%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL815-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:30:45 AM UTC 2026
% Result : Unsatisfiable 238.79s 40.06s
% Output : CNFRefutation 238.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 818
% Syntax : Number of formulae : 6928 (4615 unt; 0 typ; 0 def)
% Number of atoms : 34383 (14347 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 103510 (7669 ~;9681 |; 0 &;86160 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 112 ( 109 usr; 22 con; 0-6 aty)
% Number of variables : 24874 ( 0 ^;24874 !; 0 ?;24874 :)
% Comments :
%------------------------------------------------------------------------------
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_COMBB,type,
c_COMBB: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i > $i ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $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_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
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 ).
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 ).
thf(tp_c_Lambda_Oliftn,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i ).
thf(tp_c_Lambda_Osubstn,type,
c_Lambda_Osubstn: $i > $i > $i > $i ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(tp_c_List_Odistinct,type,
c_List_Odistinct: $i > $i > $o ).
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_Olist__update,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(tp_c_List_Olistsum,type,
c_List_Olistsum: $i > $i > $i ).
thf(tp_c_List_Omap,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i > $i ).
thf(tp_c_List_Orotate,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xmap__cong__1__1,type,
c_List_Osko__List__Xmap__cong__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xmap__eq__conv__1__1,type,
c_List_Osko__List__Xmap__eq__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xmap__ext__1__1,type,
c_List_Osko__List__Xmap__ext__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xmap__idI__1__1,type,
c_List_Osko__List__Xmap__idI__1__1: $i > $i > $i > $i ).
thf(tp_c_List_Otake,type,
c_List_Otake: $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_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_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i > $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__Xtype__induct__1__1,type,
c_Type_Osko__Type__Xtype__induct__1__1: $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_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(tp_class_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__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_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_List_Olist,type,
tc_List_Olist: $i > $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__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_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
! [V_P: $i,V_Q: $i,V_R: $i,T_b: $i,T_a: $i,T_c: $i] :
( ( c_COMBB @ V_P @ V_Q @ V_R @ T_b @ T_a @ T_c )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(4,axiom,
! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(5,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(6,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(7,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(8,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(9,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(10,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(11,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(12,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(13,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(14,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(15,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(16,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(17,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(18,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(19,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(20,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(21,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(22,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(23,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(24,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(25,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(26,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(27,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(28,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(29,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(30,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(31,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(32,axiom,
c_Type_Otypings @ v_e____ @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(33,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_s ) @ V_k )
= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(34,axiom,
! [V_e: $i,V_i: $i,V_U: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_Ts )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__types_0) ).
thf(35,axiom,
! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(39,axiom,
c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argsT_0) ).
thf(40,axiom,
! [V_e: $i,V_u: $i,V_i: $i,V_ts: $i,V_Ts: $i,V_T: $i] :
( ( c_Type_Otypings @ V_e @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_u ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_Ts )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ tc_Type_Otype ) @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substs__lemma_0) ).
thf(41,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_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/sandbox2/benchmark/theBenchmark.p',cls_uT_H_0) ).
thf(43,axiom,
! [V_t: $i,V_ts: $i,V_u: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_u ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__map_0) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',cls_T_0) ).
thf(45,axiom,
! [V_ts: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_ts @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
thf(46,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 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(47,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 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(48,axiom,
! [V_g: $i,V_f: $i,V_xs: $i,T_c: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_g @ ( c_List_Omap @ V_f @ V_xs @ T_c @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ V_g @ V_f @ T_b @ ( tc_fun @ T_a @ T_a ) @ T_c ) @ V_xs @ V_a @ T_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__map_0) ).
thf(49,axiom,
! [V_t: $i,V_ts: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__map_0) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',cls_shift__commute_0) ).
thf(51,axiom,
! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',cls_varT_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(57,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(59,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',cls_headT_0) ).
thf(61,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeI_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/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(64,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(65,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(66,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(70,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 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(71,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 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_1) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',cls_type__induct_0) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',cls_type__induct_1) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
thf(80,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b )
= ( c_List_Ofoldr @ ( c_COMBC @ V_f @ T_a @ T_b @ T_a ) @ ( c_List_Orev @ V_xs @ T_b ) @ V_a @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr_0) ).
thf(81,axiom,
! [V_f: $i,V_xs: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a )
= ( c_List_Ofoldl @ ( c_COMBC @ V_f @ T_b @ T_a @ T_a ) @ V_a @ ( c_List_Orev @ V_xs @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
thf(82,axiom,
! [V_t: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_argT_0) ).
thf(84,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(85,axiom,
! [V_k: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) ) @ V_u ) @ V_k )
= V_u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(86,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_s ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_s ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
thf(90,axiom,
! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(91,axiom,
! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__update_0) ).
thf(92,axiom,
! [V_f: $i,V_g: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ V_f @ V_g @ V_xs @ T_b @ T_a ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ V_f @ V_g @ V_xs @ T_b @ T_a ) ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
= ( c_List_Omap @ V_g @ V_xs @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__conv_2) ).
thf(93,axiom,
! [V_f: $i,V_g: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__cong__1__1 @ V_f @ V_g @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__cong__1__1 @ V_f @ V_g @ V_x @ T_a @ T_b ) ) )
| ( ( c_List_Omap @ V_f @ V_x @ T_a @ T_b )
= ( c_List_Omap @ V_g @ V_x @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__cong_1) ).
thf(94,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(95,axiom,
! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(96,axiom,
! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(97,axiom,
! [V_f: $i,V_g: $i,V_xs: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Omap @ V_g @ V_xs @ T_c @ T_b ) @ T_b @ T_a )
= ( c_List_Omap @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_xs @ T_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__map_0) ).
thf(98,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(99,axiom,
! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__map_0) ).
thf(100,axiom,
! [V_f: $i,V_g: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__ext__1__1 @ V_f @ V_g @ V_xs @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__ext__1__1 @ V_f @ V_g @ V_xs @ T_a @ T_b ) ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_a @ T_b )
= ( c_List_Omap @ V_g @ V_xs @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__ext_1) ).
thf(101,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__map_0) ).
thf(102,axiom,
! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orotate @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__map_0) ).
thf(103,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).
thf(104,axiom,
! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).
thf(105,axiom,
! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(106,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
thf(107,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(108,axiom,
! [V_xs: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_b )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_0) ).
thf(109,axiom,
! [V_f: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__idI__1__1 @ V_f @ V_xs @ T_a ) )
!= ( c_List_Osko__List__Xmap__idI__1__1 @ V_f @ V_xs @ T_a ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_a @ T_a )
= V_xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__idI_1) ).
thf(110,axiom,
! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__map_0) ).
thf(111,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(112,axiom,
! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(113,axiom,
! [T_a: $i,T_b: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Omap @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_b ) @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__0_0) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(122,axiom,
! [V_c: $i] :
( ( c_Nat_Osize__class_Osize @ V_c @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_size__char_0) ).
thf(123,axiom,
! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_1) ).
thf(125,axiom,
! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
thf(128,axiom,
( ( c_Orderings_Obot__class_Obot @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__nat__def_0) ).
thf(129,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(130,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(133,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(134,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(135,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(136,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(137,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(138,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(143,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(144,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(145,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(146,axiom,
! [V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(148,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(149,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(150,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(151,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(152,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(153,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(154,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(155,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(156,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(157,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(158,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(163,axiom,
! [V_n: $i,V_i: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ V_i ) @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',cls_listsum__append_0) ).
thf(166,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(167,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(168,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(169,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(170,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(172,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(173,axiom,
! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(174,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(175,axiom,
! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).
thf(176,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(177,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(178,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(179,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(180,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(181,axiom,
! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(182,axiom,
! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(184,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(185,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(186,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(188,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(195,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(198,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(199,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(200,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(201,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(202,axiom,
! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(203,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(204,axiom,
! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(205,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(207,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(208,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(209,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(210,axiom,
! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).
thf(211,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(220,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(221,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(226,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/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(229,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(232,axiom,
! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(233,axiom,
! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(234,axiom,
! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(235,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/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(237,axiom,
! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ V_m @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(238,axiom,
! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(241,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(242,axiom,
! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(243,axiom,
! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(244,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(245,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(246,axiom,
! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(247,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(248,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(249,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(250,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(251,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(255,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(258,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(259,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(260,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(261,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(262,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/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(264,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(265,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(266,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(267,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(268,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(270,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(271,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(272,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(273,axiom,
! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(275,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(276,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/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(278,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(279,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(280,axiom,
! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(283,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(284,axiom,
! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(285,axiom,
! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
thf(287,axiom,
! [V_m: $i,V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate @ V_m @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Orotate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).
thf(288,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(289,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(290,axiom,
! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(292,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(293,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/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(296,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(297,axiom,
! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',cls_abs_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(303,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__take_0) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(306,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ 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_Oone__class_Oone @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_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 @ 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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(309,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(310,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(311,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/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(312,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(314,axiom,
! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( c_Suc @ V_k ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__lift_0) ).
thf(315,axiom,
! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(316,axiom,
! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0621
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).
thf(317,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(318,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(319,axiom,
! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(320,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(321,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(322,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(323,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
thf(324,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/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(326,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(327,axiom,
! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ 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/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(328,axiom,
! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(329,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(330,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_xs @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).
thf(331,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(332,axiom,
! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(333,axiom,
! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(334,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(335,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(336,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(337,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(339,axiom,
! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(340,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(341,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ 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/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(342,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/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(343,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(344,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(345,axiom,
! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(346,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(347,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(348,axiom,
! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(349,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(350,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/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(351,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(352,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_0) ).
thf(353,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) ) @ V_u ) @ V_i )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__gt_0) ).
thf(354,axiom,
! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(355,axiom,
! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(356,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__rev_0) ).
thf(357,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(358,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).
thf(359,axiom,
! [V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).
thf(360,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(361,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(362,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).
thf(363,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(364,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(365,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(366,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(367,axiom,
! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__append_0) ).
thf(368,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__0_0) ).
thf(369,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__add_0) ).
thf(370,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',cls_drop__drop_0) ).
thf(372,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/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(374,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(375,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__Suc_0) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I35_J_0) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).
thf(378,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I27_J_0) ).
thf(379,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 @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__lt_0) ).
thf(380,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/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(383,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
thf(384,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(385,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(386,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(389,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/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(390,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(391,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(393,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(394,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(395,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(396,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(397,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(398,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(399,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(400,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(401,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/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
thf(402,axiom,
! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(403,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(404,axiom,
! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).
thf(405,axiom,
! [T_a: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(406,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/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
thf(407,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/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(411,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(412,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(413,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(414,axiom,
! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(415,axiom,
! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(416,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(417,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(419,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(420,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(421,axiom,
! [V_n: $i] :
( ( V_n
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
thf(422,axiom,
! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
thf(423,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(424,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(425,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(426,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(428,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(429,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(430,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(431,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(432,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(434,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(435,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(436,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__drop_0) ).
thf(437,axiom,
! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(438,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__all_0) ).
thf(439,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
thf(440,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(441,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(442,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(443,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_0) ).
thf(444,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(445,axiom,
! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(447,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/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(448,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(449,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(450,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(451,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) @ ( c_Suc @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(452,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(454,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(456,axiom,
! [V_t: $i,V_v: $i,V_i: $i,V_j: $i,V_u: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_v ) @ V_i ) ) @ ( c_Suc @ V_j ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_v ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) @ V_v ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__subst_0) ).
thf(457,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).
thf(458,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_0) ).
thf(459,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).
thf(460,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
thf(461,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
thf(462,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
thf(463,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
thf(464,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
thf(465,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
thf(466,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
thf(467,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
thf(468,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
thf(469,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
thf(470,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
thf(471,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
thf(472,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
thf(473,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
thf(474,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
thf(475,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
thf(476,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
thf(477,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
thf(478,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
thf(479,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
thf(480,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
thf(481,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
thf(482,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
thf(483,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
thf(484,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
thf(485,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
thf(486,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
thf(488,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
thf(489,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
thf(490,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
thf(491,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
thf(492,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
thf(493,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
thf(494,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
thf(495,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/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(496,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/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(497,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/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(498,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(499,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(500,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/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(501,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/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(502,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/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(504,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(505,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(506,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/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(507,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(508,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(509,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(510,axiom,
! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(511,axiom,
! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(512,axiom,
! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(513,axiom,
! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(514,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/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(515,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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(516,axiom,
! [V_k: $i,T_a: $i,T_b: $i,V_lst: $i] :
( ( c_List_Omap @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_lst @ T_b @ T_a )
= ( c_List_Oreplicate @ ( c_Nat_Osize__class_Osize @ V_lst @ ( tc_List_Olist @ T_b ) ) @ V_k @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate__const_0) ).
thf(517,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
thf(518,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(519,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(520,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
thf(521,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/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(522,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/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(523,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(524,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/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(525,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(526,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/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(527,axiom,
! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(528,axiom,
! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(529,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__length01_0) ).
thf(530,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(531,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/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
thf(532,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/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(533,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/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(534,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/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(535,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(536,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(537,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(538,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(539,axiom,
! [V_pwr: $i,V_x: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I33_J_0) ).
thf(540,axiom,
! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
thf(541,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/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
thf(542,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(543,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_xs @ T_a ) @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).
thf(544,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/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
thf(545,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(546,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/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(547,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/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(548,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/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(549,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__drop_0) ).
thf(550,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__append_0) ).
thf(551,axiom,
! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(552,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(553,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/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(554,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(555,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(556,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(557,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(558,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(559,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(560,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/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(561,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/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(562,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate_0) ).
thf(563,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/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(564,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/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
thf(565,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/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(566,axiom,
! [V_j: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(567,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ V_n ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
thf(568,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/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(569,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append1_0) ).
thf(570,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append_0) ).
thf(571,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(572,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/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(573,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/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(574,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(575,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(576,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(577,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/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(578,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/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(579,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(580,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(581,axiom,
! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
thf(582,axiom,
! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(583,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/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(584,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/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(585,axiom,
! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).
thf(586,axiom,
! [V_x: $i,V_ys: $i,T_a: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
thf(587,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(588,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(589,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(590,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/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(591,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(592,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(593,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(594,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ 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/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(595,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/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(596,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(597,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/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(598,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/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(599,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(600,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(601,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(602,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(603,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/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(604,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/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(605,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(606,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(607,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(608,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(609,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/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(610,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/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(611,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/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(612,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/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(613,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(614,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(615,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(616,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(617,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(618,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(619,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(620,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/sandbox2/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(621,axiom,
! [V_i: $i,V_j: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Otake @ V_j @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__add_0) ).
thf(622,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(623,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(624,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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(625,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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(626,axiom,
! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(627,axiom,
! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(628,axiom,
! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0622
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).
thf(629,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(630,axiom,
! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) @ V_k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
thf(631,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/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
thf(632,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/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(633,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/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(634,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/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(635,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/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(636,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(637,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(638,axiom,
! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(639,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(640,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(641,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(642,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/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(643,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/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(644,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/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(645,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/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(646,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(647,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(648,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/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(649,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/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(650,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(651,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(652,axiom,
! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(653,axiom,
! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(654,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(655,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(656,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/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(657,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/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(658,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(659,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(660,axiom,
! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(661,axiom,
! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(662,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(663,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(664,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/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(665,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/sandbox2/benchmark/theBenchmark.p',cls_type__induct_2) ).
thf(666,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) ) @ V_s ) @ V_x )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(667,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/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_0) ).
thf(668,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(669,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(670,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(671,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(672,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(673,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(674,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(675,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(676,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__drop_0) ).
thf(677,axiom,
! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(678,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/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
thf(679,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(680,axiom,
! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(681,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__take_0) ).
thf(682,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/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(683,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/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(684,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/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(685,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/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(686,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/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(687,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/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(688,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/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(689,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(690,axiom,
! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Odrop @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_m @ ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__drop_0) ).
thf(691,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/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).
thf(692,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/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(693,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(694,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(695,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(696,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(697,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(698,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(699,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(700,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(701,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(702,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/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(703,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(704,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(705,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(706,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(707,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(708,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(709,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(710,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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(711,axiom,
! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otake @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__take_0) ).
thf(712,axiom,
! [V_m: $i,V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_Suc @ V_m ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(713,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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(714,axiom,
! [V_xs_092_060_094isub_0621: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).
thf(715,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/sandbox2/benchmark/theBenchmark.p',cls_listsum_0) ).
thf(716,axiom,
! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(717,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(718,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(719,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__all_0) ).
thf(720,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist__update @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_x @ T_a ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append_1) ).
thf(721,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
thf(722,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/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(723,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(724,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(725,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).
thf(726,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/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
thf(727,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/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
thf(728,axiom,
! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
thf(729,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/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(730,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ 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/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(731,axiom,
! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(732,axiom,
! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(733,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/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(734,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
thf(735,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/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(736,axiom,
! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(737,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(738,axiom,
! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(739,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(740,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(741,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(742,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/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(743,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(744,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(745,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(746,axiom,
! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
thf(747,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(748,axiom,
! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(749,axiom,
! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(750,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/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(751,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/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(752,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/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(753,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/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(754,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/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(755,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(756,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(757,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(758,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(759,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/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
thf(760,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/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_1) ).
thf(761,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/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(762,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/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(763,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
thf(764,axiom,
! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(765,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(766,axiom,
! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(767,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(768,axiom,
! [V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Odistinct @ V_ys @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(769,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(770,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/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(771,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/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(772,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/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(773,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/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(774,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/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(775,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/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(776,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/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(777,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/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(778,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
thf(779,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
thf(780,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
thf(781,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/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(782,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/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(783,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/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(784,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/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(785,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/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(786,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/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_2) ).
thf(787,axiom,
! [V_xs: $i,V_k: $i,V_y: $i,T_a: $i] :
( ( ( c_List_Orev @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_a ) @ T_a )
= ( c_List_Olist__update @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_k @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_y @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__update_0) ).
thf(788,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/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(789,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/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(790,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(791,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(792,axiom,
! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a )
= V_ys_092_060_094isub_0622 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).
thf(793,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(794,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/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_1) ).
thf(795,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(796,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(797,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(798,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/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(799,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/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(800,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/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(801,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/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(802,axiom,
! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__append_0) ).
thf(803,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(804,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(805,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(806,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/sandbox2/benchmark/theBenchmark.p',cls_lem0_0) ).
thf(807,axiom,
! [V_a: $i,V_list: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_a @ V_list @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_list @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osize_I4_J_0) ).
thf(808,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(809,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
thf(810,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
thf(811,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(812,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(813,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/sandbox2/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
thf(814,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(815,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(816,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(817,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(818,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[817]) ).
thf(819,negated_conjecture,
~ ( c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(820,plain,
$false = $false,
inference(unfold_def,[status(thm)],[818]) ).
thf(821,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(822,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(823,plain,
( ( ! [V_P: $i,V_Q: $i,V_R: $i,T_b: $i,T_a: $i,T_c: $i] :
( ( c_COMBB @ V_P @ V_Q @ V_R @ T_b @ T_a @ T_c )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(824,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(825,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(826,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(827,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(828,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(829,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(830,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(831,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(832,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(833,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(834,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(835,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(836,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(837,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(838,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(839,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(840,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(841,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(842,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(843,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(844,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(845,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(846,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(847,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(848,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(849,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)],[29]) ).
thf(850,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)],[30]) ).
thf(851,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)],[31]) ).
thf(852,plain,
( ( c_Type_Otypings @ v_e____ @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____ )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(853,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_s ) @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(854,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_Ts )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(855,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(856,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)],[36]) ).
thf(857,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)],[37]) ).
thf(858,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)],[38]) ).
thf(859,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)],[39]) ).
thf(860,plain,
( ( ! [V_e: $i,V_u: $i,V_i: $i,V_ts: $i,V_Ts: $i,V_T: $i] :
( ( c_Type_Otypings @ V_e @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_u ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_Ts )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ tc_Type_Otype ) @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(861,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(862,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(863,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_u ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(864,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)],[44]) ).
thf(865,plain,
( ( ! [V_ts: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_ts @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(866,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 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(867,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 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(868,plain,
( ( ! [V_g: $i,V_f: $i,V_xs: $i,T_c: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_g @ ( c_List_Omap @ V_f @ V_xs @ T_c @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ V_g @ V_f @ T_b @ ( tc_fun @ T_a @ T_a ) @ T_c ) @ V_xs @ V_a @ T_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(869,plain,
( ( ! [V_t: $i,V_ts: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(870,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)],[50]) ).
thf(871,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(872,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)],[52]) ).
thf(873,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(874,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(875,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(876,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(877,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(878,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)],[58]) ).
thf(879,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(880,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)],[60]) ).
thf(881,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(882,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)],[62]) ).
thf(883,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(884,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(885,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(886,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(887,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)],[67]) ).
thf(888,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)],[68]) ).
thf(889,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)],[69]) ).
thf(890,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 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(891,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 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(892,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)],[72]) ).
thf(893,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)],[73]) ).
thf(894,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)],[74]) ).
thf(895,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)],[75]) ).
thf(896,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)],[76]) ).
thf(897,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)],[77]) ).
thf(898,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)],[78]) ).
thf(899,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)],[79]) ).
thf(900,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b )
= ( c_List_Ofoldr @ ( c_COMBC @ V_f @ T_a @ T_b @ T_a ) @ ( c_List_Orev @ V_xs @ T_b ) @ V_a @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(901,plain,
( ( ! [V_f: $i,V_xs: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a )
= ( c_List_Ofoldl @ ( c_COMBC @ V_f @ T_b @ T_a @ T_a ) @ V_a @ ( c_List_Orev @ V_xs @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(902,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(903,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)],[83]) ).
thf(904,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(905,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) ) @ V_u ) @ V_k )
= V_u ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(906,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_s ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_s ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(907,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)],[87]) ).
thf(908,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)],[88]) ).
thf(909,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)],[89]) ).
thf(910,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(911,plain,
( ( ! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(912,plain,
( ( ! [V_f: $i,V_g: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ V_f @ V_g @ V_xs @ T_b @ T_a ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ V_f @ V_g @ V_xs @ T_b @ T_a ) ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
= ( c_List_Omap @ V_g @ V_xs @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(913,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__cong__1__1 @ V_f @ V_g @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__cong__1__1 @ V_f @ V_g @ V_x @ T_a @ T_b ) ) )
| ( ( c_List_Omap @ V_f @ V_x @ T_a @ T_b )
= ( c_List_Omap @ V_g @ V_x @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(914,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(915,plain,
( ( ! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(916,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(917,plain,
( ( ! [V_f: $i,V_g: $i,V_xs: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Omap @ V_g @ V_xs @ T_c @ T_b ) @ T_b @ T_a )
= ( c_List_Omap @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_xs @ T_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(918,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(919,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(920,plain,
( ( ! [V_f: $i,V_g: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__ext__1__1 @ V_f @ V_g @ V_xs @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__ext__1__1 @ V_f @ V_g @ V_xs @ T_a @ T_b ) ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_a @ T_b )
= ( c_List_Omap @ V_g @ V_xs @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(921,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(922,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orotate @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(923,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(924,plain,
( ( ! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(925,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(926,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(927,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(928,plain,
( ( ! [V_xs: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_b )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(929,plain,
( ( ! [V_f: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__idI__1__1 @ V_f @ V_xs @ T_a ) )
!= ( c_List_Osko__List__Xmap__idI__1__1 @ V_f @ V_xs @ T_a ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_a @ T_a )
= V_xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(930,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(931,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(932,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(933,plain,
( ( ! [T_a: $i,T_b: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Omap @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_b ) @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(934,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)],[114]) ).
thf(935,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)],[115]) ).
thf(936,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)],[116]) ).
thf(937,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)],[117]) ).
thf(938,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)],[118]) ).
thf(939,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)],[119]) ).
thf(940,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)],[120]) ).
thf(941,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)],[121]) ).
thf(942,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)],[122]) ).
thf(943,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(944,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)],[124]) ).
thf(945,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)],[125]) ).
thf(946,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)],[126]) ).
thf(947,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)],[127]) ).
thf(948,plain,
( ( ( c_Orderings_Obot__class_Obot @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(949,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(950,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)],[130]) ).
thf(951,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)],[131]) ).
thf(952,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)],[132]) ).
thf(953,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)],[133]) ).
thf(954,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)],[134]) ).
thf(955,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(956,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)],[136]) ).
thf(957,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)],[137]) ).
thf(958,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)],[138]) ).
thf(959,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)],[139]) ).
thf(960,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)],[140]) ).
thf(961,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)],[141]) ).
thf(962,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)],[142]) ).
thf(963,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)],[143]) ).
thf(964,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)],[144]) ).
thf(965,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(966,plain,
( ( ! [V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(967,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)],[147]) ).
thf(968,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)],[148]) ).
thf(969,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)],[149]) ).
thf(970,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)],[150]) ).
thf(971,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)],[151]) ).
thf(972,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)],[152]) ).
thf(973,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)],[153]) ).
thf(974,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)],[154]) ).
thf(975,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)],[155]) ).
thf(976,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)],[156]) ).
thf(977,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)],[157]) ).
thf(978,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)],[158]) ).
thf(979,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)],[159]) ).
thf(980,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)],[160]) ).
thf(981,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)],[161]) ).
thf(982,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)],[162]) ).
thf(983,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)],[163]) ).
thf(984,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)],[164]) ).
thf(985,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)],[165]) ).
thf(986,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)],[166]) ).
thf(987,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)],[167]) ).
thf(988,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)],[168]) ).
thf(989,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)],[169]) ).
thf(990,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)],[170]) ).
thf(991,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)],[171]) ).
thf(992,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(993,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)],[173]) ).
thf(994,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(995,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(996,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)],[176]) ).
thf(997,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)],[177]) ).
thf(998,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)],[178]) ).
thf(999,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)],[179]) ).
thf(1000,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(1001,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(1002,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(1003,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)],[183]) ).
thf(1004,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)],[184]) ).
thf(1005,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)],[185]) ).
thf(1006,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)],[186]) ).
thf(1007,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)],[187]) ).
thf(1008,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(1009,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)],[189]) ).
thf(1010,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)],[190]) ).
thf(1011,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)],[191]) ).
thf(1012,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)],[192]) ).
thf(1013,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)],[193]) ).
thf(1014,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)],[194]) ).
thf(1015,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)],[195]) ).
thf(1016,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)],[196]) ).
thf(1017,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)],[197]) ).
thf(1018,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)],[198]) ).
thf(1019,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)],[199]) ).
thf(1020,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)],[200]) ).
thf(1021,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)],[201]) ).
thf(1022,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(1023,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)],[203]) ).
thf(1024,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(1025,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)],[205]) ).
thf(1026,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)],[206]) ).
thf(1027,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)],[207]) ).
thf(1028,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)],[208]) ).
thf(1029,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)],[209]) ).
thf(1030,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(1031,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)],[211]) ).
thf(1032,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)],[212]) ).
thf(1033,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)],[213]) ).
thf(1034,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)],[214]) ).
thf(1035,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)],[215]) ).
thf(1036,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)],[216]) ).
thf(1037,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)],[217]) ).
thf(1038,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)],[218]) ).
thf(1039,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)],[219]) ).
thf(1040,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(1041,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(1042,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)],[222]) ).
thf(1043,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)],[223]) ).
thf(1044,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)],[224]) ).
thf(1045,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)],[225]) ).
thf(1046,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)],[226]) ).
thf(1047,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)],[227]) ).
thf(1048,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)],[228]) ).
thf(1049,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)],[229]) ).
thf(1050,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)],[230]) ).
thf(1051,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)],[231]) ).
thf(1052,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(1053,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(1054,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(1055,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)],[235]) ).
thf(1056,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)],[236]) ).
thf(1057,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)],[237]) ).
thf(1058,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)],[238]) ).
thf(1059,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)],[239]) ).
thf(1060,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)],[240]) ).
thf(1061,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)],[241]) ).
thf(1062,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)],[242]) ).
thf(1063,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(1064,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(1065,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)],[245]) ).
thf(1066,plain,
( ( ! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(1067,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)],[247]) ).
thf(1068,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)],[248]) ).
thf(1069,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(1070,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)],[250]) ).
thf(1071,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)],[251]) ).
thf(1072,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)],[252]) ).
thf(1073,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)],[253]) ).
thf(1074,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)],[254]) ).
thf(1075,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)],[255]) ).
thf(1076,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)],[256]) ).
thf(1077,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)],[257]) ).
thf(1078,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)],[258]) ).
thf(1079,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)],[259]) ).
thf(1080,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)],[260]) ).
thf(1081,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(1082,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)],[262]) ).
thf(1083,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)],[263]) ).
thf(1084,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)],[264]) ).
thf(1085,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)],[265]) ).
thf(1086,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)],[266]) ).
thf(1087,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)],[267]) ).
thf(1088,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)],[268]) ).
thf(1089,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)],[269]) ).
thf(1090,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(1091,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)],[271]) ).
thf(1092,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)],[272]) ).
thf(1093,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(1094,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)],[274]) ).
thf(1095,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)],[275]) ).
thf(1096,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)],[276]) ).
thf(1097,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)],[277]) ).
thf(1098,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)],[278]) ).
thf(1099,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)],[279]) ).
thf(1100,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)],[280]) ).
thf(1101,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)],[281]) ).
thf(1102,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)],[282]) ).
thf(1103,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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)],[283]) ).
thf(1104,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(1105,plain,
( ( ! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(1106,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)],[286]) ).
thf(1107,plain,
( ( ! [V_m: $i,V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate @ V_m @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Orotate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(1108,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(1109,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(1110,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(1111,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)],[291]) ).
thf(1112,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(1113,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)],[293]) ).
thf(1114,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)],[294]) ).
thf(1115,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)],[295]) ).
thf(1116,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(1117,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(1118,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)],[298]) ).
thf(1119,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)],[299]) ).
thf(1120,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)],[300]) ).
thf(1121,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(1122,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(1123,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(1124,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)],[304]) ).
thf(1125,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(1126,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ 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_Oone__class_Oone @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(1127,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)],[307]) ).
thf(1128,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)],[308]) ).
thf(1129,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)],[309]) ).
thf(1130,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(1131,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)],[311]) ).
thf(1132,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(1133,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)],[313]) ).
thf(1134,plain,
( ( ! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( c_Suc @ V_k ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(1135,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(1136,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0621
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(1137,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)],[317]) ).
thf(1138,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)],[318]) ).
thf(1139,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)],[319]) ).
thf(1140,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)],[320]) ).
thf(1141,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(1142,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(1143,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(1144,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)],[324]) ).
thf(1145,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)],[325]) ).
thf(1146,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(1147,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ 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)],[327]) ).
thf(1148,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)],[328]) ).
thf(1149,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(1150,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_xs @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(1151,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)],[331]) ).
thf(1152,plain,
( ( ! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(1154,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(1155,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(1156,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(1157,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)],[337]) ).
thf(1158,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)],[338]) ).
thf(1159,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(1160,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(1161,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ 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)],[341]) ).
thf(1162,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)],[342]) ).
thf(1163,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)],[343]) ).
thf(1164,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)],[344]) ).
thf(1165,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1166,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)],[346]) ).
thf(1167,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)],[347]) ).
thf(1168,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(1169,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(1170,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)],[350]) ).
thf(1171,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(1172,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(1173,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) ) @ V_u ) @ V_i )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(1174,plain,
( ( ! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(1175,plain,
( ( ! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(1176,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(1177,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)],[357]) ).
thf(1178,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1179,plain,
( ( ! [V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(1180,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(1181,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1182,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(1183,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(1184,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)],[364]) ).
thf(1185,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)],[365]) ).
thf(1186,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(1187,plain,
( ( ! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(1188,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(1189,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)],[369]) ).
thf(1190,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)],[370]) ).
thf(1191,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)],[371]) ).
thf(1192,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)],[372]) ).
thf(1193,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)],[373]) ).
thf(1194,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(1195,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)],[375]) ).
thf(1196,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)],[376]) ).
thf(1197,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)],[377]) ).
thf(1198,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)],[378]) ).
thf(1199,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 @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(1200,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)],[380]) ).
thf(1201,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)],[381]) ).
thf(1202,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)],[382]) ).
thf(1203,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(1204,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(1205,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)],[385]) ).
thf(1206,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)],[386]) ).
thf(1207,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)],[387]) ).
thf(1208,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)],[388]) ).
thf(1209,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)],[389]) ).
thf(1210,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)],[390]) ).
thf(1211,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)],[391]) ).
thf(1212,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)],[392]) ).
thf(1213,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)],[393]) ).
thf(1214,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)],[394]) ).
thf(1215,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(1216,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(1217,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)],[397]) ).
thf(1218,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)],[398]) ).
thf(1219,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)],[399]) ).
thf(1220,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)],[400]) ).
thf(1221,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)],[401]) ).
thf(1222,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1223,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1224,plain,
( ( ! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1225,plain,
( ( ! [T_a: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1226,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)],[406]) ).
thf(1227,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)],[407]) ).
thf(1228,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)],[408]) ).
thf(1229,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)],[409]) ).
thf(1230,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)],[410]) ).
thf(1231,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)],[411]) ).
thf(1232,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)],[412]) ).
thf(1233,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)],[413]) ).
thf(1234,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)],[414]) ).
thf(1235,plain,
( ( ! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1236,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)],[416]) ).
thf(1237,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)],[417]) ).
thf(1238,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)],[418]) ).
thf(1239,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)],[419]) ).
thf(1240,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)],[420]) ).
thf(1241,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1242,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1243,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)],[423]) ).
thf(1244,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)],[424]) ).
thf(1245,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)],[425]) ).
thf(1246,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)],[426]) ).
thf(1247,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)],[427]) ).
thf(1248,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)],[428]) ).
thf(1249,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)],[429]) ).
thf(1250,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)],[430]) ).
thf(1251,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)],[431]) ).
thf(1252,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)],[432]) ).
thf(1253,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)],[433]) ).
thf(1254,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(1255,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(1256,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(1257,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1258,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1259,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1260,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1261,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)],[441]) ).
thf(1262,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)],[442]) ).
thf(1263,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1264,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)],[444]) ).
thf(1265,plain,
( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1266,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)],[446]) ).
thf(1267,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)],[447]) ).
thf(1268,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)],[448]) ).
thf(1269,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1270,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1271,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)],[451]) ).
thf(1272,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1273,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)],[453]) ).
thf(1274,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)],[454]) ).
thf(1275,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)],[455]) ).
thf(1276,plain,
( ( ! [V_t: $i,V_v: $i,V_i: $i,V_j: $i,V_u: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_v ) @ V_i ) ) @ ( c_Suc @ V_j ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_v ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) @ V_v ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1277,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1278,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)],[458]) ).
thf(1279,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)],[459]) ).
thf(1280,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)],[460]) ).
thf(1281,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)],[461]) ).
thf(1282,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)],[462]) ).
thf(1283,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)],[463]) ).
thf(1284,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)],[464]) ).
thf(1285,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)],[465]) ).
thf(1286,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)],[466]) ).
thf(1287,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)],[467]) ).
thf(1288,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)],[468]) ).
thf(1289,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)],[469]) ).
thf(1290,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)],[470]) ).
thf(1291,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)],[471]) ).
thf(1292,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)],[472]) ).
thf(1293,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)],[473]) ).
thf(1294,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)],[474]) ).
thf(1295,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)],[475]) ).
thf(1296,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)],[476]) ).
thf(1297,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)],[477]) ).
thf(1298,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)],[478]) ).
thf(1299,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)],[479]) ).
thf(1300,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)],[480]) ).
thf(1301,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)],[481]) ).
thf(1302,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)],[482]) ).
thf(1303,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)],[483]) ).
thf(1304,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)],[484]) ).
thf(1305,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)],[485]) ).
thf(1306,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)],[486]) ).
thf(1307,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)],[487]) ).
thf(1308,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)],[488]) ).
thf(1309,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)],[489]) ).
thf(1310,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)],[490]) ).
thf(1311,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)],[491]) ).
thf(1312,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)],[492]) ).
thf(1313,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)],[493]) ).
thf(1314,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1315,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)],[495]) ).
thf(1316,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)],[496]) ).
thf(1317,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)],[497]) ).
thf(1318,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)],[498]) ).
thf(1319,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)],[499]) ).
thf(1320,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)],[500]) ).
thf(1321,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)],[501]) ).
thf(1322,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)],[502]) ).
thf(1323,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)],[503]) ).
thf(1324,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)],[504]) ).
thf(1325,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)],[505]) ).
thf(1326,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)],[506]) ).
thf(1327,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)],[507]) ).
thf(1328,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)],[508]) ).
thf(1329,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)],[509]) ).
thf(1330,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)],[510]) ).
thf(1331,plain,
( ( ! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1332,plain,
( ( ! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1333,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1334,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)],[514]) ).
thf(1335,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)],[515]) ).
thf(1336,plain,
( ( ! [V_k: $i,T_a: $i,T_b: $i,V_lst: $i] :
( ( c_List_Omap @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_lst @ T_b @ T_a )
= ( c_List_Oreplicate @ ( c_Nat_Osize__class_Osize @ V_lst @ ( tc_List_Olist @ T_b ) ) @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1337,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1338,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)],[518]) ).
thf(1339,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)],[519]) ).
thf(1340,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1341,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)],[521]) ).
thf(1342,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)],[522]) ).
thf(1343,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)],[523]) ).
thf(1344,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)],[524]) ).
thf(1345,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)],[525]) ).
thf(1346,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)],[526]) ).
thf(1347,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)],[527]) ).
thf(1348,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1349,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1350,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1351,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)],[531]) ).
thf(1352,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)],[532]) ).
thf(1353,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)],[533]) ).
thf(1354,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)],[534]) ).
thf(1355,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)],[535]) ).
thf(1356,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)],[536]) ).
thf(1357,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)],[537]) ).
thf(1358,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)],[538]) ).
thf(1359,plain,
( ( ! [V_pwr: $i,V_x: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= 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)],[539]) ).
thf(1360,plain,
( ( ! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1361,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)],[541]) ).
thf(1362,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1363,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_xs @ T_a ) @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1364,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)],[544]) ).
thf(1365,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)],[545]) ).
thf(1366,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)],[546]) ).
thf(1367,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)],[547]) ).
thf(1368,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)],[548]) ).
thf(1369,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1370,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1371,plain,
( ( ! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1372,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1373,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)],[553]) ).
thf(1374,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)],[554]) ).
thf(1375,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)],[555]) ).
thf(1376,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)],[556]) ).
thf(1377,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1378,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1379,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)],[559]) ).
thf(1380,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)],[560]) ).
thf(1381,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)],[561]) ).
thf(1382,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1383,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)],[563]) ).
thf(1384,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)],[564]) ).
thf(1385,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)],[565]) ).
thf(1386,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)],[566]) ).
thf(1387,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ V_n ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1388,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)],[568]) ).
thf(1389,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1390,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1391,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1392,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)],[572]) ).
thf(1393,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)],[573]) ).
thf(1394,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)],[574]) ).
thf(1395,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)],[575]) ).
thf(1396,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)],[576]) ).
thf(1397,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)],[577]) ).
thf(1398,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)],[578]) ).
thf(1399,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)],[579]) ).
thf(1400,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)],[580]) ).
thf(1401,plain,
( ( ! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(1402,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1403,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)],[583]) ).
thf(1404,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)],[584]) ).
thf(1405,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(1406,plain,
( ( ! [V_x: $i,V_ys: $i,T_a: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1407,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)],[587]) ).
thf(1408,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)],[588]) ).
thf(1409,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)],[589]) ).
thf(1410,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)],[590]) ).
thf(1411,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1412,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1413,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)],[593]) ).
thf(1414,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[594]) ).
thf(1415,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)],[595]) ).
thf(1416,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)],[596]) ).
thf(1417,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)],[597]) ).
thf(1418,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)],[598]) ).
thf(1419,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)],[599]) ).
thf(1420,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)],[600]) ).
thf(1421,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)],[601]) ).
thf(1422,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)],[602]) ).
thf(1423,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)],[603]) ).
thf(1424,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)],[604]) ).
thf(1425,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)],[605]) ).
thf(1426,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)],[606]) ).
thf(1427,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)],[607]) ).
thf(1428,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)],[608]) ).
thf(1429,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)],[609]) ).
thf(1430,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)],[610]) ).
thf(1431,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)],[611]) ).
thf(1432,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)],[612]) ).
thf(1433,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)],[613]) ).
thf(1434,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)],[614]) ).
thf(1435,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)],[615]) ).
thf(1436,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(1437,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(1438,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)],[618]) ).
thf(1439,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(1440,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)],[620]) ).
thf(1441,plain,
( ( ! [V_i: $i,V_j: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Otake @ V_j @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(1442,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)],[622]) ).
thf(1443,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)],[623]) ).
thf(1444,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)],[624]) ).
thf(1445,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)],[625]) ).
thf(1446,plain,
( ( ! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(1447,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(1448,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0622
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(1449,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(1450,plain,
( ( ! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) @ V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(1451,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)],[631]) ).
thf(1452,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)],[632]) ).
thf(1453,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)],[633]) ).
thf(1454,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)],[634]) ).
thf(1455,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)],[635]) ).
thf(1456,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)],[636]) ).
thf(1457,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)],[637]) ).
thf(1458,plain,
( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(1459,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(1460,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)],[640]) ).
thf(1461,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)],[641]) ).
thf(1462,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)],[642]) ).
thf(1463,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)],[643]) ).
thf(1464,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)],[644]) ).
thf(1465,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)],[645]) ).
thf(1466,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)],[646]) ).
thf(1467,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(1468,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)],[648]) ).
thf(1469,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)],[649]) ).
thf(1470,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(1471,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)],[651]) ).
thf(1472,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)],[652]) ).
thf(1473,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)],[653]) ).
thf(1474,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(1475,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)],[655]) ).
thf(1476,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)],[656]) ).
thf(1477,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)],[657]) ).
thf(1478,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)],[658]) ).
thf(1479,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)],[659]) ).
thf(1480,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)],[660]) ).
thf(1481,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)],[661]) ).
thf(1482,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(1483,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_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)],[663]) ).
thf(1484,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)],[664]) ).
thf(1485,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)],[665]) ).
thf(1486,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) ) @ V_s ) @ V_x )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(1487,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)],[667]) ).
thf(1488,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)],[668]) ).
thf(1489,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)],[669]) ).
thf(1490,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)],[670]) ).
thf(1491,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)],[671]) ).
thf(1492,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)],[672]) ).
thf(1493,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)],[673]) ).
thf(1494,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)],[674]) ).
thf(1495,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)],[675]) ).
thf(1496,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(1497,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(1498,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)],[678]) ).
thf(1499,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(1500,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(1501,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(1502,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)],[682]) ).
thf(1503,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)],[683]) ).
thf(1504,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)],[684]) ).
thf(1505,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)],[685]) ).
thf(1506,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)],[686]) ).
thf(1507,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)],[687]) ).
thf(1508,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)],[688]) ).
thf(1509,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)],[689]) ).
thf(1510,plain,
( ( ! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Odrop @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_m @ ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(1511,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)],[691]) ).
thf(1512,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)],[692]) ).
thf(1513,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)],[693]) ).
thf(1514,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)],[694]) ).
thf(1515,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)],[695]) ).
thf(1516,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)],[696]) ).
thf(1517,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)],[697]) ).
thf(1518,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)],[698]) ).
thf(1519,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)],[699]) ).
thf(1520,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)],[700]) ).
thf(1521,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)],[701]) ).
thf(1522,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)],[702]) ).
thf(1523,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)],[703]) ).
thf(1524,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)],[704]) ).
thf(1525,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)],[705]) ).
thf(1526,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)],[706]) ).
thf(1527,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)],[707]) ).
thf(1528,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)],[708]) ).
thf(1529,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(1530,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)],[710]) ).
thf(1531,plain,
( ( ! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otake @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[711]) ).
thf(1532,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)],[712]) ).
thf(1533,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)],[713]) ).
thf(1534,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[714]) ).
thf(1535,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)],[715]) ).
thf(1536,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)],[716]) ).
thf(1537,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)],[717]) ).
thf(1538,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)],[718]) ).
thf(1539,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[719]) ).
thf(1540,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist__update @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_x @ T_a ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(1541,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[721]) ).
thf(1542,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)],[722]) ).
thf(1543,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)],[723]) ).
thf(1544,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[724]) ).
thf(1545,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(1546,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)],[726]) ).
thf(1547,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)],[727]) ).
thf(1548,plain,
( ( ! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[728]) ).
thf(1549,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)],[729]) ).
thf(1550,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ 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)],[730]) ).
thf(1551,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[731]) ).
thf(1552,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(1553,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)],[733]) ).
thf(1554,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[734]) ).
thf(1555,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)],[735]) ).
thf(1556,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(1557,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)],[737]) ).
thf(1558,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)],[738]) ).
thf(1559,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[739]) ).
thf(1560,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)],[740]) ).
thf(1561,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)],[741]) ).
thf(1562,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)],[742]) ).
thf(1563,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)],[743]) ).
thf(1564,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)],[744]) ).
thf(1565,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)],[745]) ).
thf(1566,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[746]) ).
thf(1567,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)],[747]) ).
thf(1568,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[748]) ).
thf(1569,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[749]) ).
thf(1570,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)],[750]) ).
thf(1571,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)],[751]) ).
thf(1572,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)],[752]) ).
thf(1573,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)],[753]) ).
thf(1574,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)],[754]) ).
thf(1575,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)],[755]) ).
thf(1576,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)],[756]) ).
thf(1577,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)],[757]) ).
thf(1578,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)],[758]) ).
thf(1579,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)],[759]) ).
thf(1580,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)],[760]) ).
thf(1581,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)],[761]) ).
thf(1582,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)],[762]) ).
thf(1583,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[763]) ).
thf(1584,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(1585,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[765]) ).
thf(1586,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[766]) ).
thf(1587,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(1588,plain,
( ( ! [V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Odistinct @ V_ys @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(1589,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[769]) ).
thf(1590,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)],[770]) ).
thf(1591,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)],[771]) ).
thf(1592,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)],[772]) ).
thf(1593,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)],[773]) ).
thf(1594,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)],[774]) ).
thf(1595,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)],[775]) ).
thf(1596,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)],[776]) ).
thf(1597,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)],[777]) ).
thf(1598,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)],[778]) ).
thf(1599,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)],[779]) ).
thf(1600,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)],[780]) ).
thf(1601,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)],[781]) ).
thf(1602,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)],[782]) ).
thf(1603,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)],[783]) ).
thf(1604,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)],[784]) ).
thf(1605,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)],[785]) ).
thf(1606,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)],[786]) ).
thf(1607,plain,
( ( ! [V_xs: $i,V_k: $i,V_y: $i,T_a: $i] :
( ( ( c_List_Orev @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_a ) @ T_a )
= ( c_List_Olist__update @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_k @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_y @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(1608,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)],[788]) ).
thf(1609,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)],[789]) ).
thf(1610,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)],[790]) ).
thf(1611,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[791]) ).
thf(1612,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a )
= V_ys_092_060_094isub_0622 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[792]) ).
thf(1613,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[793]) ).
thf(1614,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)],[794]) ).
thf(1615,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)],[795]) ).
thf(1616,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)],[796]) ).
thf(1617,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)],[797]) ).
thf(1618,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)],[798]) ).
thf(1619,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)],[799]) ).
thf(1620,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)],[800]) ).
thf(1621,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)],[801]) ).
thf(1622,plain,
( ( ! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[802]) ).
thf(1623,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)],[803]) ).
thf(1624,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[804]) ).
thf(1625,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)],[805]) ).
thf(1626,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)],[806]) ).
thf(1627,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_a @ V_list @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_list @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[807]) ).
thf(1628,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)],[808]) ).
thf(1629,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)],[809]) ).
thf(1630,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)],[810]) ).
thf(1631,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[811]) ).
thf(1632,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[812]) ).
thf(1633,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)],[813]) ).
thf(1634,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)],[814]) ).
thf(1635,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)],[815]) ).
thf(1636,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)],[816]) ).
thf(1637,plain,
( ( ~ ( c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____ ) )
= $true ),
inference(unfold_def,[status(thm)],[819]) ).
thf(1638,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[820]) ).
thf(1639,plain,
( ( ~ ( c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____ ) )
= $true ),
inference(copy,[status(thm)],[1637]) ).
thf(1640,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)],[1636]) ).
thf(1641,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)],[1635]) ).
thf(1642,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)],[1634]) ).
thf(1643,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)],[1633]) ).
thf(1644,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1632]) ).
thf(1645,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1631]) ).
thf(1646,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)],[1630]) ).
thf(1647,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)],[1629]) ).
thf(1648,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)],[1628]) ).
thf(1649,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_a @ V_list @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_list @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1627]) ).
thf(1650,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)],[1626]) ).
thf(1651,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)],[1625]) ).
thf(1652,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1624]) ).
thf(1653,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)],[1623]) ).
thf(1654,plain,
( ( ! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1622]) ).
thf(1655,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)],[1621]) ).
thf(1656,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)],[1620]) ).
thf(1657,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)],[1619]) ).
thf(1658,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)],[1618]) ).
thf(1659,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)],[1617]) ).
thf(1660,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)],[1616]) ).
thf(1661,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)],[1615]) ).
thf(1662,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)],[1614]) ).
thf(1663,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1613]) ).
thf(1664,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a )
= V_ys_092_060_094isub_0622 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1612]) ).
thf(1665,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1611]) ).
thf(1666,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)],[1610]) ).
thf(1667,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)],[1609]) ).
thf(1668,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)],[1608]) ).
thf(1669,plain,
( ( ! [V_xs: $i,V_k: $i,V_y: $i,T_a: $i] :
( ( ( c_List_Orev @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_a ) @ T_a )
= ( c_List_Olist__update @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_k @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_y @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1607]) ).
thf(1670,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)],[1606]) ).
thf(1671,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)],[1605]) ).
thf(1672,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)],[1604]) ).
thf(1673,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)],[1603]) ).
thf(1674,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)],[1602]) ).
thf(1675,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)],[1601]) ).
thf(1676,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)],[1600]) ).
thf(1677,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)],[1599]) ).
thf(1678,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)],[1598]) ).
thf(1679,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)],[1597]) ).
thf(1680,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)],[1596]) ).
thf(1681,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)],[1595]) ).
thf(1682,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)],[1594]) ).
thf(1683,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)],[1593]) ).
thf(1684,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)],[1592]) ).
thf(1685,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)],[1591]) ).
thf(1686,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)],[1590]) ).
thf(1687,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1589]) ).
thf(1688,plain,
( ( ! [V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Odistinct @ V_ys @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1588]) ).
thf(1689,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1587]) ).
thf(1690,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[1586]) ).
thf(1691,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1585]) ).
thf(1692,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1584]) ).
thf(1693,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1583]) ).
thf(1694,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)],[1582]) ).
thf(1695,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)],[1581]) ).
thf(1696,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)],[1580]) ).
thf(1697,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)],[1579]) ).
thf(1698,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)],[1578]) ).
thf(1699,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)],[1577]) ).
thf(1700,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)],[1576]) ).
thf(1701,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)],[1575]) ).
thf(1702,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)],[1574]) ).
thf(1703,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)],[1573]) ).
thf(1704,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)],[1572]) ).
thf(1705,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)],[1571]) ).
thf(1706,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)],[1570]) ).
thf(1707,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1569]) ).
thf(1708,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[1568]) ).
thf(1709,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)],[1567]) ).
thf(1710,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1566]) ).
thf(1711,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)],[1565]) ).
thf(1712,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)],[1564]) ).
thf(1713,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)],[1563]) ).
thf(1714,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)],[1562]) ).
thf(1715,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)],[1561]) ).
thf(1716,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)],[1560]) ).
thf(1717,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1559]) ).
thf(1718,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)],[1558]) ).
thf(1719,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)],[1557]) ).
thf(1720,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1556]) ).
thf(1721,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)],[1555]) ).
thf(1722,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1554]) ).
thf(1723,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)],[1553]) ).
thf(1724,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1552]) ).
thf(1725,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1551]) ).
thf(1726,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ 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)],[1550]) ).
thf(1727,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)],[1549]) ).
thf(1728,plain,
( ( ! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1548]) ).
thf(1729,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)],[1547]) ).
thf(1730,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)],[1546]) ).
thf(1731,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1545]) ).
thf(1732,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1544]) ).
thf(1733,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)],[1543]) ).
thf(1734,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)],[1542]) ).
thf(1735,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1541]) ).
thf(1736,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist__update @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_x @ T_a ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1540]) ).
thf(1737,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1539]) ).
thf(1738,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)],[1538]) ).
thf(1739,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)],[1537]) ).
thf(1740,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)],[1536]) ).
thf(1741,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)],[1535]) ).
thf(1742,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1534]) ).
thf(1743,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)],[1533]) ).
thf(1744,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)],[1532]) ).
thf(1745,plain,
( ( ! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otake @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1531]) ).
thf(1746,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)],[1530]) ).
thf(1747,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1529]) ).
thf(1748,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)],[1528]) ).
thf(1749,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)],[1527]) ).
thf(1750,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)],[1526]) ).
thf(1751,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)],[1525]) ).
thf(1752,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)],[1524]) ).
thf(1753,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)],[1523]) ).
thf(1754,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)],[1522]) ).
thf(1755,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)],[1521]) ).
thf(1756,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)],[1520]) ).
thf(1757,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)],[1519]) ).
thf(1758,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)],[1518]) ).
thf(1759,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)],[1517]) ).
thf(1760,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)],[1516]) ).
thf(1761,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)],[1515]) ).
thf(1762,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)],[1514]) ).
thf(1763,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)],[1513]) ).
thf(1764,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)],[1512]) ).
thf(1765,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)],[1511]) ).
thf(1766,plain,
( ( ! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Odrop @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_m @ ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1510]) ).
thf(1767,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)],[1509]) ).
thf(1768,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)],[1508]) ).
thf(1769,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)],[1507]) ).
thf(1770,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)],[1506]) ).
thf(1771,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)],[1505]) ).
thf(1772,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)],[1504]) ).
thf(1773,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)],[1503]) ).
thf(1774,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)],[1502]) ).
thf(1775,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1501]) ).
thf(1776,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1500]) ).
thf(1777,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1499]) ).
thf(1778,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)],[1498]) ).
thf(1779,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[1497]) ).
thf(1780,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1496]) ).
thf(1781,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)],[1495]) ).
thf(1782,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)],[1494]) ).
thf(1783,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)],[1493]) ).
thf(1784,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)],[1492]) ).
thf(1785,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)],[1491]) ).
thf(1786,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)],[1490]) ).
thf(1787,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)],[1489]) ).
thf(1788,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)],[1488]) ).
thf(1789,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)],[1487]) ).
thf(1790,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) ) @ V_s ) @ V_x )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[1486]) ).
thf(1791,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)],[1485]) ).
thf(1792,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)],[1484]) ).
thf(1793,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)],[1483]) ).
thf(1794,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1482]) ).
thf(1795,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)],[1481]) ).
thf(1796,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)],[1480]) ).
thf(1797,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)],[1479]) ).
thf(1798,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)],[1478]) ).
thf(1799,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)],[1477]) ).
thf(1800,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)],[1476]) ).
thf(1801,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)],[1475]) ).
thf(1802,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1474]) ).
thf(1803,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)],[1473]) ).
thf(1804,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)],[1472]) ).
thf(1805,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)],[1471]) ).
thf(1806,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1470]) ).
thf(1807,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)],[1469]) ).
thf(1808,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)],[1468]) ).
thf(1809,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1467]) ).
thf(1810,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)],[1466]) ).
thf(1811,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)],[1465]) ).
thf(1812,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)],[1464]) ).
thf(1813,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)],[1463]) ).
thf(1814,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)],[1462]) ).
thf(1815,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)],[1461]) ).
thf(1816,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)],[1460]) ).
thf(1817,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1459]) ).
thf(1818,plain,
( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1458]) ).
thf(1819,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)],[1457]) ).
thf(1820,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)],[1456]) ).
thf(1821,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)],[1455]) ).
thf(1822,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)],[1454]) ).
thf(1823,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)],[1453]) ).
thf(1824,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)],[1452]) ).
thf(1825,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)],[1451]) ).
thf(1826,plain,
( ( ! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[1450]) ).
thf(1827,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(1828,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0622
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(1829,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1447]) ).
thf(1830,plain,
( ( ! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ) )
= $true ),
inference(copy,[status(thm)],[1446]) ).
thf(1831,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)],[1445]) ).
thf(1832,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)],[1444]) ).
thf(1833,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(1834,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)],[1442]) ).
thf(1835,plain,
( ( ! [V_i: $i,V_j: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Otake @ V_j @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1441]) ).
thf(1836,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)],[1440]) ).
thf(1837,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1439]) ).
thf(1838,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)],[1438]) ).
thf(1839,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1437]) ).
thf(1840,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(1841,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)],[1435]) ).
thf(1842,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)],[1434]) ).
thf(1843,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)],[1433]) ).
thf(1844,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)],[1432]) ).
thf(1845,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)],[1431]) ).
thf(1846,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)],[1430]) ).
thf(1847,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)],[1429]) ).
thf(1848,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)],[1428]) ).
thf(1849,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)],[1427]) ).
thf(1850,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)],[1426]) ).
thf(1851,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)],[1425]) ).
thf(1852,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)],[1424]) ).
thf(1853,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)],[1423]) ).
thf(1854,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)],[1422]) ).
thf(1855,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)],[1421]) ).
thf(1856,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)],[1420]) ).
thf(1857,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)],[1419]) ).
thf(1858,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)],[1418]) ).
thf(1859,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)],[1417]) ).
thf(1860,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)],[1416]) ).
thf(1861,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)],[1415]) ).
thf(1862,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[1414]) ).
thf(1863,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)],[1413]) ).
thf(1864,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1412]) ).
thf(1865,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1411]) ).
thf(1866,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)],[1410]) ).
thf(1867,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)],[1409]) ).
thf(1868,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)],[1408]) ).
thf(1869,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)],[1407]) ).
thf(1870,plain,
( ( ! [V_x: $i,V_ys: $i,T_a: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1406]) ).
thf(1871,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1405]) ).
thf(1872,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)],[1404]) ).
thf(1873,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)],[1403]) ).
thf(1874,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1402]) ).
thf(1875,plain,
( ( ! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[1401]) ).
thf(1876,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)],[1400]) ).
thf(1877,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)],[1399]) ).
thf(1878,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)],[1398]) ).
thf(1879,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)],[1397]) ).
thf(1880,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)],[1396]) ).
thf(1881,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)],[1395]) ).
thf(1882,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)],[1394]) ).
thf(1883,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)],[1393]) ).
thf(1884,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)],[1392]) ).
thf(1885,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1391]) ).
thf(1886,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1390]) ).
thf(1887,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1389]) ).
thf(1888,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)],[1388]) ).
thf(1889,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ V_n ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1387]) ).
thf(1890,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)],[1386]) ).
thf(1891,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)],[1385]) ).
thf(1892,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)],[1384]) ).
thf(1893,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)],[1383]) ).
thf(1894,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1382]) ).
thf(1895,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)],[1381]) ).
thf(1896,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)],[1380]) ).
thf(1897,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)],[1379]) ).
thf(1898,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1378]) ).
thf(1899,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1377]) ).
thf(1900,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)],[1376]) ).
thf(1901,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)],[1375]) ).
thf(1902,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)],[1374]) ).
thf(1903,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)],[1373]) ).
thf(1904,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1372]) ).
thf(1905,plain,
( ( ! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1371]) ).
thf(1906,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1370]) ).
thf(1907,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1369]) ).
thf(1908,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)],[1368]) ).
thf(1909,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)],[1367]) ).
thf(1910,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)],[1366]) ).
thf(1911,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)],[1365]) ).
thf(1912,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)],[1364]) ).
thf(1913,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_xs @ T_a ) @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1363]) ).
thf(1914,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1362]) ).
thf(1915,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)],[1361]) ).
thf(1916,plain,
( ( ! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1360]) ).
thf(1917,plain,
( ( ! [V_pwr: $i,V_x: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1359]) ).
thf(1918,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)],[1358]) ).
thf(1919,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)],[1357]) ).
thf(1920,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)],[1356]) ).
thf(1921,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)],[1355]) ).
thf(1922,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)],[1354]) ).
thf(1923,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)],[1353]) ).
thf(1924,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)],[1352]) ).
thf(1925,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)],[1351]) ).
thf(1926,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1350]) ).
thf(1927,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1349]) ).
thf(1928,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1348]) ).
thf(1929,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)],[1347]) ).
thf(1930,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)],[1346]) ).
thf(1931,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)],[1345]) ).
thf(1932,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)],[1344]) ).
thf(1933,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)],[1343]) ).
thf(1934,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)],[1342]) ).
thf(1935,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)],[1341]) ).
thf(1936,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1340]) ).
thf(1937,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)],[1339]) ).
thf(1938,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)],[1338]) ).
thf(1939,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1337]) ).
thf(1940,plain,
( ( ! [V_k: $i,T_a: $i,T_b: $i,V_lst: $i] :
( ( c_List_Omap @ ( c_COMBK @ V_k @ T_a @ T_b ) @ V_lst @ T_b @ T_a )
= ( c_List_Oreplicate @ ( c_Nat_Osize__class_Osize @ V_lst @ ( tc_List_Olist @ T_b ) ) @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1336]) ).
thf(1941,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)],[1335]) ).
thf(1942,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)],[1334]) ).
thf(1943,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1333]) ).
thf(1944,plain,
( ( ! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1332]) ).
thf(1945,plain,
( ( ! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1331]) ).
thf(1946,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)],[1330]) ).
thf(1947,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)],[1329]) ).
thf(1948,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)],[1328]) ).
thf(1949,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)],[1327]) ).
thf(1950,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)],[1326]) ).
thf(1951,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)],[1325]) ).
thf(1952,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)],[1324]) ).
thf(1953,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)],[1323]) ).
thf(1954,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)],[1322]) ).
thf(1955,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)],[1321]) ).
thf(1956,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)],[1320]) ).
thf(1957,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)],[1319]) ).
thf(1958,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)],[1318]) ).
thf(1959,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)],[1317]) ).
thf(1960,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)],[1316]) ).
thf(1961,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)],[1315]) ).
thf(1962,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1314]) ).
thf(1963,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)],[1313]) ).
thf(1964,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)],[1312]) ).
thf(1965,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)],[1311]) ).
thf(1966,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)],[1310]) ).
thf(1967,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)],[1309]) ).
thf(1968,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)],[1308]) ).
thf(1969,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)],[1307]) ).
thf(1970,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)],[1306]) ).
thf(1971,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)],[1305]) ).
thf(1972,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)],[1304]) ).
thf(1973,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)],[1303]) ).
thf(1974,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)],[1302]) ).
thf(1975,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)],[1301]) ).
thf(1976,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)],[1300]) ).
thf(1977,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)],[1299]) ).
thf(1978,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)],[1298]) ).
thf(1979,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)],[1297]) ).
thf(1980,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)],[1296]) ).
thf(1981,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)],[1295]) ).
thf(1982,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)],[1294]) ).
thf(1983,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)],[1293]) ).
thf(1984,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)],[1292]) ).
thf(1985,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)],[1291]) ).
thf(1986,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)],[1290]) ).
thf(1987,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)],[1289]) ).
thf(1988,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)],[1288]) ).
thf(1989,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)],[1287]) ).
thf(1990,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)],[1286]) ).
thf(1991,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)],[1285]) ).
thf(1992,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)],[1284]) ).
thf(1993,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)],[1283]) ).
thf(1994,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)],[1282]) ).
thf(1995,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)],[1281]) ).
thf(1996,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)],[1280]) ).
thf(1997,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)],[1279]) ).
thf(1998,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)],[1278]) ).
thf(1999,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1277]) ).
thf(2000,plain,
( ( ! [V_t: $i,V_v: $i,V_i: $i,V_j: $i,V_u: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_v ) @ V_i ) ) @ ( c_Suc @ V_j ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_v ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) @ V_v ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1276]) ).
thf(2001,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)],[1275]) ).
thf(2002,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)],[1274]) ).
thf(2003,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)],[1273]) ).
thf(2004,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1272]) ).
thf(2005,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)],[1271]) ).
thf(2006,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(2007,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(2008,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)],[1268]) ).
thf(2009,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)],[1267]) ).
thf(2010,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)],[1266]) ).
thf(2011,plain,
( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(2012,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)],[1264]) ).
thf(2013,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(2014,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)],[1262]) ).
thf(2015,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)],[1261]) ).
thf(2016,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(2017,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1259]) ).
thf(2018,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1258]) ).
thf(2019,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(2020,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(2021,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(2022,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1254]) ).
thf(2023,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)],[1253]) ).
thf(2024,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)],[1252]) ).
thf(2025,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)],[1251]) ).
thf(2026,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)],[1250]) ).
thf(2027,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)],[1249]) ).
thf(2028,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)],[1248]) ).
thf(2029,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)],[1247]) ).
thf(2030,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)],[1246]) ).
thf(2031,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)],[1245]) ).
thf(2032,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)],[1244]) ).
thf(2033,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)],[1243]) ).
thf(2034,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(2035,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1241]) ).
thf(2036,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)],[1240]) ).
thf(2037,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)],[1239]) ).
thf(2038,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)],[1238]) ).
thf(2039,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)],[1237]) ).
thf(2040,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)],[1236]) ).
thf(2041,plain,
( ( ! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(2042,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)],[1234]) ).
thf(2043,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)],[1233]) ).
thf(2044,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)],[1232]) ).
thf(2045,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)],[1231]) ).
thf(2046,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)],[1230]) ).
thf(2047,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)],[1229]) ).
thf(2048,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)],[1228]) ).
thf(2049,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)],[1227]) ).
thf(2050,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)],[1226]) ).
thf(2051,plain,
( ( ! [T_a: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1225]) ).
thf(2052,plain,
( ( ! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1224]) ).
thf(2053,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1223]) ).
thf(2054,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ) )
= $true ),
inference(copy,[status(thm)],[1222]) ).
thf(2055,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)],[1221]) ).
thf(2056,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)],[1220]) ).
thf(2057,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)],[1219]) ).
thf(2058,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)],[1218]) ).
thf(2059,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)],[1217]) ).
thf(2060,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(2061,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(2062,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)],[1214]) ).
thf(2063,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)],[1213]) ).
thf(2064,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)],[1212]) ).
thf(2065,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)],[1211]) ).
thf(2066,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)],[1210]) ).
thf(2067,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)],[1209]) ).
thf(2068,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)],[1208]) ).
thf(2069,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)],[1207]) ).
thf(2070,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)],[1206]) ).
thf(2071,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)],[1205]) ).
thf(2072,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(2073,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(2074,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)],[1202]) ).
thf(2075,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)],[1201]) ).
thf(2076,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)],[1200]) ).
thf(2077,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 @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(2078,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)],[1198]) ).
thf(2079,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)],[1197]) ).
thf(2080,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)],[1196]) ).
thf(2081,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)],[1195]) ).
thf(2082,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(2083,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)],[1193]) ).
thf(2084,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)],[1192]) ).
thf(2085,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)],[1191]) ).
thf(2086,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)],[1190]) ).
thf(2087,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)],[1189]) ).
thf(2088,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(2089,plain,
( ( ! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(2090,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(2091,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)],[1185]) ).
thf(2092,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)],[1184]) ).
thf(2093,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1183]) ).
thf(2094,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1182]) ).
thf(2095,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(2096,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(2097,plain,
( ( ! [V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1179]) ).
thf(2098,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(2099,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)],[1177]) ).
thf(2100,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(2101,plain,
( ( ! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(2102,plain,
( ( ! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(2103,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) ) @ V_u ) @ V_i )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(2104,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(2105,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(2106,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)],[1170]) ).
thf(2107,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(2108,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(2109,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)],[1167]) ).
thf(2110,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)],[1166]) ).
thf(2111,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1165]) ).
thf(2112,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)],[1164]) ).
thf(2113,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)],[1163]) ).
thf(2114,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)],[1162]) ).
thf(2115,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ 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)],[1161]) ).
thf(2116,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(2117,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(2118,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)],[1158]) ).
thf(2119,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)],[1157]) ).
thf(2120,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(2121,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(2122,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(2123,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(2124,plain,
( ( ! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(2125,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)],[1151]) ).
thf(2126,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_xs @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(2127,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(2128,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)],[1148]) ).
thf(2129,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ 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)],[1147]) ).
thf(2130,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(2131,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)],[1145]) ).
thf(2132,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)],[1144]) ).
thf(2133,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1143]) ).
thf(2134,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(2135,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1141]) ).
thf(2136,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)],[1140]) ).
thf(2137,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)],[1139]) ).
thf(2138,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)],[1138]) ).
thf(2139,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)],[1137]) ).
thf(2140,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0621
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(2141,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1135]) ).
thf(2142,plain,
( ( ! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( c_Suc @ V_k ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1134]) ).
thf(2143,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)],[1133]) ).
thf(2144,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1132]) ).
thf(2145,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)],[1131]) ).
thf(2146,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1130]) ).
thf(2147,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)],[1129]) ).
thf(2148,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)],[1128]) ).
thf(2149,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)],[1127]) ).
thf(2150,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ 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_Oone__class_Oone @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(2151,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)],[1125]) ).
thf(2152,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)],[1124]) ).
thf(2153,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(2154,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)],[1122]) ).
thf(2155,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)],[1121]) ).
thf(2156,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)],[1120]) ).
thf(2157,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)],[1119]) ).
thf(2158,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)],[1118]) ).
thf(2159,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1117]) ).
thf(2160,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1116]) ).
thf(2161,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)],[1115]) ).
thf(2162,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)],[1114]) ).
thf(2163,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)],[1113]) ).
thf(2164,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1112]) ).
thf(2165,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)],[1111]) ).
thf(2166,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(2167,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(2168,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(2169,plain,
( ( ! [V_m: $i,V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate @ V_m @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Orotate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(2170,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)],[1106]) ).
thf(2171,plain,
( ( ! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(2172,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(2173,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)],[1103]) ).
thf(2174,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)],[1102]) ).
thf(2175,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)],[1101]) ).
thf(2176,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)],[1100]) ).
thf(2177,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)],[1099]) ).
thf(2178,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)],[1098]) ).
thf(2179,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)],[1097]) ).
thf(2180,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)],[1096]) ).
thf(2181,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)],[1095]) ).
thf(2182,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)],[1094]) ).
thf(2183,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1093]) ).
thf(2184,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)],[1092]) ).
thf(2185,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)],[1091]) ).
thf(2186,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(2187,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)],[1089]) ).
thf(2188,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)],[1088]) ).
thf(2189,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)],[1087]) ).
thf(2190,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)],[1086]) ).
thf(2191,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)],[1085]) ).
thf(2192,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)],[1084]) ).
thf(2193,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)],[1083]) ).
thf(2194,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)],[1082]) ).
thf(2195,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(2196,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)],[1080]) ).
thf(2197,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)],[1079]) ).
thf(2198,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)],[1078]) ).
thf(2199,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)],[1077]) ).
thf(2200,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)],[1076]) ).
thf(2201,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)],[1075]) ).
thf(2202,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)],[1074]) ).
thf(2203,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)],[1073]) ).
thf(2204,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)],[1072]) ).
thf(2205,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)],[1071]) ).
thf(2206,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)],[1070]) ).
thf(2207,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1069]) ).
thf(2208,plain,
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(2209,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)],[1067]) ).
thf(2210,plain,
( ( ! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(2211,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)],[1065]) ).
thf(2212,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1064]) ).
thf(2213,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(2214,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)],[1062]) ).
thf(2215,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)],[1061]) ).
thf(2216,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)],[1060]) ).
thf(2217,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)],[1059]) ).
thf(2218,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)],[1058]) ).
thf(2219,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)],[1057]) ).
thf(2220,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)],[1056]) ).
thf(2221,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)],[1055]) ).
thf(2222,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(2223,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(2224,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(2225,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)],[1051]) ).
thf(2226,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)],[1050]) ).
thf(2227,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)],[1049]) ).
thf(2228,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)],[1048]) ).
thf(2229,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)],[1047]) ).
thf(2230,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)],[1046]) ).
thf(2231,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)],[1045]) ).
thf(2232,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)],[1044]) ).
thf(2233,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)],[1043]) ).
thf(2234,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)],[1042]) ).
thf(2235,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(2236,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(2237,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)],[1039]) ).
thf(2238,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)],[1038]) ).
thf(2239,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)],[1037]) ).
thf(2240,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)],[1036]) ).
thf(2241,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)],[1035]) ).
thf(2242,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)],[1034]) ).
thf(2243,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)],[1033]) ).
thf(2244,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)],[1032]) ).
thf(2245,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)],[1031]) ).
thf(2246,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(2247,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)],[1029]) ).
thf(2248,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)],[1028]) ).
thf(2249,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)],[1027]) ).
thf(2250,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)],[1026]) ).
thf(2251,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)],[1025]) ).
thf(2252,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(2253,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)],[1023]) ).
thf(2254,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(2255,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)],[1021]) ).
thf(2256,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)],[1020]) ).
thf(2257,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)],[1019]) ).
thf(2258,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)],[1018]) ).
thf(2259,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)],[1017]) ).
thf(2260,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)],[1016]) ).
thf(2261,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)],[1015]) ).
thf(2262,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)],[1014]) ).
thf(2263,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)],[1013]) ).
thf(2264,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)],[1012]) ).
thf(2265,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)],[1011]) ).
thf(2266,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)],[1010]) ).
thf(2267,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)],[1009]) ).
thf(2268,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(2269,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)],[1007]) ).
thf(2270,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)],[1006]) ).
thf(2271,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)],[1005]) ).
thf(2272,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)],[1004]) ).
thf(2273,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)],[1003]) ).
thf(2274,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(2275,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(2276,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(2277,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)],[999]) ).
thf(2278,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)],[998]) ).
thf(2279,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)],[997]) ).
thf(2280,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)],[996]) ).
thf(2281,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[995]) ).
thf(2282,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[994]) ).
thf(2283,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)],[993]) ).
thf(2284,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(2285,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)],[991]) ).
thf(2286,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)],[990]) ).
thf(2287,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)],[989]) ).
thf(2288,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)],[988]) ).
thf(2289,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)],[987]) ).
thf(2290,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)],[986]) ).
thf(2291,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)],[985]) ).
thf(2292,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)],[984]) ).
thf(2293,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)],[983]) ).
thf(2294,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)],[982]) ).
thf(2295,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)],[981]) ).
thf(2296,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)],[980]) ).
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_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(2298,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)],[978]) ).
thf(2299,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)],[977]) ).
thf(2300,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)],[976]) ).
thf(2301,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)],[975]) ).
thf(2302,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)],[974]) ).
thf(2303,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)],[973]) ).
thf(2304,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)],[972]) ).
thf(2305,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)],[971]) ).
thf(2306,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)],[970]) ).
thf(2307,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)],[969]) ).
thf(2308,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)],[968]) ).
thf(2309,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)],[967]) ).
thf(2310,plain,
( ( ! [V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(2311,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(2312,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)],[964]) ).
thf(2313,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)],[963]) ).
thf(2314,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)],[962]) ).
thf(2315,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)],[961]) ).
thf(2316,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)],[960]) ).
thf(2317,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)],[959]) ).
thf(2318,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)],[958]) ).
thf(2319,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)],[957]) ).
thf(2320,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)],[956]) ).
thf(2321,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)],[955]) ).
thf(2322,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)],[954]) ).
thf(2323,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)],[953]) ).
thf(2324,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)],[952]) ).
thf(2325,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)],[951]) ).
thf(2326,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)],[950]) ).
thf(2327,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)],[949]) ).
thf(2328,plain,
( ( ( c_Orderings_Obot__class_Obot @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(2329,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)],[947]) ).
thf(2330,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)],[946]) ).
thf(2331,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)],[945]) ).
thf(2332,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)],[944]) ).
thf(2333,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(2334,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)],[942]) ).
thf(2335,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)],[941]) ).
thf(2336,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)],[940]) ).
thf(2337,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)],[939]) ).
thf(2338,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)],[938]) ).
thf(2339,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)],[937]) ).
thf(2340,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)],[936]) ).
thf(2341,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)],[935]) ).
thf(2342,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)],[934]) ).
thf(2343,plain,
( ( ! [T_a: $i,T_b: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Omap @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_b ) @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(2344,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(2345,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(2346,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(2347,plain,
( ( ! [V_f: $i,V_xs: $i,T_a: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__idI__1__1 @ V_f @ V_xs @ T_a ) )
!= ( c_List_Osko__List__Xmap__idI__1__1 @ V_f @ V_xs @ T_a ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_a @ T_a )
= V_xs ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(2348,plain,
( ( ! [V_xs: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_b )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(2349,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(2350,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(2351,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(2352,plain,
( ( ! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(2353,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(2354,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orotate @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(2355,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(2356,plain,
( ( ! [V_f: $i,V_g: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__ext__1__1 @ V_f @ V_g @ V_xs @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__ext__1__1 @ V_f @ V_g @ V_xs @ T_a @ T_b ) ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_a @ T_b )
= ( c_List_Omap @ V_g @ V_xs @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(2357,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(2358,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(2359,plain,
( ( ! [V_f: $i,V_g: $i,V_xs: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Omap @ V_g @ V_xs @ T_c @ T_b ) @ T_b @ T_a )
= ( c_List_Omap @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_xs @ T_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(2360,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(2361,plain,
( ( ! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(2362,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(2363,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__cong__1__1 @ V_f @ V_g @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__cong__1__1 @ V_f @ V_g @ V_x @ T_a @ T_b ) ) )
| ( ( c_List_Omap @ V_f @ V_x @ T_a @ T_b )
= ( c_List_Omap @ V_g @ V_x @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(2364,plain,
( ( ! [V_f: $i,V_g: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ V_f @ V_g @ V_xs @ T_b @ T_a ) )
!= ( hAPP @ V_g @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ V_f @ V_g @ V_xs @ T_b @ T_a ) ) )
| ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
= ( c_List_Omap @ V_g @ V_xs @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(2365,plain,
( ( ! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(2366,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(2367,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)],[909]) ).
thf(2368,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)],[908]) ).
thf(2369,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)],[907]) ).
thf(2370,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_s ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_s ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(2371,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) ) @ V_u ) @ V_k )
= V_u ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(2372,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(2373,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)],[903]) ).
thf(2374,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(2375,plain,
( ( ! [V_f: $i,V_xs: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a )
= ( c_List_Ofoldl @ ( c_COMBC @ V_f @ T_b @ T_a @ T_a ) @ V_a @ ( c_List_Orev @ V_xs @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(2376,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b )
= ( c_List_Ofoldr @ ( c_COMBC @ V_f @ T_a @ T_b @ T_a ) @ ( c_List_Orev @ V_xs @ T_b ) @ V_a @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(2377,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)],[899]) ).
thf(2378,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)],[898]) ).
thf(2379,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)],[897]) ).
thf(2380,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)],[896]) ).
thf(2381,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)],[895]) ).
thf(2382,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)],[894]) ).
thf(2383,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)],[893]) ).
thf(2384,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)],[892]) ).
thf(2385,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 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(2386,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 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(2387,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)],[889]) ).
thf(2388,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)],[888]) ).
thf(2389,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)],[887]) ).
thf(2390,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(2391,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(2392,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(2393,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)],[883]) ).
thf(2394,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)],[882]) ).
thf(2395,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(2396,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)],[880]) ).
thf(2397,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(2398,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)],[878]) ).
thf(2399,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(2400,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)],[876]) ).
thf(2401,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)],[875]) ).
thf(2402,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)],[874]) ).
thf(2403,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)],[873]) ).
thf(2404,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)],[872]) ).
thf(2405,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(2406,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)],[870]) ).
thf(2407,plain,
( ( ! [V_t: $i,V_ts: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(2408,plain,
( ( ! [V_g: $i,V_f: $i,V_xs: $i,T_c: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_g @ ( c_List_Omap @ V_f @ V_xs @ T_c @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ V_g @ V_f @ T_b @ ( tc_fun @ T_a @ T_a ) @ T_c ) @ V_xs @ V_a @ T_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(2409,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 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(2410,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 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(2411,plain,
( ( ! [V_ts: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_ts @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(2412,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)],[864]) ).
thf(2413,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_u ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(2414,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)],[862]) ).
thf(2415,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(2416,plain,
( ( ! [V_e: $i,V_u: $i,V_i: $i,V_ts: $i,V_Ts: $i,V_T: $i] :
( ( c_Type_Otypings @ V_e @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_u ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_Ts )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ tc_Type_Otype ) @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(2417,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)],[859]) ).
thf(2418,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)],[858]) ).
thf(2419,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)],[857]) ).
thf(2420,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)],[856]) ).
thf(2421,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(2422,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_Ts )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(2423,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_s ) @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(2424,plain,
( ( c_Type_Otypings @ v_e____ @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____ )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(2425,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)],[851]) ).
thf(2426,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)],[850]) ).
thf(2427,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)],[849]) ).
thf(2428,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(2429,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(2430,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(2431,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(2432,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(2433,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(2434,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(2435,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(2436,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(2437,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(2438,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(2439,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(2440,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(2441,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(2442,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(2443,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(2444,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(2445,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(2446,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(2447,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(2448,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(2449,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(2450,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(2451,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(2452,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(2453,plain,
( ( ! [V_P: $i,V_Q: $i,V_R: $i,T_b: $i,T_a: $i,T_c: $i] :
( ( c_COMBB @ V_P @ V_Q @ V_R @ T_b @ T_a @ T_c )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(2454,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(2455,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)],[821]) ).
thf(2456,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1638]) ).
thf(2457,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)],[1953]) ).
thf(2458,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)],[2229]) ).
thf(2459,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)],[2185]) ).
thf(2460,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)],[1659]) ).
thf(2461,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)],[2187]) ).
thf(2462,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2107]) ).
thf(2463,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Omap @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Omap @ SX0 @ SX4 @ SX2 @ SX3 ) )
| ( ( c_Nat_Osize__class_Osize @ SX1 @ ( tc_List_Olist @ SX2 ) )
= ( c_Nat_Osize__class_Osize @ SX4 @ ( tc_List_Olist @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2350]) ).
thf(2464,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)],[1831]) ).
thf(2465,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)],[2214]) ).
thf(2466,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)],[1954]) ).
thf(2467,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)],[2184]) ).
thf(2468,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)],[2263]) ).
thf(2469,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)],[2221]) ).
thf(2470,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)],[2228]) ).
thf(2471,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)],[2003]) ).
thf(2472,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Omap @ SX1 @ SX2 @ SX3 @ SX0 ) )
| ( SX2
= ( c_List_Olist_ONil @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2351]) ).
thf(2473,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( SX1
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ SX3 @ SX2 ) @ SX4 @ SX2 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1828]) ).
thf(2474,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)],[1846]) ).
thf(2475,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ SX0 @ SX1 ) @ SX3 @ SX1 ) @ SX1 )
!= SX3 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 )
!= SX0 )
| ( SX2
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ SX0 @ SX1 ) )
| ( ( c_List_Oappend @ SX2 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ SX0 @ SX1 ) @ SX3 @ SX1 ) @ SX1 )
= ( c_List_Oappend @ SX0 @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2246]) ).
thf(2476,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)],[2297]) ).
thf(2477,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)],[2001]) ).
thf(2478,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2236]) ).
thf(2479,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)],[2147]) ).
thf(2480,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 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ~ ( c_Type_Otyping @ SX5 @ SX3 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX3 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SX5 @ SX4 @ SX1 @ tc_Type_Otype ) @ SX2 @ SX6 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2385]) ).
thf(2481,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)],[2220]) ).
thf(2482,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)],[2175]) ).
thf(2483,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)],[1877]) ).
thf(2484,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)],[2106]) ).
thf(2485,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX1 @ SX3 @ SX0 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SX0 ) @ SX1 @ SX0 )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2093]) ).
thf(2486,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ SX0 @ ( c_List_Osko__List__Xmap__idI__1__1 @ SX0 @ SX1 @ SX2 ) )
!= ( c_List_Osko__List__Xmap__idI__1__1 @ SX0 @ SX1 @ SX2 ) )
| ( ( c_List_Omap @ SX0 @ SX1 @ SX2 @ SX2 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2347]) ).
thf(2487,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)],[2271]) ).
thf(2488,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)],[2196]) ).
thf(2489,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)],[2384]) ).
thf(2490,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ SX0 @ SX2 )
= SX3 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2281]) ).
thf(2491,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Oone__class_Oone @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2186]) ).
thf(2492,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)],[2377]) ).
thf(2493,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i,SX9: $i,SX10: $i] :
( ( ( hAPP @ SX0 @ ( hAPP @ SX1 @ SX2 ) )
!= ( hAPP @ SX3 @ ( hAPP @ SX4 @ SX5 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SX0 @ SX1 @ SX6 @ SX7 @ SX8 ) @ SX2 )
= ( hAPP @ ( c_Fun_Ocomp @ SX3 @ SX4 @ SX9 @ SX7 @ SX10 ) @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2275]) ).
thf(2494,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)],[1719]) ).
thf(2495,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Orev @ SX1 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2108]) ).
thf(2496,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)],[1657]) ).
thf(2497,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Otake @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1939]) ).
thf(2498,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ( ( c_Fun_Ocomp @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
!= ( c_Fun_Ocomp @ SX5 @ SX6 @ SX7 @ SX3 @ SX4 ) )
| ( ( hAPP @ SX0 @ ( hAPP @ SX1 @ SX8 ) )
= ( hAPP @ SX5 @ ( hAPP @ SX6 @ SX8 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2274]) ).
thf(2499,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)],[2002]) ).
thf(2500,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)],[2231]) ).
thf(2501,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)],[2216]) ).
thf(2502,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)],[1960]) ).
thf(2503,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)],[2296]) ).
thf(2504,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ SX0 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
!= ( hAPP @ SX1 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) )
| ( ( c_List_Omap @ SX0 @ SX2 @ SX3 @ SX4 )
= ( c_List_Omap @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2364]) ).
thf(2505,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)],[1872]) ).
thf(2506,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)],[2037]) ).
thf(2507,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)],[2295]) ).
thf(2508,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)],[1955]) ).
thf(2509,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)],[1653]) ).
thf(2510,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ SX0 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
!= ( hAPP @ SX1 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) )
| ( ( c_List_Omap @ SX0 @ SX2 @ SX3 @ SX4 )
= ( c_List_Omap @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2356]) ).
thf(2511,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1869]) ).
thf(2512,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)],[2265]) ).
thf(2513,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)],[1951]) ).
thf(2514,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( SX0
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ SX3 @ SX2 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2140]) ).
thf(2515,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)],[1873]) ).
thf(2516,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)],[2260]) ).
thf(2517,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 )
!= SX0 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SX2 @ SX3 @ SX1 )
= ( c_List_Oappend @ SX0 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) @ SX3 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1871]) ).
thf(2518,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)],[1867]) ).
thf(2519,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)],[2038]) ).
thf(2520,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)],[2262]) ).
thf(2521,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)],[1808]) ).
thf(2522,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2269]) ).
thf(2523,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2132]) ).
thf(2524,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)],[2338]) ).
thf(2525,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2222]) ).
thf(2526,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)],[1805]) ).
thf(2527,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)],[1931]) ).
thf(2528,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)],[2418]) ).
thf(2529,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orotate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2116]) ).
thf(2530,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[2235]) ).
thf(2531,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)],[2197]) ).
thf(2532,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)],[2289]) ).
thf(2533,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)],[2378]) ).
thf(2534,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)],[2193]) ).
thf(2535,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2090]) ).
thf(2536,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)],[1868]) ).
thf(2537,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)],[1847]) ).
thf(2538,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Omap @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Olist_ONil @ SX3 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2345]) ).
thf(2539,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ SX3 @ SX1 ) )
| ( SX0
= ( c_List_Oappend @ ( c_List_Orev @ SX3 @ SX1 ) @ ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1818]) ).
thf(2540,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)],[1866]) ).
thf(2541,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)],[2261]) ).
thf(2542,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)],[1714]) ).
thf(2543,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Olist__update @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Olist_ONil @ SX3 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2183]) ).
thf(2544,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2127]) ).
thf(2545,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)],[2047]) ).
thf(2546,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)],[2287]) ).
thf(2547,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)],[1952]) ).
thf(2548,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)],[1804]) ).
thf(2549,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)],[2402]) ).
thf(2550,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)],[1832]) ).
thf(2551,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)],[2099]) ).
thf(2552,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2195]) ).
thf(2553,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1833]) ).
thf(2554,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)],[1768]) ).
thf(2555,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1720]) ).
thf(2556,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX2
= ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1732]) ).
thf(2557,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1834]) ).
thf(2558,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) )
| ( ( c_List_Oappend @ SX0 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) @ SX1 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1875]) ).
thf(2559,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2212]) ).
thf(2560,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ SX0 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
!= ( hAPP @ SX1 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) )
| ( ( c_List_Omap @ SX0 @ SX2 @ SX3 @ SX4 )
= ( c_List_Omap @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2363]) ).
thf(2561,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) )
| ( ( c_List_Oappend @ SX0 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) @ SX3 @ SX1 ) @ SX1 )
= ( c_List_Oappend @ SX2 @ SX3 @ SX1 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1742]) ).
thf(2562,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)],[2152]) ).
thf(2563,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2213]) ).
thf(2564,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)],[2046]) ).
thf(2565,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[2131]) ).
thf(2566,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Type_Otype_OAtom @ SX0 )
!= ( c_Type_Otype_OAtom @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1697]) ).
thf(2567,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)],[2217]) ).
thf(2568,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2223]) ).
thf(2569,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ SX0 @ SX2 ) @ SX1 @ SX2 )
= SX4 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1664]) ).
thf(2570,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 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ~ ( c_Type_Otyping @ SX5 @ SX3 @ SX0 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX3 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SX5 @ SX4 @ SX0 @ tc_Type_Otype ) @ SX2 @ SX6 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2386]) ).
thf(2571,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)],[2230]) ).
thf(2572,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2272]) ).
thf(2573,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)],[2049]) ).
thf(2574,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)],[1950]) ).
thf(2575,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)],[2290]) ).
thf(2576,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)],[1751]) ).
thf(2577,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)],[2015]) ).
thf(2578,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Odrop @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX1 @ ( tc_List_Olist @ SX2 ) ) @ SX0 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2017]) ).
thf(2579,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)],[2379]) ).
thf(2580,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)],[2048]) ).
thf(2581,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)],[1891]) ).
thf(2582,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)],[1656]) ).
thf(2583,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)],[1961]) ).
thf(2584,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)],[2288]) ).
thf(2585,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)],[1803]) ).
thf(2586,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1838]) ).
thf(2587,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)],[2419]) ).
thf(2588,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)],[2198]) ).
thf(2589,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)],[1807]) ).
thf(2590,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)],[1956]) ).
thf(2591,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)],[2294]) ).
thf(2592,plain,
( ( c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_u____ ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_Ts____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(2593,plain,
! [SV1: $i] :
( ( ! [SY2547: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV1 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ SY2547 ) @ SY2547 ) @ SV1 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SY2547 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2594,plain,
! [SV2: $i] :
( ( ! [SY2548: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV2 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SY2548 @ SV2 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SY2548 ) @ SY2548 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2595,plain,
! [SV3: $i] :
( ( ( SV3
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV3 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2596,plain,
! [SV4: $i] :
( ( ! [SY2549: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ SV4 ) @ ( c_Suc @ SY2549 ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ SV4 @ SY2549 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2597,plain,
! [SV5: $i] :
( ( ( c_Suc @ SV5 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV5 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2598,plain,
! [SV6: $i] :
( ( ( c_Suc @ SV6 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2599,plain,
! [SV7: $i] :
( ( ! [SY2550: $i,SY2551: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV7 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2550 @ SV7 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2551 @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SY2550 @ SY2551 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2600,plain,
! [SV8: $i] :
( ( ! [SY2552: $i,SY2553: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV8 )
| ( c_lessequals @ SY2552 @ SY2553 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2552 @ SV8 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2553 @ SV8 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2601,plain,
! [SV9: $i] :
( ( ! [SY2554: $i,SY2555: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV9 @ SY2554 @ SY2555 ) @ ( tc_List_Olist @ SY2555 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SY2554 @ ( tc_List_Olist @ SY2555 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2602,plain,
! [SV10: $i] :
( ( ! [SY2556: $i,SY2557: $i] :
( ( c_HOL_Oord__class_Oless @ SV10 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2556 ) @ SY2557 ) @ tc_nat )
| ~ ( c_lessequals @ SV10 @ SY2556 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2557 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2603,plain,
! [SV11: $i] :
( ( ! [SY2558: $i,SY2559: $i,SY2560: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( c_HOL_Oord__class_Oless @ SY2558 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SY2559 ) @ SY2560 ) @ SV11 )
| ~ ( c_lessequals @ SY2558 @ SY2560 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SY2559 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2604,plain,
! [SV12: $i] :
( ( ! [SY2561: $i] : ( c_List_Olistsp @ SV12 @ ( c_List_Olist_ONil @ SY2561 ) @ SY2561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2605,plain,
! [SV13: $i] :
( ( ! [SY2562: $i,SY2563: $i,SY2564: $i] :
( ( c_List_Odrop @ SV13 @ ( c_List_Oappend @ SY2562 @ SY2563 @ SY2564 ) @ SY2564 )
= ( c_List_Oappend @ ( c_List_Odrop @ SV13 @ SY2562 @ SY2564 ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Nat_Osize__class_Osize @ SY2562 @ ( tc_List_Olist @ SY2564 ) ) @ tc_nat ) @ SY2563 @ SY2564 ) @ SY2564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2606,plain,
! [SV14: $i] :
( ( ! [SY2565: $i,SY2566: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV14 @ SY2565 @ tc_nat ) ) @ SY2566 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2565 ) @ SY2566 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2565 @ SV14 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2607,plain,
! [SV15: $i] :
( ( ! [SY2567: $i,SY2568: $i,SY2569: $i] :
( ~ ( class_Orderings_Olinorder @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY2567 @ SY2568 @ SV15 ) @ SY2569 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SY2568 @ SY2569 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SY2567 @ SY2569 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2608,plain,
! [SV16: $i] :
( ( ! [SY2570: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV16 @ SY2570 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV16 @ SY2570 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2609,plain,
! [SV17: $i] :
( ( ! [SY2571: $i,SY2572: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV17 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SY2571 @ SY2572 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SY2571 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2610,plain,
! [SV18: $i] :
( ( ! [SY2573: $i] :
( ( hBOOL @ ( hAPP @ SV18 @ SY2573 ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV18 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2611,plain,
! [SV19: $i] :
( ( ! [SY2574: $i] :
( ( c_List_Otake @ SV19 @ ( c_List_Olist_ONil @ SY2574 ) @ SY2574 )
= ( c_List_Olist_ONil @ SY2574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2612,plain,
! [SV20: $i] :
( ( ! [SY2575: $i,SY2576: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ ( c_Power_Opower__class_Opower @ SY2575 @ SY2576 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ SY2575 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2613,plain,
! [SV21: $i] :
( ( ! [SY2577: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV21 )
| ~ ( class_Power_Opower @ SV21 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ ( c_Suc @ SY2577 ) @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2614,plain,
! [SV22: $i] :
( ( ! [SY2578: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV22 ) @ ( c_Suc @ SY2578 ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV22 ) @ SY2578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2615,plain,
! [SV23: $i] :
( ( ! [SY2579: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV23 ) ) @ SY2579 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV23 ) @ SY2579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2616,plain,
! [SV24: $i] :
( ( ! [SY2580: $i,SY2581: $i,SY2582: $i] :
( ( ( c_List_Orev @ ( c_List_Olist__update @ SV24 @ SY2580 @ SY2581 @ SY2582 ) @ SY2582 )
= ( c_List_Olist__update @ ( c_List_Orev @ SV24 @ SY2582 ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SY2582 ) ) @ SY2580 @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY2581 @ SY2582 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2580 @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SY2582 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2617,plain,
! [SV25: $i] :
( ( ! [SY2583: $i,SY2584: $i] :
( ( hBOOL @ ( hAPP @ SV25 @ SY2583 ) )
| ( hBOOL @ ( hAPP @ SV25 @ SY2584 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2584 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV25 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2618,plain,
! [SV26: $i] :
( ( ! [SY2585: $i] : ( c_HOL_Oord__class_Oless @ SV26 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV26 ) @ SY2585 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2619,plain,
! [SV27: $i] :
( ( ! [SY2586: $i] : ( c_HOL_Oord__class_Oless @ SV27 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2586 ) @ SV27 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2620,plain,
! [SV28: $i] :
( ( ! [SY2587: $i] : ( c_HOL_Oord__class_Oless @ SV28 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV28 ) @ SY2587 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2621,plain,
! [SV29: $i] :
( ( ! [SY2588: $i,SY2589: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SY2588 ) @ SY2589 @ tc_nat )
| ~ ( c_lessequals @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SY2589 @ SY2588 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2588 @ SY2589 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2622,plain,
! [SV30: $i] :
( ( ! [SY2590: $i,SY2591: $i] :
( ( c_lessequals @ SV30 @ ( c_HOL_Ominus__class_Ominus @ SY2590 @ SY2591 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV30 ) @ SY2591 ) @ SY2590 @ tc_nat )
| ~ ( c_lessequals @ SY2591 @ SY2590 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2623,plain,
! [SV31: $i] :
( ( ! [SY2592: $i,SY2593: $i,SY2594: $i] :
( ~ ( class_Orderings_Olinorder @ SV31 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2592 @ SY2593 @ SV31 ) @ SY2594 @ SV31 )
| ~ ( c_lessequals @ SY2593 @ SY2594 @ SV31 )
| ~ ( c_lessequals @ SY2592 @ SY2594 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2624,plain,
! [SV32: $i] :
( ( ! [SY2595: $i,SY2596: $i,SY2597: $i] :
( ~ ( class_Orderings_Olinorder @ SV32 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2595 @ SY2596 @ SV32 ) @ SY2597 @ SV32 )
| ~ ( c_lessequals @ SY2596 @ SY2597 @ SV32 )
| ~ ( c_lessequals @ SY2595 @ SY2597 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2625,plain,
! [SV33: $i] :
( ( ! [SY2598: $i,SY2599: $i,SY2600: $i] :
( ~ ( class_Orderings_Olinorder @ SV33 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2598 @ SY2599 @ SV33 ) @ SY2600 @ SV33 )
| ~ ( c_lessequals @ SY2599 @ SY2600 @ SV33 )
| ~ ( c_lessequals @ SY2598 @ SY2600 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2626,plain,
! [SV34: $i] :
( ( ! [SY2601: $i,SY2602: $i] :
( ~ ( class_Orderings_Olinorder @ SV34 )
| ( c_lessequals @ SY2601 @ ( c_Orderings_Oord__class_Omax @ SY2601 @ SY2602 @ SV34 ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2627,plain,
! [SV35: $i] :
( ( ! [SY2603: $i,SY2604: $i] :
( ~ ( class_Orderings_Olinorder @ SV35 )
| ( c_lessequals @ SY2603 @ ( c_Orderings_Oord__class_Omax @ SY2604 @ SY2603 @ SV35 ) @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2628,plain,
! [SV36: $i] :
( ( ! [SY2605: $i] :
( ( c_List_Oappend @ SV36 @ ( c_List_Olist_ONil @ SY2605 ) @ SY2605 )
= SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2629,plain,
! [SV37: $i] :
( ( ! [SY2606: $i] :
( SV37
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2606 ) @ SV37 @ SY2606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2630,plain,
! [SV38: $i] :
( ( ! [SY2607: $i] :
( SV38
= ( c_List_Oappend @ SV38 @ ( c_List_Olist_ONil @ SY2607 ) @ SY2607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2631,plain,
! [SV39: $i] :
( ( ! [SY2608: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV39 ) @ SY2608 @ SV39 )
= SY2608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2632,plain,
! [SV40: $i] :
( ( ! [SY2609: $i] :
( SV40
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2609 ) @ SV40 @ SY2609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2633,plain,
! [SV41: $i] :
( ( ! [SY2610: $i] :
( ~ ( class_Orderings_Obot @ SV41 )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV41 ) @ SY2610 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2634,plain,
! [SV42: $i] :
( ( ! [SY2611: $i,SY2612: $i] :
( ( c_List_Odistinct @ SV42 @ SY2611 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV42 @ SY2612 @ SY2611 ) @ SY2611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2635,plain,
! [SV43: $i] :
( ( ! [SY2613: $i,SY2614: $i] :
( ( c_List_Odistinct @ SV43 @ SY2613 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SY2614 @ SV43 @ SY2613 ) @ SY2613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2636,plain,
! [SV44: $i] :
( ( ! [SY2615: $i] :
( SV44
= ( c_List_Orev @ ( c_List_Orev @ SV44 @ SY2615 ) @ SY2615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2637,plain,
! [SV45: $i] :
( ( ! [SY2616: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV45 @ SY2616 ) @ SY2616 )
= SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2638,plain,
! [SV46: $i] :
( ( ! [SY2617: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV46 @ SY2617 ) @ SY2617 )
= SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2639,plain,
! [SV47: $i] :
( ( ! [SY2618: $i,SY2619: $i,SY2620: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV47 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2618 @ SY2619 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SY2618 @ SY2620 @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SY2618 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SY2618 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SY2620 @ SY2619 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2640,plain,
! [SV48: $i] :
( ( ! [SY2621: $i,SY2622: $i] :
( SV48
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV48 @ ( tc_List_Olist @ SY2621 ) ) @ ( c_List_Oappend @ SV48 @ SY2622 @ SY2621 ) @ SY2621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2641,plain,
! [SV49: $i] :
( ( ! [SY2623: $i,SY2624: $i,SY2625: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
| ( c_lessequals @ SY2623 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SY2624 ) @ SY2625 ) @ SV49 )
| ~ ( c_lessequals @ SY2623 @ SY2625 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SY2624 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2642,plain,
! [SV50: $i] :
( ( ! [SY2626: $i,SY2627: $i,SY2628: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SY2626 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SY2627 ) @ SY2628 ) @ SV50 )
| ~ ( c_lessequals @ SY2626 @ SY2627 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SY2628 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2643,plain,
! [SV51: $i] :
( ( ! [SY2629: $i] :
( ( hBOOL @ ( hAPP @ SV51 @ SY2629 ) )
| ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV51 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2644,plain,
! [SV52: $i] :
( ( ! [SY2630: $i] :
( ( c_lessequals @ ( c_Suc @ SV52 ) @ SY2630 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV52 @ SY2630 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2645,plain,
! [SV53: $i] :
( ( ! [SY2631: $i] :
( ( c_HOL_Oord__class_Oless @ SV53 @ SY2631 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV53 ) @ SY2631 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2646,plain,
! [SV54: $i] :
( ( ! [SY2632: $i] :
( ( c_lessequals @ ( c_Suc @ SV54 ) @ SY2632 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY2632 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2647,plain,
! [SV55: $i] :
( ( ! [SY2633: $i] :
( ( c_HOL_Oord__class_Oless @ SV55 @ SY2633 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV55 ) @ SY2633 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2648,plain,
! [SV56: $i] :
( ( ! [SY2634: $i,SY2635: $i] :
( ( c_HOL_Oord__class_Oless @ SV56 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2634 ) @ SY2635 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ SY2634 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2649,plain,
! [SV57: $i] :
( ( ! [SY2636: $i,SY2637: $i] :
( ( c_HOL_Oord__class_Oless @ SV57 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2636 ) @ SY2637 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SY2637 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2650,plain,
! [SV58: $i] :
( ( ! [SY2638: $i,SY2639: $i] :
( ( c_HOL_Oord__class_Oless @ SV58 @ SY2638 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SY2639 ) @ SY2638 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2651,plain,
! [SV59: $i] :
( ( ! [SY2640: $i,SY2641: $i] :
( ( c_HOL_Oord__class_Oless @ SV59 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2640 ) @ SY2641 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV59 @ SY2640 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2652,plain,
! [SV60: $i] :
( ( ! [SY2642: $i,SY2643: $i] :
( ( c_HOL_Oord__class_Oless @ SV60 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2642 ) @ SY2643 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV60 @ SY2643 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2653,plain,
! [SV61: $i] :
( ( ! [SY2644: $i,SY2645: $i,SY2646: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV61 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2644 @ SY2645 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SY2644 @ SY2646 @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ SY2644 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SY2644 @ SV61 )
| ~ ( c_lessequals @ SY2646 @ SY2645 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2654,plain,
! [SV62: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV62 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= SV62 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2655,plain,
! [SV63: $i] :
( ( ! [SY2647: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV63 ) @ SY2647 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV63 @ SY2647 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY2647 @ SV63 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2656,plain,
! [SV64: $i] :
( ( ! [SY2648: $i,SY2649: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV64 ) @ SY2648 @ SY2649 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV64 @ SY2648 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2649 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2657,plain,
! [SV65: $i] :
( ( ! [SY2650: $i,SY2651: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY2650 ) @ SY2651 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY2651 ) @ SY2650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2658,plain,
! [SV66: $i] :
( ( ! [SY2652: $i,SY2653: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV66 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SY2652 ) @ SY2653 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SY2653 ) @ SY2652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2659,plain,
! [SV67: $i] :
( ( ! [SY2654: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV67 ) @ SY2654 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2654 ) @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2660,plain,
! [SV68: $i] :
( ( ! [SY2655: $i,SY2656: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SY2655 ) @ SY2656 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SY2656 ) @ SY2655 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2661,plain,
! [SV69: $i] :
( ( ! [SY2657: $i,SY2658: $i,SY2659: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV69 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY2657 ) @ SY2658 ) @ SY2659 @ SV69 @ SV69 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY2657 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY2658 @ SY2659 @ SV69 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2662,plain,
! [SV70: $i] :
( ( ! [SY2660: $i,SY2661: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV70 @ SY2660 @ SY2661 ) @ SY2661 )
= ( c_List_Oreplicate @ SV70 @ SY2660 @ SY2661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2663,plain,
! [SV71: $i] :
( ( ! [SY2662: $i,SY2663: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SY2662 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SY2663 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2663 @ SV71 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2663 @ SY2662 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2664,plain,
! [SV72: $i] :
( ( ! [SY2664: $i,SY2665: $i] :
( ( ( hAPP @ SV72 @ SY2664 )
= SY2665 )
| ~ ( c_Type_Otyping @ SV72 @ ( c_Lambda_OdB_OVar @ SY2664 ) @ SY2665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2665,plain,
! [SV73: $i] :
( ( ! [SY2666: $i,SY2667: $i,SY2668: $i] :
( ( c_List_Otake @ ( c_Suc @ SV73 ) @ ( c_List_Olist_OCons @ SY2666 @ SY2667 @ SY2668 ) @ SY2668 )
= ( c_List_Olist_OCons @ SY2666 @ ( c_List_Otake @ SV73 @ SY2667 @ SY2668 ) @ SY2668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2666,plain,
! [SV74: $i] :
( ( ! [SY2669: $i,SY2670: $i,SY2671: $i] :
( ~ ( class_Orderings_Olinorder @ SV74 )
| ( c_lessequals @ SY2669 @ SY2670 @ SV74 )
| ( c_lessequals @ SY2669 @ SY2671 @ SV74 )
| ~ ( c_lessequals @ SY2669 @ ( c_Orderings_Oord__class_Omax @ SY2671 @ SY2670 @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2667,plain,
! [SV75: $i] :
( ( ! [SY2672: $i,SY2673: $i,SY2674: $i] :
( ( c_List_Olistsp @ SV75 @ SY2672 @ SY2673 )
| ~ ( c_List_Olistsp @ SV75 @ ( c_List_Oappend @ SY2674 @ SY2672 @ SY2673 ) @ SY2673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2668,plain,
! [SV76: $i] :
( ( ! [SY2675: $i,SY2676: $i,SY2677: $i] :
( ( c_List_Olistsp @ SV76 @ SY2675 @ SY2676 )
| ~ ( c_List_Olistsp @ SV76 @ ( c_List_Oappend @ SY2675 @ SY2677 @ SY2676 ) @ SY2676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2669,plain,
! [SV77: $i] :
( ( ! [SY2678: $i,SY2679: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV77 ) ) @ SY2678 ) @ SY2679 )
= ( c_Lambda_OdB_OVar @ SV77 ) )
| ( SV77 = SY2679 )
| ( c_HOL_Oord__class_Oless @ SY2679 @ SV77 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2670,plain,
! [SV78: $i] :
( ( ! [SY2680: $i,SY2681: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV78 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ ( c_HOL_Ominus__class_Ominus @ SY2680 @ SY2681 @ SV78 ) ) @ SY2681 )
= SY2680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2671,plain,
! [SV79: $i] :
( ( ! [SY2682: $i,SY2683: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV79 @ ( tc_List_Olist @ SY2682 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SY2683 @ SV79 @ SY2682 ) @ ( tc_List_Olist @ SY2682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2672,plain,
! [SV80: $i] :
( ( ! [SY2684: $i,SY2685: $i] :
( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2684 ) @ SY2685 ) @ SY2684 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV80 @ SY2685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2673,plain,
! [SV81: $i] :
( ( ! [SY2686: $i,SY2687: $i] :
( ~ ( hBOOL @ ( hAPP @ SV81 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2686 ) @ SY2687 ) @ SY2686 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV81 @ SY2687 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2674,plain,
! [SV82: $i] :
( ( ! [SY2688: $i,SY2689: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV82 @ SY2688 @ SY2689 ) @ SY2689 )
= ( c_List_Olist_OCons @ SV82 @ ( c_List_Olist_ONil @ SY2689 ) @ SY2689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2675,plain,
! [SV83: $i] :
( ( ! [SY2690: $i,SY2691: $i,SY2692: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV83 ) @ SY2690 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2691 ) @ SY2692 ) @ tc_nat )
| ~ ( c_lessequals @ SY2690 @ SY2692 @ tc_nat )
| ~ ( c_lessequals @ SV83 @ SY2691 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2676,plain,
! [SV84: $i] :
( ( ! [SY2693: $i,SY2694: $i,SY2695: $i,SY2696: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SY2693 ) @ SY2694 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SY2695 ) @ SY2696 ) @ SV84 )
| ~ ( c_lessequals @ SY2694 @ SY2696 @ SV84 )
| ~ ( c_lessequals @ SY2693 @ SY2695 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2677,plain,
! [SV85: $i] :
( ( ! [SY2697: $i,SY2698: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV85 @ SY2697 @ SY2698 ) @ ( tc_List_Olist @ SY2698 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SY2697 @ ( tc_List_Olist @ SY2698 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2678,plain,
! [SV86: $i] :
( ( ! [SY2699: $i,SY2700: $i,SY2701: $i,SY2702: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV86 @ SY2699 @ SY2700 ) @ SY2701 @ SY2702 @ SY2700 )
= ( c_List_Oappend @ SV86 @ ( c_List_Olist__update @ SY2699 @ ( c_HOL_Ominus__class_Ominus @ SY2701 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SY2700 ) ) @ tc_nat ) @ SY2702 @ SY2700 ) @ SY2700 ) )
| ( c_HOL_Oord__class_Oless @ SY2701 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SY2700 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2679,plain,
! [SV87: $i] :
( ( ! [SY2703: $i,SY2704: $i] :
( ( ( c_List_Otake @ SV87 @ SY2703 @ SY2704 )
= SY2703 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY2703 @ ( tc_List_Olist @ SY2704 ) ) @ SV87 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2680,plain,
! [SV88: $i] :
( ( ! [SY2705: $i] :
( ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SY2705 ) @ tc_nat )
| ~ ( c_lessequals @ SV88 @ SY2705 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2681,plain,
! [SV89: $i] :
( ( ! [SY2706: $i] :
( ( c_lessequals @ SV89 @ SY2706 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV89 @ ( c_Suc @ SY2706 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2682,plain,
! [SV90: $i] :
( ( ~ ( c_lessequals @ SV90 @ SV90 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV90 @ ( c_Suc @ SV90 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2683,plain,
! [SV91: $i] :
( ( ! [SY2707: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV91 )
| ( ( c_List_Olistsum @ SY2707 @ SV91 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SY2707 @ SV91 @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2684,plain,
! [SV92: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV92 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2685,plain,
! [SV93: $i] :
( ( ! [SY2708: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV93 @ SY2708 @ tc_nat ) @ ( c_Suc @ SV93 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2686,plain,
! [SV94: $i] :
( ( ! [SY2709: $i,SY2710: $i,SY2711: $i] :
( ( c_List_Odrop @ SV94 @ ( c_List_Otake @ SY2709 @ SY2710 @ SY2711 ) @ SY2711 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SY2709 @ SV94 @ tc_nat ) @ ( c_List_Odrop @ SV94 @ SY2710 @ SY2711 ) @ SY2711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2687,plain,
! [SV95: $i] :
( ( ! [SY2712: $i,SY2713: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY2712 ) @ SY2713 ) @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SY2713 @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SY2712 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2688,plain,
! [SV96: $i] :
( ( ! [SY2714: $i,SY2715: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV96 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2714 @ ( c_Suc @ SY2715 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SY2714 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SY2714 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2689,plain,
! [SV97: $i] :
( ( ! [SY2716: $i,SY2717: $i,SY2718: $i] :
( ~ ( class_Orderings_Opreorder @ SV97 )
| ( c_HOL_Oord__class_Oless @ SY2716 @ SY2717 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SY2718 @ SY2717 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SY2716 @ SY2718 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2690,plain,
! [SV98: $i] :
( ( ! [SY2719: $i,SY2720: $i,SY2721: $i] :
( ~ ( class_Orderings_Oorder @ SV98 )
| ( c_HOL_Oord__class_Oless @ SY2719 @ SY2720 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY2719 @ SY2721 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY2721 @ SY2720 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2691,plain,
! [SV99: $i] :
( ( ! [SY2722: $i,SY2723: $i] :
( ~ ( class_Orderings_Olinorder @ SV99 )
| ( ( c_Orderings_Oord__class_Omax @ SY2722 @ SY2723 @ SV99 )
= SY2723 )
| ~ ( c_lessequals @ SY2722 @ SY2723 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2692,plain,
! [SV100: $i] :
( ( ! [SY2724: $i,SY2725: $i] :
( ~ ( class_Orderings_Olinorder @ SV100 )
| ( ( c_Orderings_Oord__class_Omax @ SY2724 @ SY2725 @ SV100 )
= SY2724 )
| ~ ( c_lessequals @ SY2725 @ SY2724 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2693,plain,
! [SV101: $i] :
( ( ! [SY2726: $i,SY2727: $i,SY2728: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SY2726 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SY2727 ) @ SY2728 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SY2726 ) @ SY2727 ) ) @ SY2728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2694,plain,
! [SV102: $i] :
( ( ! [SY2729: $i,SY2730: $i,SY2731: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV102 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SY2729 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SY2730 ) @ SY2731 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SY2730 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SY2729 ) @ SY2731 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2695,plain,
! [SV103: $i] :
( ( ! [SY2732: $i,SY2733: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2732 ) @ SY2733 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2732 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ SY2733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2696,plain,
! [SV104: $i] :
( ( ! [SY2734: $i,SY2735: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV104 ) @ SY2734 ) ) @ SY2735 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV104 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2734 ) @ SY2735 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2697,plain,
! [SV105: $i] :
( ( ! [SY2736: $i,SY2737: $i,SY2738: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SY2736 ) @ SY2737 ) ) @ SY2738 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SY2736 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SY2737 ) @ SY2738 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2698,plain,
! [SV106: $i] :
( ( ! [SY2739: $i,SY2740: $i,SY2741: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV106 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SY2739 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SY2740 ) @ SY2741 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SY2740 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SY2739 ) @ SY2741 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2699,plain,
! [SV107: $i] :
( ( ! [SY2742: $i,SY2743: $i,SY2744: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV107 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SY2742 ) @ SY2743 ) ) @ SY2744 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SY2742 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SY2743 ) @ SY2744 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2700,plain,
! [SV108: $i] :
( ( ! [SY2745: $i,SY2746: $i,SY2747: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV108 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SY2745 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SY2746 ) @ SY2747 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SY2745 ) @ SY2746 ) ) @ SY2747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2701,plain,
! [SV109: $i] :
( ( ! [SY2748: $i,SY2749: $i,SY2750: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV109 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SY2748 ) @ SY2749 ) ) @ SY2750 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SY2748 ) @ SY2750 ) ) @ SY2749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2702,plain,
! [SV110: $i] :
( ( ! [SY2751: $i,SY2752: $i,SY2753: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY2751 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY2752 ) @ SY2753 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY2752 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY2751 ) @ SY2753 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2703,plain,
! [SV111: $i] :
( ( ! [SY2754: $i,SY2755: $i,SY2756: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY2754 ) @ SY2755 ) ) @ SY2756 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY2754 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY2755 ) @ SY2756 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2704,plain,
! [SV112: $i] :
( ( ! [SY2757: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV112 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2757 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2757 ) @ SV112 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2705,plain,
! [SV113: $i] :
( ( ! [SY2758: $i,SY2759: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV113 @ SY2758 @ SY2759 ) @ SY2759 )
= ( c_List_Olist_OCons @ SV113 @ SY2758 @ SY2759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2706,plain,
! [SV114: $i] :
( ( ! [SY2760: $i,SY2761: $i,SY2762: $i] :
( ( c_List_Otake @ SV114 @ ( c_List_Odrop @ SY2760 @ SY2761 @ SY2762 ) @ SY2762 )
= ( c_List_Odrop @ SY2760 @ ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV114 ) @ SY2760 ) @ SY2761 @ SY2762 ) @ SY2762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2707,plain,
! [SV115: $i] :
( ( ! [SY2763: $i,SY2764: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV115 ) @ SY2763 @ SY2764 )
= ( c_List_Olist_OCons @ SY2763 @ ( c_List_Oreplicate @ SV115 @ SY2763 @ SY2764 ) @ SY2764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2708,plain,
! [SV116: $i] :
( ( ! [SY2765: $i,SY2766: $i] :
( ( c_lessequals @ SV116 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2765 ) @ SY2766 ) @ tc_nat )
| ~ ( c_lessequals @ SV116 @ SY2766 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2709,plain,
! [SV117: $i] :
( ( ! [SY2767: $i,SY2768: $i] :
( ( c_lessequals @ SV117 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2767 ) @ SY2768 ) @ tc_nat )
| ~ ( c_lessequals @ SV117 @ SY2767 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2710,plain,
! [SV118: $i] :
( ( ! [SY2769: $i,SY2770: $i] :
( ( c_lessequals @ SV118 @ SY2769 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2770 ) @ SV118 ) @ SY2769 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2711,plain,
! [SV119: $i] :
( ( ! [SY2771: $i,SY2772: $i] :
( ( c_lessequals @ SV119 @ SY2771 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV119 ) @ SY2772 ) @ SY2771 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2712,plain,
! [SV120: $i] :
( ( ! [SY2773: $i,SY2774: $i] :
( ( c_lessequals @ SV120 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2773 ) @ SY2774 ) @ tc_nat )
| ~ ( c_lessequals @ SV120 @ SY2774 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2713,plain,
! [SV121: $i] :
( ( ! [SY2775: $i,SY2776: $i] :
( ( c_lessequals @ SV121 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2775 ) @ SY2776 ) @ tc_nat )
| ~ ( c_lessequals @ SV121 @ SY2775 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2714,plain,
! [SV122: $i] :
( ( ! [SY2777: $i,SY2778: $i] :
( ( c_List_Orev @ ( c_List_Otake @ SV122 @ SY2777 @ SY2778 ) @ SY2778 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SY2777 @ ( tc_List_Olist @ SY2778 ) ) @ SV122 @ tc_nat ) @ ( c_List_Orev @ SY2777 @ SY2778 ) @ SY2778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2715,plain,
! [SV123: $i] :
( ( ! [SY2779: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV123 ) ) @ SY2779 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV123 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ SV123 @ SY2779 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2716,plain,
! [SV124: $i] :
( ( ! [SY2780: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV124 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV124 ) @ SY2780 @ SV124 )
= ( c_HOL_Oone__class_Oone @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2717,plain,
! [SV125: $i] :
( ( ! [SY2781: $i,SY2782: $i,SY2783: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV125 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SY2781 @ SY2782 @ SV125 ) @ SY2783 @ SV125 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SY2781 @ SY2783 @ SV125 ) @ ( c_HOL_Ominus__class_Ominus @ SY2782 @ SY2783 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2718,plain,
! [SV126: $i] :
( ( ! [SY2784: $i,SY2785: $i,SY2786: $i] :
( ( hAPP @ ( c_COMBK @ SV126 @ SY2784 @ SY2785 ) @ SY2786 )
= SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2719,plain,
! [SV127: $i] :
( ( ! [SY2787: $i,SY2788: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ SV127 @ SY2787 @ SY2788 ) @ SY2788 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SY2787 @ ( tc_List_Olist @ SY2788 ) ) @ SV127 @ tc_nat ) @ ( c_List_Orev @ SY2787 @ SY2788 ) @ SY2788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2720,plain,
! [SV128: $i] :
( ( ! [SY2789: $i,SY2790: $i] :
( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SY2789 @ SY2790 @ SV128 )
| ( c_lessequals @ SY2790 @ SY2789 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2721,plain,
! [SV129: $i] :
( ( ! [SY2791: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ~ ( c_lessequals @ SY2791 @ SY2791 @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SY2791 @ SY2791 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2722,plain,
! [SV130: $i] :
( ( ! [SY2792: $i] :
( ~ ( class_Orderings_Olinorder @ SV130 )
| ( c_HOL_Oord__class_Oless @ SY2792 @ SY2792 @ SV130 )
| ( c_lessequals @ SY2792 @ SY2792 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2723,plain,
! [SV131: $i] :
( ( ! [SY2793: $i,SY2794: $i] :
( ~ ( class_Orderings_Olinorder @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SY2793 @ SY2794 @ SV131 )
| ~ ( c_lessequals @ SY2794 @ SY2793 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2724,plain,
! [SV132: $i] :
( ( ! [SY2795: $i,SY2796: $i] :
( ~ ( class_Orderings_Olinorder @ SV132 )
| ( c_lessequals @ SY2795 @ SY2796 @ SV132 )
| ( c_HOL_Oord__class_Oless @ SY2796 @ SY2795 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2725,plain,
! [SV133: $i] :
( ( ! [SY2797: $i,SY2798: $i] :
( ~ ( class_Orderings_Olinorder @ SV133 )
| ~ ( c_lessequals @ SY2797 @ SY2798 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SY2798 @ SY2797 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2726,plain,
! [SV134: $i] :
( ( ! [SY2799: $i,SY2800: $i] :
( ~ ( class_Orderings_Olinorder @ SV134 )
| ( c_HOL_Oord__class_Oless @ SY2799 @ SY2800 @ SV134 )
| ( c_lessequals @ SY2800 @ SY2799 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2727,plain,
! [SV135: $i] :
( ( ! [SY2801: $i,SY2802: $i] :
( ~ ( class_Orderings_Opreorder @ SV135 )
| ~ ( c_lessequals @ SY2801 @ SY2802 @ SV135 )
| ~ ( c_HOL_Oord__class_Oless @ SY2802 @ SY2801 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2728,plain,
! [SV136: $i] :
( ( ! [SY2803: $i] :
( ( hBOOL @ ( hAPP @ SV136 @ SY2803 ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV136 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2729,plain,
! [SV137: $i] :
( ( ! [SY2804: $i] :
( ( c_HOL_Oord__class_Oless @ SV137 @ SV137 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV137 ) ) @ SY2804 ) @ SV137 )
= SY2804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2730,plain,
! [SV138: $i] :
( ( ! [SY2805: $i] :
( ( hBOOL @ ( hAPP @ SV138 @ SY2805 ) )
| ~ ( hBOOL @ ( hAPP @ SV138 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2731,plain,
! [SV139: $i] :
( ( ! [SY2806: $i,SY2807: $i,SY2808: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
| ( c_HOL_Oord__class_Oless @ SY2806 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SY2807 ) @ SY2808 ) @ SV139 )
| ~ ( c_HOL_Oord__class_Oless @ SY2806 @ SY2808 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SY2807 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2732,plain,
! [SV140: $i] :
( ( ! [SY2809: $i,SY2810: $i,SY2811: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV140 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2809 @ SY2810 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SY2809 @ SY2811 @ SV140 ) @ SV140 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SY2809 @ SV140 )
| ~ ( c_lessequals @ SY2810 @ SY2811 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2733,plain,
! [SV141: $i] :
( ( ! [SY2812: $i,SY2813: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SY2812 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SY2813 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2813 @ SY2812 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2734,plain,
! [SV142: $i] :
( ( ! [SY2814: $i,SY2815: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV142 @ SY2814 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2815 @ SY2814 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV142 @ SY2815 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2735,plain,
! [SV143: $i] :
( ( ! [SY2816: $i,SY2817: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SY2816 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2817 @ SY2816 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV143 @ SY2817 @ tc_nat )
| ~ ( c_lessequals @ SY2816 @ SY2817 @ tc_nat )
| ~ ( c_lessequals @ SY2816 @ SV143 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2736,plain,
! [SV144: $i] :
( ( ! [SY2818: $i,SY2819: $i] :
( ( c_lessequals @ SV144 @ SY2818 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SY2819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2818 @ SY2819 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2819 @ SY2818 @ tc_nat )
| ~ ( c_lessequals @ SY2819 @ SV144 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2737,plain,
! [SV145: $i] :
( ( ! [SY2820: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV145 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV145 ) @ SY2820 ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2738,plain,
! [SV146: $i] :
( ( ! [SY2821: $i,SY2822: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV146 @ SY2821 @ tc_nat ) @ SY2822 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV146 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2821 ) @ SY2822 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2739,plain,
! [SV147: $i] :
( ( ! [SY2823: $i,SY2824: $i,SY2825: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV147 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2823 @ SY2824 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SY2825 @ SY2824 @ SV147 ) @ SV147 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SY2823 @ SV147 )
| ~ ( c_lessequals @ SY2823 @ SY2825 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2740,plain,
! [SV148: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV148 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV148 )
= ( c_HOL_Oone__class_Oone @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2741,plain,
! [SV149: $i] :
( ( ! [SY2826: $i,SY2827: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV149 @ SY2826 @ SY2827 ) @ SY2827 )
= ( c_List_Oappend @ ( c_List_Orev @ SY2826 @ SY2827 ) @ ( c_List_Olist_OCons @ SV149 @ ( c_List_Olist_ONil @ SY2827 ) @ SY2827 ) @ SY2827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2742,plain,
! [SV150: $i] :
( ( ! [SY2828: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV150 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SY2828 ) @ SV150 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ ( c_HOL_Oone__class_Oone @ SV150 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2828 @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2743,plain,
! [SV151: $i] :
( ( ! [SY2829: $i,SY2830: $i,SY2831: $i,SY2832: $i,SY2833: $i] :
( ( c_List_Ofoldl @ SV151 @ SY2829 @ ( c_List_Olist_OCons @ SY2830 @ SY2831 @ SY2832 ) @ SY2833 @ SY2832 )
= ( c_List_Ofoldl @ SV151 @ ( hAPP @ ( hAPP @ SV151 @ SY2829 ) @ SY2830 ) @ SY2831 @ SY2833 @ SY2832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2744,plain,
! [SV152: $i] :
( ( ! [SY2834: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV152 ) ) @ SY2834 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV152 ) @ ( c_Suc @ SY2834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2745,plain,
! [SV153: $i] :
( ( ! [SY2835: $i,SY2836: $i,SY2837: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV153 ) @ ( c_List_Olist_OCons @ SY2835 @ SY2836 @ SY2837 ) @ SY2837 )
= ( c_List_Odrop @ SV153 @ SY2836 @ SY2837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2746,plain,
! [SV154: $i] :
( ( ! [SY2838: $i,SY2839: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ SY2838 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2839 ) @ SY2838 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV154 @ SY2839 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2747,plain,
! [SV155: $i] :
( ( ! [SY2840: $i,SY2841: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SY2840 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SY2841 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY2840 @ SY2841 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2748,plain,
! [SV156: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV156 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2749,plain,
! [SV157: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV157 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2750,plain,
! [SV158: $i] :
( ( ! [SY2842: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV158 @ ( c_List_Olist_ONil @ SY2842 ) @ SY2842 ) @ SY2842 )
= ( c_List_Olist_OCons @ SV158 @ ( c_List_Olist_ONil @ SY2842 ) @ SY2842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2751,plain,
! [SV159: $i] :
( ( ! [SY2843: $i,SY2844: $i,SY2845: $i] :
( ~ ( class_Orderings_Olinorder @ SV159 )
| ( c_HOL_Oord__class_Oless @ SY2843 @ ( c_Orderings_Oord__class_Omax @ SY2844 @ SY2845 @ SV159 ) @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SY2843 @ SY2844 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2752,plain,
! [SV160: $i] :
( ( ! [SY2846: $i,SY2847: $i,SY2848: $i] :
( ~ ( class_Orderings_Olinorder @ SV160 )
| ( c_HOL_Oord__class_Oless @ SY2846 @ ( c_Orderings_Oord__class_Omax @ SY2847 @ SY2848 @ SV160 ) @ SV160 )
| ~ ( c_HOL_Oord__class_Oless @ SY2846 @ SY2848 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2753,plain,
! [SV161: $i] :
( ( ! [SY2849: $i,SY2850: $i,SY2851: $i] :
( ~ ( class_Orderings_Olinorder @ SV161 )
| ( c_HOL_Oord__class_Oless @ SY2849 @ ( c_Orderings_Oord__class_Omax @ SY2850 @ SY2851 @ SV161 ) @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SY2849 @ SY2850 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2754,plain,
! [SV162: $i] :
( ( ! [SY2852: $i,SY2853: $i,SY2854: $i] :
( ~ ( class_Orderings_Olinorder @ SV162 )
| ( c_HOL_Oord__class_Oless @ SY2852 @ ( c_Orderings_Oord__class_Omax @ SY2853 @ SY2854 @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SY2852 @ SY2854 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2755,plain,
! [SV163: $i] :
( ( ! [SY2855: $i,SY2856: $i,SY2857: $i] :
( ~ ( class_Orderings_Olinorder @ SV163 )
| ( c_HOL_Oord__class_Oless @ SY2855 @ SY2856 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY2855 @ SY2857 @ SV163 ) @ SY2856 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2756,plain,
! [SV164: $i] :
( ( ! [SY2858: $i] :
( ( c_List_Odrop @ SV164 @ ( c_List_Olist_ONil @ SY2858 ) @ SY2858 )
= ( c_List_Olist_ONil @ SY2858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2757,plain,
! [SV165: $i] :
( ( ! [SY2859: $i,SY2860: $i,SY2861: $i,SY2862: $i,SY2863: $i,SY2864: $i,SY2865: $i,SY2866: $i] :
( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SY2859 @ SY2860 ) @ SY2861 ) ) @ ( hAPP @ ( hAPP @ SY2859 @ SY2860 ) @ SY2862 ) )
= ( hAPP @ ( hAPP @ SY2859 @ SY2860 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2861 ) @ SY2862 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2863 @ SV165 @ SY2859 @ SY2864 @ SY2865 @ SY2866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2758,plain,
! [SV166: $i] :
( ( ! [SY2867: $i,SY2868: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ SV166 ) @ SY2867 @ SY2868 )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV166 @ SY2867 @ SY2868 ) ) @ SY2868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2759,plain,
! [SV167: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2760,plain,
! [SV168: $i] :
( ( ! [SY2869: $i,SY2870: $i,SY2871: $i,SY2872: $i,SY2873: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV168 @ SY2869 @ SY2870 @ SY2871 @ SY2872 ) @ SY2873 )
= ( hAPP @ SV168 @ ( hAPP @ SY2869 @ SY2873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2761,plain,
! [SV169: $i] :
( ( ! [SY2874: $i,SY2875: $i,SY2876: $i,SY2877: $i,SY2878: $i] :
( ( hAPP @ SV169 @ ( hAPP @ SY2874 @ SY2875 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV169 @ SY2874 @ SY2876 @ SY2877 @ SY2878 ) @ SY2875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2762,plain,
! [SV170: $i] :
( ( ! [SY2879: $i,SY2880: $i,SY2881: $i] :
( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SY2879 ) @ SY2880 @ SY2881 )
= ( c_List_Oappend @ ( c_List_Otake @ SV170 @ SY2880 @ SY2881 ) @ ( c_List_Otake @ SY2879 @ ( c_List_Odrop @ SV170 @ SY2880 @ SY2881 ) @ SY2881 ) @ SY2881 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SY2879 ) @ ( c_Nat_Osize__class_Osize @ SY2880 @ ( tc_List_Olist @ SY2881 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2763,plain,
! [SV171: $i] :
( ( ! [SY2882: $i,SY2883: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV171 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SY2882 @ SY2883 @ SV171 @ SV171 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SY2883 @ SY2882 @ SV171 @ SV171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2764,plain,
! [SV172: $i] :
( ( ! [SY2884: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV172 )
| ( ( c_Power_Opower__class_Opower @ SY2884 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV172 )
= SY2884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2765,plain,
! [SV173: $i] :
( ( ! [SY2885: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV173 )
| ( ( c_Power_Opower__class_Opower @ SY2885 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV173 )
= SY2885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2766,plain,
! [SV174: $i] :
( ( ! [SY2886: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV174 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ SY2886 ) @ SY2886 ) @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ SY2886 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2767,plain,
! [SV175: $i] :
( ( ! [SY2887: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV175 )
| ( c_HOL_Oord__class_Oless @ SY2887 @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SY2887 ) @ SY2887 ) @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2768,plain,
! [SV176: $i] :
( ( ! [SY2888: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV176 )
| ( c_HOL_Oord__class_Oless @ SY2888 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SY2888 ) @ SY2888 ) @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2769,plain,
! [SV177: $i] :
( ( ! [SY2889: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV177 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV177 ) @ SY2889 ) @ SY2889 ) @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ SY2889 @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2770,plain,
! [SV178: $i] :
( ( ! [SY2890: $i,SY2891: $i,SY2892: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV178 )
| ( c_HOL_Oord__class_Oless @ SY2890 @ SY2891 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SY2891 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2890 @ SY2892 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SY2891 @ SY2892 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2771,plain,
! [SV179: $i] :
( ( ! [SY2893: $i,SY2894: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV179 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SY2893 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SY2894 @ SV179 @ SV179 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SY2893 @ SY2894 @ SV179 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2772,plain,
! [SV180: $i] :
( ( ! [SY2895: $i,SY2896: $i,SY2897: $i] :
( ~ ( class_Orderings_Olinorder @ SV180 )
| ( c_lessequals @ SY2895 @ SY2896 @ SV180 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2897 @ SY2895 @ SV180 ) @ SY2896 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2773,plain,
! [SV181: $i] :
( ( ! [SY2898: $i,SY2899: $i,SY2900: $i] :
( ~ ( class_Orderings_Olinorder @ SV181 )
| ( c_lessequals @ SY2898 @ SY2899 @ SV181 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2898 @ SY2900 @ SV181 ) @ SY2899 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2774,plain,
! [SV182: $i] :
( ( ! [SY2901: $i,SY2902: $i,SY2903: $i] :
( ~ ( class_Orderings_Olinorder @ SV182 )
| ( c_lessequals @ SY2901 @ ( c_Orderings_Oord__class_Omax @ SY2902 @ SY2903 @ SV182 ) @ SV182 )
| ~ ( c_lessequals @ SY2901 @ SY2903 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2775,plain,
! [SV183: $i] :
( ( ! [SY2904: $i,SY2905: $i,SY2906: $i] :
( ~ ( class_Orderings_Olinorder @ SV183 )
| ( c_lessequals @ SY2904 @ ( c_Orderings_Oord__class_Omax @ SY2905 @ SY2906 @ SV183 ) @ SV183 )
| ~ ( c_lessequals @ SY2904 @ SY2905 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2776,plain,
! [SV184: $i] :
( ( ! [SY2907: $i,SY2908: $i,SY2909: $i] :
( ~ ( class_Orderings_Olinorder @ SV184 )
| ( c_lessequals @ SY2907 @ ( c_Orderings_Oord__class_Omax @ SY2908 @ SY2909 @ SV184 ) @ SV184 )
| ~ ( c_lessequals @ SY2907 @ SY2909 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2777,plain,
! [SV185: $i] :
( ( ! [SY2910: $i,SY2911: $i,SY2912: $i] :
( ~ ( class_Orderings_Olinorder @ SV185 )
| ( c_lessequals @ SY2910 @ ( c_Orderings_Oord__class_Omax @ SY2911 @ SY2912 @ SV185 ) @ SV185 )
| ~ ( c_lessequals @ SY2910 @ SY2911 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2778,plain,
! [SV186: $i] :
( ( ! [SY2913: $i,SY2914: $i,SY2915: $i] :
( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_lessequals @ SY2913 @ SY2914 @ SV186 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2915 @ SY2913 @ SV186 ) @ SY2914 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2779,plain,
! [SV187: $i] :
( ( ! [SY2916: $i,SY2917: $i,SY2918: $i] :
( ~ ( class_Orderings_Olinorder @ SV187 )
| ( c_lessequals @ SY2916 @ SY2917 @ SV187 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2916 @ SY2918 @ SV187 ) @ SY2917 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2780,plain,
! [SV188: $i] :
( ( ! [SY2919: $i,SY2920: $i] :
( ( c_lessequals @ SV188 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2919 ) @ SY2920 ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV188 @ SY2920 @ tc_nat ) @ SY2919 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2781,plain,
! [SV189: $i] :
( ( ! [SY2921: $i,SY2922: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV189 @ SY2921 @ tc_nat ) @ SY2922 @ tc_nat )
| ~ ( c_lessequals @ SV189 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2922 ) @ SY2921 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2782,plain,
! [SV190: $i] :
( ( ! [SY2923: $i,SY2924: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV190 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ ( c_Power_Opower__class_Opower @ SY2923 @ SY2924 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SY2923 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2783,plain,
! [SV191: $i] :
( ( ! [SY2925: $i,SY2926: $i,SY2927: $i] :
( ~ ( class_Orderings_Olinorder @ SV191 )
| ( c_HOL_Oord__class_Oless @ SY2925 @ SY2926 @ SV191 )
| ( c_HOL_Oord__class_Oless @ SY2925 @ SY2927 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SY2925 @ ( c_Orderings_Oord__class_Omax @ SY2927 @ SY2926 @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2784,plain,
! [SV192: $i] :
( ( ! [SY2928: $i,SY2929: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SY2928 ) @ SY2929 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2928 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SY2928 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2929 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2785,plain,
! [SV193: $i] :
( ( ! [SY2930: $i,SY2931: $i,SY2932: $i] :
( ( c_List_Ofoldl @ SV193 @ SY2930 @ ( c_List_Olist_ONil @ SY2931 ) @ SY2932 @ SY2931 )
= SY2930 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2786,plain,
! [SV194: $i] :
( ( ! [SY2933: $i,SY2934: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV194 ) @ SY2933 @ SY2934 )
= ( c_Lambda_OdB_OVar @ SV194 ) )
| ( SV194 = SY2934 )
| ( c_HOL_Oord__class_Oless @ SY2934 @ SV194 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2787,plain,
! [SV195: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV195 ) @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2788,plain,
! [SV196: $i] :
( ( ! [SY2935: $i,SY2936: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV196 @ SY2935 @ SY2936 ) @ ( tc_List_Olist @ SY2936 ) ) @ ( c_Nat_Osize__class_Osize @ SY2935 @ ( tc_List_Olist @ SY2936 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2789,plain,
! [SV197: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV197 ) @ ( tc_List_Olist @ SV197 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2790,plain,
! [SV198: $i] :
( ( ! [SY2937: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV198 ) @ ( c_Suc @ SY2937 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV198 @ SY2937 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2791,plain,
! [SV199: $i] :
( ( ! [SY2938: $i,SY2939: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SY2938 ) @ SY2939 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SY2939 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ SY2938 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2792,plain,
! [SV200: $i] :
( ( ! [SY2940: $i,SY2941: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SY2940 ) @ SY2941 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_lessequals @ SY2941 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SY2940 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2793,plain,
! [SV201: $i] :
( ( ! [SY2942: $i] :
( ( SV201 = SY2942 )
| ( c_HOL_Oord__class_Oless @ SV201 @ SY2942 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV201 @ ( c_Suc @ SY2942 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2794,plain,
! [SV202: $i] :
( ( ! [SY2943: $i] :
( ( SV202 = SY2943 )
| ~ ( c_HOL_Oord__class_Oless @ SY2943 @ ( c_Suc @ SV202 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2943 @ SV202 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2795,plain,
! [SV203: $i] :
( ( ! [SY2944: $i] :
( ( SV203 = SY2944 )
| ~ ( c_HOL_Oord__class_Oless @ SV203 @ ( c_Suc @ SY2944 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV203 @ SY2944 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2796,plain,
! [SV204: $i] :
( ( ! [SY2945: $i,SY2946: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ SY2945 ) @ SY2946 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ ( c_HOL_Ominus__class_Ominus @ SY2945 @ SY2946 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY2946 @ SY2945 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2797,plain,
! [SV205: $i] :
( ( ! [SY2947: $i,SY2948: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SY2947 ) @ SY2948 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV205 @ SY2948 @ tc_nat ) ) @ SY2947 ) )
| ~ ( c_lessequals @ SY2948 @ SV205 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2798,plain,
! [SV206: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV206 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ ( c_HOL_Oone__class_Oone @ SV206 ) @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2799,plain,
! [SV207: $i] :
( ( ! [SY2949: $i,SY2950: $i,SY2951: $i,SY2952: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV207 @ SY2949 @ SY2950 ) @ SY2951 @ SY2952 @ SY2950 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV207 @ SY2951 @ SY2952 @ SY2950 ) @ SY2949 @ SY2950 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2951 @ ( c_Nat_Osize__class_Osize @ SV207 @ ( tc_List_Olist @ SY2950 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2800,plain,
! [SV208: $i] :
( ( ! [SY2953: $i,SY2954: $i,SY2955: $i,SY2956: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV208 @ SY2953 @ SY2954 ) @ SY2955 @ SY2956 @ SY2954 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV208 @ SY2955 @ SY2956 @ SY2954 ) @ SY2953 @ SY2954 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2955 @ ( c_Nat_Osize__class_Osize @ SV208 @ ( tc_List_Olist @ SY2954 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2801,plain,
! [SV209: $i] :
( ( ! [SY2957: $i,SY2958: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV209 @ ( c_HOL_Ominus__class_Ominus @ SY2957 @ SY2958 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV209 ) @ SY2958 ) @ SY2957 @ tc_nat ) )
| ~ ( c_lessequals @ SY2958 @ SY2957 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2802,plain,
! [SV210: $i] :
( ( ! [SY2959: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV210 ) @ SY2959 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV210 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ SY2959 ) ) )
| ( SV210
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2803,plain,
! [SV211: $i] :
( ( ! [SY2960: $i,SY2961: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV211 @ SY2960 @ tc_nat ) @ SY2961 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV211 @ SY2961 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2804,plain,
! [SV212: $i] :
( ( ! [SY2962: $i,SY2963: $i,SY2964: $i] :
( ( c_Type_Otype_Otype__rec @ SV212 @ SY2962 @ ( c_Type_Otype_OAtom @ SY2963 ) @ SY2964 )
= ( hAPP @ SV212 @ SY2963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2805,plain,
! [SV213: $i] :
( ( ! [SY2965: $i,SY2966: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SY2965 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2966 @ SY2965 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ SV213 @ SY2966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2806,plain,
! [SV214: $i] :
( ( ! [SY2967: $i,SY2968: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ SV214 @ SY2967 @ SY2968 ) @ ( tc_List_Olist @ SY2968 ) )
= ( c_Nat_Osize__class_Osize @ SY2967 @ ( tc_List_Olist @ SY2968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2807,plain,
! [SV215: $i] :
( ( ! [SY2969: $i] :
( ( c_List_Olist_ONil @ SV215 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2969 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2808,plain,
! [SV216: $i] :
( ( ! [SY2970: $i,SY2971: $i] :
( ~ ( class_Orderings_Opreorder @ SV216 )
| ( c_HOL_Oord__class_Oless @ SY2970 @ SY2971 @ SV216 )
| ( c_lessequals @ SY2971 @ SY2970 @ SV216 )
| ~ ( c_lessequals @ SY2970 @ SY2971 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2809,plain,
! [SV217: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV217 @ SV217 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2810,plain,
! [SV218: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV218 @ SV218 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2811,plain,
! [SV219: $i] :
( ( ! [SY2972: $i] :
( ~ ( class_Orderings_Oorder @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ SY2972 @ SY2972 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2812,plain,
! [SV220: $i] :
( ( ! [SY2973: $i] :
( ~ ( class_Orderings_Olinorder @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SY2973 @ SY2973 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2813,plain,
! [SV221: $i] :
( ( ! [SY2974: $i] :
( ~ ( class_Orderings_Opreorder @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SY2974 @ SY2974 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2814,plain,
! [SV222: $i] :
( ( ! [SY2975: $i] :
( ~ ( c_lessequals @ SV222 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2975 ) @ SV222 ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2975 ) @ SV222 ) @ SV222 @ tc_nat )
= SY2975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2815,plain,
! [SV223: $i] :
( ( ! [SY2976: $i,SY2977: $i] :
( ( ( c_Lambda_Oliftn @ SV223 @ ( c_Lambda_OdB_OVar @ SY2976 ) @ SY2977 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2976 ) @ SV223 ) ) )
| ( c_HOL_Oord__class_Oless @ SY2976 @ SY2977 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2816,plain,
! [SV224: $i] :
( ( ! [SY2978: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV224 ) ) @ SY2978 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV224 ) @ SY2978 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2817,plain,
! [SV225: $i] :
( ( ! [SY2979: $i,SY2980: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ SV225 @ SY2979 @ SY2980 ) @ ( tc_List_Olist @ SY2980 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV225 @ ( tc_List_Olist @ SY2980 ) ) ) @ ( c_Nat_Osize__class_Osize @ SY2979 @ ( tc_List_Olist @ SY2980 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2818,plain,
! [SV226: $i] :
( ( ! [SY2981: $i,SY2982: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ SV226 @ SY2981 @ SY2982 ) @ ( tc_List_Olist @ SY2982 ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SY2981 @ ( tc_List_Olist @ SY2982 ) ) @ SV226 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2819,plain,
! [SV227: $i] :
( ( ! [SY2983: $i,SY2984: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SY2983 ) @ SY2984 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SY2984 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SY2983 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2820,plain,
! [SV228: $i] :
( ( ! [SY2985: $i] : ( c_lessequals @ SV228 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV228 ) @ SY2985 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2821,plain,
! [SV229: $i] :
( ( ! [SY2986: $i] : ( c_lessequals @ SV229 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2986 ) @ SV229 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2822,plain,
! [SV230: $i] :
( ( ! [SY2987: $i] : ( c_lessequals @ SV230 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV230 ) @ SY2987 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2823,plain,
! [SV231: $i] :
( ( ! [SY2988: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV231 @ SY2988 @ tc_nat ) ) @ SY2988 )
= ( c_Orderings_Oord__class_Omax @ SV231 @ SY2988 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2824,plain,
! [SV232: $i] :
( ( ! [SY2989: $i,SY2990: $i,SY2991: $i] :
( ( ( c_List_Otake @ SV232 @ ( c_List_Olist_OCons @ SY2989 @ SY2990 @ SY2991 ) @ SY2991 )
= ( c_List_Olist_OCons @ SY2989 @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV232 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY2990 @ SY2991 ) @ SY2991 ) )
| ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2825,plain,
! [SV233: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV233 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV233 ) @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2826,plain,
! [SV234: $i] :
( ( ! [SY2992: $i,SY2993: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV234 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SY2992 @ SY2993 @ SV234 ) @ SV234 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SY2992 ) @ ( c_List_Olistsum @ SY2993 @ SV234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2827,plain,
! [SV235: $i] :
( ( ! [SY2994: $i,SY2995: $i] :
( ( c_Lambda_Oliftn @ SV235 @ ( c_Lambda_OdB_OAbs @ SY2994 ) @ SY2995 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV235 @ SY2994 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2995 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2828,plain,
! [SV236: $i] :
( ( ! [SY2996: $i,SY2997: $i,SY2998: $i,SY2999: $i,SY3000: $i,SY3001: $i] :
( ( ( hAPP @ ( hAPP @ SV236 @ SY2996 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SY2996 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2997 @ SY2998 @ SV236 @ SY2999 @ SY3000 @ SY3001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2829,plain,
! [SV237: $i] :
( ( ! [SY3002: $i,SY3003: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV237 )
| ( c_HOL_Oord__class_Oless @ SY3002 @ SY3003 @ SV237 )
| ( c_HOL_Oord__class_Oless @ SY3003 @ SY3002 @ SV237 )
| ( SY3003 = SY3002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2830,plain,
! [SV238: $i] :
( ( ! [SY3004: $i,SY3005: $i] :
( ~ ( class_Orderings_Olinorder @ SV238 )
| ( SY3004 = SY3005 )
| ( c_HOL_Oord__class_Oless @ SY3005 @ SY3004 @ SV238 )
| ( c_HOL_Oord__class_Oless @ SY3004 @ SY3005 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2831,plain,
! [SV239: $i] :
( ( ! [SY3006: $i] :
( ( SV239 = SY3006 )
| ~ ( c_lessequals @ SY3006 @ SV239 @ tc_nat )
| ~ ( c_lessequals @ SV239 @ SY3006 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2832,plain,
! [SV240: $i] :
( ( ! [SY3007: $i] :
( ( c_HOL_Oord__class_Oless @ SV240 @ SY3007 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3007 @ SV240 @ tc_nat )
| ( SY3007 = SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2833,plain,
! [SV241: $i] :
( ( ! [SY3008: $i,SY3009: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV241 @ SY3008 ) @ SY3009 ) )
| ( c_HOL_Oord__class_Oless @ SY3008 @ SY3009 @ tc_nat )
| ( SY3009 = SY3008 )
| ( c_HOL_Oord__class_Oless @ SY3009 @ SY3008 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2834,plain,
! [SV242: $i] :
( ( ! [SY3010: $i,SY3011: $i,SY3012: $i,SY3013: $i] :
( ( SV242 = SY3010 )
| ~ ( c_Type_Otyping @ SY3011 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3012 ) @ SY3013 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3010 )
| ~ ( c_Type_Otyping @ SY3011 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3012 ) @ SY3013 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2835,plain,
! [SV243: $i] :
( ( ! [SY3014: $i,SY3015: $i,SY3016: $i] :
( ~ ( class_Orderings_Olinorder @ SV243 )
| ( c_HOL_Oord__class_Oless @ SY3014 @ SY3015 @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY3016 @ SY3014 @ SV243 ) @ SY3015 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2836,plain,
! [SV244: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV244 )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV244 ) @ SV244 )
= ( c_HOL_Ozero__class_Ozero @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2837,plain,
! [SV245: $i] :
( ( ! [SY3017: $i,SY3018: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV245 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SY3017 @ SY3018 @ SV245 ) @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3018 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SY3017 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2838,plain,
! [SV246: $i] :
( ( ! [SY3019: $i,SY3020: $i] :
( ( ( c_List_Orotate @ SV246 @ SY3019 @ SY3020 )
= SY3019 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY3019 @ ( tc_List_Olist @ SY3020 ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2839,plain,
! [SV247: $i] :
( ( ! [SY3021: $i,SY3022: $i,SY3023: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV247 ) @ SY3021 ) @ SY3022 ) ) @ SY3023 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV247 ) @ SY3023 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3021 ) @ SY3023 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3022 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3023 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3022 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2840,plain,
! [SV248: $i] :
( ( ! [SY3024: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV248 @ SY3024 @ tc_nat ) @ SV248 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2841,plain,
! [SV249: $i] :
( ( ! [SY3025: $i] : ( c_Type_Otyping @ SV249 @ ( c_Lambda_OdB_OVar @ SY3025 ) @ ( hAPP @ SV249 @ SY3025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2842,plain,
! [SV250: $i] :
( ( ! [SY3026: $i,SY3027: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SY3026 ) @ SY3027 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SY3027 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SY3026 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2843,plain,
! [SV251: $i] :
( ( ! [SY3028: $i,SY3029: $i,SY3030: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV251 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3028 @ SY3029 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SY3030 @ SY3029 @ SV251 ) @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3029 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SY3028 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SY3028 @ SY3030 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2844,plain,
! [SV252: $i] :
( ( ! [SY3031: $i,SY3032: $i,SY3033: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV252 @ SY3031 @ SY3032 ) @ SY3033 @ SY3032 )
= ( c_List_Olist_OCons @ SV252 @ ( c_List_Oappend @ SY3031 @ SY3033 @ SY3032 ) @ SY3032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2845,plain,
! [SV253: $i] :
( ( ! [SY3034: $i,SY3035: $i,SY3036: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV253 @ SY3034 @ SY3035 ) @ SY3036 @ SY3035 )
= ( c_List_Olist_OCons @ SV253 @ ( c_List_Oappend @ SY3034 @ SY3036 @ SY3035 ) @ SY3035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2846,plain,
! [SV254: $i] :
( ( ! [SY3037: $i,SY3038: $i] :
( SV254
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY3037 @ ( tc_List_Olist @ SY3038 ) ) @ ( c_List_Oappend @ SY3037 @ SV254 @ SY3038 ) @ SY3038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2847,plain,
! [SV255: $i] :
( ( ! [SY3039: $i,SY3040: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SY3039 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3040 @ SY3039 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV255 @ SY3040 @ tc_nat ) )
| ~ ( c_lessequals @ SY3039 @ SY3040 @ tc_nat )
| ~ ( c_lessequals @ SY3039 @ SV255 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2848,plain,
! [SV256: $i] :
( ( ! [SY3041: $i,SY3042: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SY3041 @ tc_nat ) @ SY3042 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SY3042 @ tc_nat ) @ SY3041 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2849,plain,
! [SV257: $i] :
( ( ! [SY3043: $i,SY3044: $i,SY3045: $i] :
( ( c_List_Omap @ ( c_COMBK @ SV257 @ SY3043 @ SY3044 ) @ SY3045 @ SY3044 @ SY3043 )
= ( c_List_Oreplicate @ ( c_Nat_Osize__class_Osize @ SY3045 @ ( tc_List_Olist @ SY3044 ) ) @ SV257 @ SY3043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2850,plain,
! [SV258: $i] :
( ( ! [SY3046: $i,SY3047: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SY3046 ) @ SY3047 ) @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SY3047 @ SV258 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SY3046 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2851,plain,
! [SV259: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SY3048 ) @ SY3049 ) @ SV259 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SY3049 @ SV259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SY3048 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2852,plain,
! [SV260: $i] :
( ( ! [SY3050: $i,SY3051: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV260 ) @ SY3050 @ SY3051 @ SV260 )
= ( c_List_Olist_ONil @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2853,plain,
! [SV261: $i] :
( ( ! [SY3052: $i,SY3053: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV261 ) @ SY3052 @ SY3053 @ SV261 )
= ( c_List_Olist_ONil @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2854,plain,
! [SV262: $i] :
( ( ! [SY3054: $i,SY3055: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV262 ) @ SY3054 @ SY3055 @ SV262 )
= ( c_List_Olist_ONil @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2855,plain,
! [SV263: $i] :
( ( ! [SY3056: $i,SY3057: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV263 @ SY3056 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3057 @ SY3056 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3056 @ SV263 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV263 @ SY3057 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2856,plain,
! [SV264: $i] :
( ( ! [SY3058: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV264 ) @ SY3058 @ tc_nat )
| ( ( c_Suc @ SV264 )
= SY3058 )
| ~ ( c_HOL_Oord__class_Oless @ SV264 @ SY3058 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2857,plain,
! [SV265: $i] :
( ( ! [SY3059: $i] :
( ~ ( c_lessequals @ SV265 @ SY3059 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SY3059 ) @ SV265 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2858,plain,
! [SV266: $i] :
( ( ! [SY3060: $i] :
( ( c_lessequals @ ( c_Suc @ SV266 ) @ SY3060 @ tc_nat )
| ( c_lessequals @ SY3060 @ SV266 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2859,plain,
! [SV267: $i] :
( ( ! [SY3061: $i,SY3062: $i,SY3063: $i] :
( ( c_List_Olist_OCons @ SV267 @ ( c_List_Oappend @ SY3061 @ SY3062 @ SY3063 ) @ SY3063 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV267 @ SY3061 @ SY3063 ) @ SY3062 @ SY3063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2860,plain,
! [SV268: $i] :
( ( ! [SY3064: $i,SY3065: $i,SY3066: $i] :
( ( c_List_Olist_OCons @ SV268 @ ( c_List_Oappend @ SY3064 @ SY3065 @ SY3066 ) @ SY3066 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV268 @ SY3064 @ SY3066 ) @ SY3065 @ SY3066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2861,plain,
! [SV269: $i] :
( ( ! [SY3067: $i,SY3068: $i] :
( ( c_lessequals @ SV269 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3067 ) @ SV269 ) @ SY3068 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3068 @ SY3067 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2862,plain,
! [SV270: $i] :
( ( ! [SY3069: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV270 @ ( tc_List_Olist @ SY3069 ) ) @ tc_nat )
| ( SV270
= ( c_List_Olist_ONil @ SY3069 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2863,plain,
! [SV271: $i] :
( ( ! [SY3070: $i,SY3071: $i,SY3072: $i,SY3073: $i,SY3074: $i,SY3075: $i,SY3076: $i,SY3077: $i] :
( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SY3070 @ SY3071 ) @ SY3072 ) ) @ SY3073 )
= ( hAPP @ ( hAPP @ SY3070 @ ( hAPP @ ( hAPP @ SV271 @ SY3071 ) @ SY3073 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SY3072 ) @ SY3073 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3074 @ SY3070 @ SV271 @ SY3075 @ SY3076 @ SY3077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2864,plain,
! [SV272: $i] :
( ( ! [SY3078: $i,SY3079: $i,SY3080: $i,SY3081: $i,SY3082: $i,SY3083: $i,SY3084: $i,SY3085: $i] :
( ( ( hAPP @ ( hAPP @ SV272 @ SY3078 ) @ ( hAPP @ ( hAPP @ SY3079 @ SY3080 ) @ SY3081 ) )
= ( hAPP @ ( hAPP @ SY3079 @ ( hAPP @ ( hAPP @ SV272 @ SY3078 ) @ SY3080 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SY3078 ) @ SY3081 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3079 @ SV272 @ SY3082 @ SY3083 @ SY3084 @ SY3085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2865,plain,
! [SV273: $i] :
( ( ! [SY3086: $i,SY3087: $i,SY3088: $i,SY3089: $i,SY3090: $i,SY3091: $i,SY3092: $i] :
( ( ( hAPP @ ( hAPP @ SV273 @ SY3086 ) @ SY3087 )
= ( hAPP @ ( hAPP @ SV273 @ SY3087 ) @ SY3086 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3088 @ SV273 @ SY3089 @ SY3090 @ SY3091 @ SY3092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2866,plain,
! [SV274: $i] :
( ( ! [SY3093: $i,SY3094: $i,SY3095: $i,SY3096: $i,SY3097: $i,SY3098: $i,SY3099: $i,SY3100: $i] :
( ( ( hAPP @ ( hAPP @ SV274 @ SY3093 ) @ ( hAPP @ ( hAPP @ SV274 @ SY3094 ) @ SY3095 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SY3093 ) @ SY3094 ) ) @ SY3095 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3096 @ SV274 @ SY3097 @ SY3098 @ SY3099 @ SY3100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2867,plain,
! [SV275: $i] :
( ( ! [SY3101: $i,SY3102: $i,SY3103: $i,SY3104: $i,SY3105: $i,SY3106: $i] :
( ( ( hAPP @ ( hAPP @ SV275 @ SY3101 ) @ SY3102 )
= SY3102 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3103 @ SV275 @ SY3104 @ SY3105 @ SY3101 @ SY3106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2868,plain,
! [SV276: $i] :
( ( ! [SY3107: $i,SY3108: $i,SY3109: $i,SY3110: $i,SY3111: $i,SY3112: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SY3107 ) @ SY3108 )
= SY3107 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3109 @ SV276 @ SY3110 @ SY3107 @ SY3111 @ SY3112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2869,plain,
! [SV277: $i] :
( ( ! [SY3113: $i,SY3114: $i,SY3115: $i,SY3116: $i,SY3117: $i,SY3118: $i,SY3119: $i] :
( ( ( hAPP @ ( hAPP @ SV277 @ SY3113 ) @ SY3114 )
= ( hAPP @ ( hAPP @ SV277 @ SY3114 ) @ SY3113 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SY3115 @ SY3116 @ SY3117 @ SY3118 @ SY3119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2870,plain,
! [SV278: $i] :
( ( ! [SY3120: $i,SY3121: $i,SY3122: $i,SY3123: $i,SY3124: $i,SY3125: $i,SY3126: $i,SY3127: $i] :
( ( ( hAPP @ ( hAPP @ SV278 @ SY3120 ) @ ( hAPP @ ( hAPP @ SV278 @ SY3121 ) @ SY3122 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SY3120 ) @ SY3121 ) ) @ SY3122 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SY3123 @ SY3124 @ SY3125 @ SY3126 @ SY3127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2871,plain,
! [SV279: $i] :
( ( ! [SY3128: $i,SY3129: $i,SY3130: $i,SY3131: $i,SY3132: $i,SY3133: $i] :
( ( ( hAPP @ ( hAPP @ SV279 @ SY3128 ) @ SY3129 )
= SY3129 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SY3130 @ SY3131 @ SY3128 @ SY3132 @ SY3133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2872,plain,
! [SV280: $i] :
( ( ! [SY3134: $i,SY3135: $i,SY3136: $i,SY3137: $i,SY3138: $i,SY3139: $i,SY3140: $i,SY3141: $i] :
( ( ( hAPP @ ( hAPP @ SV280 @ SY3134 ) @ ( hAPP @ ( hAPP @ SV280 @ SY3135 ) @ SY3136 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SY3134 ) @ SY3135 ) ) @ SY3136 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SY3137 @ SY3138 @ SY3139 @ SY3140 @ SY3141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2873,plain,
! [SV281: $i] :
( ( ! [SY3142: $i,SY3143: $i,SY3144: $i,SY3145: $i,SY3146: $i,SY3147: $i,SY3148: $i] :
( ( ( hAPP @ ( hAPP @ SV281 @ SY3142 ) @ SY3143 )
= ( hAPP @ ( hAPP @ SV281 @ SY3143 ) @ SY3142 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SY3144 @ SY3145 @ SY3146 @ SY3147 @ SY3148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2874,plain,
! [SV282: $i] :
( ( ! [SY3149: $i,SY3150: $i,SY3151: $i,SY3152: $i,SY3153: $i,SY3154: $i,SY3155: $i,SY3156: $i] :
( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SY3149 ) @ SY3150 ) ) @ SY3151 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SY3149 ) @ SY3151 ) ) @ SY3150 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SY3152 @ SY3153 @ SY3154 @ SY3155 @ SY3156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2875,plain,
! [SV283: $i] :
( ( ! [SY3157: $i,SY3158: $i,SY3159: $i,SY3160: $i,SY3161: $i,SY3162: $i,SY3163: $i,SY3164: $i] :
( ( ( hAPP @ ( hAPP @ SV283 @ SY3157 ) @ ( hAPP @ ( hAPP @ SV283 @ SY3158 ) @ SY3159 ) )
= ( hAPP @ ( hAPP @ SV283 @ SY3158 ) @ ( hAPP @ ( hAPP @ SV283 @ SY3157 ) @ SY3159 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SY3160 @ SY3161 @ SY3162 @ SY3163 @ SY3164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2876,plain,
! [SV284: $i] :
( ( ! [SY3165: $i,SY3166: $i,SY3167: $i,SY3168: $i,SY3169: $i,SY3170: $i,SY3171: $i,SY3172: $i] :
( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SY3165 ) @ SY3166 ) ) @ SY3167 )
= ( hAPP @ ( hAPP @ SV284 @ SY3165 ) @ ( hAPP @ ( hAPP @ SV284 @ SY3166 ) @ SY3167 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SY3168 @ SY3169 @ SY3170 @ SY3171 @ SY3172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2877,plain,
! [SV285: $i] :
( ( ! [SY3173: $i,SY3174: $i,SY3175: $i,SY3176: $i,SY3177: $i,SY3178: $i,SY3179: $i,SY3180: $i,SY3181: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SY3173 ) @ SY3174 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SY3175 ) @ SY3176 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SY3173 ) @ SY3175 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SY3174 ) @ SY3176 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SY3177 @ SY3178 @ SY3179 @ SY3180 @ SY3181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2878,plain,
! [SV286: $i] :
( ( ! [SY3182: $i,SY3183: $i,SY3184: $i,SY3185: $i,SY3186: $i,SY3187: $i,SY3188: $i,SY3189: $i] :
( ( ( hAPP @ ( hAPP @ SV286 @ SY3182 ) @ ( hAPP @ ( hAPP @ SV286 @ SY3183 ) @ SY3184 ) )
= ( hAPP @ ( hAPP @ SV286 @ SY3183 ) @ ( hAPP @ ( hAPP @ SV286 @ SY3182 ) @ SY3184 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3185 @ SV286 @ SY3186 @ SY3187 @ SY3188 @ SY3189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2879,plain,
! [SV287: $i] :
( ( ! [SY3190: $i,SY3191: $i,SY3192: $i,SY3193: $i,SY3194: $i,SY3195: $i,SY3196: $i,SY3197: $i] :
( ( ( hAPP @ ( hAPP @ SV287 @ SY3190 ) @ ( hAPP @ ( hAPP @ SV287 @ SY3191 ) @ SY3192 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SY3190 ) @ SY3191 ) ) @ SY3192 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3193 @ SV287 @ SY3194 @ SY3195 @ SY3196 @ SY3197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2880,plain,
! [SV288: $i] :
( ( ! [SY3198: $i,SY3199: $i,SY3200: $i,SY3201: $i,SY3202: $i,SY3203: $i,SY3204: $i,SY3205: $i] :
( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SY3198 ) @ SY3199 ) ) @ SY3200 )
= ( hAPP @ ( hAPP @ SV288 @ SY3198 ) @ ( hAPP @ ( hAPP @ SV288 @ SY3199 ) @ SY3200 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3201 @ SV288 @ SY3202 @ SY3203 @ SY3204 @ SY3205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2881,plain,
! [SV289: $i] :
( ( ! [SY3206: $i,SY3207: $i,SY3208: $i,SY3209: $i,SY3210: $i,SY3211: $i,SY3212: $i,SY3213: $i] :
( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SY3206 ) @ SY3207 ) ) @ SY3208 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SY3206 ) @ SY3208 ) ) @ SY3207 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3209 @ SV289 @ SY3210 @ SY3211 @ SY3212 @ SY3213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2882,plain,
! [SV290: $i] :
( ( ! [SY3214: $i,SY3215: $i,SY3216: $i,SY3217: $i,SY3218: $i,SY3219: $i,SY3220: $i,SY3221: $i,SY3222: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SY3214 ) @ SY3215 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SY3216 ) @ SY3217 ) )
= ( hAPP @ ( hAPP @ SV290 @ SY3216 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SY3214 ) @ SY3215 ) ) @ SY3217 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3218 @ SV290 @ SY3219 @ SY3220 @ SY3221 @ SY3222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2883,plain,
! [SV291: $i] :
( ( ! [SY3223: $i,SY3224: $i,SY3225: $i,SY3226: $i,SY3227: $i,SY3228: $i,SY3229: $i,SY3230: $i,SY3231: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SY3223 ) @ SY3224 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SY3225 ) @ SY3226 ) )
= ( hAPP @ ( hAPP @ SV291 @ SY3223 ) @ ( hAPP @ ( hAPP @ SV291 @ SY3224 ) @ ( hAPP @ ( hAPP @ SV291 @ SY3225 ) @ SY3226 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3227 @ SV291 @ SY3228 @ SY3229 @ SY3230 @ SY3231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2884,plain,
! [SV292: $i] :
( ( ! [SY3232: $i,SY3233: $i,SY3234: $i,SY3235: $i,SY3236: $i,SY3237: $i,SY3238: $i,SY3239: $i,SY3240: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SY3232 ) @ SY3233 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SY3234 ) @ SY3235 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SY3232 ) @ SY3234 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SY3233 ) @ SY3235 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3236 @ SV292 @ SY3237 @ SY3238 @ SY3239 @ SY3240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2885,plain,
! [SV293: $i] :
( ( ! [SY3241: $i,SY3242: $i,SY3243: $i,SY3244: $i,SY3245: $i,SY3246: $i] :
( ( ( hAPP @ ( hAPP @ SV293 @ SY3241 ) @ SY3242 )
= SY3241 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3243 @ SV293 @ SY3244 @ SY3245 @ SY3242 @ SY3246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2886,plain,
! [SV294: $i] :
( ( ! [SY3247: $i,SY3248: $i,SY3249: $i,SY3250: $i,SY3251: $i,SY3252: $i] :
( ( ( hAPP @ ( hAPP @ SV294 @ SY3247 ) @ SY3248 )
= SY3248 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3249 @ SV294 @ SY3250 @ SY3251 @ SY3247 @ SY3252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2887,plain,
! [SV295: $i] :
( ( ! [SY3253: $i,SY3254: $i,SY3255: $i,SY3256: $i,SY3257: $i,SY3258: $i] :
( ( ( hAPP @ ( hAPP @ SV295 @ SY3253 ) @ SY3254 )
= SY3254 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3255 @ SV295 @ SY3256 @ SY3254 @ SY3257 @ SY3258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2888,plain,
! [SV296: $i] :
( ( ! [SY3259: $i,SY3260: $i,SY3261: $i,SY3262: $i,SY3263: $i,SY3264: $i] :
( ( ( hAPP @ ( hAPP @ SV296 @ SY3259 ) @ SY3260 )
= SY3259 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3261 @ SV296 @ SY3262 @ SY3259 @ SY3263 @ SY3264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2889,plain,
! [SV297: $i] :
( ( ! [SY3265: $i,SY3266: $i,SY3267: $i,SY3268: $i,SY3269: $i,SY3270: $i,SY3271: $i,SY3272: $i] :
( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SY3265 @ SY3266 ) @ SY3267 ) ) @ SY3268 )
= ( hAPP @ ( hAPP @ SY3265 @ ( hAPP @ ( hAPP @ SV297 @ SY3266 ) @ SY3268 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SY3267 ) @ SY3268 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3265 @ SV297 @ SY3269 @ SY3270 @ SY3271 @ SY3272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2890,plain,
! [SV298: $i] :
( ( ! [SY3273: $i,SY3274: $i,SY3275: $i,SY3276: $i,SY3277: $i,SY3278: $i,SY3279: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ SY3273 ) @ SY3274 )
= ( hAPP @ ( hAPP @ SV298 @ SY3274 ) @ SY3273 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3275 @ SV298 @ SY3276 @ SY3277 @ SY3278 @ SY3279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2891,plain,
! [SV299: $i] :
( ( ! [SY3280: $i,SY3281: $i,SY3282: $i,SY3283: $i,SY3284: $i,SY3285: $i] :
( ( ( hAPP @ ( hAPP @ SV299 @ SY3280 ) @ SY3281 )
= SY3280 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SY3282 @ SY3283 @ SY3281 @ SY3284 @ SY3285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2892,plain,
! [SV300: $i] :
( ( ! [SY3286: $i,SY3287: $i,SY3288: $i,SY3289: $i,SY3290: $i,SY3291: $i] :
( ( ( hAPP @ ( hAPP @ SV300 @ SY3286 ) @ SY3287 )
= SY3287 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SY3288 @ SY3289 @ SY3286 @ SY3290 @ SY3291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2893,plain,
! [SV301: $i] :
( ( ! [SY3292: $i,SY3293: $i,SY3294: $i,SY3295: $i,SY3296: $i,SY3297: $i] :
( ( ( hAPP @ ( hAPP @ SV301 @ SY3292 ) @ SY3292 )
= ( hAPP @ ( hAPP @ SY3293 @ ( hAPP @ ( hAPP @ SV301 @ SY3294 ) @ SY3294 ) ) @ SY3292 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SY3293 @ SY3295 @ SY3296 @ SY3294 @ SY3297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2894,plain,
! [SV302: $i] :
( ( ! [SY3298: $i,SY3299: $i,SY3300: $i,SY3301: $i,SY3302: $i,SY3303: $i,SY3304: $i] :
( ( ( hAPP @ ( hAPP @ SV302 @ SY3298 ) @ ( hAPP @ ( hAPP @ SY3299 @ SY3300 ) @ SY3298 ) )
= ( hAPP @ ( hAPP @ SY3299 @ ( hAPP @ ( hAPP @ SV302 @ SY3300 ) @ SY3301 ) ) @ SY3298 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SY3299 @ SY3302 @ SY3303 @ SY3301 @ SY3304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2895,plain,
! [SV303: $i] :
( ( ! [SY3305: $i,SY3306: $i,SY3307: $i,SY3308: $i,SY3309: $i,SY3310: $i,SY3311: $i] :
( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SY3305 @ SY3306 ) @ SY3307 ) ) @ SY3307 )
= ( hAPP @ ( hAPP @ SY3305 @ ( hAPP @ ( hAPP @ SV303 @ SY3306 ) @ SY3308 ) ) @ SY3307 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SY3305 @ SY3309 @ SY3310 @ SY3308 @ SY3311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2896,plain,
! [SV304: $i] :
( ( ! [SY3312: $i,SY3313: $i,SY3314: $i,SY3315: $i,SY3316: $i,SY3317: $i,SY3318: $i,SY3319: $i] :
( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SY3312 @ SY3313 ) @ SY3314 ) ) @ ( hAPP @ ( hAPP @ SY3312 @ SY3315 ) @ SY3314 ) )
= ( hAPP @ ( hAPP @ SY3312 @ ( hAPP @ ( hAPP @ SV304 @ SY3313 ) @ SY3315 ) ) @ SY3314 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SY3312 @ SY3316 @ SY3317 @ SY3318 @ SY3319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2897,plain,
! [SV305: $i] :
( ( ! [SY3320: $i,SY3321: $i,SY3322: $i] :
( ~ ( hBOOL @ ( hAPP @ SV305 @ ( c_Type_Otype_Otype__case @ SY3320 @ SY3321 @ ( c_Type_Otype_OAtom @ SY3322 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV305 @ ( hAPP @ SY3320 @ SY3322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2898,plain,
! [SV306: $i] :
( ( ! [SY3323: $i,SY3324: $i,SY3325: $i] :
( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_Type_Otype_Otype__case @ SY3323 @ SY3324 @ ( c_Type_Otype_OAtom @ SY3325 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV306 @ ( hAPP @ SY3323 @ SY3325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2899,plain,
! [SV307: $i] :
( ( ! [SY3326: $i,SY3327: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV307 @ SY3326 @ SY3327 ) @ SY3327 )
= SY3326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2900,plain,
! [SV308: $i] :
( ( ! [SY3328: $i,SY3329: $i,SY3330: $i,SY3331: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3328 ) @ SY3329 ) ) @ ( c_Suc @ SY3330 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3331 ) @ SY3328 ) @ SY3330 ) ) @ SY3329 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ SY3331 ) @ SY3329 ) ) @ SY3328 ) @ SY3330 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3329 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3330 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2901,plain,
! [SV309: $i] :
( ( ! [SY3332: $i,SY3333: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ SV309 @ SY3332 @ SY3333 ) @ ( c_List_Odrop @ SV309 @ SY3332 @ SY3333 ) @ SY3333 )
= SY3332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2902,plain,
! [SV310: $i] :
( ( ! [SY3334: $i,SY3335: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV310 ) @ SY3334 @ tc_nat ) @ ( c_Suc @ SY3335 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV310 @ SY3334 @ tc_nat ) @ SY3335 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2903,plain,
! [SV311: $i] :
( ( ! [SY3336: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV311 @ ( c_Suc @ SY3336 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV311 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY3336 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2904,plain,
! [SV312: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV312 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2905,plain,
! [SV313: $i] :
( ( ! [SY3337: $i,SY3338: $i,SY3339: $i,SY3340: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SY3337 ) @ SY3338 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SY3339 ) @ SY3340 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SY3337 ) @ SY3339 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SY3338 ) @ SY3340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2906,plain,
! [SV314: $i] :
( ( ! [SY3341: $i,SY3342: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SY3341 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SY3342 ) )
| ~ ( c_Lambda_Obeta @ SY3341 @ SY3342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2907,plain,
! [SV315: $i] :
( ( ! [SY3343: $i,SY3344: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV315 ) @ SY3343 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3344 ) @ SY3343 ) )
| ~ ( c_Lambda_Obeta @ SV315 @ SY3344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2908,plain,
! [SV316: $i] :
( ( ! [SY3345: $i,SY3346: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV316 @ SY3345 ) @ ( c_List_Olist_OCons @ SY3346 @ ( c_List_Olist_ONil @ SY3345 ) @ SY3345 ) @ SY3345 ) @ SY3345 )
= ( c_List_Olist_OCons @ SY3346 @ SV316 @ SY3345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2909,plain,
! [SV317: $i] :
( ( ! [SY3347: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV317 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3347 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2910,plain,
! [SV318: $i] :
( ( ! [SY3348: $i,SY3349: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV318 ) @ SY3348 @ SY3349 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV318 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3349 @ SV318 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2911,plain,
! [SV319: $i] :
( ( ! [SY3350: $i,SY3351: $i] :
( ~ ( class_Orderings_Olinorder @ SV319 )
| ( ( c_Orderings_Oord__class_Omax @ SY3350 @ SY3351 @ SV319 )
= ( c_Orderings_Oord__class_Omax @ SY3351 @ SY3350 @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2912,plain,
! [SV320: $i] :
( ( ! [SY3352: $i,SY3353: $i] :
( ( ( c_Lambda_Oliftn @ SV320 @ ( c_Lambda_OdB_OVar @ SY3352 ) @ SY3353 )
= ( c_Lambda_OdB_OVar @ SY3352 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3352 @ SY3353 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2913,plain,
! [SV321: $i] :
( ( ! [SY3354: $i,SY3355: $i] :
( ( ( c_List_Odrop @ SV321 @ SY3354 @ SY3355 )
= ( c_List_Olist_ONil @ SY3355 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY3354 @ ( tc_List_Olist @ SY3355 ) ) @ SV321 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2914,plain,
! [SV322: $i] :
( ( c_lessequals @ ( c_Suc @ SV322 ) @ ( c_Suc @ SV322 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2915,plain,
! [SV323: $i] :
( ( ! [SY3356: $i,SY3357: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ SV323 @ SY3356 @ SY3357 ) @ SY3357 )
| ~ ( c_List_Odistinct @ SY3356 @ SY3357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2916,plain,
! [SV324: $i] :
( ( ! [SY3358: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ SV324 @ SY3358 ) @ SY3358 )
| ~ ( c_List_Odistinct @ SV324 @ SY3358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2917,plain,
! [SV325: $i] :
( ( ! [SY3359: $i] :
( ( c_List_Odistinct @ SV325 @ SY3359 )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ SV325 @ SY3359 ) @ SY3359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2918,plain,
! [SV326: $i] :
( ( ! [SY3360: $i,SY3361: $i,SY3362: $i] :
( ( c_List_Odrop @ SV326 @ ( c_List_Oreplicate @ SY3360 @ SY3361 @ SY3362 ) @ SY3362 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SY3360 @ SV326 @ tc_nat ) @ SY3361 @ SY3362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2919,plain,
! [SV327: $i] :
( ( ! [SY3363: $i] :
( ( c_HOL_Oord__class_Oless @ SV327 @ SY3363 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3363 @ SV327 @ tc_nat )
| ( SY3363 = SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2920,plain,
! [SV328: $i] :
( ( ! [SY3364: $i,SY3365: $i] :
( ~ ( class_Orderings_Oorder @ SV328 )
| ( SY3364 = SY3365 )
| ~ ( c_lessequals @ SY3365 @ SY3364 @ SV328 )
| ~ ( c_lessequals @ SY3364 @ SY3365 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2921,plain,
! [SV329: $i] :
( ( ! [SY3366: $i,SY3367: $i] :
( ~ ( class_Orderings_Olinorder @ SV329 )
| ( c_HOL_Oord__class_Oless @ SY3366 @ SY3367 @ SV329 )
| ( c_HOL_Oord__class_Oless @ SY3367 @ SY3366 @ SV329 )
| ( SY3367 = SY3366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2922,plain,
! [SV330: $i] :
( ( ! [SY3368: $i,SY3369: $i] :
( ~ ( class_Orderings_Oorder @ SV330 )
| ( SY3368 = SY3369 )
| ~ ( c_lessequals @ SY3369 @ SY3368 @ SV330 )
| ~ ( c_lessequals @ SY3368 @ SY3369 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2923,plain,
! [SV331: $i] :
( ( ! [SY3370: $i,SY3371: $i] :
( ~ ( class_Orderings_Oorder @ SV331 )
| ( SY3370 = SY3371 )
| ~ ( c_lessequals @ SY3370 @ SY3371 @ SV331 )
| ~ ( c_lessequals @ SY3371 @ SY3370 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2924,plain,
! [SV332: $i] :
( ( ! [SY3372: $i,SY3373: $i,SY3374: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV332 @ SY3372 @ SY3373 ) @ ( c_List_Oreplicate @ SY3374 @ SY3372 @ SY3373 ) @ SY3373 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY3374 @ SY3372 @ SY3373 ) @ ( c_List_Oreplicate @ SV332 @ SY3372 @ SY3373 ) @ SY3373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2925,plain,
! [SV333: $i] :
( ( ! [SY3375: $i,SY3376: $i] :
( ~ ( class_Orderings_Olinorder @ SV333 )
| ( c_HOL_Oord__class_Oless @ SY3375 @ SY3376 @ SV333 )
| ( SY3376 = SY3375 )
| ( c_HOL_Oord__class_Oless @ SY3376 @ SY3375 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2926,plain,
! [SV334: $i] :
( ( ! [SY3377: $i,SY3378: $i] :
( ~ ( class_Orderings_Olinorder @ SV334 )
| ( SY3377 = SY3378 )
| ( c_HOL_Oord__class_Oless @ SY3377 @ SY3378 @ SV334 )
| ( c_HOL_Oord__class_Oless @ SY3378 @ SY3377 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2927,plain,
! [SV335: $i] :
( ( ! [SY3379: $i,SY3380: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV335 )
| ( c_lessequals @ SY3379 @ SY3380 @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY3379 @ SY3380 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2928,plain,
! [SV336: $i] :
( ( ! [SY3381: $i,SY3382: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV336 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY3381 @ SY3382 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ SY3381 @ SY3382 @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2929,plain,
! [SV337: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV337 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV337 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV337 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2930,plain,
! [SV338: $i] :
( ( ( SV338
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV338 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV338 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2931,plain,
! [SV339: $i] :
( ( ! [SY3383: $i] :
( ~ ( class_Orderings_Olinorder @ SV339 )
| ( ( c_Orderings_Oord__class_Omax @ SY3383 @ SY3383 @ SV339 )
= SY3383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2932,plain,
! [SV340: $i] :
( ( ! [SY3384: $i,SY3385: $i,SY3386: $i,SY3387: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SY3384 ) @ SY3385 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SY3386 ) @ SY3387 ) @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SY3385 @ SY3387 @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SY3384 @ SY3386 @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2933,plain,
! [SV341: $i] :
( ( ! [SY3388: $i,SY3389: $i,SY3390: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV341 ) @ SY3388 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3389 ) @ SY3390 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3388 @ SY3390 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV341 @ SY3389 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2934,plain,
! [SV342: $i] :
( ( ! [SY3391: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV342 ) @ SY3391 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY3391 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2935,plain,
! [SV343: $i] :
( ( ! [SY3392: $i] :
( ( c_lessequals @ SV343 @ SY3392 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV343 @ SY3392 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2936,plain,
! [SV344: $i] :
( ( ! [SY3393: $i] :
( ( c_lessequals @ SV344 @ SY3393 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV344 @ SY3393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2937,plain,
! [SV345: $i] :
( ( ! [SY3394: $i,SY3395: $i] :
( ~ ( class_Orderings_Oorder @ SV345 )
| ( c_lessequals @ SY3394 @ SY3395 @ SV345 )
| ~ ( c_HOL_Oord__class_Oless @ SY3394 @ SY3395 @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2938,plain,
! [SV346: $i] :
( ( ! [SY3396: $i,SY3397: $i] :
( ~ ( class_Orderings_Opreorder @ SV346 )
| ( c_lessequals @ SY3396 @ SY3397 @ SV346 )
| ~ ( c_HOL_Oord__class_Oless @ SY3396 @ SY3397 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2939,plain,
! [SV347: $i] :
( ( ! [SY3398: $i,SY3399: $i,SY3400: $i,SY3401: $i] :
( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3398 ) @ SY3399 ) @ SY3400 )
| ~ ( c_Type_Otyping @ SV347 @ SY3399 @ SY3401 )
| ~ ( c_Type_Otyping @ SV347 @ SY3398 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY3401 ) @ SY3400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2940,plain,
! [SV348: $i] :
( ( c_List_Odistinct @ ( c_List_Olist_ONil @ SV348 ) @ SV348 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2941,plain,
! [SV349: $i] :
( ( ! [SY3402: $i,SY3403: $i,SY3404: $i] :
( ( ( c_List_Olist__update @ SV349 @ SY3402 @ SY3403 @ SY3404 )
= ( c_List_Oappend @ ( c_List_Otake @ SY3402 @ SV349 @ SY3404 ) @ ( c_List_Olist_OCons @ SY3403 @ ( c_List_Odrop @ ( c_Suc @ SY3402 ) @ SV349 @ SY3404 ) @ SY3404 ) @ SY3404 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3402 @ ( c_Nat_Osize__class_Osize @ SV349 @ ( tc_List_Olist @ SY3404 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2942,plain,
! [SV350: $i] :
( ( ! [SY3405: $i,SY3406: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV350 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ ( c_Power_Opower__class_Opower @ SY3405 @ ( c_Suc @ SY3406 ) @ SV350 ) @ SV350 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ SY3405 @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2943,plain,
! [SV351: $i] :
( ( ! [SY3407: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV351 ) @ SY3407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2944,plain,
! [SV352: $i] :
( ( ! [SY3408: $i,SY3409: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SY3408 @ SY3409 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV352 ) @ SY3409 ) @ ( c_Suc @ SY3408 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY3409 @ SY3408 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2945,plain,
! [SV353: $i] :
( ( ! [SY3410: $i,SY3411: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV353 )
| ( c_HOL_Oord__class_Oless @ SY3410 @ SY3411 @ SV353 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY3410 @ SY3411 @ SV353 ) @ ( c_HOL_Ozero__class_Ozero @ SV353 ) @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2946,plain,
! [SV354: $i] :
( ( ! [SY3412: $i,SY3413: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV354 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY3412 @ SY3413 @ SV354 ) @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV354 )
| ~ ( c_HOL_Oord__class_Oless @ SY3412 @ SY3413 @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2947,plain,
! [SV355: $i] :
( ( ! [SY3414: $i,SY3415: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV355 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3414 @ SV355 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3415 @ SV355 ) @ SV355 )
| ~ ( c_HOL_Oord__class_Oless @ SY3414 @ SY3415 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2948,plain,
! [SV356: $i] :
( ( ! [SY3416: $i,SY3417: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV356 )
| ( c_HOL_Oord__class_Oless @ SY3416 @ SY3417 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3416 @ SV356 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3417 @ SV356 ) @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2949,plain,
! [SV357: $i] :
( ( c_HOL_Oord__class_Oless @ SV357 @ ( c_Suc @ SV357 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2950,plain,
! [SV358: $i] :
( ( c_HOL_Oord__class_Oless @ SV358 @ ( c_Suc @ SV358 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2951,plain,
! [SV359: $i] :
( ( ! [SY3418: $i,SY3419: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV359 ) @ SY3418 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3419 @ SY3418 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV359 @ SY3419 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2952,plain,
! [SV360: $i] :
( ( ! [SY3420: $i,SY3421: $i,SY3422: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV360 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SY3420 ) @ SY3421 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SY3422 ) @ SY3421 ) @ SV360 )
| ~ ( c_lessequals @ SY3420 @ SY3422 @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2953,plain,
! [SV361: $i] :
( ( ! [SY3423: $i,SY3424: $i,SY3425: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV361 )
| ( c_lessequals @ SY3423 @ SY3424 @ SV361 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SY3423 ) @ SY3425 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SY3424 ) @ SY3425 ) @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2954,plain,
! [SV362: $i] :
( ( ! [SY3426: $i,SY3427: $i,SY3428: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV362 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SY3426 ) @ SY3427 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SY3426 ) @ SY3428 ) @ SV362 )
| ~ ( c_lessequals @ SY3427 @ SY3428 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2955,plain,
! [SV363: $i] :
( ( ! [SY3429: $i,SY3430: $i,SY3431: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV363 )
| ( c_lessequals @ SY3429 @ SY3430 @ SV363 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SY3431 ) @ SY3429 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SY3431 ) @ SY3430 ) @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2956,plain,
! [SV364: $i] :
( ( ! [SY3432: $i,SY3433: $i,SY3434: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV364 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SY3432 ) @ SY3433 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SY3434 ) @ SY3433 ) @ SV364 )
| ~ ( c_lessequals @ SY3432 @ SY3434 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2957,plain,
! [SV365: $i] :
( ( ! [SY3435: $i,SY3436: $i,SY3437: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV365 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SY3435 ) @ SY3436 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SY3435 ) @ SY3437 ) @ SV365 )
| ~ ( c_lessequals @ SY3436 @ SY3437 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2958,plain,
! [SV366: $i] :
( ( ! [SY3438: $i,SY3439: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV366 ) @ SY3438 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3439 ) @ SY3438 ) @ tc_nat )
| ~ ( c_lessequals @ SV366 @ SY3439 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2959,plain,
! [SV367: $i] :
( ( ! [SY3440: $i,SY3441: $i] :
( ( c_lessequals @ SV367 @ SY3440 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3441 ) @ SV367 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3441 ) @ SY3440 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2960,plain,
! [SV368: $i] :
( ( ! [SY3442: $i,SY3443: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SY3442 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SY3443 ) @ tc_nat )
| ~ ( c_lessequals @ SY3442 @ SY3443 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2961,plain,
! [SV369: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV369 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV369 ) @ ( c_HOL_Oone__class_Oone @ SV369 ) @ SV369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2962,plain,
! [SV370: $i] :
( ( ! [SY3444: $i,SY3445: $i,SY3446: $i] :
( ( ( c_List_Olist__update @ SV370 @ SY3444 @ SY3445 @ SY3446 )
= SV370 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SY3446 ) ) @ SY3444 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2963,plain,
! [SV371: $i] :
( ( ! [SY3447: $i] :
( ~ ( c_lessequals @ SV371 @ SY3447 @ tc_nat )
| ( SY3447
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3447 @ SV371 @ tc_nat ) ) @ SV371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2964,plain,
! [SV372: $i] :
( ( ! [SY3448: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV372 ) @ ( c_HOL_Ominus__class_Ominus @ SY3448 @ SV372 @ tc_nat ) )
= SY3448 )
| ~ ( c_lessequals @ SV372 @ SY3448 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2965,plain,
! [SV373: $i] :
( ( ! [SY3449: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV373 @ SY3449 @ tc_nat ) ) @ SY3449 )
= SV373 )
| ~ ( c_lessequals @ SY3449 @ SV373 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2966,plain,
! [SV374: $i] :
( ( ! [SY3450: $i,SY3451: $i,SY3452: $i,SY3453: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV374 @ SY3450 @ SY3451 @ SY3452 ) @ SY3453 )
= ( hAPP @ SV374 @ ( c_HOL_Ominus__class_Ominus @ SY3453 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3450 @ SY3453 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2967,plain,
! [SV375: $i] :
( ( ! [SY3454: $i,SY3455: $i,SY3456: $i,SY3457: $i,SY3458: $i,SY3459: $i,SY3460: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SY3454 ) @ ( hAPP @ ( hAPP @ SY3455 @ SY3454 ) @ SY3456 ) )
= ( hAPP @ ( hAPP @ SY3455 @ SY3454 ) @ ( c_Suc @ SY3456 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3457 @ SV375 @ SY3455 @ SY3458 @ SY3459 @ SY3460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2968,plain,
! [SV376: $i] :
( ( ! [SY3461: $i,SY3462: $i,SY3463: $i,SY3464: $i,SY3465: $i,SY3466: $i,SY3467: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SY3461 @ SY3462 ) @ SY3463 ) ) @ SY3462 )
= ( hAPP @ ( hAPP @ SY3461 @ SY3462 ) @ ( c_Suc @ SY3463 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3464 @ SV376 @ SY3461 @ SY3465 @ SY3466 @ SY3467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2969,plain,
! [SV377: $i] :
( ( ! [SY3468: $i,SY3469: $i,SY3470: $i,SY3471: $i,SY3472: $i,SY3473: $i,SY3474: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SY3468 ) @ ( c_Suc @ SY3469 ) )
= ( hAPP @ ( hAPP @ SY3470 @ SY3468 ) @ ( hAPP @ ( hAPP @ SV377 @ SY3468 ) @ SY3469 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3471 @ SY3470 @ SV377 @ SY3472 @ SY3473 @ SY3474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2970,plain,
! [SV378: $i] :
( ( ! [SY3475: $i,SY3476: $i,SY3477: $i,SY3478: $i,SY3479: $i,SY3480: $i,SY3481: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ SY3475 ) @ ( c_Suc @ SY3476 ) )
= ( hAPP @ ( hAPP @ SY3477 @ SY3475 ) @ ( hAPP @ ( hAPP @ SV378 @ SY3475 ) @ SY3476 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3478 @ SY3477 @ SV378 @ SY3479 @ SY3480 @ SY3481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2971,plain,
! [SV379: $i] :
( ( ! [SY3482: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV379 )
| ( c_HOL_Oord__class_Oless @ SY3482 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SY3482 ) @ ( c_HOL_Oone__class_Oone @ SV379 ) ) @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2972,plain,
! [SV380: $i] :
( ( ! [SY3483: $i,SY3484: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ ( c_HOL_Ominus__class_Ominus @ SY3483 @ SY3484 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ SY3483 ) @ SY3484 @ tc_nat ) )
| ~ ( c_lessequals @ SY3484 @ SY3483 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2973,plain,
! [SV381: $i] :
( ( ! [SY3485: $i,SY3486: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV381 @ SY3485 @ tc_nat ) ) @ SY3486 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV381 ) @ SY3486 ) @ SY3485 @ tc_nat ) )
| ~ ( c_lessequals @ SY3485 @ SV381 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2974,plain,
! [SV382: $i] :
( ( ! [SY3487: $i,SY3488: $i,SY3489: $i] :
( ( c_List_Odrop @ SV382 @ ( c_List_Odrop @ SY3487 @ SY3488 @ SY3489 ) @ SY3489 )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV382 ) @ SY3487 ) @ SY3488 @ SY3489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2975,plain,
! [SV383: $i] :
( ( ! [SY3490: $i,SY3491: $i,SY3492: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV383 )
| ( c_lessequals @ SY3490 @ SY3491 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SY3491 @ SV383 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3490 @ ( c_Suc @ SY3492 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SY3491 @ ( c_Suc @ SY3492 ) @ SV383 ) @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2976,plain,
! [SV384: $i] :
( ( ! [SY3493: $i,SY3494: $i,SY3495: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV384 ) @ SY3493 ) @ SY3494 @ SY3495 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV384 @ SY3494 @ SY3495 ) @ ( c_List_Oreplicate @ SY3493 @ SY3494 @ SY3495 ) @ SY3495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2977,plain,
! [SV385: $i] :
( ( ! [SY3496: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV385 @ SY3496 )
= ( c_List_Olist_ONil @ SY3496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2978,plain,
! [SV386: $i] :
( ( ! [SY3497: $i,SY3498: $i,SY3499: $i] :
( ( c_List_Otake @ SV386 @ ( c_List_Oappend @ SY3497 @ SY3498 @ SY3499 ) @ SY3499 )
= ( c_List_Oappend @ ( c_List_Otake @ SV386 @ SY3497 @ SY3499 ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV386 @ ( c_Nat_Osize__class_Osize @ SY3497 @ ( tc_List_Olist @ SY3499 ) ) @ tc_nat ) @ SY3498 @ SY3499 ) @ SY3499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2979,plain,
! [SV387: $i] :
( ( ! [SY3500: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV387 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV387 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3500 @ SV387 ) @ SV387 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3500 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2980,plain,
! [SV388: $i] :
( ( ! [SY3501: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV388 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3501 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV388 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3501 @ SV388 ) @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2981,plain,
! [SV389: $i] :
( ( ! [SY3502: $i,SY3503: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV389 @ SY3502 @ SY3503 ) @ SY3503 )
= ( c_List_Olist_ONil @ SY3503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2982,plain,
! [SV390: $i] :
( ( ! [SY3504: $i] :
( ~ ( class_Power_Opower @ SV390 )
| ( ( c_Power_Opower__class_Opower @ SY3504 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV390 )
= ( c_HOL_Oone__class_Oone @ SV390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2983,plain,
! [SV391: $i] :
( ( ! [SY3505: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV391 )
| ( ( c_Power_Opower__class_Opower @ SY3505 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV391 )
= ( c_HOL_Oone__class_Oone @ SV391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2984,plain,
! [SV392: $i] :
( ( ! [SY3506: $i,SY3507: $i] :
( ( c_List_Odistinct @ SV392 @ SY3506 )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ SY3507 @ SV392 @ SY3506 ) @ SY3506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2985,plain,
! [SV393: $i] :
( ( ! [SY3508: $i,SY3509: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ SV393 @ SY3508 @ SY3509 ) @ SY3509 )
| ~ ( c_List_Odistinct @ SY3508 @ SY3509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2986,plain,
! [SV394: $i] :
( ( ! [SY3510: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV394 )
| ( ( c_List_Olistsum @ ( c_List_Orev @ SY3510 @ SV394 ) @ SV394 )
= ( c_List_Olistsum @ SY3510 @ SV394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2987,plain,
! [SV395: $i] :
( ( ! [SY3511: $i,SY3512: $i,SY3513: $i] :
( ( c_List_Olistsp @ SV395 @ ( c_List_Oappend @ SY3511 @ SY3512 @ SY3513 ) @ SY3513 )
| ~ ( c_List_Olistsp @ SV395 @ SY3512 @ SY3513 )
| ~ ( c_List_Olistsp @ SV395 @ SY3511 @ SY3513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2988,plain,
! [SV396: $i] :
( ( ! [SY3514: $i,SY3515: $i,SY3516: $i,SY3517: $i,SY3518: $i,SY3519: $i] :
( ( c_Fun_Ocomp @ SV396 @ ( c_Fun_Ocomp @ SY3514 @ SY3515 @ SY3516 @ SY3517 @ SY3518 ) @ SY3517 @ SY3519 @ SY3518 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV396 @ SY3514 @ SY3517 @ SY3519 @ SY3516 ) @ SY3515 @ SY3516 @ SY3519 @ SY3518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2989,plain,
! [SV397: $i] :
( ( ! [SY3520: $i,SY3521: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV397 ) ) @ SY3520 ) @ SY3521 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV397 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3521 @ SV397 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2990,plain,
! [SV398: $i] :
( ( ! [SY3522: $i,SY3523: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV398 ) ) @ SY3522 ) @ SY3523 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV398 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3523 @ SV398 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2991,plain,
! [SV399: $i] :
( ( ! [SY3524: $i,SY3525: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV399 @ SY3524 @ SY3525 ) @ ( tc_List_Olist @ SY3525 ) )
= SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2992,plain,
! [SV400: $i] :
( ( ! [SY3526: $i] :
( ( c_lessequals @ SV400 @ SY3526 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV400 ) @ SY3526 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2993,plain,
! [SV401: $i] :
( ( ! [SY3527: $i] :
( ( c_lessequals @ SV401 @ ( c_Suc @ SY3527 ) @ tc_nat )
| ~ ( c_lessequals @ SV401 @ SY3527 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2994,plain,
! [SV402: $i] :
( ( ~ ( c_lessequals @ ( c_Suc @ SV402 ) @ SV402 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2995,plain,
! [SV403: $i] :
( ( ! [SY3528: $i,SY3529: $i] :
( ( c_HOL_Oord__class_Oless @ SV403 @ SY3528 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SY3529 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3528 @ SY3529 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3529 @ SY3528 @ tc_nat )
| ~ ( c_lessequals @ SY3529 @ SV403 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2996,plain,
! [SV404: $i] :
( ( ! [SY3530: $i,SY3531: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SY3530 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3531 @ SY3530 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV404 @ SY3531 @ tc_nat )
| ~ ( c_lessequals @ SY3530 @ SY3531 @ tc_nat )
| ~ ( c_lessequals @ SY3530 @ SV404 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2997,plain,
! [SV405: $i] :
( ( ! [SY3532: $i,SY3533: $i,SY3534: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV405 )
| ( c_HOL_Oord__class_Oless @ SY3532 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SY3533 ) @ SY3534 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ SY3532 @ SY3534 @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SY3533 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2998,plain,
! [SV406: $i] :
( ( ! [SY3535: $i,SY3536: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV406 ) ) @ SY3535 ) @ SY3536 )
= ( c_Lambda_OdB_OVar @ SV406 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV406 @ SY3536 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2999,plain,
! [SV407: $i] :
( ( ! [SY3537: $i,SY3538: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV407 ) @ ( c_Lambda_OdB_OVar @ SY3537 ) ) @ SY3538 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(3000,plain,
! [SV408: $i] :
( ( ! [SY3539: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV408 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV408 ) @ SY3539 ) @ SY3539 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_lessequals @ SY3539 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(3001,plain,
! [SV409: $i] :
( ( ! [SY3540: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV409 )
| ( c_lessequals @ SY3540 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV409 ) @ SY3540 ) @ SY3540 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(3002,plain,
! [SV410: $i] :
( ( ! [SY3541: $i,SY3542: $i,SY3543: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3541 @ SY3542 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SY3541 @ SY3543 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ SY3542 @ SY3543 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SY3541 @ SV410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(3003,plain,
! [SV411: $i] :
( ( ! [SY3544: $i,SY3545: $i,SY3546: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV411 )
| ( c_HOL_Oord__class_Oless @ SY3544 @ SY3545 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3546 @ SY3544 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SY3546 @ SY3545 @ SV411 ) @ SV411 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SY3546 @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(3004,plain,
! [SV412: $i] :
( ( ! [SY3547: $i,SY3548: $i,SY3549: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3547 @ SY3548 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SY3547 @ SY3549 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SY3547 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SY3548 @ SY3549 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(3005,plain,
! [SV413: $i] :
( ( ! [SY3550: $i,SY3551: $i,SY3552: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV413 )
| ( c_HOL_Oord__class_Oless @ SY3550 @ SY3551 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3552 @ SY3550 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SY3552 @ SY3551 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SY3552 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(3006,plain,
! [SV414: $i] :
( ( ! [SY3553: $i,SY3554: $i,SY3555: $i] :
( ( c_Lambda_Oliftn @ SV414 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3553 ) @ SY3554 ) @ SY3555 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV414 @ SY3553 @ SY3555 ) ) @ ( c_Lambda_Oliftn @ SV414 @ SY3554 @ SY3555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(3007,plain,
! [SV415: $i] :
( ( ! [SY3556: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV415 @ SY3556 )
= ( c_List_Olist_ONil @ SY3556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(3008,plain,
! [SV416: $i] :
( ( ! [SY3557: $i,SY3558: $i,SY3559: $i] :
( ( ( c_List_Odrop @ SV416 @ ( c_List_Olist_OCons @ SY3557 @ SY3558 @ SY3559 ) @ SY3559 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY3558 @ SY3559 ) )
| ( SV416
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(3009,plain,
! [SV417: $i] :
( ( ! [SY3560: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV417 @ ( c_HOL_Ominus__class_Ominus @ SV417 @ SY3560 @ tc_nat ) @ tc_nat )
= SY3560 )
| ~ ( c_lessequals @ SY3560 @ SV417 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(3010,plain,
! [SV418: $i] :
( ( ! [SY3561: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV418 ) ) @ SY3561 )
= ( c_Lambda_OdB_OVar @ SV418 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV418 @ SY3561 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(3011,plain,
! [SV419: $i] :
( ( ! [SY3562: $i] :
( ( c_List_Orotate @ SV419 @ ( c_List_Olist_ONil @ SY3562 ) @ SY3562 )
= ( c_List_Olist_ONil @ SY3562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(3012,plain,
! [SV420: $i] :
( ( ! [SY3563: $i,SY3564: $i,SY3565: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV420 @ SY3563 @ SY3564 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3565 @ SY3564 )
= ( c_List_Olist_OCons @ SY3565 @ SY3563 @ SY3564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(3013,plain,
! [SV421: $i] :
( ( ! [SY3566: $i] :
( ( c_HOL_Oord__class_Oless @ SV421 @ SV421 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV421 ) @ SY3566 @ SV421 )
= ( c_Lambda_Oliftn @ SV421 @ SY3566 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(3014,plain,
! [SV422: $i] :
( ( ! [SY3567: $i,SY3568: $i,SY3569: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV422 @ SY3567 @ SY3568 @ SY3569 ) @ ( tc_List_Olist @ SY3569 ) )
= ( c_Nat_Osize__class_Osize @ SV422 @ ( tc_List_Olist @ SY3569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(3015,plain,
! [SV423: $i] :
( ( ! [SY3570: $i] :
( ( SV423
= ( c_Suc @ SY3570 ) )
| ( c_lessequals @ SV423 @ SY3570 @ tc_nat )
| ~ ( c_lessequals @ SV423 @ ( c_Suc @ SY3570 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(3016,plain,
! [SV424: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV424 @ SV424 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV424 @ ( c_Suc @ SV424 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(3017,plain,
! [SV425: $i] :
( ( ! [SY3571: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV425 @ SY3571 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3571 @ ( c_Suc @ SV425 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(3018,plain,
! [SV426: $i] :
( ( ! [SY3572: $i] :
( ( c_HOL_Oord__class_Oless @ SV426 @ ( c_Suc @ SY3572 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3572 @ SV426 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(3019,plain,
! [SV427: $i] :
( ( ! [SY3573: $i,SY3574: $i,SY3575: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV427 ) @ SY3573 ) @ SY3574 ) ) @ SY3575 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV427 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3575 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3573 ) @ SY3575 ) ) @ SY3574 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3574 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3575 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(3020,plain,
! [SV428: $i] :
( ( ! [SY3576: $i,SY3577: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SY3576 ) ) @ ( c_Suc @ SY3577 ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SY3577 ) ) @ SY3576 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3576 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3577 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(3021,plain,
! [SV429: $i] :
( ( ! [SY3578: $i,SY3579: $i] :
( ( c_List_Olist_OCons @ SV429 @ SY3578 @ SY3579 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY3579 ) @ ( c_List_Olist_OCons @ SV429 @ SY3578 @ SY3579 ) @ SY3579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(3022,plain,
! [SV430: $i] :
( ( ! [SY3580: $i] :
( ( c_List_Olist_OCons @ SV430 @ ( c_List_Olist_ONil @ SY3580 ) @ SY3580 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV430 @ ( c_List_Olist_ONil @ SY3580 ) @ SY3580 ) @ SY3580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(3023,plain,
! [SV431: $i] :
( ( ! [SY3581: $i,SY3582: $i,SY3583: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV431 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ ( c_Orderings_Oord__class_Omax @ SY3581 @ SY3582 @ SV431 ) ) @ SY3583 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SY3581 ) @ SY3583 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SY3582 ) @ SY3583 ) @ SV431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(3024,plain,
! [SV432: $i] :
( ( ! [SY3584: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV432 ) @ ( c_Lambda_OdB_OVar @ SY3584 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(3025,plain,
! [SV433: $i] :
( ( ! [SY3585: $i,SY3586: $i,SY3587: $i] :
( ~ ( class_Orderings_Olinorder @ SV433 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SY3585 @ SY3586 @ SV433 ) @ SY3587 @ SV433 )
= ( c_Orderings_Oord__class_Omax @ SY3585 @ ( c_Orderings_Oord__class_Omax @ SY3586 @ SY3587 @ SV433 ) @ SV433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(3026,plain,
! [SV434: $i] :
( ( ! [SY3588: $i,SY3589: $i,SY3590: $i] :
( ~ ( class_Orderings_Olinorder @ SV434 )
| ( ( c_Orderings_Oord__class_Omax @ SY3588 @ ( c_Orderings_Oord__class_Omax @ SY3589 @ SY3590 @ SV434 ) @ SV434 )
= ( c_Orderings_Oord__class_Omax @ SY3589 @ ( c_Orderings_Oord__class_Omax @ SY3588 @ SY3590 @ SV434 ) @ SV434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(3027,plain,
! [SV435: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV435 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV435 ) @ ( c_HOL_Oone__class_Oone @ SV435 ) ) @ ( c_HOL_Oone__class_Oone @ SV435 ) ) @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(3028,plain,
! [SV436: $i] :
( ( ( c_List_Olist_ONil @ SV436 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV436 ) @ ( c_List_Olist_ONil @ SV436 ) @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(3029,plain,
! [SV437: $i] :
( ( ! [SY3591: $i,SY3592: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ SV437 @ SY3591 @ SY3592 ) @ SY3592 )
| ~ ( c_List_Odistinct @ SY3591 @ SY3592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(3030,plain,
! [SV438: $i] :
( ( ! [SY3593: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV438 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3593 @ SV438 ) @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(3031,plain,
! [SV439: $i] :
( ( ! [SY3594: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV439 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3594 @ SV439 ) @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(3032,plain,
! [SV440: $i] :
( ( ! [SY3595: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV440 ) @ ( c_Lambda_OdB_OAbs @ SY3595 ) )
| ~ ( c_Lambda_Obeta @ SV440 @ SY3595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(3033,plain,
! [SV441: $i] :
( ( ! [SY3596: $i,SY3597: $i] :
( ~ ( class_Orderings_Olinorder @ SV441 )
| ( ( c_Orderings_Oord__class_Omax @ SY3596 @ ( c_Orderings_Oord__class_Omax @ SY3596 @ SY3597 @ SV441 ) @ SV441 )
= ( c_Orderings_Oord__class_Omax @ SY3596 @ SY3597 @ SV441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(3034,plain,
! [SV442: $i] :
( ( ! [SY3598: $i,SY3599: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV442 @ SY3598 @ SY3599 ) @ ( c_List_Olist_OCons @ SY3598 @ ( c_List_Olist_ONil @ SY3599 ) @ SY3599 ) @ SY3599 )
= ( c_List_Olist_OCons @ SY3598 @ ( c_List_Oreplicate @ SV442 @ SY3598 @ SY3599 ) @ SY3599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(3035,plain,
! [SV443: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_ONil @ SV443 ) @ SV443 )
= ( c_List_Olist_ONil @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(3036,plain,
! [SV444: $i] :
( ( ! [SY3600: $i,SY3601: $i,SY3602: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV444 ) @ SY3600 ) @ SY3601 @ SY3602 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV444 @ SY3601 @ SY3602 ) ) @ ( c_Lambda_Osubstn @ SY3600 @ SY3601 @ SY3602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(3037,plain,
! [SV445: $i] :
( ( ! [SY3603: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV445 ) @ SY3603 ) @ SY3603 @ tc_nat )
= SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(3038,plain,
! [SV446: $i] :
( ( ! [SY3604: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV446 ) @ SY3604 ) @ SV446 @ tc_nat )
= SY3604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(3039,plain,
! [SV447: $i] :
( ( ! [SY3605: $i,SY3606: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV447 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SY3605 ) @ SY3606 ) @ SY3606 @ SV447 )
= SY3605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(3040,plain,
! [SV448: $i] :
( ( ! [SY3607: $i,SY3608: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV448 @ SY3607 @ SY3608 ) @ SY3608 )
= ( c_List_Oappend @ ( c_List_Orev @ SY3607 @ SY3608 ) @ ( c_List_Orev @ SV448 @ SY3608 ) @ SY3608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(3041,plain,
! [SV449: $i] :
( ( ! [SY3609: $i,SY3610: $i,SY3611: $i,SY3612: $i,SY3613: $i] :
( ( c_List_Ofoldl @ SV449 @ SY3609 @ ( c_List_Oappend @ SY3610 @ SY3611 @ SY3612 ) @ SY3613 @ SY3612 )
= ( c_List_Ofoldl @ SV449 @ ( c_List_Ofoldl @ SV449 @ SY3609 @ SY3610 @ SY3613 @ SY3612 ) @ SY3611 @ SY3613 @ SY3612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(3042,plain,
! [SV450: $i] :
( ( ! [SY3614: $i,SY3615: $i,SY3616: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV450 )
| ( c_lessequals @ SY3614 @ SY3615 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3616 @ SY3614 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SY3616 @ SY3615 @ SV450 ) @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SY3616 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(3043,plain,
! [SV451: $i] :
( ( ! [SY3617: $i,SY3618: $i,SY3619: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV451 )
| ( c_lessequals @ SY3617 @ SY3618 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3619 @ SY3617 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SY3619 @ SY3618 @ SV451 ) @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SY3619 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(3044,plain,
! [SV452: $i] :
( ( ! [SY3620: $i,SY3621: $i,SY3622: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV452 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3620 @ SY3621 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SY3620 @ SY3622 @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ SY3621 @ SY3622 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SY3620 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(3045,plain,
! [SV453: $i] :
( ( ! [SY3623: $i,SY3624: $i,SY3625: $i] :
( ( c_List_Orotate @ SV453 @ ( c_List_Orotate @ SY3623 @ SY3624 @ SY3625 ) @ SY3625 )
= ( c_List_Orotate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV453 ) @ SY3623 ) @ SY3624 @ SY3625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(3046,plain,
! [SV454: $i] :
( ( ! [SY3626: $i,SY3627: $i,SY3628: $i] :
( ( c_Type_Otype_Otype__case @ SV454 @ SY3626 @ ( c_Type_Otype_OAtom @ SY3627 ) @ SY3628 )
= ( hAPP @ SV454 @ SY3627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(3047,plain,
! [SV455: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV455 ) @ ( tc_List_Olist @ SV455 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(3048,plain,
! [SV456: $i] :
( ( ! [SY3629: $i,SY3630: $i] :
( ( c_List_Odistinct @ SV456 @ SY3629 )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ SY3630 @ SV456 @ SY3629 ) @ SY3629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(3049,plain,
! [SV457: $i] :
( ( ! [SY3631: $i,SY3632: $i,SY3633: $i,SY3634: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY3631 ) @ SY3632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY3633 ) @ SY3634 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SY3632 @ SY3634 @ SV457 )
| ~ ( c_lessequals @ SY3631 @ SY3633 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(3050,plain,
! [SV458: $i] :
( ( ! [SY3635: $i,SY3636: $i,SY3637: $i,SY3638: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SY3635 ) @ SY3636 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SY3637 ) @ SY3638 ) @ SV458 )
| ~ ( c_lessequals @ SY3636 @ SY3638 @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SY3635 @ SY3637 @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(3051,plain,
! [SV459: $i] :
( ( ! [SY3639: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV459 ) @ ( c_Suc @ SY3639 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV459 @ SY3639 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(3052,plain,
! [SV460: $i] :
( ( ! [SY3640: $i] :
( ( c_HOL_Oord__class_Oless @ SV460 @ SY3640 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV460 ) @ ( c_Suc @ SY3640 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(3053,plain,
! [SV461: $i] :
( ( ! [SY3641: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV461 ) @ ( c_Suc @ SY3641 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV461 @ SY3641 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(3054,plain,
! [SV462: $i] :
( ( ! [SY3642: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV462 ) @ SY3642 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3642 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(3055,plain,
! [SV463: $i] :
( ( ! [SY3643: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV463 ) @ SY3643 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(3056,plain,
! [SV464: $i] :
( ( ! [SY3644: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV464 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ SY3644 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV464 ) @ SY3644 ) @ SY3644 ) @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(3057,plain,
! [SV465: $i] :
( ( ! [SY3645: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV465 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV465 ) @ SY3645 ) @ SY3645 ) @ SV465 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SY3645 @ SV465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(3058,plain,
! [SV466: $i] :
( ( ! [SY3646: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV466 )
| ~ ( class_Int_Onumber__ring @ SV466 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3646 @ SY3646 @ SV466 )
= ( c_HOL_Ozero__class_Ozero @ SV466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(3059,plain,
! [SV467: $i] :
( ( ! [SY3647: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV467 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3647 @ SY3647 @ SV467 )
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(3060,plain,
! [SV468: $i] :
( ( ! [SY3648: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV468 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3648 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
= SY3648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(3061,plain,
! [SV469: $i] :
( ( ! [SY3649: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV469 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3649 @ SY3649 @ SV469 )
= ( c_HOL_Ozero__class_Ozero @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(3062,plain,
! [SV470: $i] :
( ( ! [SY3650: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV470 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3650 @ SY3650 @ SV470 )
= ( c_HOL_Ozero__class_Ozero @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(3063,plain,
! [SV471: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV471 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(3064,plain,
! [SV472: $i] :
( ( ! [SY3651: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV472 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) ) @ SY3651 )
= SY3651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(3065,plain,
! [SV473: $i] :
( ( ! [SY3652: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV473 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV473 ) @ ( c_HOL_Ozero__class_Ozero @ SV473 ) ) @ SY3652 )
= SY3652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(3066,plain,
! [SV474: $i] :
( ( ! [SY3653: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV474 )
| ~ ( class_Int_Onumber__ring @ SV474 )
| ( SY3653
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV474 ) @ SY3653 ) @ ( c_HOL_Ozero__class_Ozero @ SV474 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(3067,plain,
! [SV475: $i] :
( ( ! [SY3654: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV475 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV475 ) @ SY3654 ) @ ( c_HOL_Ozero__class_Ozero @ SV475 ) )
= SY3654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(3068,plain,
! [SV476: $i] :
( ( ! [SY3655: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV476 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV476 ) @ ( c_HOL_Ozero__class_Ozero @ SV476 ) ) @ SY3655 )
= SY3655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(3069,plain,
! [SV477: $i] :
( ( ! [SY3656: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV477 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV477 ) @ SY3656 ) @ ( c_HOL_Ozero__class_Ozero @ SV477 ) )
= SY3656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(3070,plain,
! [SV478: $i] :
( ( ! [SY3657: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV478 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV478 ) @ SY3657 ) @ ( c_HOL_Ozero__class_Ozero @ SV478 ) )
= SY3657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(3071,plain,
! [SV479: $i] :
( ( ! [SY3658: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV479 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV479 ) @ ( c_HOL_Ozero__class_Ozero @ SV479 ) ) @ SY3658 )
= SY3658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(3072,plain,
! [SV480: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV480 )
| ~ ( class_Power_Opower @ SV480 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV480 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV480 )
= ( c_HOL_Oone__class_Oone @ SV480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(3073,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)],[2209]) ).
thf(3074,plain,
! [SV481: $i] :
( ( ! [SY3659: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV481 @ SY3659 )
= SV481 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(3075,plain,
! [SV482: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV482 @ tc_nat )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(3076,plain,
! [SV483: $i] :
( ( ( SV483
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV483 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(3077,plain,
! [SV484: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV484 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV484 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(3078,plain,
! [SV485: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV485 @ SV485 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(3079,plain,
! [SV486: $i] :
( ( ! [SY3660: $i,SY3661: $i,SY3662: $i,SY3663: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SY3660 @ SY3661 @ SY3662 ) @ SY3662 ) @ ( c_Nat_Osize__class_Osize @ SV486 @ ( tc_List_Olist @ SY3662 ) ) @ SY3663 @ SY3662 )
= ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SY3663 @ SY3661 @ SY3662 ) @ SY3662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(3080,plain,
! [SV487: $i] :
( ( ! [SY3664: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV487 ) @ SY3664 ) @ SV487 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(3081,plain,
! [SV488: $i] :
( ( ! [SY3665: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV488 ) @ SY3665 ) @ SY3665 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(3082,plain,
! [SV489: $i] :
( ( ! [SY3666: $i,SY3667: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV489 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SY3666 @ SY3667 @ tc_nat ) @ SV489 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3666 @ SV489 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3667 @ SV489 ) @ SV489 ) )
| ~ ( c_lessequals @ SY3667 @ SY3666 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(3083,plain,
! [SV490: $i] :
( ( ! [SY3668: $i,SY3669: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV490 ) @ ( c_List_Olist_OCons @ SY3668 @ SY3669 @ SV490 ) @ SV490 )
= ( c_List_Olist_OCons @ SY3668 @ SY3669 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(3084,plain,
! [SV491: $i] :
( ( ! [SY3670: $i,SY3671: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV491 ) @ SY3670 ) @ SY3671 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV491 @ ( c_HOL_Ominus__class_Ominus @ SY3671 @ SY3670 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(3085,plain,
! [SV492: $i] :
( ( ! [SY3672: $i,SY3673: $i] :
( ( c_HOL_Oord__class_Oless @ SV492 @ ( c_HOL_Ominus__class_Ominus @ SY3672 @ SY3673 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SY3673 ) @ SY3672 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(3086,plain,
! [SV493: $i] :
( ( ! [SY3674: $i,SY3675: $i,SY3676: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV493 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SY3674 ) @ SY3675 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SY3676 ) @ SY3675 ) @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SY3674 @ SY3676 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(3087,plain,
! [SV494: $i] :
( ( ! [SY3677: $i,SY3678: $i,SY3679: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV494 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SY3677 ) @ SY3678 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SY3679 ) @ SY3678 ) @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SY3677 @ SY3679 @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(3088,plain,
! [SV495: $i] :
( ( ! [SY3680: $i,SY3681: $i,SY3682: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV495 )
| ( c_HOL_Oord__class_Oless @ SY3680 @ SY3681 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SY3680 ) @ SY3682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SY3681 ) @ SY3682 ) @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(3089,plain,
! [SV496: $i] :
( ( ! [SY3683: $i,SY3684: $i,SY3685: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV496 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SY3683 ) @ SY3684 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SY3683 ) @ SY3685 ) @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SY3684 @ SY3685 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(3090,plain,
! [SV497: $i] :
( ( ! [SY3686: $i,SY3687: $i,SY3688: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV497 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SY3686 ) @ SY3687 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SY3686 ) @ SY3688 ) @ SV497 )
| ~ ( c_HOL_Oord__class_Oless @ SY3687 @ SY3688 @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(3091,plain,
! [SV498: $i] :
( ( ! [SY3689: $i,SY3690: $i,SY3691: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV498 )
| ( c_HOL_Oord__class_Oless @ SY3689 @ SY3690 @ SV498 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SY3691 ) @ SY3689 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SY3691 ) @ SY3690 ) @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(3092,plain,
! [SV499: $i] :
( ( ! [SY3692: $i,SY3693: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV499 ) @ SY3692 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3693 ) @ SY3692 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV499 @ SY3693 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(3093,plain,
! [SV500: $i] :
( ( ! [SY3694: $i,SY3695: $i] :
( ( c_HOL_Oord__class_Oless @ SV500 @ SY3694 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3695 ) @ SV500 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3695 ) @ SY3694 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(3094,plain,
! [SV501: $i] :
( ( ! [SY3696: $i,SY3697: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SY3696 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SY3697 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3696 @ SY3697 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(3095,plain,
! [SV502: $i] :
( ( ! [SY3698: $i,SY3699: $i,SY3700: $i] :
( ~ ( class_Orderings_Oorder @ SV502 )
| ( c_lessequals @ SY3698 @ SY3699 @ SV502 )
| ~ ( c_lessequals @ SY3698 @ SY3700 @ SV502 )
| ~ ( c_lessequals @ SY3700 @ SY3699 @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(3096,plain,
! [SV503: $i] :
( ( ! [SY3701: $i,SY3702: $i,SY3703: $i] :
( ~ ( class_Orderings_Oorder @ SV503 )
| ( c_HOL_Oord__class_Oless @ SY3701 @ SY3702 @ SV503 )
| ~ ( c_lessequals @ SY3701 @ SY3703 @ SV503 )
| ~ ( c_HOL_Oord__class_Oless @ SY3703 @ SY3702 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(3097,plain,
! [SV504: $i] :
( ( ! [SY3704: $i,SY3705: $i,SY3706: $i] :
( ~ ( class_Orderings_Oorder @ SV504 )
| ( c_HOL_Oord__class_Oless @ SY3704 @ SY3705 @ SV504 )
| ~ ( c_HOL_Oord__class_Oless @ SY3704 @ SY3706 @ SV504 )
| ~ ( c_lessequals @ SY3706 @ SY3705 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(3098,plain,
! [SV505: $i] :
( ( ! [SY3707: $i,SY3708: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SY3707 ) @ SY3708 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SY3708 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SY3707 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(3099,plain,
! [SV506: $i] :
( ( ! [SY3709: $i,SY3710: $i,SY3711: $i] :
( ~ ( class_Orderings_Opreorder @ SV506 )
| ( c_lessequals @ SY3709 @ SY3710 @ SV506 )
| ~ ( c_lessequals @ SY3711 @ SY3710 @ SV506 )
| ~ ( c_lessequals @ SY3709 @ SY3711 @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(3100,plain,
! [SV507: $i] :
( ( c_lessequals @ SV507 @ SV507 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(3101,plain,
! [SV508: $i] :
( ( ! [SY3712: $i,SY3713: $i] :
( ( c_lessequals @ SV508 @ SY3712 @ tc_nat )
| ~ ( c_lessequals @ SY3713 @ SY3712 @ tc_nat )
| ~ ( c_lessequals @ SV508 @ SY3713 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(3102,plain,
! [SV509: $i] :
( ( c_lessequals @ SV509 @ SV509 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(3103,plain,
! [SV510: $i] :
( ( ! [SY3714: $i] :
( ~ ( class_Orderings_Oorder @ SV510 )
| ( c_lessequals @ SY3714 @ SY3714 @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(3104,plain,
! [SV511: $i] :
( ( ! [SY3715: $i] :
( ~ ( class_Orderings_Opreorder @ SV511 )
| ( c_lessequals @ SY3715 @ SY3715 @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(3105,plain,
! [SV512: $i] :
( ( ! [SY3716: $i,SY3717: $i,SY3718: $i] :
( ~ ( class_Orderings_Opreorder @ SV512 )
| ( c_HOL_Oord__class_Oless @ SY3716 @ SY3717 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SY3718 @ SY3717 @ SV512 )
| ~ ( c_lessequals @ SY3716 @ SY3718 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(3106,plain,
! [SV513: $i] :
( ( ! [SY3719: $i,SY3720: $i,SY3721: $i] :
( ~ ( class_Orderings_Opreorder @ SV513 )
| ( c_HOL_Oord__class_Oless @ SY3719 @ SY3720 @ SV513 )
| ~ ( c_lessequals @ SY3721 @ SY3720 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ SY3719 @ SY3721 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(3107,plain,
! [SV514: $i] :
( ( ! [SY3722: $i,SY3723: $i,SY3724: $i,SY3725: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
| ( c_lessequals @ SY3722 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SY3723 ) @ SY3724 ) @ SV514 )
| ~ ( c_lessequals @ SY3725 @ SY3724 @ SV514 )
| ~ ( c_lessequals @ SY3722 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SY3723 ) @ SY3725 ) @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(3108,plain,
! [SV515: $i] :
( ( ! [SY3726: $i,SY3727: $i,SY3728: $i] :
( ( c_Type_Otyping @ SV515 @ SY3726 @ SY3727 )
| ~ ( c_Lambda_Obeta @ SY3728 @ SY3726 )
| ~ ( c_Type_Otyping @ SV515 @ SY3728 @ SY3727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(3109,plain,
! [SV516: $i] :
( ( ! [SY3729: $i,SY3730: $i] :
( ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3729 @ SY3730 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ominus__class_Ominus @ SY3729 @ SY3730 @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(3110,plain,
! [SV517: $i] :
( ( ! [SY3731: $i,SY3732: $i,SY3733: $i,SY3734: $i,SY3735: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SY3731 @ SY3732 @ SY3733 ) @ SY3734 @ SY3735 @ SY3733 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SY3734 @ SY3735 @ SY3733 ) @ SY3731 @ SY3732 @ SY3733 ) )
| ( SY3731 = SY3734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(3111,plain,
! [SV518: $i] :
( ( ! [SY3736: $i] :
( ( SV518 = SY3736 )
| ~ ( c_HOL_Oord__class_Oless @ SV518 @ ( c_Suc @ SY3736 ) @ tc_nat )
| ~ ( c_lessequals @ SY3736 @ SV518 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(3112,plain,
! [SV519: $i] :
( ( ! [SY3737: $i,SY3738: $i,SY3739: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV519 @ SY3737 @ SY3738 ) @ ( c_List_Olist_OCons @ SY3737 @ SY3739 @ SY3738 ) @ SY3738 )
= ( c_List_Olist_OCons @ SY3737 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV519 @ SY3737 @ SY3738 ) @ SY3739 @ SY3738 ) @ SY3738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(3113,plain,
! [SV520: $i] :
( ( ( c_List_Olist_ONil @ SV520 )
= ( c_List_Orev @ ( c_List_Olist_ONil @ SV520 ) @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(3114,plain,
! [SV521: $i] :
( ( ! [SY3740: $i] :
( ( c_HOL_Oord__class_Oless @ SV521 @ SY3740 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3740 @ SV521 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(3115,plain,
! [SV522: $i] :
( ( ! [SY3741: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV522 @ SY3741 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3741 @ SV522 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(3116,plain,
! [SV523: $i] :
( ( ! [SY3742: $i] :
( ( c_HOL_Oord__class_Oless @ SV523 @ SY3742 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV523 ) @ SY3742 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(3117,plain,
! [SV524: $i] :
( ( ! [SY3743: $i] :
( ( c_HOL_Oord__class_Oless @ SV524 @ ( c_Suc @ SY3743 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV524 @ SY3743 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(3118,plain,
! [SV525: $i] :
( ( ! [SY3744: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV525 @ SY3744 ) @ ( tc_List_Olist @ SY3744 ) )
= ( c_Nat_Osize__class_Osize @ SV525 @ ( tc_List_Olist @ SY3744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(3119,plain,
! [SV526: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV526 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV526 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV526 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(3120,plain,
! [SV527: $i] :
( ( ! [SY3745: $i,SY3746: $i,SY3747: $i,SY3748: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV527 @ SY3745 @ SY3746 ) @ ( c_Suc @ SY3747 ) @ SY3748 @ SY3746 )
= ( c_List_Olist_OCons @ SV527 @ ( c_List_Olist__update @ SY3745 @ SY3747 @ SY3748 @ SY3746 ) @ SY3746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(3121,plain,
! [SV528: $i] :
( ( ! [SY3749: $i,SY3750: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV528 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3749 ) @ SY3750 ) @ SV528 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV528 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3749 @ SV528 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3750 @ SV528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(3122,plain,
! [SV529: $i] :
( ( ! [SY3751: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SY3751 @ tc_nat ) @ SV529 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV529 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3751 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(3123,plain,
! [SV530: $i] :
( ( ! [SY3752: $i,SY3753: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV530 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SY3752 @ SY3753 @ SV530 ) @ SV530 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV530 ) @ ( c_List_Olistsum @ SY3752 @ SV530 ) ) @ ( c_List_Olistsum @ SY3753 @ SV530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(3124,plain,
! [SV531: $i] :
( ( ! [SY3754: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV531 ) @ ( c_HOL_Ominus__class_Ominus @ SY3754 @ SV531 @ tc_nat ) )
= SY3754 )
| ( c_HOL_Oord__class_Oless @ SY3754 @ SV531 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(3125,plain,
! [SV532: $i] :
( ( ! [SY3755: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV532 @ ( c_Suc @ SY3755 ) @ tc_nat ) @ SV532 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV532 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(3126,plain,
! [SV533: $i] :
( ( ! [SY3756: $i,SY3757: $i] :
( ~ ( class_Orderings_Oorder @ SV533 )
| ( c_HOL_Oord__class_Oless @ SY3756 @ SY3757 @ SV533 )
| ( SY3757 = SY3756 )
| ~ ( c_lessequals @ SY3756 @ SY3757 @ SV533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(3127,plain,
! [SV534: $i] :
( ( ! [SY3758: $i,SY3759: $i] :
( ~ ( class_Orderings_Oorder @ SV534 )
| ( c_HOL_Oord__class_Oless @ SY3758 @ SY3759 @ SV534 )
| ~ ( c_lessequals @ SY3758 @ SY3759 @ SV534 )
| ( SY3759 = SY3758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(3128,plain,
! [SV535: $i] :
( ( ! [SY3760: $i] :
( ( c_HOL_Oord__class_Oless @ SV535 @ SY3760 @ tc_nat )
| ( SV535 = SY3760 )
| ~ ( c_lessequals @ SV535 @ SY3760 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(3129,plain,
! [SV536: $i] :
( ( ! [SY3761: $i] :
( ( SV536 = SY3761 )
| ( c_HOL_Oord__class_Oless @ SV536 @ SY3761 @ tc_nat )
| ~ ( c_lessequals @ SV536 @ SY3761 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(3130,plain,
! [SV537: $i] :
( ( ! [SY3762: $i] :
( ( c_HOL_Oord__class_Oless @ SV537 @ SY3762 @ tc_nat )
| ( SV537 = SY3762 )
| ~ ( c_lessequals @ SV537 @ SY3762 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(3131,plain,
! [SV538: $i] :
( ( ! [SY3763: $i,SY3764: $i] :
( ~ ( class_Orderings_Oorder @ SV538 )
| ( SY3763 = SY3764 )
| ( c_HOL_Oord__class_Oless @ SY3763 @ SY3764 @ SV538 )
| ~ ( c_lessequals @ SY3763 @ SY3764 @ SV538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(3132,plain,
! [SV539: $i] :
( ( ! [SY3765: $i,SY3766: $i] :
( ~ ( class_Orderings_Oorder @ SV539 )
| ( c_HOL_Oord__class_Oless @ SY3765 @ SY3766 @ SV539 )
| ( SY3765 = SY3766 )
| ~ ( c_lessequals @ SY3765 @ SY3766 @ SV539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(3133,plain,
! [SV540: $i] :
( ( ! [SY3767: $i,SY3768: $i] :
( ~ ( class_Orderings_Oorder @ SV540 )
| ( c_HOL_Oord__class_Oless @ SY3767 @ SY3768 @ SV540 )
| ( SY3767 = SY3768 )
| ~ ( c_lessequals @ SY3767 @ SY3768 @ SV540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(3134,plain,
! [SV541: $i] :
( ( ! [SY3769: $i,SY3770: $i] :
( ~ ( class_Orderings_Oorder @ SV541 )
| ( c_HOL_Oord__class_Oless @ SY3769 @ SY3770 @ SV541 )
| ~ ( c_lessequals @ SY3769 @ SY3770 @ SV541 )
| ( SY3769 = SY3770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(3135,plain,
! [SV542: $i] :
( ( ! [SY3771: $i,SY3772: $i] :
( ~ ( class_Orderings_Olinorder @ SV542 )
| ( SY3771 = SY3772 )
| ~ ( c_lessequals @ SY3771 @ SY3772 @ SV542 )
| ( c_HOL_Oord__class_Oless @ SY3771 @ SY3772 @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(3136,plain,
! [SV543: $i] :
( ( ! [SY3773: $i,SY3774: $i] :
( ~ ( class_Orderings_Olinorder @ SV543 )
| ( SY3773 = SY3774 )
| ( c_HOL_Oord__class_Oless @ SY3773 @ SY3774 @ SV543 )
| ~ ( c_lessequals @ SY3773 @ SY3774 @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(3137,plain,
! [SV544: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV544 ) @ ( c_List_Olist_ONil @ SV544 ) @ SV544 )
= ( c_List_Olist_ONil @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(3138,plain,
! [SV545: $i] :
( ( ! [SY3775: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ SV545 ) ) @ SY3775 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV545 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3775 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(3139,plain,
! [SV546: $i] :
( ( ! [SY3776: $i,SY3777: $i,SY3778: $i,SY3779: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV546 @ SY3776 @ SY3777 @ SY3778 ) @ SY3776 @ SY3779 @ SY3778 )
= ( c_List_Olist__update @ SV546 @ SY3776 @ SY3779 @ SY3778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(3140,plain,
! [SV547: $i] :
( ( ! [SY3780: $i] :
( ( c_lessequals @ SV547 @ SY3780 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV547 ) @ ( c_Suc @ SY3780 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(3141,plain,
! [SV548: $i] :
( ( ! [SY3781: $i] :
( ( c_lessequals @ ( c_Suc @ SV548 ) @ ( c_Suc @ SY3781 ) @ tc_nat )
| ~ ( c_lessequals @ SV548 @ SY3781 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(3142,plain,
! [SV549: $i] :
( ( ! [SY3782: $i,SY3783: $i,SY3784: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV549 @ SY3782 @ SY3783 ) @ SY3784 @ SY3783 )
= ( c_List_Oappend @ SV549 @ ( c_List_Oappend @ SY3782 @ SY3784 @ SY3783 ) @ SY3783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(3143,plain,
! [SV550: $i] :
( ( ! [SY3785: $i,SY3786: $i,SY3787: $i] :
( ( c_List_Oappend @ SV550 @ ( c_List_Oappend @ SY3785 @ SY3786 @ SY3787 ) @ SY3787 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV550 @ SY3785 @ SY3787 ) @ SY3786 @ SY3787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(3144,plain,
! [SV551: $i] :
( ( ! [SY3788: $i,SY3789: $i,SY3790: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV551 @ SY3788 @ SY3789 ) @ SY3790 @ SY3789 )
= ( c_List_Oappend @ SV551 @ ( c_List_Oappend @ SY3788 @ SY3790 @ SY3789 ) @ SY3789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(3145,plain,
! [SV552: $i] :
( ( ! [SY3791: $i,SY3792: $i,SY3793: $i] :
( ( c_List_Oappend @ SV552 @ ( c_List_Oappend @ SY3791 @ SY3792 @ SY3793 ) @ SY3793 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV552 @ SY3791 @ SY3793 ) @ SY3792 @ SY3793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(3146,plain,
! [SV553: $i] :
( ( ! [SY3794: $i,SY3795: $i] :
( ~ ( class_Orderings_Oorder @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SY3794 @ SY3795 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SY3795 @ SY3794 @ SV553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(3147,plain,
! [SV554: $i] :
( ( ! [SY3796: $i,SY3797: $i] :
( ~ ( class_Orderings_Olinorder @ SV554 )
| ~ ( c_HOL_Oord__class_Oless @ SY3796 @ SY3797 @ SV554 )
| ~ ( c_HOL_Oord__class_Oless @ SY3797 @ SY3796 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(3148,plain,
! [SV555: $i] :
( ( ! [SY3798: $i] :
( ( c_lessequals @ SV555 @ SY3798 @ tc_nat )
| ( c_lessequals @ SY3798 @ SV555 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(3149,plain,
! [SV556: $i] :
( ( ! [SY3799: $i,SY3800: $i] :
( ~ ( class_Orderings_Olinorder @ SV556 )
| ( c_lessequals @ SY3799 @ SY3800 @ SV556 )
| ( c_lessequals @ SY3800 @ SY3799 @ SV556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(3150,plain,
! [SV557: $i] :
( ( ! [SY3801: $i,SY3802: $i] :
( ~ ( class_Orderings_Opreorder @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ SY3801 @ SY3802 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ SY3802 @ SY3801 @ SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(3151,plain,
! [SV558: $i] :
( ( ! [SY3803: $i,SY3804: $i] :
( ~ ( class_Orderings_Opreorder @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ SY3803 @ SY3804 @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ SY3804 @ SY3803 @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(3152,plain,
! [SV559: $i] :
( ( ! [SY3805: $i] :
( ( hBOOL @ ( hAPP @ SV559 @ SY3805 ) )
| ( hBOOL @ ( hAPP @ SV559 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV559 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV559 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(3153,plain,
! [SV560: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV560 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(3154,plain,
! [SV561: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV561 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(3155,plain,
! [SV562: $i] :
( ( ! [SY3806: $i] :
( ( hBOOL @ ( hAPP @ SV562 @ SY3806 ) )
| ( hBOOL @ ( hAPP @ SV562 @ ( v_sko__List__Xupt__Xinduct__1 @ SV562 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV562 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(3156,plain,
! [SV563: $i] :
( ( ! [SY3807: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV563 @ SY3807 )
= SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(3157,plain,
! [SV564: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV564 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(3158,plain,
! [SV565: $i] :
( ( ! [SY3808: $i] :
( ( hBOOL @ ( hAPP @ SV565 @ SY3808 ) )
| ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV565 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(3159,plain,
! [SV566: $i] :
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV566 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(3160,plain,
! [SV567: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV567 @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(3161,plain,
! [SV568: $i] :
( ( ! [SY3809: $i,SY3810: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV568 @ SY3809 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3810 @ SY3809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(3162,plain,
! [SV569: $i] :
( ( ( c_Orderings_Oord__class_Omax @ SV569 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV569 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(3163,plain,
! [SV570: $i] :
( ( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV570 @ tc_nat )
= SV570 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(3164,plain,
! [SV571: $i] :
( ( SV571
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV571 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(3165,plain,
! [SV572: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV572 )
= SV572 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(3166,plain,
! [SV573: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV573 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV573 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(3167,plain,
! [SV574: $i] :
( ( ! [SY3811: $i,SY3812: $i,SY3813: $i,SY3814: $i,SY3815: $i,SY3816: $i] :
( ( ( hAPP @ ( hAPP @ SV574 @ SY3811 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SY3812 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3813 @ SY3814 @ SV574 @ SY3815 @ SY3812 @ SY3816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(3168,plain,
! [SV575: $i] :
( ( ! [SY3817: $i,SY3818: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV575 )
| ( ( c_List_Olistsum @ ( c_List_Omap @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV575 @ SY3817 ) @ SY3818 @ SY3817 @ SV575 ) @ SV575 )
= ( c_HOL_Ozero__class_Ozero @ SV575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(3169,plain,
! [SV576: $i] :
( ( ! [SY3819: $i,SY3820: $i] :
( ( c_Lambda_Osubstn @ SV576 @ SY3819 @ SY3820 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV576 ) @ ( c_Lambda_Oliftn @ SY3820 @ SY3819 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SY3820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(3170,plain,
! [SV577: $i] :
( ( ! [SY3821: $i,SY3822: $i,SY3823: $i,SY3824: $i] :
( ( c_List_Odrop @ SV577 @ ( c_List_Omap @ SY3821 @ SY3822 @ SY3823 @ SY3824 ) @ SY3824 )
= ( c_List_Omap @ SY3821 @ ( c_List_Odrop @ SV577 @ SY3822 @ SY3823 ) @ SY3823 @ SY3824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(3171,plain,
! [SV578: $i] :
( ( ! [SY3825: $i,SY3826: $i,SY3827: $i] :
( ( c_List_Odistinct @ SV578 @ SY3825 )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ SY3826 @ SV578 @ SY3825 @ SY3827 ) @ SY3827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(3172,plain,
! [SV579: $i] :
( ( ! [SY3828: $i,SY3829: $i,SY3830: $i,SY3831: $i] :
( ( c_List_Omap @ SV579 @ ( c_List_Oappend @ SY3828 @ SY3829 @ SY3830 ) @ SY3830 @ SY3831 )
= ( c_List_Oappend @ ( c_List_Omap @ SV579 @ SY3828 @ SY3830 @ SY3831 ) @ ( c_List_Omap @ SV579 @ SY3829 @ SY3830 @ SY3831 ) @ SY3831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(3173,plain,
! [SV580: $i] :
( ( ! [SY3832: $i,SY3833: $i,SY3834: $i,SY3835: $i] :
( ( c_List_Omap @ SV580 @ ( c_List_Oreplicate @ SY3832 @ SY3833 @ SY3834 ) @ SY3834 @ SY3835 )
= ( c_List_Oreplicate @ SY3832 @ ( hAPP @ SV580 @ SY3833 ) @ SY3835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(3174,plain,
! [SV581: $i] :
( ( ! [SY3836: $i,SY3837: $i,SY3838: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV581 @ SY3836 @ SY3837 @ SY3838 ) @ ( tc_List_Olist @ SY3838 ) )
= ( c_Nat_Osize__class_Osize @ SY3836 @ ( tc_List_Olist @ SY3837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(3175,plain,
! [SV582: $i] :
( ( ! [SY3839: $i,SY3840: $i,SY3841: $i,SY3842: $i] :
( ( c_List_Orotate @ SV582 @ ( c_List_Omap @ SY3839 @ SY3840 @ SY3841 @ SY3842 ) @ SY3842 )
= ( c_List_Omap @ SY3839 @ ( c_List_Orotate @ SV582 @ SY3840 @ SY3841 ) @ SY3841 @ SY3842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(3176,plain,
! [SV583: $i] :
( ( ! [SY3843: $i,SY3844: $i,SY3845: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV583 @ SY3843 @ SY3844 @ SY3845 ) @ SY3845 )
= ( c_List_Omap @ SV583 @ ( c_List_Orev @ SY3843 @ SY3844 ) @ SY3844 @ SY3845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(3177,plain,
! [SV584: $i] :
( ( ! [SY3846: $i,SY3847: $i,SY3848: $i,SY3849: $i] :
( ( c_List_Otake @ SV584 @ ( c_List_Omap @ SY3846 @ SY3847 @ SY3848 @ SY3849 ) @ SY3849 )
= ( c_List_Omap @ SY3846 @ ( c_List_Otake @ SV584 @ SY3847 @ SY3848 ) @ SY3848 @ SY3849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(3178,plain,
! [SV585: $i] :
( ( ! [SY3850: $i,SY3851: $i] :
( ( c_List_Omap @ SV585 @ ( c_List_Olist_ONil @ SY3850 ) @ SY3850 @ SY3851 )
= ( c_List_Olist_ONil @ SY3851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(3179,plain,
! [SV586: $i] :
( ( ! [SY3852: $i,SY3853: $i,SY3854: $i,SY3855: $i,SY3856: $i] :
( ( c_List_Omap @ SV586 @ ( c_List_Omap @ SY3852 @ SY3853 @ SY3854 @ SY3855 ) @ SY3855 @ SY3856 )
= ( c_List_Omap @ ( c_Fun_Ocomp @ SV586 @ SY3852 @ SY3855 @ SY3856 @ SY3854 ) @ SY3853 @ SY3854 @ SY3856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(3180,plain,
! [SV587: $i] :
( ( ! [SY3857: $i,SY3858: $i,SY3859: $i,SY3860: $i] :
( ( c_List_Omap @ SV587 @ ( c_List_Olist_OCons @ SY3857 @ SY3858 @ SY3859 ) @ SY3859 @ SY3860 )
= ( c_List_Olist_OCons @ ( hAPP @ SV587 @ SY3857 ) @ ( c_List_Omap @ SV587 @ SY3858 @ SY3859 @ SY3860 ) @ SY3860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(3181,plain,
! [SV588: $i] :
( ( ! [SY3861: $i,SY3862: $i,SY3863: $i,SY3864: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV588 @ SY3861 ) @ ( c_List_Omap @ SV588 @ SY3862 @ SY3863 @ SY3864 ) @ SY3864 )
= ( c_List_Omap @ SV588 @ ( c_List_Olist_OCons @ SY3861 @ SY3862 @ SY3863 ) @ SY3863 @ SY3864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(3182,plain,
! [SV589: $i] :
( ( ! [SY3865: $i,SY3866: $i,SY3867: $i,SY3868: $i] :
( ( c_List_Omap @ SV589 @ ( c_List_Olist_OCons @ SY3865 @ SY3866 @ SY3867 ) @ SY3867 @ SY3868 )
= ( c_List_Olist_OCons @ ( hAPP @ SV589 @ SY3865 ) @ ( c_List_Omap @ SV589 @ SY3866 @ SY3867 @ SY3868 ) @ SY3868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(3183,plain,
! [SV590: $i] :
( ( ! [SY3869: $i,SY3870: $i,SY3871: $i,SY3872: $i,SY3873: $i] :
( ( c_List_Omap @ SV590 @ ( c_List_Olist__update @ SY3869 @ SY3870 @ SY3871 @ SY3872 ) @ SY3872 @ SY3873 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV590 @ SY3869 @ SY3872 @ SY3873 ) @ SY3870 @ ( hAPP @ SV590 @ SY3871 ) @ SY3873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(3184,plain,
! [SV591: $i] :
( ( ! [SY3874: $i,SY3875: $i] :
( ( c_List_Olist_ONil @ SV591 )
= ( c_List_Omap @ SY3874 @ ( c_List_Olist_ONil @ SY3875 ) @ SY3875 @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(3185,plain,
! [SV592: $i] :
( ( ! [SY3876: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV592 )
| ( ( c_List_Olistsum @ SY3876 @ SV592 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV592 ) @ SY3876 @ ( c_HOL_Ozero__class_Ozero @ SV592 ) @ SV592 @ SV592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(3186,plain,
! [SV593: $i] :
( ( ! [SY3877: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV593 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV593 ) @ ( c_HOL_Ozero__class_Ozero @ SV593 ) @ SY3877 @ SV593 @ SV593 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV593 ) @ SY3877 @ ( c_HOL_Ozero__class_Ozero @ SV593 ) @ SV593 @ SV593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(3187,plain,
! [SV594: $i] :
( ( ! [SY3878: $i,SY3879: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV594 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SY3878 @ SY3879 @ SV594 @ SV594 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SY3878 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SY3879 @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV594 @ SV594 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(3188,plain,
! [SV595: $i] :
( ( ! [SY3880: $i,SY3881: $i,SY3882: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV595 ) @ SY3880 ) ) @ SY3881 ) @ SY3882 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV595 ) @ SY3881 ) @ SY3882 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3880 ) @ SY3881 ) @ SY3882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(3189,plain,
! [SV596: $i] :
( ( ! [SY3883: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV596 ) ) @ SY3883 ) @ SV596 )
= SY3883 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(3190,plain,
! [SV597: $i] :
( ( ! [SY3884: $i,SY3885: $i,SY3886: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV597 ) @ SY3884 ) @ SY3885 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3886 ) @ SY3884 ) @ SY3885 ) )
| ~ ( c_Lambda_Obeta @ SV597 @ SY3886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(3191,plain,
! [SV598: $i] :
( ( ! [SY3887: $i,SY3888: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV598 ) ) @ SY3887 ) @ SY3888 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV598 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3887 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3888 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(3192,plain,
! [SV599: $i] :
( ( ! [SY3889: $i,SY3890: $i,SY3891: $i,SY3892: $i] :
( ( c_List_Ofoldr @ SV599 @ SY3889 @ SY3890 @ SY3891 @ SY3892 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV599 @ SY3891 @ SY3892 @ SY3892 ) @ SY3890 @ ( c_List_Orev @ SY3889 @ SY3891 ) @ SY3892 @ SY3891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(3193,plain,
! [SV600: $i] :
( ( ! [SY3893: $i,SY3894: $i,SY3895: $i,SY3896: $i] :
( ( c_List_Ofoldl @ SV600 @ SY3893 @ SY3894 @ SY3895 @ SY3896 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV600 @ SY3895 @ SY3896 @ SY3895 ) @ ( c_List_Orev @ SY3894 @ SY3896 ) @ SY3893 @ SY3896 @ SY3895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(3194,plain,
! [SV601: $i] :
( ( ! [SY3897: $i,SY3898: $i,SY3899: $i,SY3900: $i] :
( ( c_Type_Otype_Otype__rec @ SV601 @ SY3897 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY3898 ) @ SY3899 ) @ SY3900 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SY3897 @ SY3898 ) @ SY3899 ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SY3897 @ SY3898 @ SY3900 ) ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SY3897 @ SY3899 @ SY3900 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(3195,plain,
! [SV602: $i] :
( ( ! [SY3901: $i,SY3902: $i,SY3903: $i,SY3904: $i] :
( ( c_Type_Otype_Otype__case @ SV602 @ SY3901 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY3902 ) @ SY3903 ) @ SY3904 )
= ( hAPP @ ( hAPP @ SY3901 @ SY3902 ) @ SY3903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(3196,plain,
! [SV603: $i] :
( ( ! [SY3905: $i,SY3906: $i,SY3907: $i,SY3908: $i] :
( ~ ( hBOOL @ ( hAPP @ SV603 @ ( c_Type_Otype_Otype__case @ SY3905 @ SY3906 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY3907 ) @ SY3908 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV603 @ ( hAPP @ ( hAPP @ SY3906 @ SY3907 ) @ SY3908 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(3197,plain,
! [SV604: $i] :
( ( ! [SY3909: $i,SY3910: $i,SY3911: $i,SY3912: $i] :
( ~ ( hBOOL @ ( hAPP @ SV604 @ ( c_Type_Otype_Otype__case @ SY3909 @ SY3910 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY3911 ) @ SY3912 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV604 @ ( hAPP @ ( hAPP @ SY3910 @ SY3911 ) @ SY3912 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(3198,plain,
! [SV605: $i] :
( ( ! [SY3913: $i,SY3914: $i,SY3915: $i,SY3916: $i,SY3917: $i] :
( ( c_List_Ofoldr @ SV605 @ ( c_List_Olist_OCons @ SY3913 @ SY3914 @ SY3915 ) @ SY3916 @ SY3915 @ SY3917 )
= ( hAPP @ ( hAPP @ SV605 @ SY3913 ) @ ( c_List_Ofoldr @ SV605 @ SY3914 @ SY3916 @ SY3915 @ SY3917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(3199,plain,
! [SV606: $i] :
( ( ! [SY3918: $i,SY3919: $i,SY3920: $i,SY3921: $i,SY3922: $i] :
( ( c_List_Ofoldr @ SV606 @ ( c_List_Oappend @ SY3918 @ SY3919 @ SY3920 ) @ SY3921 @ SY3920 @ SY3922 )
= ( c_List_Ofoldr @ SV606 @ SY3918 @ ( c_List_Ofoldr @ SV606 @ SY3919 @ SY3921 @ SY3920 @ SY3922 ) @ SY3920 @ SY3922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(3200,plain,
! [SV607: $i] :
( ( ! [SY3923: $i,SY3924: $i,SY3925: $i] :
( ( c_List_Ofoldr @ SV607 @ ( c_List_Olist_ONil @ SY3923 ) @ SY3924 @ SY3923 @ SY3925 )
= SY3924 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(3201,plain,
! [SV608: $i] :
( ( ! [SY3926: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV608 ) @ SY3926 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(3202,plain,
! [SV609: $i] :
( ( ! [SY3927: $i,SY3928: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SY3927 ) ) @ SY3928 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV609 ) @ SY3928 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3927 ) @ SY3928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(3203,plain,
! [SV610: $i] :
( ( ! [SY3929: $i,SY3930: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV610 ) @ SY3929 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3930 ) @ SY3929 ) )
| ~ ( c_Lambda_Obeta @ SV610 @ SY3930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(3204,plain,
! [SV611: $i] :
( ( ! [SY3931: $i,SY3932: $i,SY3933: $i,SY3934: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV611 @ SY3931 @ SY3932 @ SY3933 ) @ SY3934 )
= ( hAPP @ SV611 @ SY3934 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3934 @ SY3931 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(3205,plain,
! [SV612: $i] :
( ( ! [SY3935: $i,SY3936: $i,SY3937: $i,SY3938: $i] :
( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3935 @ SY3936 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3937 )
| ~ ( c_Type_Otypings @ SV612 @ SY3936 @ SY3938 )
| ~ ( c_Type_Otyping @ SV612 @ SY3935 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY3938 @ SY3937 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(3206,plain,
! [SV613: $i] :
( ( ! [SY3939: $i,SY3940: $i,SY3941: $i] :
( ( c_Type_Otyping @ SV613 @ ( c_Lambda_OdB_OAbs @ SY3939 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY3940 ) @ SY3941 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV613 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3940 @ tc_Type_Otype ) @ SY3939 @ SY3941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(3207,plain,
! [SV614: $i] :
( ( ! [SY3942: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV614 )
| ~ ( class_Power_Opower @ SV614 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SY3942 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SY3942
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(3208,plain,
! [SV615: $i] :
( ( ! [SY3943: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV615 )
| ~ ( class_Power_Opower @ SV615 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV615 ) @ SY3943 @ SV615 )
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
| ( SY3943
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(3209,plain,
! [SV616: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV616 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(3210,plain,
! [SV617: $i] :
( ( ! [SY3944: $i] :
( ( c_Lambda_Osubstn @ SV617 @ SY3944 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV617 ) @ SY3944 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(3211,plain,
! [SV618: $i] :
( ( ! [SY3945: $i,SY3946: $i,SY3947: $i,SY3948: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ SY3945 @ SY3946 @ SY3947 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3948 @ SY3947 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3948 @ SY3947 ) @ ( c_Suc @ SY3945 ) @ SY3946 @ SY3947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(3212,plain,
! [SV619: $i] :
( ( ! [SY3949: $i,SY3950: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV619 @ SY3949 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3950 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV619 ) @ SY3950 ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY3950 ) @ SY3949 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(3213,plain,
! [SV620: $i] :
( ( ! [SY3951: $i,SY3952: $i,SY3953: $i,SY3954: $i,SY3955: $i,SY3956: $i] :
( ( c_List_Ofoldr @ SV620 @ ( c_List_Omap @ SY3951 @ SY3952 @ SY3953 @ SY3954 ) @ SY3955 @ SY3954 @ SY3956 )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ SV620 @ SY3951 @ SY3954 @ ( tc_fun @ SY3956 @ SY3956 ) @ SY3953 ) @ SY3952 @ SY3955 @ SY3953 @ SY3956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(3214,plain,
! [SV621: $i] :
( ( ! [SY3957: $i,SY3958: $i,SY3959: $i,SY3960: $i,SY3961: $i] :
( ~ ( c_Type_Otyping @ SV621 @ SY3957 @ SY3958 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SY3959 @ SY3958 @ tc_Type_Otype ) @ SY3960 @ SY3961 )
| ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3960 ) @ SY3957 ) @ SY3959 ) @ SY3961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(3215,plain,
! [SV622: $i] :
( ( ! [SY3962: $i,SY3963: $i,SY3964: $i,SY3965: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV622 @ SY3962 @ SY3963 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3964 ) @ SY3962 ) @ SY3965 )
| ~ ( c_Type_Otyping @ SV622 @ SY3964 @ SY3965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(3216,plain,
! [SV623: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV623 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV623 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(3217,plain,
! [SV624: $i] :
( ( ! [SY3966: $i,SY3967: $i,SY3968: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV624 @ SY3966 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3967 ) @ SY3968 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV624 ) @ SY3967 ) @ SY3968 ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY3967 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY3968 ) @ SY3966 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(3218,plain,
! [SV625: $i] :
( ( ! [SY3969: $i,SY3970: $i,SY3971: $i,SY3972: $i,SY3973: $i] :
( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY3969 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY3970 ) @ SY3971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3972 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SY3970 @ SY3973 @ tc_Type_Otype ) @ SY3971 @ SY3972 )
| ~ ( c_Type_Otyping @ SV625 @ SY3969 @ SY3973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3219,plain,
! [SV626: $i] :
( ( ! [SY3974: $i,SY3975: $i,SY3976: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV626 @ SY3974 @ SY3975 @ SY3976 ) @ SY3974 )
= SY3975 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(3220,plain,
! [SV627: $i] :
( ( ! [SY3977: $i,SY3978: $i,SY3979: $i,SY3980: $i,SY3981: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV627 @ SY3977 @ SY3978 @ SY3979 ) @ SY3980 ) @ SY3981 )
= ( hAPP @ ( hAPP @ SV627 @ SY3981 ) @ SY3980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3221,plain,
! [SV628: $i] :
( ( ! [SY3982: $i,SY3983: $i,SY3984: $i,SY3985: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV628 @ SY3982 @ SY3983 @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY3982 ) @ SY3984 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3985 )
| ~ ( c_Type_Otypings @ SV628 @ SY3984 @ SY3985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(3222,plain,
! [SV629: $i] :
( ( ! [SY3986: $i,SY3987: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV629 ) @ SY3986 ) ) @ SY3987 ) @ SY3986 )
= SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(3223,plain,
! [SV630: $i] :
( ( ! [SY3988: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV630 @ SY3988 ) )
| ~ ( class_Orderings_Opreorder @ SY3988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(3224,plain,
! [SV631: $i] :
( ( ! [SY3989: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV631 @ SY3989 ) )
| ~ ( class_Orderings_Oorder @ SY3989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3225,plain,
! [SV632: $i] :
( ( ! [SY3990: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ SV632 @ SY3990 ) )
| ~ ( class_Orderings_Obot @ SY3990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3226,plain,
! [SV633: $i] :
( ( ! [SY3991: $i,SY3992: $i,SY3993: $i,SY3994: $i,SY3995: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV633 @ SY3991 @ SY3992 @ SY3993 ) @ SY3994 ) @ SY3995 )
= ( hAPP @ ( hAPP @ SV633 @ SY3995 ) @ SY3994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3227,plain,
! [SV634: $i] :
( ( ! [SY3996: $i,SY3997: $i,SY3998: $i,SY3999: $i,SY4000: $i] :
( ( c_COMBB @ SV634 @ SY3996 @ SY3997 @ SY3998 @ SY3999 @ SY4000 )
= ( hAPP @ SV634 @ ( hAPP @ SY3996 @ SY3997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(3228,plain,
! [SV635: $i] :
( ( ! [SY4001: $i] : ( c_fequal @ SV635 @ SV635 @ SY4001 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(3229,plain,
! [SV636: $i] :
( ( ! [SY4002: $i,SY4003: $i] :
( ( SV636 = SY4002 )
| ~ ( c_fequal @ SV636 @ SY4002 @ SY4003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(3230,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(3231,plain,
! [SV637: $i] :
( ( ! [SY4004: $i,SY4005: $i,SY4006: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV637 )
| ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SY4004 ) @ SY4005 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SY4004 ) @ SY4006 ) )
| ( SY4005 = SY4006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(3232,plain,
! [SV638: $i] :
( ( ! [SY4007: $i,SY4008: $i] :
( ( SV638
!= ( c_List_Oappend @ SV638 @ SY4007 @ SY4008 ) )
| ( SY4007
= ( c_List_Olist_ONil @ SY4008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3233,plain,
! [SV639: $i] :
( ( ! [SY4009: $i,SY4010: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV639 )
| ( ( c_Power_Opower__class_Opower @ SY4009 @ SY4010 @ SV639 )
!= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
| ( SY4009
= ( c_HOL_Ozero__class_Ozero @ SV639 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(3234,plain,
! [SV640: $i] :
( ( ! [SY4011: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV640 @ SY4011 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV640 @ SY4011 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(3235,plain,
! [SV641: $i] :
( ( ! [SY4012: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV641 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV641 ) @ SY4012 ) @ SY4012 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SY4012
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3236,plain,
! [SV642: $i] :
( ( ! [SY4013: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV642 @ ( tc_List_Olist @ SY4013 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV642
= ( c_List_Olist_ONil @ SY4013 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(3237,plain,
! [SV643: $i] :
( ( ! [SY4014: $i,SY4015: $i,SY4016: $i,SY4017: $i] :
( ( ( c_List_Omap @ SV643 @ SY4014 @ SY4015 @ SY4016 )
!= ( c_List_Omap @ SV643 @ SY4017 @ SY4015 @ SY4016 ) )
| ( ( c_Nat_Osize__class_Osize @ SY4014 @ ( tc_List_Olist @ SY4015 ) )
= ( c_Nat_Osize__class_Osize @ SY4017 @ ( tc_List_Olist @ SY4015 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3238,plain,
! [SV644: $i] :
( ( ! [SY4018: $i,SY4019: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SY4018 ) @ SY4019 )
!= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SY4019 @ SV644 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SY4018 @ SV644 )
| ( SY4019
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3239,plain,
! [SV645: $i] :
( ( ! [SY4020: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV645 @ SY4020 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SY4020 @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4020 = SV645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3240,plain,
! [SV646: $i] :
( ( ! [SY4021: $i,SY4022: $i,SY4023: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV646 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SY4021 ) @ SY4022 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SY4021 ) @ SY4023 ) )
| ( SY4022 = SY4023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3241,plain,
! [SV647: $i] :
( ( ! [SY4024: $i,SY4025: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV647 )
| ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SY4024 @ SY4025 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SY4024
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3242,plain,
! [SV648: $i] :
( ( ! [SY4026: $i,SY4027: $i,SY4028: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV648 ) @ SY4026 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4027 ) @ SY4028 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV648 = SY4027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3243,plain,
! [SV649: $i] :
( ( ! [SY4029: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV649 ) @ SY4029 )
!= SV649 )
| ( SY4029
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(3244,plain,
! [SV650: $i] :
( ( ! [SY4030: $i,SY4031: $i] :
( ( ( c_List_Oappend @ SV650 @ SY4030 @ SY4031 )
!= SV650 )
| ( SY4030
= ( c_List_Olist_ONil @ SY4031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3245,plain,
! [SV651: $i] :
( ( ! [SY4032: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV651 ) @ SY4032 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV651
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV651
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(3246,plain,
! [SV652: $i] :
( ( ! [SY4033: $i,SY4034: $i,SY4035: $i] :
( ( ( c_List_Olist_ONil @ SV652 )
!= ( c_List_Omap @ SY4033 @ SY4034 @ SY4035 @ SV652 ) )
| ( SY4034
= ( c_List_Olist_ONil @ SY4035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3247,plain,
! [SV653: $i] :
( ( ! [SY4036: $i,SY4037: $i,SY4038: $i,SY4039: $i] :
( ( ( c_List_Oappend @ SV653 @ SY4036 @ SY4037 )
!= ( c_List_Oappend @ SY4038 @ SY4039 @ SY4037 ) )
| ( SY4036
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SY4037 ) ) @ SY4038 @ SY4037 ) @ SY4039 @ SY4037 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SY4037 ) ) @ ( c_Nat_Osize__class_Osize @ SY4038 @ ( tc_List_Olist @ SY4037 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3248,plain,
! [SV654: $i] :
( ( ! [SY4040: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV654 ) @ SY4040 ) )
| ( SY4040
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV654
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3249,plain,
! [SV655: $i] :
( ( ! [SY4041: $i,SY4042: $i,SY4043: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SY4041 ) ) @ SY4042 @ SY4041 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY4042 @ ( tc_List_Olist @ SY4041 ) ) @ SV655 @ SY4041 ) @ SY4043 @ SY4041 ) @ SY4041 )
!= SY4043 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SY4041 ) ) @ SY4042 @ SY4041 )
!= SV655 )
| ( SY4042
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY4042 @ ( tc_List_Olist @ SY4041 ) ) @ SV655 @ SY4041 ) )
| ( ( c_List_Oappend @ SY4042 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY4042 @ ( tc_List_Olist @ SY4041 ) ) @ SV655 @ SY4041 ) @ SY4043 @ SY4041 ) @ SY4041 )
= ( c_List_Oappend @ SV655 @ SY4043 @ SY4041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(3250,plain,
! [SV656: $i] :
( ( ! [SY4044: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV656 ) @ SY4044 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV656
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4044
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(3251,plain,
! [SV657: $i] :
( ( ! [SY4045: $i,SY4046: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV657 @ SY4045 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4046 @ SY4045 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV657 = SY4046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3252,plain,
! [SV658: $i] :
( ( SV658
!= ( c_Suc @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(3253,plain,
! [SV659: $i] :
( ( ! [SY4047: $i,SY4048: $i,SY4049: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV659 )
| ( ( c_Power_Opower__class_Opower @ SY4047 @ ( c_Suc @ SY4048 ) @ SV659 )
!= ( c_Power_Opower__class_Opower @ SY4049 @ ( c_Suc @ SY4048 ) @ SV659 ) )
| ( SY4047 = SY4049 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SY4049 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SY4047 @ SV659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(3254,plain,
! [SV660: $i] :
( ( ! [SY4050: $i,SY4051: $i,SY4052: $i,SY4053: $i,SY4054: $i,SY4055: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SY4050 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY4051 ) @ SY4052 ) @ SY4053 ) ) )
| ~ ( c_Type_Otyping @ SY4054 @ SY4052 @ SY4050 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY4052 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY4054 @ SY4053 @ SY4050 @ tc_Type_Otype ) @ SY4051 @ SY4055 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY4051 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(3255,plain,
! [SV661: $i] :
( ( ! [SY4056: $i] :
( ( SV661
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV661 ) @ SY4056 ) )
| ( SY4056
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(3256,plain,
! [SV662: $i] :
( ( ! [SY4057: $i,SY4058: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV662 ) @ SY4057 )
!= ( c_Lambda_OdB_OVar @ SY4058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3257,plain,
! [SV663: $i] :
( ( ! [SY4059: $i,SY4060: $i] :
( ( c_Lambda_OdB_OVar @ SV663 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4059 ) @ SY4060 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(3258,plain,
! [SV664: $i] :
( ( ! [SY4061: $i,SY4062: $i] :
( ( ( c_List_Olist_ONil @ SV664 )
!= ( c_List_Oreplicate @ SY4061 @ SY4062 @ SV664 ) )
| ( SY4061
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(3259,plain,
! [SV665: $i] :
( ( ! [SY4063: $i,SY4064: $i,SY4065: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV665 )
| ( ( c_Power_Opower__class_Opower @ SY4063 @ SY4064 @ SV665 )
!= ( c_Power_Opower__class_Opower @ SY4063 @ SY4065 @ SV665 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SY4063 @ SV665 )
| ( SY4064 = SY4065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3260,plain,
! [SV666: $i] :
( ( ! [SY4066: $i,SY4067: $i] :
( ( ( hAPP @ SV666 @ ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SY4066 @ SY4067 ) )
!= ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SY4066 @ SY4067 ) )
| ( ( c_List_Omap @ SV666 @ SY4066 @ SY4067 @ SY4067 )
= SY4066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(3261,plain,
! [SV667: $i] :
( ( ! [SY4068: $i,SY4069: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV667 ) @ SY4068 )
!= ( c_Lambda_OdB_OAbs @ SY4069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3262,plain,
! [SV668: $i] :
( ( ! [SY4070: $i,SY4071: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV668 )
| ~ ( class_Int_Onumber__ring @ SV668 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4070 @ SY4071 @ SV668 )
!= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
| ( SY4070 = SY4071 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3263,plain,
! [SV669: $i] :
( ( ! [SY4072: $i,SY4073: $i] :
( ( c_Type_Otype_OAtom @ SV669 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4072 ) @ SY4073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(3264,plain,
! [SV670: $i] :
( ( ! [SY4074: $i,SY4075: $i,SY4076: $i,SY4077: $i] :
( ( ( c_List_Oappend @ SV670 @ SY4074 @ SY4075 )
!= ( c_List_Oappend @ SY4076 @ SY4077 @ SY4075 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY4076 @ ( tc_List_Olist @ SY4075 ) ) @ SV670 @ SY4075 )
= SY4076 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV670 @ ( tc_List_Olist @ SY4075 ) ) @ ( c_Nat_Osize__class_Osize @ SY4076 @ ( tc_List_Olist @ SY4075 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(3265,plain,
! [SV671: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV671 )
| ( ( c_HOL_Oone__class_Oone @ SV671 )
!= ( c_HOL_Ozero__class_Ozero @ SV671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3266,plain,
! [SV672: $i] :
( ( ! [SY4078: $i,SY4079: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV672 ) @ SY4078 )
!= ( c_Type_Otype_OAtom @ SY4079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3267,plain,
! [SV673: $i] :
( ( ! [SY4080: $i,SY4081: $i,SY4082: $i,SY4083: $i,SY4084: $i,SY4085: $i,SY4086: $i,SY4087: $i,SY4088: $i,SY4089: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SY4080 @ SY4081 ) )
!= ( hAPP @ SY4082 @ ( hAPP @ SY4083 @ SY4084 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SY4080 @ SY4085 @ SY4086 @ SY4087 ) @ SY4081 )
= ( hAPP @ ( c_Fun_Ocomp @ SY4082 @ SY4083 @ SY4088 @ SY4086 @ SY4089 ) @ SY4084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3268,plain,
! [SV674: $i] :
( ( ! [SY4090: $i,SY4091: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV674 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY4090 @ SV674 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY4091 @ SV674 ) )
| ( SY4090 = SY4091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3269,plain,
! [SV675: $i] :
( ( ! [SY4092: $i] :
( ( ( c_List_Olist_ONil @ SV675 )
!= ( c_List_Orev @ SY4092 @ SV675 ) )
| ( SY4092
= ( c_List_Olist_ONil @ SV675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3270,plain,
! [SV676: $i] :
( ( ! [SY4093: $i,SY4094: $i,SY4095: $i] :
( ( ( c_List_Oappend @ SV676 @ SY4093 @ SY4094 )
!= ( c_List_Oappend @ SV676 @ SY4095 @ SY4094 ) )
| ( SY4093 = SY4095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3271,plain,
! [SV677: $i] :
( ( ! [SY4096: $i,SY4097: $i] :
( ( ( c_List_Otake @ SV677 @ SY4096 @ SY4097 )
!= ( c_List_Olist_ONil @ SY4097 ) )
| ( SY4096
= ( c_List_Olist_ONil @ SY4097 ) )
| ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(3272,plain,
! [SV678: $i] :
( ( ! [SY4098: $i,SY4099: $i,SY4100: $i,SY4101: $i,SY4102: $i,SY4103: $i,SY4104: $i,SY4105: $i] :
( ( ( c_Fun_Ocomp @ SV678 @ SY4098 @ SY4099 @ SY4100 @ SY4101 )
!= ( c_Fun_Ocomp @ SY4102 @ SY4103 @ SY4104 @ SY4100 @ SY4101 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SY4098 @ SY4105 ) )
= ( hAPP @ SY4102 @ ( hAPP @ SY4103 @ SY4105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(3273,plain,
! [SV679: $i] :
( ( ! [SY4106: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV679 ) @ SY4106 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4106
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4106
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(3274,plain,
! [SV680: $i] :
( ( ! [SY4107: $i,SY4108: $i] :
( ( SV680
!= ( c_List_Oappend @ SY4107 @ SV680 @ SY4108 ) )
| ( SY4107
= ( c_List_Olist_ONil @ SY4108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(3275,plain,
! [SV681: $i] :
( ( ! [SY4109: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV681 ) @ SY4109 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4109
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(3276,plain,
! [SV682: $i] :
( ( ! [SY4110: $i,SY4111: $i] :
( ( c_List_Olist_OCons @ SV682 @ SY4110 @ SY4111 )
!= ( c_List_Olist_ONil @ SY4111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3277,plain,
! [SV683: $i] :
( ( ! [SY4112: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV683 ) @ SY4112 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4112
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV683
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(3278,plain,
! [SV684: $i] :
( ( ! [SY4113: $i,SY4114: $i,SY4115: $i,SY4116: $i] :
( ( ( hAPP @ SV684 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SY4113 @ SY4114 @ SY4115 @ SY4116 ) )
!= ( hAPP @ SY4113 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SY4113 @ SY4114 @ SY4115 @ SY4116 ) ) )
| ( ( c_List_Omap @ SV684 @ SY4114 @ SY4115 @ SY4116 )
= ( c_List_Omap @ SY4113 @ SY4114 @ SY4115 @ SY4116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3279,plain,
! [SV685: $i] :
( ( ! [SY4117: $i,SY4118: $i] :
( ( ( c_List_Oappend @ SV685 @ SY4117 @ SY4118 )
!= ( c_List_Olist_ONil @ SY4118 ) )
| ( SV685
= ( c_List_Olist_ONil @ SY4118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3280,plain,
! [SV686: $i] :
( ( ! [SY4119: $i,SY4120: $i,SY4121: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV686 ) @ SY4119 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4120 ) @ SY4121 ) )
| ( SY4119 = SY4121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(3281,plain,
! [SV687: $i] :
( ( ! [SY4122: $i,SY4123: $i,SY4124: $i,SY4125: $i] :
( ( ( c_List_Oappend @ SV687 @ ( c_List_Olist_OCons @ SY4122 @ ( c_List_Olist_ONil @ SY4123 ) @ SY4123 ) @ SY4123 )
!= ( c_List_Oappend @ SY4124 @ ( c_List_Olist_OCons @ SY4125 @ ( c_List_Olist_ONil @ SY4123 ) @ SY4123 ) @ SY4123 ) )
| ( SY4122 = SY4125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(3282,plain,
! [SV688: $i] :
( ( ! [SY4126: $i,SY4127: $i,SY4128: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV688 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SY4126 ) @ SY4127 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SY4126 ) @ SY4128 ) )
| ( SY4127 = SY4128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(3283,plain,
! [SV689: $i] :
( ( ! [SY4129: $i,SY4130: $i,SY4131: $i,SY4132: $i] :
( ( ( c_List_Oreplicate @ SV689 @ SY4129 @ SY4130 )
!= ( c_List_Oreplicate @ SY4131 @ SY4132 @ SY4130 ) )
| ( SV689 = SY4131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3284,plain,
! [SV690: $i] :
( ( ! [SY4133: $i,SY4134: $i,SY4135: $i,SY4136: $i] :
( ( ( hAPP @ SV690 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SY4133 @ SY4134 @ SY4135 @ SY4136 ) )
!= ( hAPP @ SY4133 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SY4133 @ SY4134 @ SY4135 @ SY4136 ) ) )
| ( ( c_List_Omap @ SV690 @ SY4134 @ SY4135 @ SY4136 )
= ( c_List_Omap @ SY4133 @ SY4134 @ SY4135 @ SY4136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(3285,plain,
! [SV691: $i] :
( ( ! [SY4137: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV691 )
!= ( c_Lambda_OdB_OAbs @ SY4137 ) )
| ( SV691 = SY4137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(3286,plain,
! [SV692: $i] :
( ( ! [SY4138: $i,SY4139: $i] :
( ( c_Lambda_OdB_OAbs @ SV692 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4138 ) @ SY4139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3287,plain,
! [SV693: $i] :
( ( ! [SY4140: $i,SY4141: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV693 ) @ SY4140 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4141 ) @ SY4140 ) )
| ( SV693 = SY4141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(3288,plain,
! [SV694: $i] :
( ( ! [SY4142: $i,SY4143: $i,SY4144: $i,SY4145: $i] :
( ( ( c_List_Oappend @ SV694 @ SY4142 @ SY4143 )
!= ( c_List_Oappend @ SY4144 @ SY4145 @ SY4143 ) )
| ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SY4143 ) ) @ SY4144 @ SY4143 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SY4143 ) ) @ ( c_Nat_Osize__class_Osize @ SY4144 @ ( tc_List_Olist @ SY4143 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(3289,plain,
! [SV695: $i] :
( ( ! [SY4146: $i,SY4147: $i] :
( ( ( c_List_Oappend @ SV695 @ SY4146 @ SY4147 )
!= ( c_List_Olist_ONil @ SY4147 ) )
| ( SY4146
= ( c_List_Olist_ONil @ SY4147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(3290,plain,
! [SV696: $i] :
( ( ! [SY4148: $i,SY4149: $i,SY4150: $i,SY4151: $i] :
( ( ( c_List_Olist_OCons @ SV696 @ SY4148 @ SY4149 )
!= ( c_List_Olist_OCons @ SY4150 @ SY4151 @ SY4149 ) )
| ( SV696 = SY4150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3291,plain,
! [SV697: $i] :
( ( ! [SY4152: $i,SY4153: $i,SY4154: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SY4152 ) ) @ SY4153 @ SY4152 )
!= SV697 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY4153 @ ( tc_List_Olist @ SY4152 ) ) @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SY4152 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SY4153 @ SY4154 @ SY4152 )
= ( c_List_Oappend @ SV697 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SY4152 ) ) @ SY4153 @ SY4152 ) @ SY4154 @ SY4152 ) @ SY4152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(3292,plain,
! [SV698: $i] :
( ( ! [SY4155: $i,SY4156: $i] :
( ( ( c_List_Olist_ONil @ SV698 )
!= ( c_List_Oappend @ SY4155 @ SY4156 @ SV698 ) )
| ( SY4155
= ( c_List_Olist_ONil @ SV698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(3293,plain,
! [SV699: $i] :
( ( ! [SY4157: $i,SY4158: $i,SY4159: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV699 ) @ SY4157 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4158 ) @ SY4159 ) )
| ( SV699 = SY4158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(3294,plain,
! [SV700: $i] :
( ( ! [SY4160: $i,SY4161: $i,SY4162: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV700 ) @ SY4160 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4161 ) @ SY4162 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4160 = SY4162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(3295,plain,
! [SV701: $i] :
( ( ! [SY4163: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV701 ) @ SY4163 ) )
| ( SV701
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV701
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3296,plain,
! [SV702: $i] :
( ( ! [SY4164: $i] :
( ( ( c_Lambda_OdB_OVar @ SV702 )
!= ( c_Lambda_OdB_OVar @ SY4164 ) )
| ( SV702 = SY4164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3297,plain,
! [SV703: $i] :
( ( ! [SY4165: $i,SY4166: $i] :
( SV703
!= ( c_List_Olist_OCons @ SY4165 @ SV703 @ SY4166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3298,plain,
! [SV704: $i] :
( ( ! [SY4167: $i,SY4168: $i,SY4169: $i,SY4170: $i] :
( ( ( c_List_Oreplicate @ SV704 @ SY4167 @ SY4168 )
!= ( c_List_Oreplicate @ SY4169 @ SY4170 @ SY4168 ) )
| ( SY4167 = SY4170 )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3299,plain,
! [SV705: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV705 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3300,plain,
! [SV706: $i] :
( ( ! [SY4171: $i,SY4172: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SY4171 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY4172 @ SY4171 @ tc_nat ) )
| ~ ( c_lessequals @ SY4171 @ SY4172 @ tc_nat )
| ~ ( c_lessequals @ SY4171 @ SV706 @ tc_nat )
| ( SV706 = SY4172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(3301,plain,
! [SV707: $i] :
( ( ! [SY4173: $i,SY4174: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV707 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4173 @ SY4174 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV707 )
= SY4173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3302,plain,
! [SV708: $i] :
( ( ! [SY4175: $i,SY4176: $i,SY4177: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV708 ) @ SY4175 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4176 ) @ SY4177 ) )
| ( SV708 = SY4176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3303,plain,
! [SV709: $i] :
( ( ! [SY4178: $i,SY4179: $i] :
( ( ( c_List_Orotate @ SV709 @ SY4178 @ SY4179 )
!= ( c_List_Olist_ONil @ SY4179 ) )
| ( SY4178
= ( c_List_Olist_ONil @ SY4179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(3304,plain,
! [SV710: $i] :
( ( ( c_Suc @ SV710 )
!= SV710 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3305,plain,
! [SV711: $i] :
( ( ! [SY4180: $i,SY4181: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV711 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4180 @ SY4181 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SY4180 = SY4181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3306,plain,
! [SV712: $i] :
( ( ! [SY4182: $i,SY4183: $i,SY4184: $i,SY4185: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4182 @ SY4183 @ SV712 )
!= ( c_HOL_Ominus__class_Ominus @ SY4184 @ SY4185 @ SV712 ) )
| ( c_HOL_Oord__class_Oless @ SY4184 @ SY4185 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SY4182 @ SY4183 @ SV712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3307,plain,
! [SV713: $i] :
( ( ! [SY4186: $i,SY4187: $i,SY4188: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV713 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4186 ) @ SY4187 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SY4188 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SY4187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(3308,plain,
! [SV714: $i] :
( ( ! [SY4189: $i,SY4190: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV714 )
| ~ ( class_Int_Onumber__ring @ SV714 )
| ( SY4189
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SY4189 ) @ SY4190 ) )
| ( SY4190
= ( c_HOL_Ozero__class_Ozero @ SV714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3309,plain,
! [SV715: $i] :
( ( ! [SY4191: $i,SY4192: $i] :
( ( ( c_List_Orev @ SV715 @ SY4191 )
!= ( c_List_Orev @ SY4192 @ SY4191 ) )
| ( SV715 = SY4192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(3310,plain,
! [SV716: $i] :
( ( ! [SY4193: $i,SY4194: $i] :
( ( ( c_List_Olist_ONil @ SV716 )
!= ( c_List_Oappend @ SY4193 @ SY4194 @ SV716 ) )
| ( SY4194
= ( c_List_Olist_ONil @ SV716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(3311,plain,
! [SV717: $i] :
( ( ! [SY4195: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV717 ) @ SY4195 ) )
| ( SV717
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4195
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3312,plain,
! [SV718: $i] :
( ( ! [SY4196: $i,SY4197: $i,SY4198: $i] :
( ( ( c_List_Omap @ SV718 @ SY4196 @ SY4197 @ SY4198 )
!= ( c_List_Olist_ONil @ SY4198 ) )
| ( SY4196
= ( c_List_Olist_ONil @ SY4197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(3313,plain,
! [SV719: $i] :
( ( ! [SY4199: $i,SY4200: $i,SY4201: $i] :
( ( ( c_List_Orev @ SV719 @ SY4199 )
!= ( c_List_Olist_OCons @ SY4200 @ SY4201 @ SY4199 ) )
| ( SV719
= ( c_List_Oappend @ ( c_List_Orev @ SY4201 @ SY4199 ) @ ( c_List_Olist_OCons @ SY4200 @ ( c_List_Olist_ONil @ SY4199 ) @ SY4199 ) @ SY4199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3314,plain,
! [SV720: $i] :
( ( ! [SY4202: $i,SY4203: $i,SY4204: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV720 ) @ SY4202 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4203 ) @ SY4204 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3315,plain,
! [SV721: $i] :
( ( ! [SY4205: $i,SY4206: $i,SY4207: $i,SY4208: $i] :
( ( ( c_List_Olist_OCons @ SV721 @ SY4205 @ SY4206 )
!= ( c_List_Olist_OCons @ SY4207 @ SY4208 @ SY4206 ) )
| ( SY4205 = SY4208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3316,plain,
! [SV722: $i] :
( ( ! [SY4209: $i,SY4210: $i,SY4211: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV722 ) @ SY4209 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4210 ) @ SY4211 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4210 @ SY4209 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV722 @ SY4211 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3317,plain,
! [SV723: $i] :
( ( ! [SY4212: $i,SY4213: $i,SY4214: $i] :
( ( ( c_List_Olist__update @ SV723 @ SY4212 @ SY4213 @ SY4214 )
!= ( c_List_Olist_ONil @ SY4214 ) )
| ( SV723
= ( c_List_Olist_ONil @ SY4214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3318,plain,
! [SV724: $i] :
( ( ! [SY4215: $i] :
( ( ( c_List_Orev @ SV724 @ SY4215 )
!= ( c_List_Olist_ONil @ SY4215 ) )
| ( SV724
= ( c_List_Olist_ONil @ SY4215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3319,plain,
! [SV725: $i] :
( ( ! [SY4216: $i,SY4217: $i,SY4218: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV725 ) @ SY4216 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4217 ) @ SY4218 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV725 = SY4217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3320,plain,
! [SV726: $i] :
( ( ! [SY4219: $i,SY4220: $i,SY4221: $i,SY4222: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4219 @ SY4220 @ SV726 )
!= ( c_HOL_Ominus__class_Ominus @ SY4221 @ SY4222 @ SV726 ) )
| ( c_lessequals @ SY4222 @ SY4221 @ SV726 )
| ~ ( c_lessequals @ SY4220 @ SY4219 @ SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3321,plain,
! [SV727: $i] :
( ( ! [SY4223: $i,SY4224: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SY4223 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SY4224 ) )
| ( SY4223 = SY4224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3322,plain,
! [SV728: $i] :
( ( ! [SY4225: $i,SY4226: $i,SY4227: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV728 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4225 @ SY4225 @ SV728 )
!= ( c_HOL_Ominus__class_Ominus @ SY4226 @ SY4227 @ SV728 ) )
| ( SY4226 = SY4227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3323,plain,
! [SV729: $i] :
( ( ! [SY4228: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV729 )
| ~ ( class_Power_Opower @ SV729 )
| ( ( c_Power_Opower__class_Opower @ SY4228 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3324,plain,
! [SV730: $i] :
( ( ! [SY4229: $i,SY4230: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SY4229 ) @ SY4230 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SY4230 @ SV730 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SY4229 @ SV730 )
| ( SY4229
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3325,plain,
! [SV731: $i] :
( ( ! [SY4231: $i,SY4232: $i] :
( ( ( c_List_Oreplicate @ SV731 @ SY4231 @ SY4232 )
!= ( c_List_Olist_ONil @ SY4232 ) )
| ( SV731
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3326,plain,
! [SV732: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV732 )
| ( ( c_HOL_Ozero__class_Ozero @ SV732 )
!= ( c_HOL_Oone__class_Oone @ SV732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3327,plain,
! [SV733: $i] :
( ( ! [SY4233: $i] :
( ( ( c_Suc @ SV733 )
!= ( c_Suc @ SY4233 ) )
| ( SV733 = SY4233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3328,plain,
! [SV734: $i] :
( ( ! [SY4234: $i,SY4235: $i,SY4236: $i,SY4237: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV734 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SY4234 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SY4235 ) @ SY4236 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SY4235 ) @ SY4237 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SY4234 ) @ SY4236 )
= SY4237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3329,plain,
! [SV735: $i] :
( ( ! [SY4238: $i,SY4239: $i] :
( ( ( c_List_Orev @ SV735 @ SY4238 )
!= ( c_List_Olist_OCons @ SY4239 @ ( c_List_Olist_ONil @ SY4238 ) @ SY4238 ) )
| ( SV735
= ( c_List_Olist_OCons @ SY4239 @ ( c_List_Olist_ONil @ SY4238 ) @ SY4238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3330,plain,
! [SV736: $i] :
( ( ! [SY4240: $i,SY4241: $i] :
( ( ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SY4240 ) @ SY4240 )
!= ( c_List_Orev @ SY4241 @ SY4240 ) )
| ( SY4241
= ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SY4240 ) @ SY4240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3331,plain,
! [SV737: $i] :
( ( ! [SY4242: $i] :
( ( ( c_Suc @ SV737 )
!= ( c_Suc @ SY4242 ) )
| ( SV737 = SY4242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3332,plain,
! [SV738: $i] :
( ( ! [SY4243: $i,SY4244: $i] :
( ( SV738
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SY4243 ) ) @ SY4244 @ SY4243 ) )
| ( ( c_List_Oappend @ SV738 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SY4243 ) ) @ SY4244 @ SY4243 ) @ SY4243 )
= SY4244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3333,plain,
! [SV739: $i] :
( ( ( c_Suc @ SV739 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3334,plain,
! [SV740: $i] :
( ( ! [SY4245: $i,SY4246: $i,SY4247: $i,SY4248: $i] :
( ( ( hAPP @ SV740 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SY4245 @ SY4246 @ SY4247 @ SY4248 ) )
!= ( hAPP @ SY4245 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SY4245 @ SY4246 @ SY4247 @ SY4248 ) ) )
| ( ( c_List_Omap @ SV740 @ SY4246 @ SY4247 @ SY4248 )
= ( c_List_Omap @ SY4245 @ SY4246 @ SY4247 @ SY4248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3335,plain,
! [SV741: $i] :
( ( ! [SY4249: $i,SY4250: $i,SY4251: $i] :
( ( SV741
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SY4249 ) ) @ SY4250 @ SY4249 ) )
| ( ( c_List_Oappend @ SV741 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SY4249 ) ) @ SY4250 @ SY4249 ) @ SY4251 @ SY4249 ) @ SY4249 )
= ( c_List_Oappend @ SY4250 @ SY4251 @ SY4249 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SY4249 ) ) @ ( c_Nat_Osize__class_Osize @ SY4250 @ ( tc_List_Olist @ SY4249 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3336,plain,
! [SV742: $i] :
( ( ! [SY4252: $i,SY4253: $i,SY4254: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV742 ) ) @ SY4252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4253 ) @ SY4254 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3337,plain,
! [SV743: $i] :
( ( ( c_Suc @ SV743 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3338,plain,
! [SV744: $i] :
( ( ! [SY4255: $i,SY4256: $i,SY4257: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV744 ) @ SY4255 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4256 ) @ SY4257 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4255 = SY4257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3339,plain,
! [SV745: $i] :
( ( ! [SY4258: $i,SY4259: $i] :
( ( c_List_Olist_OCons @ SV745 @ SY4258 @ SY4259 )
!= SY4258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3340,plain,
! [SV746: $i] :
( ( ! [SY4260: $i] :
( ( ( c_Type_Otype_OAtom @ SV746 )
!= ( c_Type_Otype_OAtom @ SY4260 ) )
| ( SV746 = SY4260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3341,plain,
! [SV747: $i] :
( ( ! [SY4261: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV747 ) @ SY4261 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV747
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3342,plain,
! [SV748: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV748 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3343,plain,
! [SV749: $i] :
( ( ! [SY4262: $i,SY4263: $i,SY4264: $i,SY4265: $i] :
( ( ( c_List_Oappend @ SV749 @ SY4262 @ SY4263 )
!= ( c_List_Oappend @ SY4264 @ SY4265 @ SY4263 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY4264 @ ( tc_List_Olist @ SY4263 ) ) @ SV749 @ SY4263 ) @ SY4262 @ SY4263 )
= SY4265 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV749 @ ( tc_List_Olist @ SY4263 ) ) @ ( c_Nat_Osize__class_Osize @ SY4264 @ ( tc_List_Olist @ SY4263 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3344,plain,
! [SV750: $i] :
( ( ! [SY4266: $i,SY4267: $i,SY4268: $i,SY4269: $i,SY4270: $i,SY4271: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SY4266 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY4267 ) @ SY4268 ) @ SY4269 ) ) )
| ~ ( c_Type_Otyping @ SY4270 @ SY4268 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY4268 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY4270 @ SY4269 @ SV750 @ tc_Type_Otype ) @ SY4267 @ SY4271 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY4267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3345,plain,
! [SV751: $i] :
( ( ! [SY4272: $i,SY4273: $i] :
( ( ( c_List_Oappend @ SV751 @ SY4272 @ SY4273 )
!= SY4272 )
| ( SV751
= ( c_List_Olist_ONil @ SY4273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3346,plain,
! [SV752: $i] :
( ( ! [SY4274: $i] :
( ( c_Lambda_OdB_OAbs @ SV752 )
!= ( c_Lambda_OdB_OVar @ SY4274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3347,plain,
! [SV753: $i] :
( ( ! [SY4275: $i,SY4276: $i] :
( ( c_List_Olist_ONil @ SV753 )
!= ( c_List_Olist_OCons @ SY4275 @ SY4276 @ SV753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3348,plain,
! [SV754: $i] :
( ( ! [SY4277: $i,SY4278: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SY4277 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SY4278 ) )
| ( SY4277 = SY4278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3349,plain,
! [SV755: $i] :
( ( ! [SY4279: $i,SY4280: $i,SY4281: $i,SY4282: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4279 @ SY4280 @ SV755 )
!= ( c_HOL_Ominus__class_Ominus @ SY4281 @ SY4282 @ SV755 ) )
| ( c_HOL_Oord__class_Oless @ SY4279 @ SY4280 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SY4281 @ SY4282 @ SV755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3350,plain,
! [SV756: $i] :
( ( ! [SY4283: $i,SY4284: $i] :
( ~ ( class_Orderings_Olinorder @ SV756 )
| ( ( c_Orderings_Oord__class_Omax @ SY4283 @ SY4284 @ SV756 )
!= SY4284 )
| ( c_lessequals @ SY4283 @ SY4284 @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3351,plain,
! [SV757: $i] :
( ( ! [SY4285: $i,SY4286: $i,SY4287: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV757 )
| ( ( c_Power_Opower__class_Opower @ SY4285 @ SY4286 @ SV757 )
!= ( c_Power_Opower__class_Opower @ SY4287 @ SY4286 @ SV757 ) )
| ( SY4285 = SY4287 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4286 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SY4287 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SY4285 @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(3352,plain,
! [SV758: $i] :
( ( ! [SY4288: $i,SY4289: $i] :
( ( ( c_List_Odrop @ SV758 @ SY4288 @ SY4289 )
!= ( c_List_Olist_ONil @ SY4289 ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY4288 @ ( tc_List_Olist @ SY4289 ) ) @ SV758 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3353,plain,
! [SV759: $i] :
( ( ! [SY4290: $i,SY4291: $i,SY4292: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4290 ) @ SY4291 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY4292 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY4290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3354,plain,
! [SV760: $i] :
( ( ! [SY4293: $i,SY4294: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV760 @ SY4293 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY4294 ) )
| ( SV760
= ( c_Lambda_OdB_OAbs @ SY4294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3355,plain,
! [SV761: $i] :
( ( ! [SY4295: $i,SY4296: $i] :
( ( ( c_Lambda_OdB_OVar @ SV761 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4295 @ SY4296 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV761 )
= SY4295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3356,plain,
! [SV762: $i] :
( ( ! [SY4297: $i,SY4298: $i,SY4299: $i] :
( ( ( c_List_Oappend @ SV762 @ SY4297 @ SY4298 )
!= ( c_List_Oappend @ SY4299 @ SY4297 @ SY4298 ) )
| ( SV762 = SY4299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3357,plain,
! [SV763: $i] :
( ( ! [SY4300: $i,SY4301: $i] :
( ( c_List_Olist_OCons @ SV763 @ SY4300 @ SY4301 )
!= ( c_List_Olist_ONil @ SY4301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3358,plain,
! [SV764: $i] :
( ( ! [SY4302: $i,SY4303: $i,SY4304: $i,SY4305: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4302 @ SY4303 @ SV764 )
!= ( c_HOL_Ominus__class_Ominus @ SY4304 @ SY4305 @ SV764 ) )
| ( c_lessequals @ SY4303 @ SY4302 @ SV764 )
| ~ ( c_lessequals @ SY4305 @ SY4304 @ SV764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3359,plain,
! [SV765: $i] :
( ( ! [SY4306: $i,SY4307: $i,SY4308: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV765 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4306 @ SY4307 @ SV765 )
!= ( c_HOL_Ominus__class_Ominus @ SY4308 @ SY4308 @ SV765 ) )
| ( SY4306 = SY4307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3360,plain,
! [SV766: $i] :
( ( ! [SY4309: $i] :
( ( c_Lambda_OdB_OVar @ SV766 )
!= ( c_Lambda_OdB_OAbs @ SY4309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3361,plain,
! [SV767: $i] :
( ( ! [SY4310: $i,SY4311: $i,SY4312: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV767 ) @ SY4310 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4311 ) @ SY4312 ) )
| ( SY4310 = SY4312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3362,plain,
! [SV768: $i] :
( ( ! [SY4313: $i,SY4314: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV768 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4313 @ SY4314 @ SV768 )
!= ( c_HOL_Ozero__class_Ozero @ SV768 ) )
| ( SY4313 = SY4314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3363,plain,
! [SV769: $i] :
( ( ! [SY4315: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV769 ) @ SY4315 ) )
| ( SY4315
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3364,plain,
! [SV770: $i] :
( ( ! [SY4316: $i,SY4317: $i,SY4318: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV770 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SY4316 ) @ SY4317 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SY4318 ) @ SY4317 ) )
| ( SY4316 = SY4318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3365,plain,
! [SV771: $i] :
( ( ! [SY4319: $i,SY4320: $i,SY4321: $i,SY4322: $i] :
( ( ( c_List_Oappend @ SV771 @ ( c_List_Olist_OCons @ SY4319 @ ( c_List_Olist_ONil @ SY4320 ) @ SY4320 ) @ SY4320 )
!= ( c_List_Oappend @ SY4321 @ ( c_List_Olist_OCons @ SY4322 @ ( c_List_Olist_ONil @ SY4320 ) @ SY4320 ) @ SY4320 ) )
| ( SV771 = SY4321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3366,plain,
! [SV772: $i,SV1: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV1 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ SV772 ) @ SV772 ) @ SV1 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV772 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3367,plain,
! [SV773: $i,SV2: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV2 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV773 @ SV2 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV773 ) @ SV773 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3368,plain,
! [SV3: $i] :
( ( ( SV3
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV3 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2595]) ).
thf(3369,plain,
! [SV774: $i,SV4: $i] :
( ( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ SV4 ) @ ( c_Suc @ SV774 ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ SV4 @ SV774 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3370,plain,
! [SV775: $i,SV7: $i] :
( ( ! [SY4323: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV7 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV7 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4323 @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV775 @ SY4323 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3371,plain,
! [SV776: $i,SV8: $i] :
( ( ! [SY4324: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV8 )
| ( c_lessequals @ SV776 @ SY4324 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV776 @ SV8 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4324 @ SV8 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3372,plain,
! [SV777: $i,SV9: $i] :
( ( ! [SY4325: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV9 @ SV777 @ SY4325 ) @ ( tc_List_Olist @ SY4325 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV777 @ ( tc_List_Olist @ SY4325 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3373,plain,
! [SV778: $i,SV10: $i] :
( ( ! [SY4326: $i] :
( ( c_HOL_Oord__class_Oless @ SV10 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV778 ) @ SY4326 ) @ tc_nat )
| ~ ( c_lessequals @ SV10 @ SV778 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4326 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3374,plain,
! [SV779: $i,SV11: $i] :
( ( ! [SY4327: $i,SY4328: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SY4327 ) @ SY4328 ) @ SV11 )
| ~ ( c_lessequals @ SV779 @ SY4328 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SY4327 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3375,plain,
! [SV780: $i,SV12: $i] :
( ( c_List_Olistsp @ SV12 @ ( c_List_Olist_ONil @ SV780 ) @ SV780 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3376,plain,
! [SV781: $i,SV13: $i] :
( ( ! [SY4329: $i,SY4330: $i] :
( ( c_List_Odrop @ SV13 @ ( c_List_Oappend @ SV781 @ SY4329 @ SY4330 ) @ SY4330 )
= ( c_List_Oappend @ ( c_List_Odrop @ SV13 @ SV781 @ SY4330 ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Nat_Osize__class_Osize @ SV781 @ ( tc_List_Olist @ SY4330 ) ) @ tc_nat ) @ SY4329 @ SY4330 ) @ SY4330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3377,plain,
! [SV782: $i,SV14: $i] :
( ( ! [SY4331: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV14 @ SV782 @ tc_nat ) ) @ SY4331 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV782 ) @ SY4331 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV782 @ SV14 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3378,plain,
! [SV783: $i,SV15: $i] :
( ( ! [SY4332: $i,SY4333: $i] :
( ~ ( class_Orderings_Olinorder @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SY4332 @ SV15 ) @ SY4333 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SY4332 @ SY4333 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV783 @ SY4333 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3379,plain,
! [SV784: $i,SV16: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV16 @ SV784 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV16 @ SV784 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3380,plain,
! [SV785: $i,SV17: $i] :
( ( ! [SY4334: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV17 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV785 @ SY4334 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV785 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3381,plain,
! [SV786: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ SV786 ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV18 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3382,plain,
! [SV787: $i,SV19: $i] :
( ( ( c_List_Otake @ SV19 @ ( c_List_Olist_ONil @ SV787 ) @ SV787 )
= ( c_List_Olist_ONil @ SV787 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3383,plain,
! [SV788: $i,SV20: $i] :
( ( ! [SY4335: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV788 @ SY4335 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ SV788 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3384,plain,
! [SV789: $i,SV21: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV21 )
| ~ ( class_Power_Opower @ SV21 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ ( c_Suc @ SV789 ) @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3385,plain,
! [SV790: $i,SV22: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV22 ) @ ( c_Suc @ SV790 ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV22 ) @ SV790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3386,plain,
! [SV791: $i,SV23: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV23 ) ) @ SV791 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV23 ) @ SV791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3387,plain,
! [SV792: $i,SV24: $i] :
( ( ! [SY4336: $i,SY4337: $i] :
( ( ( c_List_Orev @ ( c_List_Olist__update @ SV24 @ SV792 @ SY4336 @ SY4337 ) @ SY4337 )
= ( c_List_Olist__update @ ( c_List_Orev @ SV24 @ SY4337 ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SY4337 ) ) @ SV792 @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY4336 @ SY4337 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV792 @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SY4337 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3388,plain,
! [SV793: $i,SV25: $i] :
( ( ! [SY4338: $i] :
( ( hBOOL @ ( hAPP @ SV25 @ SV793 ) )
| ( hBOOL @ ( hAPP @ SV25 @ SY4338 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4338 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV25 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3389,plain,
! [SV794: $i,SV26: $i] :
( ( c_HOL_Oord__class_Oless @ SV26 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV26 ) @ SV794 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3390,plain,
! [SV795: $i,SV27: $i] :
( ( c_HOL_Oord__class_Oless @ SV27 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV795 ) @ SV27 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3391,plain,
! [SV796: $i,SV28: $i] :
( ( c_HOL_Oord__class_Oless @ SV28 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV28 ) @ SV796 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3392,plain,
! [SV797: $i,SV29: $i] :
( ( ! [SY4339: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV797 ) @ SY4339 @ tc_nat )
| ~ ( c_lessequals @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SY4339 @ SV797 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV797 @ SY4339 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3393,plain,
! [SV798: $i,SV30: $i] :
( ( ! [SY4340: $i] :
( ( c_lessequals @ SV30 @ ( c_HOL_Ominus__class_Ominus @ SV798 @ SY4340 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV30 ) @ SY4340 ) @ SV798 @ tc_nat )
| ~ ( c_lessequals @ SY4340 @ SV798 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3394,plain,
! [SV799: $i,SV31: $i] :
( ( ! [SY4341: $i,SY4342: $i] :
( ~ ( class_Orderings_Olinorder @ SV31 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SY4341 @ SV31 ) @ SY4342 @ SV31 )
| ~ ( c_lessequals @ SY4341 @ SY4342 @ SV31 )
| ~ ( c_lessequals @ SV799 @ SY4342 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3395,plain,
! [SV800: $i,SV32: $i] :
( ( ! [SY4343: $i,SY4344: $i] :
( ~ ( class_Orderings_Olinorder @ SV32 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SY4343 @ SV32 ) @ SY4344 @ SV32 )
| ~ ( c_lessequals @ SY4343 @ SY4344 @ SV32 )
| ~ ( c_lessequals @ SV800 @ SY4344 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3396,plain,
! [SV801: $i,SV33: $i] :
( ( ! [SY4345: $i,SY4346: $i] :
( ~ ( class_Orderings_Olinorder @ SV33 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SY4345 @ SV33 ) @ SY4346 @ SV33 )
| ~ ( c_lessequals @ SY4345 @ SY4346 @ SV33 )
| ~ ( c_lessequals @ SV801 @ SY4346 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3397,plain,
! [SV802: $i,SV34: $i] :
( ( ! [SY4347: $i] :
( ~ ( class_Orderings_Olinorder @ SV34 )
| ( c_lessequals @ SV802 @ ( c_Orderings_Oord__class_Omax @ SV802 @ SY4347 @ SV34 ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3398,plain,
! [SV803: $i,SV35: $i] :
( ( ! [SY4348: $i] :
( ~ ( class_Orderings_Olinorder @ SV35 )
| ( c_lessequals @ SV803 @ ( c_Orderings_Oord__class_Omax @ SY4348 @ SV803 @ SV35 ) @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3399,plain,
! [SV804: $i,SV36: $i] :
( ( ( c_List_Oappend @ SV36 @ ( c_List_Olist_ONil @ SV804 ) @ SV804 )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3400,plain,
! [SV805: $i,SV37: $i] :
( ( SV37
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV805 ) @ SV37 @ SV805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3401,plain,
! [SV806: $i,SV38: $i] :
( ( SV38
= ( c_List_Oappend @ SV38 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3402,plain,
! [SV807: $i,SV39: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV39 ) @ SV807 @ SV39 )
= SV807 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3403,plain,
! [SV808: $i,SV40: $i] :
( ( SV40
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV808 ) @ SV40 @ SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3404,plain,
! [SV809: $i,SV41: $i] :
( ( ~ ( class_Orderings_Obot @ SV41 )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV41 ) @ SV809 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3405,plain,
! [SV810: $i,SV42: $i] :
( ( ! [SY4349: $i] :
( ( c_List_Odistinct @ SV42 @ SV810 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV42 @ SY4349 @ SV810 ) @ SV810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3406,plain,
! [SV811: $i,SV43: $i] :
( ( ! [SY4350: $i] :
( ( c_List_Odistinct @ SV43 @ SV811 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SY4350 @ SV43 @ SV811 ) @ SV811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3407,plain,
! [SV812: $i,SV44: $i] :
( ( SV44
= ( c_List_Orev @ ( c_List_Orev @ SV44 @ SV812 ) @ SV812 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3408,plain,
! [SV813: $i,SV45: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV45 @ SV813 ) @ SV813 )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3409,plain,
! [SV814: $i,SV46: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV46 @ SV814 ) @ SV814 )
= SV46 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3410,plain,
! [SV815: $i,SV47: $i] :
( ( ! [SY4351: $i,SY4352: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV47 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SY4351 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SY4352 @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SY4352 @ SY4351 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3411,plain,
! [SV816: $i,SV48: $i] :
( ( ! [SY4353: $i] :
( SV48
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV48 @ ( tc_List_Olist @ SV816 ) ) @ ( c_List_Oappend @ SV48 @ SY4353 @ SV816 ) @ SV816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3412,plain,
! [SV817: $i,SV49: $i] :
( ( ! [SY4354: $i,SY4355: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
| ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SY4354 ) @ SY4355 ) @ SV49 )
| ~ ( c_lessequals @ SV817 @ SY4355 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SY4354 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3413,plain,
! [SV818: $i,SV50: $i] :
( ( ! [SY4356: $i,SY4357: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SY4356 ) @ SY4357 ) @ SV50 )
| ~ ( c_lessequals @ SV818 @ SY4356 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SY4357 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3414,plain,
! [SV819: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ SV51 @ SV819 ) )
| ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV51 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3415,plain,
! [SV820: $i,SV52: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV52 ) @ SV820 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV52 @ SV820 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3416,plain,
! [SV821: $i,SV53: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV53 @ SV821 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV53 ) @ SV821 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(3417,plain,
! [SV822: $i,SV54: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV54 ) @ SV822 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV822 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3418,plain,
! [SV823: $i,SV55: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV55 @ SV823 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV55 ) @ SV823 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3419,plain,
! [SV824: $i,SV56: $i] :
( ( ! [SY4358: $i] :
( ( c_HOL_Oord__class_Oless @ SV56 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV824 ) @ SY4358 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ SV824 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3420,plain,
! [SV825: $i,SV57: $i] :
( ( ! [SY4359: $i] :
( ( c_HOL_Oord__class_Oless @ SV57 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV825 ) @ SY4359 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SY4359 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(3421,plain,
! [SV826: $i,SV58: $i] :
( ( ! [SY4360: $i] :
( ( c_HOL_Oord__class_Oless @ SV58 @ SV826 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SY4360 ) @ SV826 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3422,plain,
! [SV827: $i,SV59: $i] :
( ( ! [SY4361: $i] :
( ( c_HOL_Oord__class_Oless @ SV59 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV827 ) @ SY4361 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV59 @ SV827 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3423,plain,
! [SV828: $i,SV60: $i] :
( ( ! [SY4362: $i] :
( ( c_HOL_Oord__class_Oless @ SV60 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV828 ) @ SY4362 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV60 @ SY4362 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3424,plain,
! [SV829: $i,SV61: $i] :
( ( ! [SY4363: $i,SY4364: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV61 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SY4363 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SY4364 @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
| ~ ( c_lessequals @ SY4364 @ SY4363 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3425,plain,
! [SV830: $i,SV63: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV63 ) @ SV830 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV63 @ SV830 @ tc_nat ) ) )
| ~ ( c_lessequals @ SV830 @ SV63 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3426,plain,
! [SV831: $i,SV64: $i] :
( ( ! [SY4365: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV64 ) @ SV831 @ SY4365 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV64 @ SV831 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4365 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3427,plain,
! [SV832: $i,SV65: $i] :
( ( ! [SY4366: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV832 ) @ SY4366 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY4366 ) @ SV832 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3428,plain,
! [SV833: $i,SV66: $i] :
( ( ! [SY4367: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV66 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SV833 ) @ SY4367 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SY4367 ) @ SV833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3429,plain,
! [SV834: $i,SV67: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV67 ) @ SV834 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV834 ) @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3430,plain,
! [SV835: $i,SV68: $i] :
( ( ! [SY4368: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV835 ) @ SY4368 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SY4368 ) @ SV835 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3431,plain,
! [SV836: $i,SV69: $i] :
( ( ! [SY4369: $i,SY4370: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV69 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ SY4369 ) @ SY4370 @ SV69 @ SV69 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY4369 @ SY4370 @ SV69 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3432,plain,
! [SV837: $i,SV70: $i] :
( ( ! [SY4371: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV70 @ SV837 @ SY4371 ) @ SY4371 )
= ( c_List_Oreplicate @ SV70 @ SV837 @ SY4371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3433,plain,
! [SV838: $i,SV71: $i] :
( ( ! [SY4372: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV838 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SY4372 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4372 @ SV71 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4372 @ SV838 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3434,plain,
! [SV839: $i,SV72: $i] :
( ( ! [SY4373: $i] :
( ( ( hAPP @ SV72 @ SV839 )
= SY4373 )
| ~ ( c_Type_Otyping @ SV72 @ ( c_Lambda_OdB_OVar @ SV839 ) @ SY4373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3435,plain,
! [SV840: $i,SV73: $i] :
( ( ! [SY4374: $i,SY4375: $i] :
( ( c_List_Otake @ ( c_Suc @ SV73 ) @ ( c_List_Olist_OCons @ SV840 @ SY4374 @ SY4375 ) @ SY4375 )
= ( c_List_Olist_OCons @ SV840 @ ( c_List_Otake @ SV73 @ SY4374 @ SY4375 ) @ SY4375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3436,plain,
! [SV841: $i,SV74: $i] :
( ( ! [SY4376: $i,SY4377: $i] :
( ~ ( class_Orderings_Olinorder @ SV74 )
| ( c_lessequals @ SV841 @ SY4376 @ SV74 )
| ( c_lessequals @ SV841 @ SY4377 @ SV74 )
| ~ ( c_lessequals @ SV841 @ ( c_Orderings_Oord__class_Omax @ SY4377 @ SY4376 @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3437,plain,
! [SV842: $i,SV75: $i] :
( ( ! [SY4378: $i,SY4379: $i] :
( ( c_List_Olistsp @ SV75 @ SV842 @ SY4378 )
| ~ ( c_List_Olistsp @ SV75 @ ( c_List_Oappend @ SY4379 @ SV842 @ SY4378 ) @ SY4378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3438,plain,
! [SV843: $i,SV76: $i] :
( ( ! [SY4380: $i,SY4381: $i] :
( ( c_List_Olistsp @ SV76 @ SV843 @ SY4380 )
| ~ ( c_List_Olistsp @ SV76 @ ( c_List_Oappend @ SV843 @ SY4381 @ SY4380 ) @ SY4380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3439,plain,
! [SV844: $i,SV77: $i] :
( ( ! [SY4382: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV77 ) ) @ SV844 ) @ SY4382 )
= ( c_Lambda_OdB_OVar @ SV77 ) )
| ( SV77 = SY4382 )
| ( c_HOL_Oord__class_Oless @ SY4382 @ SV77 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3440,plain,
! [SV845: $i,SV78: $i] :
( ( ! [SY4383: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV78 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ ( c_HOL_Ominus__class_Ominus @ SV845 @ SY4383 @ SV78 ) ) @ SY4383 )
= SV845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3441,plain,
! [SV846: $i,SV79: $i] :
( ( ! [SY4384: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV79 @ ( tc_List_Olist @ SV846 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SY4384 @ SV79 @ SV846 ) @ ( tc_List_Olist @ SV846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3442,plain,
! [SV847: $i,SV80: $i] :
( ( ! [SY4385: $i] :
( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV847 ) @ SY4385 ) @ SV847 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV80 @ SY4385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3443,plain,
! [SV848: $i,SV81: $i] :
( ( ! [SY4386: $i] :
( ~ ( hBOOL @ ( hAPP @ SV81 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV848 ) @ SY4386 ) @ SV848 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV81 @ SY4386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3444,plain,
! [SV849: $i,SV82: $i] :
( ( ! [SY4387: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV82 @ SV849 @ SY4387 ) @ SY4387 )
= ( c_List_Olist_OCons @ SV82 @ ( c_List_Olist_ONil @ SY4387 ) @ SY4387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2674]) ).
thf(3445,plain,
! [SV850: $i,SV83: $i] :
( ( ! [SY4388: $i,SY4389: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV83 ) @ SV850 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4388 ) @ SY4389 ) @ tc_nat )
| ~ ( c_lessequals @ SV850 @ SY4389 @ tc_nat )
| ~ ( c_lessequals @ SV83 @ SY4388 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3446,plain,
! [SV851: $i,SV84: $i] :
( ( ! [SY4390: $i,SY4391: $i,SY4392: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SY4390 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SY4391 ) @ SY4392 ) @ SV84 )
| ~ ( c_lessequals @ SY4390 @ SY4392 @ SV84 )
| ~ ( c_lessequals @ SV851 @ SY4391 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3447,plain,
! [SV852: $i,SV85: $i] :
( ( ! [SY4393: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV85 @ SV852 @ SY4393 ) @ ( tc_List_Olist @ SY4393 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV852 @ ( tc_List_Olist @ SY4393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3448,plain,
! [SV853: $i,SV86: $i] :
( ( ! [SY4394: $i,SY4395: $i,SY4396: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV86 @ SV853 @ SY4394 ) @ SY4395 @ SY4396 @ SY4394 )
= ( c_List_Oappend @ SV86 @ ( c_List_Olist__update @ SV853 @ ( c_HOL_Ominus__class_Ominus @ SY4395 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SY4394 ) ) @ tc_nat ) @ SY4396 @ SY4394 ) @ SY4394 ) )
| ( c_HOL_Oord__class_Oless @ SY4395 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SY4394 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3449,plain,
! [SV854: $i,SV87: $i] :
( ( ! [SY4397: $i] :
( ( ( c_List_Otake @ SV87 @ SV854 @ SY4397 )
= SV854 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV854 @ ( tc_List_Olist @ SY4397 ) ) @ SV87 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3450,plain,
! [SV855: $i,SV88: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SV855 ) @ tc_nat )
| ~ ( c_lessequals @ SV88 @ SV855 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3451,plain,
! [SV856: $i,SV89: $i] :
( ( ( c_lessequals @ SV89 @ SV856 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV89 @ ( c_Suc @ SV856 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3452,plain,
! [SV90: $i] :
( ( ( ~ ( c_lessequals @ SV90 @ SV90 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ ( c_Suc @ SV90 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(3453,plain,
! [SV857: $i,SV91: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV91 )
| ( ( c_List_Olistsum @ SV857 @ SV91 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV857 @ SV91 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3454,plain,
! [SV92: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV92 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2684]) ).
thf(3455,plain,
! [SV858: $i,SV93: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV93 @ SV858 @ tc_nat ) @ ( c_Suc @ SV93 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3456,plain,
! [SV859: $i,SV94: $i] :
( ( ! [SY4398: $i,SY4399: $i] :
( ( c_List_Odrop @ SV94 @ ( c_List_Otake @ SV859 @ SY4398 @ SY4399 ) @ SY4399 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV859 @ SV94 @ tc_nat ) @ ( c_List_Odrop @ SV94 @ SY4398 @ SY4399 ) @ SY4399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3457,plain,
! [SV860: $i,SV95: $i] :
( ( ! [SY4400: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV860 ) @ SY4400 ) @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SY4400 @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV860 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3458,plain,
! [SV861: $i,SV96: $i] :
( ( ! [SY4401: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV96 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV861 @ ( c_Suc @ SY4401 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV861 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3459,plain,
! [SV862: $i,SV97: $i] :
( ( ! [SY4402: $i,SY4403: $i] :
( ~ ( class_Orderings_Opreorder @ SV97 )
| ( c_HOL_Oord__class_Oless @ SV862 @ SY4402 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SY4403 @ SY4402 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV862 @ SY4403 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3460,plain,
! [SV863: $i,SV98: $i] :
( ( ! [SY4404: $i,SY4405: $i] :
( ~ ( class_Orderings_Oorder @ SV98 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SY4404 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SY4405 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY4405 @ SY4404 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3461,plain,
! [SV864: $i,SV99: $i] :
( ( ! [SY4406: $i] :
( ~ ( class_Orderings_Olinorder @ SV99 )
| ( ( c_Orderings_Oord__class_Omax @ SV864 @ SY4406 @ SV99 )
= SY4406 )
| ~ ( c_lessequals @ SV864 @ SY4406 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3462,plain,
! [SV865: $i,SV100: $i] :
( ( ! [SY4407: $i] :
( ~ ( class_Orderings_Olinorder @ SV100 )
| ( ( c_Orderings_Oord__class_Omax @ SV865 @ SY4407 @ SV100 )
= SV865 )
| ~ ( c_lessequals @ SY4407 @ SV865 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3463,plain,
! [SV866: $i,SV101: $i] :
( ( ! [SY4408: $i,SY4409: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SY4408 ) @ SY4409 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ SY4408 ) ) @ SY4409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3464,plain,
! [SV867: $i,SV102: $i] :
( ( ! [SY4410: $i,SY4411: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV102 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SY4410 ) @ SY4411 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SY4410 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ SY4411 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3465,plain,
! [SV868: $i,SV103: $i] :
( ( ! [SY4412: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV868 ) @ SY4412 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV868 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ SY4412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3466,plain,
! [SV869: $i,SV104: $i] :
( ( ! [SY4413: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV104 ) @ SV869 ) ) @ SY4413 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV104 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV869 ) @ SY4413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3467,plain,
! [SV870: $i,SV105: $i] :
( ( ! [SY4414: $i,SY4415: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ SY4414 ) ) @ SY4415 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SY4414 ) @ SY4415 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3468,plain,
! [SV871: $i,SV106: $i] :
( ( ! [SY4416: $i,SY4417: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV106 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SY4416 ) @ SY4417 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SY4416 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ SY4417 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3469,plain,
! [SV872: $i,SV107: $i] :
( ( ! [SY4418: $i,SY4419: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV107 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ SY4418 ) ) @ SY4419 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SY4418 ) @ SY4419 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3470,plain,
! [SV873: $i,SV108: $i] :
( ( ! [SY4420: $i,SY4421: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV108 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SY4420 ) @ SY4421 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ SY4420 ) ) @ SY4421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3471,plain,
! [SV874: $i,SV109: $i] :
( ( ! [SY4422: $i,SY4423: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV109 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SY4422 ) ) @ SY4423 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SY4423 ) ) @ SY4422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3472,plain,
! [SV875: $i,SV110: $i] :
( ( ! [SY4424: $i,SY4425: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY4424 ) @ SY4425 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SY4424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ SY4425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(3473,plain,
! [SV876: $i,SV111: $i] :
( ( ! [SY4426: $i,SY4427: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ SY4426 ) ) @ SY4427 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY4426 ) @ SY4427 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3474,plain,
! [SV877: $i,SV112: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV112 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV877 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV877 ) @ SV112 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3475,plain,
! [SV878: $i,SV113: $i] :
( ( ! [SY4428: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV113 @ SV878 @ SY4428 ) @ SY4428 )
= ( c_List_Olist_OCons @ SV113 @ SV878 @ SY4428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3476,plain,
! [SV879: $i,SV114: $i] :
( ( ! [SY4429: $i,SY4430: $i] :
( ( c_List_Otake @ SV114 @ ( c_List_Odrop @ SV879 @ SY4429 @ SY4430 ) @ SY4430 )
= ( c_List_Odrop @ SV879 @ ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV114 ) @ SV879 ) @ SY4429 @ SY4430 ) @ SY4430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3477,plain,
! [SV880: $i,SV115: $i] :
( ( ! [SY4431: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV115 ) @ SV880 @ SY4431 )
= ( c_List_Olist_OCons @ SV880 @ ( c_List_Oreplicate @ SV115 @ SV880 @ SY4431 ) @ SY4431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3478,plain,
! [SV881: $i,SV116: $i] :
( ( ! [SY4432: $i] :
( ( c_lessequals @ SV116 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV881 ) @ SY4432 ) @ tc_nat )
| ~ ( c_lessequals @ SV116 @ SY4432 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3479,plain,
! [SV882: $i,SV117: $i] :
( ( ! [SY4433: $i] :
( ( c_lessequals @ SV117 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV882 ) @ SY4433 ) @ tc_nat )
| ~ ( c_lessequals @ SV117 @ SV882 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3480,plain,
! [SV883: $i,SV118: $i] :
( ( ! [SY4434: $i] :
( ( c_lessequals @ SV118 @ SV883 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4434 ) @ SV118 ) @ SV883 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(3481,plain,
! [SV884: $i,SV119: $i] :
( ( ! [SY4435: $i] :
( ( c_lessequals @ SV119 @ SV884 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV119 ) @ SY4435 ) @ SV884 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(3482,plain,
! [SV885: $i,SV120: $i] :
( ( ! [SY4436: $i] :
( ( c_lessequals @ SV120 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV885 ) @ SY4436 ) @ tc_nat )
| ~ ( c_lessequals @ SV120 @ SY4436 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3483,plain,
! [SV886: $i,SV121: $i] :
( ( ! [SY4437: $i] :
( ( c_lessequals @ SV121 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV886 ) @ SY4437 ) @ tc_nat )
| ~ ( c_lessequals @ SV121 @ SV886 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3484,plain,
! [SV887: $i,SV122: $i] :
( ( ! [SY4438: $i] :
( ( c_List_Orev @ ( c_List_Otake @ SV122 @ SV887 @ SY4438 ) @ SY4438 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV887 @ ( tc_List_Olist @ SY4438 ) ) @ SV122 @ tc_nat ) @ ( c_List_Orev @ SV887 @ SY4438 ) @ SY4438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3485,plain,
! [SV888: $i,SV123: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV123 ) ) @ SV888 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV123 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ SV123 @ SV888 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3486,plain,
! [SV889: $i,SV124: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV124 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV124 ) @ SV889 @ SV124 )
= ( c_HOL_Oone__class_Oone @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3487,plain,
! [SV890: $i,SV125: $i] :
( ( ! [SY4439: $i,SY4440: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV125 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV890 @ SY4439 @ SV125 ) @ SY4440 @ SV125 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SY4440 @ SV125 ) @ ( c_HOL_Ominus__class_Ominus @ SY4439 @ SY4440 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3488,plain,
! [SV891: $i,SV126: $i] :
( ( ! [SY4441: $i,SY4442: $i] :
( ( hAPP @ ( c_COMBK @ SV126 @ SV891 @ SY4441 ) @ SY4442 )
= SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(3489,plain,
! [SV892: $i,SV127: $i] :
( ( ! [SY4443: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ SV127 @ SV892 @ SY4443 ) @ SY4443 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV892 @ ( tc_List_Olist @ SY4443 ) ) @ SV127 @ tc_nat ) @ ( c_List_Orev @ SV892 @ SY4443 ) @ SY4443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(3490,plain,
! [SV893: $i,SV128: $i] :
( ( ! [SY4444: $i] :
( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SV893 @ SY4444 @ SV128 )
| ( c_lessequals @ SY4444 @ SV893 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3491,plain,
! [SV894: $i,SV129: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV129 )
| ~ ( c_lessequals @ SV894 @ SV894 @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV894 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3492,plain,
! [SV895: $i,SV130: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV130 )
| ( c_HOL_Oord__class_Oless @ SV895 @ SV895 @ SV130 )
| ( c_lessequals @ SV895 @ SV895 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3493,plain,
! [SV896: $i,SV131: $i] :
( ( ! [SY4445: $i] :
( ~ ( class_Orderings_Olinorder @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SV896 @ SY4445 @ SV131 )
| ~ ( c_lessequals @ SY4445 @ SV896 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3494,plain,
! [SV897: $i,SV132: $i] :
( ( ! [SY4446: $i] :
( ~ ( class_Orderings_Olinorder @ SV132 )
| ( c_lessequals @ SV897 @ SY4446 @ SV132 )
| ( c_HOL_Oord__class_Oless @ SY4446 @ SV897 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3495,plain,
! [SV898: $i,SV133: $i] :
( ( ! [SY4447: $i] :
( ~ ( class_Orderings_Olinorder @ SV133 )
| ~ ( c_lessequals @ SV898 @ SY4447 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SY4447 @ SV898 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3496,plain,
! [SV899: $i,SV134: $i] :
( ( ! [SY4448: $i] :
( ~ ( class_Orderings_Olinorder @ SV134 )
| ( c_HOL_Oord__class_Oless @ SV899 @ SY4448 @ SV134 )
| ( c_lessequals @ SY4448 @ SV899 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3497,plain,
! [SV900: $i,SV135: $i] :
( ( ! [SY4449: $i] :
( ~ ( class_Orderings_Opreorder @ SV135 )
| ~ ( c_lessequals @ SV900 @ SY4449 @ SV135 )
| ~ ( c_HOL_Oord__class_Oless @ SY4449 @ SV900 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3498,plain,
! [SV901: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ SV136 @ SV901 ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV136 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3499,plain,
! [SV902: $i,SV137: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV137 @ SV137 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV137 ) ) @ SV902 ) @ SV137 )
= SV902 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3500,plain,
! [SV903: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ SV138 @ SV903 ) )
| ~ ( hBOOL @ ( hAPP @ SV138 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3501,plain,
! [SV904: $i,SV139: $i] :
( ( ! [SY4450: $i,SY4451: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
| ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SY4450 ) @ SY4451 ) @ SV139 )
| ~ ( c_HOL_Oord__class_Oless @ SV904 @ SY4451 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SY4450 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3502,plain,
! [SV905: $i,SV140: $i] :
( ( ! [SY4452: $i,SY4453: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV140 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SY4452 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SY4453 @ SV140 ) @ SV140 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 )
| ~ ( c_lessequals @ SY4452 @ SY4453 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3503,plain,
! [SV906: $i,SV141: $i] :
( ( ! [SY4454: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV906 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SY4454 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4454 @ SV906 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3504,plain,
! [SV907: $i,SV142: $i] :
( ( ! [SY4455: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV142 @ SV907 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4455 @ SV907 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV142 @ SY4455 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3505,plain,
! [SV908: $i,SV143: $i] :
( ( ! [SY4456: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SV908 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4456 @ SV908 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV143 @ SY4456 @ tc_nat )
| ~ ( c_lessequals @ SV908 @ SY4456 @ tc_nat )
| ~ ( c_lessequals @ SV908 @ SV143 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3506,plain,
! [SV909: $i,SV144: $i] :
( ( ! [SY4457: $i] :
( ( c_lessequals @ SV144 @ SV909 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SY4457 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV909 @ SY4457 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4457 @ SV909 @ tc_nat )
| ~ ( c_lessequals @ SY4457 @ SV144 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3507,plain,
! [SV910: $i,SV145: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV145 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV145 ) @ SV910 ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3508,plain,
! [SV911: $i,SV146: $i] :
( ( ! [SY4458: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV146 @ SV911 @ tc_nat ) @ SY4458 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV146 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV911 ) @ SY4458 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3509,plain,
! [SV912: $i,SV147: $i] :
( ( ! [SY4459: $i,SY4460: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV147 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SY4459 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SY4460 @ SY4459 @ SV147 ) @ SV147 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 )
| ~ ( c_lessequals @ SV912 @ SY4460 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(3510,plain,
! [SV148: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV148 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV148 )
= ( c_HOL_Oone__class_Oone @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(3511,plain,
! [SV913: $i,SV149: $i] :
( ( ! [SY4461: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV149 @ SV913 @ SY4461 ) @ SY4461 )
= ( c_List_Oappend @ ( c_List_Orev @ SV913 @ SY4461 ) @ ( c_List_Olist_OCons @ SV149 @ ( c_List_Olist_ONil @ SY4461 ) @ SY4461 ) @ SY4461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3512,plain,
! [SV914: $i,SV150: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV150 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV914 ) @ SV150 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ ( c_HOL_Oone__class_Oone @ SV150 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV914 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3513,plain,
! [SV915: $i,SV151: $i] :
( ( ! [SY4462: $i,SY4463: $i,SY4464: $i,SY4465: $i] :
( ( c_List_Ofoldl @ SV151 @ SV915 @ ( c_List_Olist_OCons @ SY4462 @ SY4463 @ SY4464 ) @ SY4465 @ SY4464 )
= ( c_List_Ofoldl @ SV151 @ ( hAPP @ ( hAPP @ SV151 @ SV915 ) @ SY4462 ) @ SY4463 @ SY4465 @ SY4464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3514,plain,
! [SV916: $i,SV152: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV152 ) ) @ SV916 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV152 ) @ ( c_Suc @ SV916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3515,plain,
! [SV917: $i,SV153: $i] :
( ( ! [SY4466: $i,SY4467: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV153 ) @ ( c_List_Olist_OCons @ SV917 @ SY4466 @ SY4467 ) @ SY4467 )
= ( c_List_Odrop @ SV153 @ SY4466 @ SY4467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3516,plain,
! [SV918: $i,SV154: $i] :
( ( ! [SY4468: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ SV918 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4468 ) @ SV918 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV154 @ SY4468 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3517,plain,
! [SV919: $i,SV155: $i] :
( ( ! [SY4469: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SV919 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SY4469 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV919 @ SY4469 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3518,plain,
! [SV920: $i,SV158: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV158 @ ( c_List_Olist_ONil @ SV920 ) @ SV920 ) @ SV920 )
= ( c_List_Olist_OCons @ SV158 @ ( c_List_Olist_ONil @ SV920 ) @ SV920 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3519,plain,
! [SV921: $i,SV159: $i] :
( ( ! [SY4470: $i,SY4471: $i] :
( ~ ( class_Orderings_Olinorder @ SV159 )
| ( c_HOL_Oord__class_Oless @ SV921 @ ( c_Orderings_Oord__class_Omax @ SY4470 @ SY4471 @ SV159 ) @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV921 @ SY4470 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3520,plain,
! [SV922: $i,SV160: $i] :
( ( ! [SY4472: $i,SY4473: $i] :
( ~ ( class_Orderings_Olinorder @ SV160 )
| ( c_HOL_Oord__class_Oless @ SV922 @ ( c_Orderings_Oord__class_Omax @ SY4472 @ SY4473 @ SV160 ) @ SV160 )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SY4473 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3521,plain,
! [SV923: $i,SV161: $i] :
( ( ! [SY4474: $i,SY4475: $i] :
( ~ ( class_Orderings_Olinorder @ SV161 )
| ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Orderings_Oord__class_Omax @ SY4474 @ SY4475 @ SV161 ) @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV923 @ SY4474 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3522,plain,
! [SV924: $i,SV162: $i] :
( ( ! [SY4476: $i,SY4477: $i] :
( ~ ( class_Orderings_Olinorder @ SV162 )
| ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Orderings_Oord__class_Omax @ SY4476 @ SY4477 @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SY4477 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(3523,plain,
! [SV925: $i,SV163: $i] :
( ( ! [SY4478: $i,SY4479: $i] :
( ~ ( class_Orderings_Olinorder @ SV163 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SY4478 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV925 @ SY4479 @ SV163 ) @ SY4478 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3524,plain,
! [SV926: $i,SV164: $i] :
( ( ( c_List_Odrop @ SV164 @ ( c_List_Olist_ONil @ SV926 ) @ SV926 )
= ( c_List_Olist_ONil @ SV926 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3525,plain,
! [SV927: $i,SV165: $i] :
( ( ! [SY4480: $i,SY4481: $i,SY4482: $i,SY4483: $i,SY4484: $i,SY4485: $i,SY4486: $i] :
( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SY4480 ) @ SY4481 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SY4480 ) @ SY4482 ) )
= ( hAPP @ ( hAPP @ SV927 @ SY4480 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4481 ) @ SY4482 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4483 @ SV165 @ SV927 @ SY4484 @ SY4485 @ SY4486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3526,plain,
! [SV928: $i,SV166: $i] :
( ( ! [SY4487: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ SV166 ) @ SV928 @ SY4487 )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV166 @ SV928 @ SY4487 ) ) @ SY4487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3527,plain,
! [SV929: $i,SV168: $i] :
( ( ! [SY4488: $i,SY4489: $i,SY4490: $i,SY4491: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV168 @ SV929 @ SY4488 @ SY4489 @ SY4490 ) @ SY4491 )
= ( hAPP @ SV168 @ ( hAPP @ SV929 @ SY4491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3528,plain,
! [SV930: $i,SV169: $i] :
( ( ! [SY4492: $i,SY4493: $i,SY4494: $i,SY4495: $i] :
( ( hAPP @ SV169 @ ( hAPP @ SV930 @ SY4492 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV169 @ SV930 @ SY4493 @ SY4494 @ SY4495 ) @ SY4492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3529,plain,
! [SV931: $i,SV170: $i] :
( ( ! [SY4496: $i,SY4497: $i] :
( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ SY4496 @ SY4497 )
= ( c_List_Oappend @ ( c_List_Otake @ SV170 @ SY4496 @ SY4497 ) @ ( c_List_Otake @ SV931 @ ( c_List_Odrop @ SV170 @ SY4496 @ SY4497 ) @ SY4497 ) @ SY4497 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ ( c_Nat_Osize__class_Osize @ SY4496 @ ( tc_List_Olist @ SY4497 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3530,plain,
! [SV932: $i,SV171: $i] :
( ( ! [SY4498: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV171 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SV932 @ SY4498 @ SV171 @ SV171 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SY4498 @ SV932 @ SV171 @ SV171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3531,plain,
! [SV933: $i,SV172: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV172 )
| ( ( c_Power_Opower__class_Opower @ SV933 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV172 )
= SV933 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3532,plain,
! [SV934: $i,SV173: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV173 )
| ( ( c_Power_Opower__class_Opower @ SV934 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV173 )
= SV934 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3533,plain,
! [SV935: $i,SV174: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV174 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ SV935 ) @ SV935 ) @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3534,plain,
! [SV936: $i,SV175: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV175 )
| ( c_HOL_Oord__class_Oless @ SV936 @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV936 ) @ SV936 ) @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3535,plain,
! [SV937: $i,SV176: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV176 )
| ( c_HOL_Oord__class_Oless @ SV937 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV937 ) @ SV937 ) @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3536,plain,
! [SV938: $i,SV177: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV177 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV177 ) @ SV938 ) @ SV938 ) @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ SV938 @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3537,plain,
! [SV939: $i,SV178: $i] :
( ( ! [SY4499: $i,SY4500: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV178 )
| ( c_HOL_Oord__class_Oless @ SV939 @ SY4499 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SY4499 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SY4500 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SY4499 @ SY4500 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3538,plain,
! [SV940: $i,SV179: $i] :
( ( ! [SY4501: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV179 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV940 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SY4501 @ SV179 @ SV179 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV940 @ SY4501 @ SV179 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3539,plain,
! [SV941: $i,SV180: $i] :
( ( ! [SY4502: $i,SY4503: $i] :
( ~ ( class_Orderings_Olinorder @ SV180 )
| ( c_lessequals @ SV941 @ SY4502 @ SV180 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY4503 @ SV941 @ SV180 ) @ SY4502 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3540,plain,
! [SV942: $i,SV181: $i] :
( ( ! [SY4504: $i,SY4505: $i] :
( ~ ( class_Orderings_Olinorder @ SV181 )
| ( c_lessequals @ SV942 @ SY4504 @ SV181 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV942 @ SY4505 @ SV181 ) @ SY4504 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3541,plain,
! [SV943: $i,SV182: $i] :
( ( ! [SY4506: $i,SY4507: $i] :
( ~ ( class_Orderings_Olinorder @ SV182 )
| ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SY4506 @ SY4507 @ SV182 ) @ SV182 )
| ~ ( c_lessequals @ SV943 @ SY4507 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(3542,plain,
! [SV944: $i,SV183: $i] :
( ( ! [SY4508: $i,SY4509: $i] :
( ~ ( class_Orderings_Olinorder @ SV183 )
| ( c_lessequals @ SV944 @ ( c_Orderings_Oord__class_Omax @ SY4508 @ SY4509 @ SV183 ) @ SV183 )
| ~ ( c_lessequals @ SV944 @ SY4508 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3543,plain,
! [SV945: $i,SV184: $i] :
( ( ! [SY4510: $i,SY4511: $i] :
( ~ ( class_Orderings_Olinorder @ SV184 )
| ( c_lessequals @ SV945 @ ( c_Orderings_Oord__class_Omax @ SY4510 @ SY4511 @ SV184 ) @ SV184 )
| ~ ( c_lessequals @ SV945 @ SY4511 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3544,plain,
! [SV946: $i,SV185: $i] :
( ( ! [SY4512: $i,SY4513: $i] :
( ~ ( class_Orderings_Olinorder @ SV185 )
| ( c_lessequals @ SV946 @ ( c_Orderings_Oord__class_Omax @ SY4512 @ SY4513 @ SV185 ) @ SV185 )
| ~ ( c_lessequals @ SV946 @ SY4512 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3545,plain,
! [SV947: $i,SV186: $i] :
( ( ! [SY4514: $i,SY4515: $i] :
( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_lessequals @ SV947 @ SY4514 @ SV186 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY4515 @ SV947 @ SV186 ) @ SY4514 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3546,plain,
! [SV948: $i,SV187: $i] :
( ( ! [SY4516: $i,SY4517: $i] :
( ~ ( class_Orderings_Olinorder @ SV187 )
| ( c_lessequals @ SV948 @ SY4516 @ SV187 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV948 @ SY4517 @ SV187 ) @ SY4516 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3547,plain,
! [SV949: $i,SV188: $i] :
( ( ! [SY4518: $i] :
( ( c_lessequals @ SV188 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SY4518 ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV188 @ SY4518 @ tc_nat ) @ SV949 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3548,plain,
! [SV950: $i,SV189: $i] :
( ( ! [SY4519: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV189 @ SV950 @ tc_nat ) @ SY4519 @ tc_nat )
| ~ ( c_lessequals @ SV189 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4519 ) @ SV950 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3549,plain,
! [SV951: $i,SV190: $i] :
( ( ! [SY4520: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV190 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ ( c_Power_Opower__class_Opower @ SV951 @ SY4520 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV951 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3550,plain,
! [SV952: $i,SV191: $i] :
( ( ! [SY4521: $i,SY4522: $i] :
( ~ ( class_Orderings_Olinorder @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV952 @ SY4521 @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV952 @ SY4522 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV952 @ ( c_Orderings_Oord__class_Omax @ SY4522 @ SY4521 @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3551,plain,
! [SV953: $i,SV192: $i] :
( ( ! [SY4523: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SV953 ) @ SY4523 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV953 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY4523 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3552,plain,
! [SV954: $i,SV193: $i] :
( ( ! [SY4524: $i,SY4525: $i] :
( ( c_List_Ofoldl @ SV193 @ SV954 @ ( c_List_Olist_ONil @ SY4524 ) @ SY4525 @ SY4524 )
= SV954 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3553,plain,
! [SV955: $i,SV194: $i] :
( ( ! [SY4526: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV194 ) @ SV955 @ SY4526 )
= ( c_Lambda_OdB_OVar @ SV194 ) )
| ( SV194 = SY4526 )
| ( c_HOL_Oord__class_Oless @ SY4526 @ SV194 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3554,plain,
! [SV195: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV195 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV195 ) @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(3555,plain,
! [SV956: $i,SV196: $i] :
( ( ! [SY4527: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV196 @ SV956 @ SY4527 ) @ ( tc_List_Olist @ SY4527 ) ) @ ( c_Nat_Osize__class_Osize @ SV956 @ ( tc_List_Olist @ SY4527 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3556,plain,
! [SV957: $i,SV198: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV198 ) @ ( c_Suc @ SV957 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV198 @ SV957 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3557,plain,
! [SV958: $i,SV199: $i] :
( ( ! [SY4528: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV958 ) @ SY4528 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SY4528 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ SV958 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3558,plain,
! [SV959: $i,SV200: $i] :
( ( ! [SY4529: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SV959 ) @ SY4529 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_lessequals @ SY4529 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SV959 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3559,plain,
! [SV960: $i,SV201: $i] :
( ( ( SV201 = SV960 )
| ( c_HOL_Oord__class_Oless @ SV201 @ SV960 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV201 @ ( c_Suc @ SV960 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3560,plain,
! [SV961: $i,SV202: $i] :
( ( ( SV202 = SV961 )
| ~ ( c_HOL_Oord__class_Oless @ SV961 @ ( c_Suc @ SV202 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV961 @ SV202 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3561,plain,
! [SV962: $i,SV203: $i] :
( ( ( SV203 = SV962 )
| ~ ( c_HOL_Oord__class_Oless @ SV203 @ ( c_Suc @ SV962 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV203 @ SV962 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3562,plain,
! [SV963: $i,SV204: $i] :
( ( ! [SY4530: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ SV963 ) @ SY4530 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SY4530 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY4530 @ SV963 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3563,plain,
! [SV964: $i,SV205: $i] :
( ( ! [SY4531: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV964 ) @ SY4531 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV205 @ SY4531 @ tc_nat ) ) @ SV964 ) )
| ~ ( c_lessequals @ SY4531 @ SV205 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3564,plain,
! [SV206: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV206 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ ( c_HOL_Oone__class_Oone @ SV206 ) @ SV206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2798]) ).
thf(3565,plain,
! [SV965: $i,SV207: $i] :
( ( ! [SY4532: $i,SY4533: $i,SY4534: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV207 @ SV965 @ SY4532 ) @ SY4533 @ SY4534 @ SY4532 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV207 @ SY4533 @ SY4534 @ SY4532 ) @ SV965 @ SY4532 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4533 @ ( c_Nat_Osize__class_Osize @ SV207 @ ( tc_List_Olist @ SY4532 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3566,plain,
! [SV966: $i,SV208: $i] :
( ( ! [SY4535: $i,SY4536: $i,SY4537: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV208 @ SV966 @ SY4535 ) @ SY4536 @ SY4537 @ SY4535 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV208 @ SY4536 @ SY4537 @ SY4535 ) @ SV966 @ SY4535 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4536 @ ( c_Nat_Osize__class_Osize @ SV208 @ ( tc_List_Olist @ SY4535 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3567,plain,
! [SV967: $i,SV209: $i] :
( ( ! [SY4538: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV209 @ ( c_HOL_Ominus__class_Ominus @ SV967 @ SY4538 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV209 ) @ SY4538 ) @ SV967 @ tc_nat ) )
| ~ ( c_lessequals @ SY4538 @ SV967 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3568,plain,
! [SV968: $i,SV210: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV210 ) @ SV968 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV210 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ SV968 ) ) )
| ( SV210
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3569,plain,
! [SV969: $i,SV211: $i] :
( ( ! [SY4539: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV211 @ SV969 @ tc_nat ) @ SY4539 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV211 @ SY4539 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3570,plain,
! [SV970: $i,SV212: $i] :
( ( ! [SY4540: $i,SY4541: $i] :
( ( c_Type_Otype_Otype__rec @ SV212 @ SV970 @ ( c_Type_Otype_OAtom @ SY4540 ) @ SY4541 )
= ( hAPP @ SV212 @ SY4540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3571,plain,
! [SV971: $i,SV213: $i] :
( ( ! [SY4542: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4542 @ SV971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ SV213 @ SY4542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3572,plain,
! [SV972: $i,SV214: $i] :
( ( ! [SY4543: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ SV214 @ SV972 @ SY4543 ) @ ( tc_List_Olist @ SY4543 ) )
= ( c_Nat_Osize__class_Osize @ SV972 @ ( tc_List_Olist @ SY4543 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3573,plain,
! [SV973: $i,SV215: $i] :
( ( ( c_List_Olist_ONil @ SV215 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV973 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3574,plain,
! [SV974: $i,SV216: $i] :
( ( ! [SY4544: $i] :
( ~ ( class_Orderings_Opreorder @ SV216 )
| ( c_HOL_Oord__class_Oless @ SV974 @ SY4544 @ SV216 )
| ( c_lessequals @ SY4544 @ SV974 @ SV216 )
| ~ ( c_lessequals @ SV974 @ SY4544 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3575,plain,
! [SV217: $i] :
( ( c_HOL_Oord__class_Oless @ SV217 @ SV217 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(3576,plain,
! [SV218: $i] :
( ( c_HOL_Oord__class_Oless @ SV218 @ SV218 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(3577,plain,
! [SV975: $i,SV219: $i] :
( ( ~ ( class_Orderings_Oorder @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ SV975 @ SV975 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3578,plain,
! [SV976: $i,SV220: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV976 @ SV976 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3579,plain,
! [SV977: $i,SV221: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV977 @ SV977 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3580,plain,
! [SV978: $i,SV222: $i] :
( ( ~ ( c_lessequals @ SV222 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV978 ) @ SV222 ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV978 ) @ SV222 ) @ SV222 @ tc_nat )
= SV978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3581,plain,
! [SV979: $i,SV223: $i] :
( ( ! [SY4545: $i] :
( ( ( c_Lambda_Oliftn @ SV223 @ ( c_Lambda_OdB_OVar @ SV979 ) @ SY4545 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV979 ) @ SV223 ) ) )
| ( c_HOL_Oord__class_Oless @ SV979 @ SY4545 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3582,plain,
! [SV980: $i,SV224: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV224 ) ) @ SV980 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV224 ) @ SV980 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3583,plain,
! [SV981: $i,SV225: $i] :
( ( ! [SY4546: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ SV225 @ SV981 @ SY4546 ) @ ( tc_List_Olist @ SY4546 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV225 @ ( tc_List_Olist @ SY4546 ) ) ) @ ( c_Nat_Osize__class_Osize @ SV981 @ ( tc_List_Olist @ SY4546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3584,plain,
! [SV982: $i,SV226: $i] :
( ( ! [SY4547: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ SV226 @ SV982 @ SY4547 ) @ ( tc_List_Olist @ SY4547 ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV982 @ ( tc_List_Olist @ SY4547 ) ) @ SV226 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3585,plain,
! [SV983: $i,SV227: $i] :
( ( ! [SY4548: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SV983 ) @ SY4548 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SY4548 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV983 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3586,plain,
! [SV984: $i,SV228: $i] :
( ( c_lessequals @ SV228 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV228 ) @ SV984 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3587,plain,
! [SV985: $i,SV229: $i] :
( ( c_lessequals @ SV229 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV985 ) @ SV229 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3588,plain,
! [SV986: $i,SV230: $i] :
( ( c_lessequals @ SV230 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV230 ) @ SV986 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3589,plain,
! [SV987: $i,SV231: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV231 @ SV987 @ tc_nat ) ) @ SV987 )
= ( c_Orderings_Oord__class_Omax @ SV231 @ SV987 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3590,plain,
! [SV988: $i,SV232: $i] :
( ( ! [SY4549: $i,SY4550: $i] :
( ( ( c_List_Otake @ SV232 @ ( c_List_Olist_OCons @ SV988 @ SY4549 @ SY4550 ) @ SY4550 )
= ( c_List_Olist_OCons @ SV988 @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV232 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY4549 @ SY4550 ) @ SY4550 ) )
| ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3591,plain,
! [SV233: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV233 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV233 ) @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(3592,plain,
! [SV989: $i,SV234: $i] :
( ( ! [SY4551: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV234 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV989 @ SY4551 @ SV234 ) @ SV234 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV989 ) @ ( c_List_Olistsum @ SY4551 @ SV234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3593,plain,
! [SV990: $i,SV235: $i] :
( ( ! [SY4552: $i] :
( ( c_Lambda_Oliftn @ SV235 @ ( c_Lambda_OdB_OAbs @ SV990 ) @ SY4552 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV235 @ SV990 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4552 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3594,plain,
! [SV991: $i,SV236: $i] :
( ( ! [SY4553: $i,SY4554: $i,SY4555: $i,SY4556: $i,SY4557: $i] :
( ( ( hAPP @ ( hAPP @ SV236 @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV991 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4553 @ SY4554 @ SV236 @ SY4555 @ SY4556 @ SY4557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3595,plain,
! [SV992: $i,SV237: $i] :
( ( ! [SY4558: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV237 )
| ( c_HOL_Oord__class_Oless @ SV992 @ SY4558 @ SV237 )
| ( c_HOL_Oord__class_Oless @ SY4558 @ SV992 @ SV237 )
| ( SY4558 = SV992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3596,plain,
! [SV993: $i,SV238: $i] :
( ( ! [SY4559: $i] :
( ~ ( class_Orderings_Olinorder @ SV238 )
| ( SV993 = SY4559 )
| ( c_HOL_Oord__class_Oless @ SY4559 @ SV993 @ SV238 )
| ( c_HOL_Oord__class_Oless @ SV993 @ SY4559 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3597,plain,
! [SV994: $i,SV239: $i] :
( ( ( SV239 = SV994 )
| ~ ( c_lessequals @ SV994 @ SV239 @ tc_nat )
| ~ ( c_lessequals @ SV239 @ SV994 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3598,plain,
! [SV995: $i,SV240: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV240 @ SV995 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV995 @ SV240 @ tc_nat )
| ( SV995 = SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3599,plain,
! [SV996: $i,SV241: $i] :
( ( ! [SY4560: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV241 @ SV996 ) @ SY4560 ) )
| ( c_HOL_Oord__class_Oless @ SV996 @ SY4560 @ tc_nat )
| ( SY4560 = SV996 )
| ( c_HOL_Oord__class_Oless @ SY4560 @ SV996 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3600,plain,
! [SV997: $i,SV242: $i] :
( ( ! [SY4561: $i,SY4562: $i,SY4563: $i] :
( ( SV242 = SV997 )
| ~ ( c_Type_Otyping @ SY4561 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4562 ) @ SY4563 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV997 )
| ~ ( c_Type_Otyping @ SY4561 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4562 ) @ SY4563 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3601,plain,
! [SV998: $i,SV243: $i] :
( ( ! [SY4564: $i,SY4565: $i] :
( ~ ( class_Orderings_Olinorder @ SV243 )
| ( c_HOL_Oord__class_Oless @ SV998 @ SY4564 @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY4565 @ SV998 @ SV243 ) @ SY4564 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3602,plain,
! [SV244: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV244 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV244 ) @ SV244 )
= ( c_HOL_Ozero__class_Ozero @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2836]) ).
thf(3603,plain,
! [SV999: $i,SV245: $i] :
( ( ! [SY4566: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV245 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SV999 @ SY4566 @ SV245 ) @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4566 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SV999 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3604,plain,
! [SV1000: $i,SV246: $i] :
( ( ! [SY4567: $i] :
( ( ( c_List_Orotate @ SV246 @ SV1000 @ SY4567 )
= SV1000 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1000 @ ( tc_List_Olist @ SY4567 ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3605,plain,
! [SV1001: $i,SV247: $i] :
( ( ! [SY4568: $i,SY4569: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV247 ) @ SV1001 ) @ SY4568 ) ) @ SY4569 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV247 ) @ SY4569 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1001 ) @ SY4569 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4568 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4569 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4568 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3606,plain,
! [SV1002: $i,SV248: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV248 @ SV1002 @ tc_nat ) @ SV248 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3607,plain,
! [SV1003: $i,SV249: $i] :
( ( c_Type_Otyping @ SV249 @ ( c_Lambda_OdB_OVar @ SV1003 ) @ ( hAPP @ SV249 @ SV1003 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3608,plain,
! [SV1004: $i,SV250: $i] :
( ( ! [SY4570: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SV1004 ) @ SY4570 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SY4570 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SV1004 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3609,plain,
! [SV1005: $i,SV251: $i] :
( ( ! [SY4571: $i,SY4572: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV251 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SY4571 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SY4572 @ SY4571 @ SV251 ) @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4571 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SY4572 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3610,plain,
! [SV1006: $i,SV252: $i] :
( ( ! [SY4573: $i,SY4574: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV252 @ SV1006 @ SY4573 ) @ SY4574 @ SY4573 )
= ( c_List_Olist_OCons @ SV252 @ ( c_List_Oappend @ SV1006 @ SY4574 @ SY4573 ) @ SY4573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3611,plain,
! [SV1007: $i,SV253: $i] :
( ( ! [SY4575: $i,SY4576: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV253 @ SV1007 @ SY4575 ) @ SY4576 @ SY4575 )
= ( c_List_Olist_OCons @ SV253 @ ( c_List_Oappend @ SV1007 @ SY4576 @ SY4575 ) @ SY4575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3612,plain,
! [SV1008: $i,SV254: $i] :
( ( ! [SY4577: $i] :
( SV254
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1008 @ ( tc_List_Olist @ SY4577 ) ) @ ( c_List_Oappend @ SV1008 @ SV254 @ SY4577 ) @ SY4577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3613,plain,
! [SV1009: $i,SV255: $i] :
( ( ! [SY4578: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1009 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4578 @ SV1009 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV255 @ SY4578 @ tc_nat ) )
| ~ ( c_lessequals @ SV1009 @ SY4578 @ tc_nat )
| ~ ( c_lessequals @ SV1009 @ SV255 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3614,plain,
! [SV1010: $i,SV256: $i] :
( ( ! [SY4579: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SV1010 @ tc_nat ) @ SY4579 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SY4579 @ tc_nat ) @ SV1010 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3615,plain,
! [SV1011: $i,SV257: $i] :
( ( ! [SY4580: $i,SY4581: $i] :
( ( c_List_Omap @ ( c_COMBK @ SV257 @ SV1011 @ SY4580 ) @ SY4581 @ SY4580 @ SV1011 )
= ( c_List_Oreplicate @ ( c_Nat_Osize__class_Osize @ SY4581 @ ( tc_List_Olist @ SY4580 ) ) @ SV257 @ SV1011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3616,plain,
! [SV1012: $i,SV258: $i] :
( ( ! [SY4582: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV1012 ) @ SY4582 ) @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SY4582 @ SV258 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1012 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3617,plain,
! [SV1013: $i,SV259: $i] :
( ( ! [SY4583: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV1013 ) @ SY4583 ) @ SV259 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SY4583 @ SV259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1013 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3618,plain,
! [SV1014: $i,SV260: $i] :
( ( ! [SY4584: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV260 ) @ SV1014 @ SY4584 @ SV260 )
= ( c_List_Olist_ONil @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3619,plain,
! [SV1015: $i,SV261: $i] :
( ( ! [SY4585: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV261 ) @ SV1015 @ SY4585 @ SV261 )
= ( c_List_Olist_ONil @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3620,plain,
! [SV1016: $i,SV262: $i] :
( ( ! [SY4586: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV262 ) @ SV1016 @ SY4586 @ SV262 )
= ( c_List_Olist_ONil @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3621,plain,
! [SV1017: $i,SV263: $i] :
( ( ! [SY4587: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV263 @ SV1017 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4587 @ SV1017 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1017 @ SV263 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV263 @ SY4587 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3622,plain,
! [SV1018: $i,SV264: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV264 ) @ SV1018 @ tc_nat )
| ( ( c_Suc @ SV264 )
= SV1018 )
| ~ ( c_HOL_Oord__class_Oless @ SV264 @ SV1018 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3623,plain,
! [SV1019: $i,SV265: $i] :
( ( ~ ( c_lessequals @ SV265 @ SV1019 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV1019 ) @ SV265 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3624,plain,
! [SV1020: $i,SV266: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV266 ) @ SV1020 @ tc_nat )
| ( c_lessequals @ SV1020 @ SV266 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3625,plain,
! [SV1021: $i,SV267: $i] :
( ( ! [SY4588: $i,SY4589: $i] :
( ( c_List_Olist_OCons @ SV267 @ ( c_List_Oappend @ SV1021 @ SY4588 @ SY4589 ) @ SY4589 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV267 @ SV1021 @ SY4589 ) @ SY4588 @ SY4589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3626,plain,
! [SV1022: $i,SV268: $i] :
( ( ! [SY4590: $i,SY4591: $i] :
( ( c_List_Olist_OCons @ SV268 @ ( c_List_Oappend @ SV1022 @ SY4590 @ SY4591 ) @ SY4591 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV268 @ SV1022 @ SY4591 ) @ SY4590 @ SY4591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3627,plain,
! [SV1023: $i,SV269: $i] :
( ( ! [SY4592: $i] :
( ( c_lessequals @ SV269 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1023 ) @ SV269 ) @ SY4592 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4592 @ SV1023 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3628,plain,
! [SV1024: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV270 @ ( tc_List_Olist @ SV1024 ) ) @ tc_nat )
| ( SV270
= ( c_List_Olist_ONil @ SV1024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3629,plain,
! [SV1025: $i,SV271: $i] :
( ( ! [SY4593: $i,SY4594: $i,SY4595: $i,SY4596: $i,SY4597: $i,SY4598: $i,SY4599: $i] :
( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SY4593 ) @ SY4594 ) ) @ SY4595 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SY4593 ) @ SY4595 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SY4594 ) @ SY4595 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4596 @ SV1025 @ SV271 @ SY4597 @ SY4598 @ SY4599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3630,plain,
! [SV1026: $i,SV272: $i] :
( ( ! [SY4600: $i,SY4601: $i,SY4602: $i,SY4603: $i,SY4604: $i,SY4605: $i,SY4606: $i] :
( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SY4600 @ SY4601 ) @ SY4602 ) )
= ( hAPP @ ( hAPP @ SY4600 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SY4601 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SY4602 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4600 @ SV272 @ SY4603 @ SY4604 @ SY4605 @ SY4606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3631,plain,
! [SV1027: $i,SV273: $i] :
( ( ! [SY4607: $i,SY4608: $i,SY4609: $i,SY4610: $i,SY4611: $i,SY4612: $i] :
( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SY4607 )
= ( hAPP @ ( hAPP @ SV273 @ SY4607 ) @ SV1027 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4608 @ SV273 @ SY4609 @ SY4610 @ SY4611 @ SY4612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3632,plain,
! [SV1028: $i,SV274: $i] :
( ( ! [SY4613: $i,SY4614: $i,SY4615: $i,SY4616: $i,SY4617: $i,SY4618: $i,SY4619: $i] :
( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SY4613 ) @ SY4614 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SY4613 ) ) @ SY4614 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4615 @ SV274 @ SY4616 @ SY4617 @ SY4618 @ SY4619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3633,plain,
! [SV1029: $i,SV275: $i] :
( ( ! [SY4620: $i,SY4621: $i,SY4622: $i,SY4623: $i,SY4624: $i] :
( ( ( hAPP @ ( hAPP @ SV275 @ SV1029 ) @ SY4620 )
= SY4620 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4621 @ SV275 @ SY4622 @ SY4623 @ SV1029 @ SY4624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3634,plain,
! [SV1030: $i,SV276: $i] :
( ( ! [SY4625: $i,SY4626: $i,SY4627: $i,SY4628: $i,SY4629: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SV1030 ) @ SY4625 )
= SV1030 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4626 @ SV276 @ SY4627 @ SV1030 @ SY4628 @ SY4629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3635,plain,
! [SV1031: $i,SV277: $i] :
( ( ! [SY4630: $i,SY4631: $i,SY4632: $i,SY4633: $i,SY4634: $i,SY4635: $i] :
( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SY4630 )
= ( hAPP @ ( hAPP @ SV277 @ SY4630 ) @ SV1031 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SY4631 @ SY4632 @ SY4633 @ SY4634 @ SY4635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3636,plain,
! [SV1032: $i,SV278: $i] :
( ( ! [SY4636: $i,SY4637: $i,SY4638: $i,SY4639: $i,SY4640: $i,SY4641: $i,SY4642: $i] :
( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SY4636 ) @ SY4637 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SY4636 ) ) @ SY4637 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SY4638 @ SY4639 @ SY4640 @ SY4641 @ SY4642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3637,plain,
! [SV1033: $i,SV279: $i] :
( ( ! [SY4643: $i,SY4644: $i,SY4645: $i,SY4646: $i,SY4647: $i] :
( ( ( hAPP @ ( hAPP @ SV279 @ SV1033 ) @ SY4643 )
= SY4643 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SY4644 @ SY4645 @ SV1033 @ SY4646 @ SY4647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3638,plain,
! [SV1034: $i,SV280: $i] :
( ( ! [SY4648: $i,SY4649: $i,SY4650: $i,SY4651: $i,SY4652: $i,SY4653: $i,SY4654: $i] :
( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SY4648 ) @ SY4649 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SY4648 ) ) @ SY4649 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SY4650 @ SY4651 @ SY4652 @ SY4653 @ SY4654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3639,plain,
! [SV1035: $i,SV281: $i] :
( ( ! [SY4655: $i,SY4656: $i,SY4657: $i,SY4658: $i,SY4659: $i,SY4660: $i] :
( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SY4655 )
= ( hAPP @ ( hAPP @ SV281 @ SY4655 ) @ SV1035 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SY4656 @ SY4657 @ SY4658 @ SY4659 @ SY4660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3640,plain,
! [SV1036: $i,SV282: $i] :
( ( ! [SY4661: $i,SY4662: $i,SY4663: $i,SY4664: $i,SY4665: $i,SY4666: $i,SY4667: $i] :
( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SY4661 ) ) @ SY4662 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SY4662 ) ) @ SY4661 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SY4663 @ SY4664 @ SY4665 @ SY4666 @ SY4667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3641,plain,
! [SV1037: $i,SV283: $i] :
( ( ! [SY4668: $i,SY4669: $i,SY4670: $i,SY4671: $i,SY4672: $i,SY4673: $i,SY4674: $i] :
( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SY4668 ) @ SY4669 ) )
= ( hAPP @ ( hAPP @ SV283 @ SY4668 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SY4669 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SY4670 @ SY4671 @ SY4672 @ SY4673 @ SY4674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3642,plain,
! [SV1038: $i,SV284: $i] :
( ( ! [SY4675: $i,SY4676: $i,SY4677: $i,SY4678: $i,SY4679: $i,SY4680: $i,SY4681: $i] :
( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SY4675 ) ) @ SY4676 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SY4675 ) @ SY4676 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SY4677 @ SY4678 @ SY4679 @ SY4680 @ SY4681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3643,plain,
! [SV1039: $i,SV285: $i] :
( ( ! [SY4682: $i,SY4683: $i,SY4684: $i,SY4685: $i,SY4686: $i,SY4687: $i,SY4688: $i,SY4689: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SY4682 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SY4683 ) @ SY4684 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SY4683 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SY4682 ) @ SY4684 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SY4685 @ SY4686 @ SY4687 @ SY4688 @ SY4689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3644,plain,
! [SV1040: $i,SV286: $i] :
( ( ! [SY4690: $i,SY4691: $i,SY4692: $i,SY4693: $i,SY4694: $i,SY4695: $i,SY4696: $i] :
( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SY4690 ) @ SY4691 ) )
= ( hAPP @ ( hAPP @ SV286 @ SY4690 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SY4691 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4692 @ SV286 @ SY4693 @ SY4694 @ SY4695 @ SY4696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3645,plain,
! [SV1041: $i,SV287: $i] :
( ( ! [SY4697: $i,SY4698: $i,SY4699: $i,SY4700: $i,SY4701: $i,SY4702: $i,SY4703: $i] :
( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SY4697 ) @ SY4698 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SY4697 ) ) @ SY4698 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4699 @ SV287 @ SY4700 @ SY4701 @ SY4702 @ SY4703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3646,plain,
! [SV1042: $i,SV288: $i] :
( ( ! [SY4704: $i,SY4705: $i,SY4706: $i,SY4707: $i,SY4708: $i,SY4709: $i,SY4710: $i] :
( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SY4704 ) ) @ SY4705 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SY4704 ) @ SY4705 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4706 @ SV288 @ SY4707 @ SY4708 @ SY4709 @ SY4710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3647,plain,
! [SV1043: $i,SV289: $i] :
( ( ! [SY4711: $i,SY4712: $i,SY4713: $i,SY4714: $i,SY4715: $i,SY4716: $i,SY4717: $i] :
( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SY4711 ) ) @ SY4712 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SY4712 ) ) @ SY4711 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4713 @ SV289 @ SY4714 @ SY4715 @ SY4716 @ SY4717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3648,plain,
! [SV1044: $i,SV290: $i] :
( ( ! [SY4718: $i,SY4719: $i,SY4720: $i,SY4721: $i,SY4722: $i,SY4723: $i,SY4724: $i,SY4725: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SY4718 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SY4719 ) @ SY4720 ) )
= ( hAPP @ ( hAPP @ SV290 @ SY4719 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SY4718 ) ) @ SY4720 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4721 @ SV290 @ SY4722 @ SY4723 @ SY4724 @ SY4725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3649,plain,
! [SV1045: $i,SV291: $i] :
( ( ! [SY4726: $i,SY4727: $i,SY4728: $i,SY4729: $i,SY4730: $i,SY4731: $i,SY4732: $i,SY4733: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SY4726 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SY4727 ) @ SY4728 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SY4726 ) @ ( hAPP @ ( hAPP @ SV291 @ SY4727 ) @ SY4728 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4729 @ SV291 @ SY4730 @ SY4731 @ SY4732 @ SY4733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3650,plain,
! [SV1046: $i,SV292: $i] :
( ( ! [SY4734: $i,SY4735: $i,SY4736: $i,SY4737: $i,SY4738: $i,SY4739: $i,SY4740: $i,SY4741: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SY4734 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SY4735 ) @ SY4736 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SY4735 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SY4734 ) @ SY4736 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4737 @ SV292 @ SY4738 @ SY4739 @ SY4740 @ SY4741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3651,plain,
! [SV1047: $i,SV293: $i] :
( ( ! [SY4742: $i,SY4743: $i,SY4744: $i,SY4745: $i,SY4746: $i] :
( ( ( hAPP @ ( hAPP @ SV293 @ SV1047 ) @ SY4742 )
= SV1047 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4743 @ SV293 @ SY4744 @ SY4745 @ SY4742 @ SY4746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3652,plain,
! [SV1048: $i,SV294: $i] :
( ( ! [SY4747: $i,SY4748: $i,SY4749: $i,SY4750: $i,SY4751: $i] :
( ( ( hAPP @ ( hAPP @ SV294 @ SV1048 ) @ SY4747 )
= SY4747 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4748 @ SV294 @ SY4749 @ SY4750 @ SV1048 @ SY4751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3653,plain,
! [SV1049: $i,SV295: $i] :
( ( ! [SY4752: $i,SY4753: $i,SY4754: $i,SY4755: $i,SY4756: $i] :
( ( ( hAPP @ ( hAPP @ SV295 @ SV1049 ) @ SY4752 )
= SY4752 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4753 @ SV295 @ SY4754 @ SY4752 @ SY4755 @ SY4756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3654,plain,
! [SV1050: $i,SV296: $i] :
( ( ! [SY4757: $i,SY4758: $i,SY4759: $i,SY4760: $i,SY4761: $i] :
( ( ( hAPP @ ( hAPP @ SV296 @ SV1050 ) @ SY4757 )
= SV1050 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4758 @ SV296 @ SY4759 @ SV1050 @ SY4760 @ SY4761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3655,plain,
! [SV1051: $i,SV297: $i] :
( ( ! [SY4762: $i,SY4763: $i,SY4764: $i,SY4765: $i,SY4766: $i,SY4767: $i,SY4768: $i] :
( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SY4762 ) @ SY4763 ) ) @ SY4764 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SY4762 ) @ SY4764 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SY4763 ) @ SY4764 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SY4765 @ SY4766 @ SY4767 @ SY4768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3656,plain,
! [SV1052: $i,SV298: $i] :
( ( ! [SY4769: $i,SY4770: $i,SY4771: $i,SY4772: $i,SY4773: $i,SY4774: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SY4769 )
= ( hAPP @ ( hAPP @ SV298 @ SY4769 ) @ SV1052 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4770 @ SV298 @ SY4771 @ SY4772 @ SY4773 @ SY4774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3657,plain,
! [SV1053: $i,SV299: $i] :
( ( ! [SY4775: $i,SY4776: $i,SY4777: $i,SY4778: $i,SY4779: $i] :
( ( ( hAPP @ ( hAPP @ SV299 @ SV1053 ) @ SY4775 )
= SV1053 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SY4776 @ SY4777 @ SY4775 @ SY4778 @ SY4779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3658,plain,
! [SV1054: $i,SV300: $i] :
( ( ! [SY4780: $i,SY4781: $i,SY4782: $i,SY4783: $i,SY4784: $i] :
( ( ( hAPP @ ( hAPP @ SV300 @ SV1054 ) @ SY4780 )
= SY4780 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SY4781 @ SY4782 @ SV1054 @ SY4783 @ SY4784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3659,plain,
! [SV1055: $i,SV301: $i] :
( ( ! [SY4785: $i,SY4786: $i,SY4787: $i,SY4788: $i,SY4789: $i] :
( ( ( hAPP @ ( hAPP @ SV301 @ SV1055 ) @ SV1055 )
= ( hAPP @ ( hAPP @ SY4785 @ ( hAPP @ ( hAPP @ SV301 @ SY4786 ) @ SY4786 ) ) @ SV1055 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SY4785 @ SY4787 @ SY4788 @ SY4786 @ SY4789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3660,plain,
! [SV1056: $i,SV302: $i] :
( ( ! [SY4790: $i,SY4791: $i,SY4792: $i,SY4793: $i,SY4794: $i,SY4795: $i] :
( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SY4790 @ SY4791 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SY4790 @ ( hAPP @ ( hAPP @ SV302 @ SY4791 ) @ SY4792 ) ) @ SV1056 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SY4790 @ SY4793 @ SY4794 @ SY4792 @ SY4795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3661,plain,
! [SV1057: $i,SV303: $i] :
( ( ! [SY4796: $i,SY4797: $i,SY4798: $i,SY4799: $i,SY4800: $i,SY4801: $i] :
( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SY4796 ) @ SY4797 ) ) @ SY4797 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SY4796 ) @ SY4798 ) ) @ SY4797 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SY4799 @ SY4800 @ SY4798 @ SY4801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3662,plain,
! [SV1058: $i,SV304: $i] :
( ( ! [SY4802: $i,SY4803: $i,SY4804: $i,SY4805: $i,SY4806: $i,SY4807: $i,SY4808: $i] :
( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SY4802 ) @ SY4803 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SY4804 ) @ SY4803 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SY4802 ) @ SY4804 ) ) @ SY4803 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SY4805 @ SY4806 @ SY4807 @ SY4808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3663,plain,
! [SV1059: $i,SV305: $i] :
( ( ! [SY4809: $i,SY4810: $i] :
( ~ ( hBOOL @ ( hAPP @ SV305 @ ( c_Type_Otype_Otype__case @ SV1059 @ SY4809 @ ( c_Type_Otype_OAtom @ SY4810 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV305 @ ( hAPP @ SV1059 @ SY4810 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3664,plain,
! [SV1060: $i,SV306: $i] :
( ( ! [SY4811: $i,SY4812: $i] :
( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_Type_Otype_Otype__case @ SV1060 @ SY4811 @ ( c_Type_Otype_OAtom @ SY4812 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV306 @ ( hAPP @ SV1060 @ SY4812 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3665,plain,
! [SV1061: $i,SV307: $i] :
( ( ! [SY4813: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV307 @ SV1061 @ SY4813 ) @ SY4813 )
= SV1061 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3666,plain,
! [SV1062: $i,SV308: $i] :
( ( ! [SY4814: $i,SY4815: $i,SY4816: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1062 ) @ SY4814 ) ) @ ( c_Suc @ SY4815 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY4816 ) @ SV1062 ) @ SY4815 ) ) @ SY4814 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ SY4816 ) @ SY4814 ) ) @ SV1062 ) @ SY4815 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4815 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3667,plain,
! [SV1063: $i,SV309: $i] :
( ( ! [SY4817: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ SV309 @ SV1063 @ SY4817 ) @ ( c_List_Odrop @ SV309 @ SV1063 @ SY4817 ) @ SY4817 )
= SV1063 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3668,plain,
! [SV1064: $i,SV310: $i] :
( ( ! [SY4818: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV310 ) @ SV1064 @ tc_nat ) @ ( c_Suc @ SY4818 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV310 @ SV1064 @ tc_nat ) @ SY4818 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3669,plain,
! [SV1065: $i,SV311: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV311 @ ( c_Suc @ SV1065 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV311 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1065 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3670,plain,
! [SV312: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV312 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV312 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(3671,plain,
! [SV1066: $i,SV313: $i] :
( ( ! [SY4819: $i,SY4820: $i,SY4821: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SY4819 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SY4820 ) @ SY4821 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SY4820 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SY4819 ) @ SY4821 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3672,plain,
! [SV1067: $i,SV314: $i] :
( ( ! [SY4822: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV1067 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SY4822 ) )
| ~ ( c_Lambda_Obeta @ SV1067 @ SY4822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3673,plain,
! [SV1068: $i,SV315: $i] :
( ( ! [SY4823: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV315 ) @ SV1068 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4823 ) @ SV1068 ) )
| ~ ( c_Lambda_Obeta @ SV315 @ SY4823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3674,plain,
! [SV1069: $i,SV316: $i] :
( ( ! [SY4824: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV316 @ SV1069 ) @ ( c_List_Olist_OCons @ SY4824 @ ( c_List_Olist_ONil @ SV1069 ) @ SV1069 ) @ SV1069 ) @ SV1069 )
= ( c_List_Olist_OCons @ SY4824 @ SV316 @ SV1069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3675,plain,
! [SV1070: $i,SV317: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV317 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1070 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3676,plain,
! [SV1071: $i,SV318: $i] :
( ( ! [SY4825: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV318 ) @ SV1071 @ SY4825 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV318 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4825 @ SV318 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3677,plain,
! [SV1072: $i,SV319: $i] :
( ( ! [SY4826: $i] :
( ~ ( class_Orderings_Olinorder @ SV319 )
| ( ( c_Orderings_Oord__class_Omax @ SV1072 @ SY4826 @ SV319 )
= ( c_Orderings_Oord__class_Omax @ SY4826 @ SV1072 @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3678,plain,
! [SV1073: $i,SV320: $i] :
( ( ! [SY4827: $i] :
( ( ( c_Lambda_Oliftn @ SV320 @ ( c_Lambda_OdB_OVar @ SV1073 ) @ SY4827 )
= ( c_Lambda_OdB_OVar @ SV1073 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1073 @ SY4827 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3679,plain,
! [SV1074: $i,SV321: $i] :
( ( ! [SY4828: $i] :
( ( ( c_List_Odrop @ SV321 @ SV1074 @ SY4828 )
= ( c_List_Olist_ONil @ SY4828 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1074 @ ( tc_List_Olist @ SY4828 ) ) @ SV321 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3680,plain,
! [SV1075: $i,SV323: $i] :
( ( ! [SY4829: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ SV323 @ SV1075 @ SY4829 ) @ SY4829 )
| ~ ( c_List_Odistinct @ SV1075 @ SY4829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3681,plain,
! [SV1076: $i,SV324: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orev @ SV324 @ SV1076 ) @ SV1076 )
| ~ ( c_List_Odistinct @ SV324 @ SV1076 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3682,plain,
! [SV1077: $i,SV325: $i] :
( ( ( c_List_Odistinct @ SV325 @ SV1077 )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ SV325 @ SV1077 ) @ SV1077 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3683,plain,
! [SV1078: $i,SV326: $i] :
( ( ! [SY4830: $i,SY4831: $i] :
( ( c_List_Odrop @ SV326 @ ( c_List_Oreplicate @ SV1078 @ SY4830 @ SY4831 ) @ SY4831 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV1078 @ SV326 @ tc_nat ) @ SY4830 @ SY4831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3684,plain,
! [SV1079: $i,SV327: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV327 @ SV1079 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1079 @ SV327 @ tc_nat )
| ( SV1079 = SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3685,plain,
! [SV1080: $i,SV328: $i] :
( ( ! [SY4832: $i] :
( ~ ( class_Orderings_Oorder @ SV328 )
| ( SV1080 = SY4832 )
| ~ ( c_lessequals @ SY4832 @ SV1080 @ SV328 )
| ~ ( c_lessequals @ SV1080 @ SY4832 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3686,plain,
! [SV1081: $i,SV329: $i] :
( ( ! [SY4833: $i] :
( ~ ( class_Orderings_Olinorder @ SV329 )
| ( c_HOL_Oord__class_Oless @ SV1081 @ SY4833 @ SV329 )
| ( c_HOL_Oord__class_Oless @ SY4833 @ SV1081 @ SV329 )
| ( SY4833 = SV1081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3687,plain,
! [SV1082: $i,SV330: $i] :
( ( ! [SY4834: $i] :
( ~ ( class_Orderings_Oorder @ SV330 )
| ( SV1082 = SY4834 )
| ~ ( c_lessequals @ SY4834 @ SV1082 @ SV330 )
| ~ ( c_lessequals @ SV1082 @ SY4834 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3688,plain,
! [SV1083: $i,SV331: $i] :
( ( ! [SY4835: $i] :
( ~ ( class_Orderings_Oorder @ SV331 )
| ( SV1083 = SY4835 )
| ~ ( c_lessequals @ SV1083 @ SY4835 @ SV331 )
| ~ ( c_lessequals @ SY4835 @ SV1083 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3689,plain,
! [SV1084: $i,SV332: $i] :
( ( ! [SY4836: $i,SY4837: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV332 @ SV1084 @ SY4836 ) @ ( c_List_Oreplicate @ SY4837 @ SV1084 @ SY4836 ) @ SY4836 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY4837 @ SV1084 @ SY4836 ) @ ( c_List_Oreplicate @ SV332 @ SV1084 @ SY4836 ) @ SY4836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3690,plain,
! [SV1085: $i,SV333: $i] :
( ( ! [SY4838: $i] :
( ~ ( class_Orderings_Olinorder @ SV333 )
| ( c_HOL_Oord__class_Oless @ SV1085 @ SY4838 @ SV333 )
| ( SY4838 = SV1085 )
| ( c_HOL_Oord__class_Oless @ SY4838 @ SV1085 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3691,plain,
! [SV1086: $i,SV334: $i] :
( ( ! [SY4839: $i] :
( ~ ( class_Orderings_Olinorder @ SV334 )
| ( SV1086 = SY4839 )
| ( c_HOL_Oord__class_Oless @ SV1086 @ SY4839 @ SV334 )
| ( c_HOL_Oord__class_Oless @ SY4839 @ SV1086 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3692,plain,
! [SV1087: $i,SV335: $i] :
( ( ! [SY4840: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV335 )
| ( c_lessequals @ SV1087 @ SY4840 @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SY4840 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3693,plain,
! [SV1088: $i,SV336: $i] :
( ( ! [SY4841: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV336 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SY4841 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ SV1088 @ SY4841 @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3694,plain,
! [SV337: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV337 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV337 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV337 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2929]) ).
thf(3695,plain,
! [SV338: $i] :
( ( ( SV338
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV338 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV338 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2930]) ).
thf(3696,plain,
! [SV1089: $i,SV339: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV339 )
| ( ( c_Orderings_Oord__class_Omax @ SV1089 @ SV1089 @ SV339 )
= SV1089 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3697,plain,
! [SV1090: $i,SV340: $i] :
( ( ! [SY4842: $i,SY4843: $i,SY4844: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SY4842 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SY4843 ) @ SY4844 ) @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SY4842 @ SY4844 @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SY4843 @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3698,plain,
! [SV1091: $i,SV341: $i] :
( ( ! [SY4845: $i,SY4846: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV341 ) @ SV1091 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4845 ) @ SY4846 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1091 @ SY4846 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV341 @ SY4845 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3699,plain,
! [SV1092: $i,SV342: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV342 ) @ SV1092 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV1092 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3700,plain,
! [SV1093: $i,SV343: $i] :
( ( ( c_lessequals @ SV343 @ SV1093 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV343 @ SV1093 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3701,plain,
! [SV1094: $i,SV344: $i] :
( ( ( c_lessequals @ SV344 @ SV1094 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV344 @ SV1094 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3702,plain,
! [SV1095: $i,SV345: $i] :
( ( ! [SY4847: $i] :
( ~ ( class_Orderings_Oorder @ SV345 )
| ( c_lessequals @ SV1095 @ SY4847 @ SV345 )
| ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SY4847 @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3703,plain,
! [SV1096: $i,SV346: $i] :
( ( ! [SY4848: $i] :
( ~ ( class_Orderings_Opreorder @ SV346 )
| ( c_lessequals @ SV1096 @ SY4848 @ SV346 )
| ~ ( c_HOL_Oord__class_Oless @ SV1096 @ SY4848 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3704,plain,
! [SV1097: $i,SV347: $i] :
( ( ! [SY4849: $i,SY4850: $i,SY4851: $i] :
( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1097 ) @ SY4849 ) @ SY4850 )
| ~ ( c_Type_Otyping @ SV347 @ SY4849 @ SY4851 )
| ~ ( c_Type_Otyping @ SV347 @ SV1097 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4851 ) @ SY4850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3705,plain,
! [SV1098: $i,SV349: $i] :
( ( ! [SY4852: $i,SY4853: $i] :
( ( ( c_List_Olist__update @ SV349 @ SV1098 @ SY4852 @ SY4853 )
= ( c_List_Oappend @ ( c_List_Otake @ SV1098 @ SV349 @ SY4853 ) @ ( c_List_Olist_OCons @ SY4852 @ ( c_List_Odrop @ ( c_Suc @ SV1098 ) @ SV349 @ SY4853 ) @ SY4853 ) @ SY4853 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1098 @ ( c_Nat_Osize__class_Osize @ SV349 @ ( tc_List_Olist @ SY4853 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3706,plain,
! [SV1099: $i,SV350: $i] :
( ( ! [SY4854: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV350 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ ( c_Power_Opower__class_Opower @ SV1099 @ ( c_Suc @ SY4854 ) @ SV350 ) @ SV350 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ SV1099 @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3707,plain,
! [SV1100: $i,SV351: $i] :
( ( ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV351 ) @ SV1100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3708,plain,
! [SV1101: $i,SV352: $i] :
( ( ! [SY4855: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SY4855 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV352 ) @ SY4855 ) @ ( c_Suc @ SV1101 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY4855 @ SV1101 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3709,plain,
! [SV1102: $i,SV353: $i] :
( ( ! [SY4856: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV353 )
| ( c_HOL_Oord__class_Oless @ SV1102 @ SY4856 @ SV353 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1102 @ SY4856 @ SV353 ) @ ( c_HOL_Ozero__class_Ozero @ SV353 ) @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3710,plain,
! [SV1103: $i,SV354: $i] :
( ( ! [SY4857: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV354 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1103 @ SY4857 @ SV354 ) @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV354 )
| ~ ( c_HOL_Oord__class_Oless @ SV1103 @ SY4857 @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3711,plain,
! [SV1104: $i,SV355: $i] :
( ( ! [SY4858: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV355 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1104 @ SV355 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4858 @ SV355 ) @ SV355 )
| ~ ( c_HOL_Oord__class_Oless @ SV1104 @ SY4858 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3712,plain,
! [SV1105: $i,SV356: $i] :
( ( ! [SY4859: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV356 )
| ( c_HOL_Oord__class_Oless @ SV1105 @ SY4859 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1105 @ SV356 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4859 @ SV356 ) @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3713,plain,
! [SV1106: $i,SV359: $i] :
( ( ! [SY4860: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV359 ) @ SV1106 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4860 @ SV1106 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV359 @ SY4860 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3714,plain,
! [SV1107: $i,SV360: $i] :
( ( ! [SY4861: $i,SY4862: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV360 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV1107 ) @ SY4861 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SY4862 ) @ SY4861 ) @ SV360 )
| ~ ( c_lessequals @ SV1107 @ SY4862 @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3715,plain,
! [SV1108: $i,SV361: $i] :
( ( ! [SY4863: $i,SY4864: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV361 )
| ( c_lessequals @ SV1108 @ SY4863 @ SV361 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1108 ) @ SY4864 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SY4863 ) @ SY4864 ) @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3716,plain,
! [SV1109: $i,SV362: $i] :
( ( ! [SY4865: $i,SY4866: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV362 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SY4865 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SY4866 ) @ SV362 )
| ~ ( c_lessequals @ SY4865 @ SY4866 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3717,plain,
! [SV1110: $i,SV363: $i] :
( ( ! [SY4867: $i,SY4868: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV363 )
| ( c_lessequals @ SV1110 @ SY4867 @ SV363 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SY4868 ) @ SV1110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SY4868 ) @ SY4867 ) @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3718,plain,
! [SV1111: $i,SV364: $i] :
( ( ! [SY4869: $i,SY4870: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV364 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV1111 ) @ SY4869 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SY4870 ) @ SY4869 ) @ SV364 )
| ~ ( c_lessequals @ SV1111 @ SY4870 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3719,plain,
! [SV1112: $i,SV365: $i] :
( ( ! [SY4871: $i,SY4872: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV365 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SY4871 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SY4872 ) @ SV365 )
| ~ ( c_lessequals @ SY4871 @ SY4872 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3720,plain,
! [SV1113: $i,SV366: $i] :
( ( ! [SY4873: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV366 ) @ SV1113 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4873 ) @ SV1113 ) @ tc_nat )
| ~ ( c_lessequals @ SV366 @ SY4873 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3721,plain,
! [SV1114: $i,SV367: $i] :
( ( ! [SY4874: $i] :
( ( c_lessequals @ SV367 @ SV1114 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4874 ) @ SV367 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4874 ) @ SV1114 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3722,plain,
! [SV1115: $i,SV368: $i] :
( ( ! [SY4875: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SY4875 ) @ tc_nat )
| ~ ( c_lessequals @ SV1115 @ SY4875 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3723,plain,
! [SV369: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV369 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV369 ) @ ( c_HOL_Oone__class_Oone @ SV369 ) @ SV369 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2961]) ).
thf(3724,plain,
! [SV1116: $i,SV370: $i] :
( ( ! [SY4876: $i,SY4877: $i] :
( ( ( c_List_Olist__update @ SV370 @ SV1116 @ SY4876 @ SY4877 )
= SV370 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SY4877 ) ) @ SV1116 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3725,plain,
! [SV1117: $i,SV371: $i] :
( ( ~ ( c_lessequals @ SV371 @ SV1117 @ tc_nat )
| ( SV1117
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1117 @ SV371 @ tc_nat ) ) @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3726,plain,
! [SV1118: $i,SV372: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV372 ) @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV372 @ tc_nat ) )
= SV1118 )
| ~ ( c_lessequals @ SV372 @ SV1118 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3727,plain,
! [SV1119: $i,SV373: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV373 @ SV1119 @ tc_nat ) ) @ SV1119 )
= SV373 )
| ~ ( c_lessequals @ SV1119 @ SV373 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3728,plain,
! [SV1120: $i,SV374: $i] :
( ( ! [SY4878: $i,SY4879: $i,SY4880: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV374 @ SV1120 @ SY4878 @ SY4879 ) @ SY4880 )
= ( hAPP @ SV374 @ ( c_HOL_Ominus__class_Ominus @ SY4880 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1120 @ SY4880 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(3729,plain,
! [SV1121: $i,SV375: $i] :
( ( ! [SY4881: $i,SY4882: $i,SY4883: $i,SY4884: $i,SY4885: $i,SY4886: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SY4881 @ SV1121 ) @ SY4882 ) )
= ( hAPP @ ( hAPP @ SY4881 @ SV1121 ) @ ( c_Suc @ SY4882 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4883 @ SV375 @ SY4881 @ SY4884 @ SY4885 @ SY4886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3730,plain,
! [SV1122: $i,SV376: $i] :
( ( ! [SY4887: $i,SY4888: $i,SY4889: $i,SY4890: $i,SY4891: $i,SY4892: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SY4887 ) @ SY4888 ) ) @ SY4887 )
= ( hAPP @ ( hAPP @ SV1122 @ SY4887 ) @ ( c_Suc @ SY4888 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4889 @ SV376 @ SV1122 @ SY4890 @ SY4891 @ SY4892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3731,plain,
! [SV1123: $i,SV377: $i] :
( ( ! [SY4893: $i,SY4894: $i,SY4895: $i,SY4896: $i,SY4897: $i,SY4898: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SY4893 ) )
= ( hAPP @ ( hAPP @ SY4894 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SY4893 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4895 @ SY4894 @ SV377 @ SY4896 @ SY4897 @ SY4898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3732,plain,
! [SV1124: $i,SV378: $i] :
( ( ! [SY4899: $i,SY4900: $i,SY4901: $i,SY4902: $i,SY4903: $i,SY4904: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SY4899 ) )
= ( hAPP @ ( hAPP @ SY4900 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SY4899 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4901 @ SY4900 @ SV378 @ SY4902 @ SY4903 @ SY4904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3733,plain,
! [SV1125: $i,SV379: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV379 )
| ( c_HOL_Oord__class_Oless @ SV1125 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV1125 ) @ ( c_HOL_Oone__class_Oone @ SV379 ) ) @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3734,plain,
! [SV1126: $i,SV380: $i] :
( ( ! [SY4905: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ ( c_HOL_Ominus__class_Ominus @ SV1126 @ SY4905 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ SV1126 ) @ SY4905 @ tc_nat ) )
| ~ ( c_lessequals @ SY4905 @ SV1126 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3735,plain,
! [SV1127: $i,SV381: $i] :
( ( ! [SY4906: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV381 @ SV1127 @ tc_nat ) ) @ SY4906 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV381 ) @ SY4906 ) @ SV1127 @ tc_nat ) )
| ~ ( c_lessequals @ SV1127 @ SV381 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3736,plain,
! [SV1128: $i,SV382: $i] :
( ( ! [SY4907: $i,SY4908: $i] :
( ( c_List_Odrop @ SV382 @ ( c_List_Odrop @ SV1128 @ SY4907 @ SY4908 ) @ SY4908 )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV382 ) @ SV1128 ) @ SY4907 @ SY4908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3737,plain,
! [SV1129: $i,SV383: $i] :
( ( ! [SY4909: $i,SY4910: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV383 )
| ( c_lessequals @ SV1129 @ SY4909 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SY4909 @ SV383 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SY4910 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SY4909 @ ( c_Suc @ SY4910 ) @ SV383 ) @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3738,plain,
! [SV1130: $i,SV384: $i] :
( ( ! [SY4911: $i,SY4912: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV384 ) @ SV1130 ) @ SY4911 @ SY4912 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV384 @ SY4911 @ SY4912 ) @ ( c_List_Oreplicate @ SV1130 @ SY4911 @ SY4912 ) @ SY4912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3739,plain,
! [SV1131: $i,SV385: $i] :
( ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV385 @ SV1131 )
= ( c_List_Olist_ONil @ SV1131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3740,plain,
! [SV1132: $i,SV386: $i] :
( ( ! [SY4913: $i,SY4914: $i] :
( ( c_List_Otake @ SV386 @ ( c_List_Oappend @ SV1132 @ SY4913 @ SY4914 ) @ SY4914 )
= ( c_List_Oappend @ ( c_List_Otake @ SV386 @ SV1132 @ SY4914 ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV386 @ ( c_Nat_Osize__class_Osize @ SV1132 @ ( tc_List_Olist @ SY4914 ) ) @ tc_nat ) @ SY4913 @ SY4914 ) @ SY4914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3741,plain,
! [SV1133: $i,SV387: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV387 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV387 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1133 @ SV387 ) @ SV387 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1133 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3742,plain,
! [SV1134: $i,SV388: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV388 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1134 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV388 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1134 @ SV388 ) @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3743,plain,
! [SV1135: $i,SV389: $i] :
( ( ! [SY4915: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV389 @ SV1135 @ SY4915 ) @ SY4915 )
= ( c_List_Olist_ONil @ SY4915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3744,plain,
! [SV1136: $i,SV390: $i] :
( ( ~ ( class_Power_Opower @ SV390 )
| ( ( c_Power_Opower__class_Opower @ SV1136 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV390 )
= ( c_HOL_Oone__class_Oone @ SV390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3745,plain,
! [SV1137: $i,SV391: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV391 )
| ( ( c_Power_Opower__class_Opower @ SV1137 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV391 )
= ( c_HOL_Oone__class_Oone @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3746,plain,
! [SV1138: $i,SV392: $i] :
( ( ! [SY4916: $i] :
( ( c_List_Odistinct @ SV392 @ SV1138 )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ SY4916 @ SV392 @ SV1138 ) @ SV1138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3747,plain,
! [SV1139: $i,SV393: $i] :
( ( ! [SY4917: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ SV393 @ SV1139 @ SY4917 ) @ SY4917 )
| ~ ( c_List_Odistinct @ SV1139 @ SY4917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3748,plain,
! [SV1140: $i,SV394: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV394 )
| ( ( c_List_Olistsum @ ( c_List_Orev @ SV1140 @ SV394 ) @ SV394 )
= ( c_List_Olistsum @ SV1140 @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3749,plain,
! [SV1141: $i,SV395: $i] :
( ( ! [SY4918: $i,SY4919: $i] :
( ( c_List_Olistsp @ SV395 @ ( c_List_Oappend @ SV1141 @ SY4918 @ SY4919 ) @ SY4919 )
| ~ ( c_List_Olistsp @ SV395 @ SY4918 @ SY4919 )
| ~ ( c_List_Olistsp @ SV395 @ SV1141 @ SY4919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3750,plain,
! [SV1142: $i,SV396: $i] :
( ( ! [SY4920: $i,SY4921: $i,SY4922: $i,SY4923: $i,SY4924: $i] :
( ( c_Fun_Ocomp @ SV396 @ ( c_Fun_Ocomp @ SV1142 @ SY4920 @ SY4921 @ SY4922 @ SY4923 ) @ SY4922 @ SY4924 @ SY4923 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV396 @ SV1142 @ SY4922 @ SY4924 @ SY4921 ) @ SY4920 @ SY4921 @ SY4924 @ SY4923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3751,plain,
! [SV1143: $i,SV397: $i] :
( ( ! [SY4925: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV397 ) ) @ SV1143 ) @ SY4925 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV397 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4925 @ SV397 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3752,plain,
! [SV1144: $i,SV398: $i] :
( ( ! [SY4926: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV398 ) ) @ SV1144 ) @ SY4926 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV398 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4926 @ SV398 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3753,plain,
! [SV1145: $i,SV399: $i] :
( ( ! [SY4927: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV399 @ SV1145 @ SY4927 ) @ ( tc_List_Olist @ SY4927 ) )
= SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3754,plain,
! [SV1146: $i,SV400: $i] :
( ( ( c_lessequals @ SV400 @ SV1146 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV400 ) @ SV1146 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3755,plain,
! [SV1147: $i,SV401: $i] :
( ( ( c_lessequals @ SV401 @ ( c_Suc @ SV1147 ) @ tc_nat )
| ~ ( c_lessequals @ SV401 @ SV1147 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3756,plain,
! [SV402: $i] :
( ( c_lessequals @ ( c_Suc @ SV402 ) @ SV402 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3757,plain,
! [SV1148: $i,SV403: $i] :
( ( ! [SY4928: $i] :
( ( c_HOL_Oord__class_Oless @ SV403 @ SV1148 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SY4928 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1148 @ SY4928 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4928 @ SV1148 @ tc_nat )
| ~ ( c_lessequals @ SY4928 @ SV403 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3758,plain,
! [SV1149: $i,SV404: $i] :
( ( ! [SY4929: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SV1149 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4929 @ SV1149 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV404 @ SY4929 @ tc_nat )
| ~ ( c_lessequals @ SV1149 @ SY4929 @ tc_nat )
| ~ ( c_lessequals @ SV1149 @ SV404 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3759,plain,
! [SV1150: $i,SV405: $i] :
( ( ! [SY4930: $i,SY4931: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV405 )
| ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SY4930 ) @ SY4931 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SY4931 @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SY4930 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3760,plain,
! [SV1151: $i,SV406: $i] :
( ( ! [SY4932: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV406 ) ) @ SV1151 ) @ SY4932 )
= ( c_Lambda_OdB_OVar @ SV406 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV406 @ SY4932 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3761,plain,
! [SV1152: $i,SV407: $i] :
( ( ! [SY4933: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV407 ) @ ( c_Lambda_OdB_OVar @ SV1152 ) ) @ SY4933 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3762,plain,
! [SV1153: $i,SV408: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV408 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV408 ) @ SV1153 ) @ SV1153 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_lessequals @ SV1153 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3763,plain,
! [SV1154: $i,SV409: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV409 )
| ( c_lessequals @ SV1154 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV409 ) @ SV1154 ) @ SV1154 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3764,plain,
! [SV1155: $i,SV410: $i] :
( ( ! [SY4934: $i,SY4935: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SY4934 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SY4935 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ SY4934 @ SY4935 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3765,plain,
! [SV1156: $i,SV411: $i] :
( ( ! [SY4936: $i,SY4937: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV411 )
| ( c_HOL_Oord__class_Oless @ SV1156 @ SY4936 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY4937 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SY4937 @ SY4936 @ SV411 ) @ SV411 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SY4937 @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3766,plain,
! [SV1157: $i,SV412: $i] :
( ( ! [SY4938: $i,SY4939: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SY4938 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SY4939 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SY4938 @ SY4939 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3767,plain,
! [SV1158: $i,SV413: $i] :
( ( ! [SY4940: $i,SY4941: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV413 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SY4940 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY4941 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SY4941 @ SY4940 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SY4941 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3768,plain,
! [SV1159: $i,SV414: $i] :
( ( ! [SY4942: $i,SY4943: $i] :
( ( c_Lambda_Oliftn @ SV414 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1159 ) @ SY4942 ) @ SY4943 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV414 @ SV1159 @ SY4943 ) ) @ ( c_Lambda_Oliftn @ SV414 @ SY4942 @ SY4943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3769,plain,
! [SV1160: $i,SV415: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV415 @ SV1160 )
= ( c_List_Olist_ONil @ SV1160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3770,plain,
! [SV1161: $i,SV416: $i] :
( ( ! [SY4944: $i,SY4945: $i] :
( ( ( c_List_Odrop @ SV416 @ ( c_List_Olist_OCons @ SV1161 @ SY4944 @ SY4945 ) @ SY4945 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY4944 @ SY4945 ) )
| ( SV416
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3008]) ).
thf(3771,plain,
! [SV1162: $i,SV417: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV417 @ ( c_HOL_Ominus__class_Ominus @ SV417 @ SV1162 @ tc_nat ) @ tc_nat )
= SV1162 )
| ~ ( c_lessequals @ SV1162 @ SV417 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3772,plain,
! [SV1163: $i,SV418: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV418 ) ) @ SV1163 )
= ( c_Lambda_OdB_OVar @ SV418 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV418 @ SV1163 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3773,plain,
! [SV1164: $i,SV419: $i] :
( ( ( c_List_Orotate @ SV419 @ ( c_List_Olist_ONil @ SV1164 ) @ SV1164 )
= ( c_List_Olist_ONil @ SV1164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3774,plain,
! [SV1165: $i,SV420: $i] :
( ( ! [SY4946: $i,SY4947: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV420 @ SV1165 @ SY4946 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4947 @ SY4946 )
= ( c_List_Olist_OCons @ SY4947 @ SV1165 @ SY4946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3775,plain,
! [SV1166: $i,SV421: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV421 @ SV421 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV421 ) @ SV1166 @ SV421 )
= ( c_Lambda_Oliftn @ SV421 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3013]) ).
thf(3776,plain,
! [SV1167: $i,SV422: $i] :
( ( ! [SY4948: $i,SY4949: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV422 @ SV1167 @ SY4948 @ SY4949 ) @ ( tc_List_Olist @ SY4949 ) )
= ( c_Nat_Osize__class_Osize @ SV422 @ ( tc_List_Olist @ SY4949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3777,plain,
! [SV1168: $i,SV423: $i] :
( ( ( SV423
= ( c_Suc @ SV1168 ) )
| ( c_lessequals @ SV423 @ SV1168 @ tc_nat )
| ~ ( c_lessequals @ SV423 @ ( c_Suc @ SV1168 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3778,plain,
! [SV424: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV424 @ SV424 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV424 @ ( c_Suc @ SV424 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3016]) ).
thf(3779,plain,
! [SV1169: $i,SV425: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV425 @ SV1169 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1169 @ ( c_Suc @ SV425 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3780,plain,
! [SV1170: $i,SV426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV426 @ ( c_Suc @ SV1170 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1170 @ SV426 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3781,plain,
! [SV1171: $i,SV427: $i] :
( ( ! [SY4950: $i,SY4951: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV427 ) @ SV1171 ) @ SY4950 ) ) @ SY4951 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV427 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4951 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1171 ) @ SY4951 ) ) @ SY4950 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4950 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4951 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3782,plain,
! [SV1172: $i,SV428: $i] :
( ( ! [SY4952: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SV1172 ) ) @ ( c_Suc @ SY4952 ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SY4952 ) ) @ SV1172 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1172 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4952 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3783,plain,
! [SV1173: $i,SV429: $i] :
( ( ! [SY4953: $i] :
( ( c_List_Olist_OCons @ SV429 @ SV1173 @ SY4953 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY4953 ) @ ( c_List_Olist_OCons @ SV429 @ SV1173 @ SY4953 ) @ SY4953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3784,plain,
! [SV1174: $i,SV430: $i] :
( ( ( c_List_Olist_OCons @ SV430 @ ( c_List_Olist_ONil @ SV1174 ) @ SV1174 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV430 @ ( c_List_Olist_ONil @ SV1174 ) @ SV1174 ) @ SV1174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3785,plain,
! [SV1175: $i,SV431: $i] :
( ( ! [SY4954: $i,SY4955: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV431 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ ( c_Orderings_Oord__class_Omax @ SV1175 @ SY4954 @ SV431 ) ) @ SY4955 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1175 ) @ SY4955 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SY4954 ) @ SY4955 ) @ SV431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3786,plain,
! [SV1176: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV432 ) @ ( c_Lambda_OdB_OVar @ SV1176 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3787,plain,
! [SV1177: $i,SV433: $i] :
( ( ! [SY4956: $i,SY4957: $i] :
( ~ ( class_Orderings_Olinorder @ SV433 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1177 @ SY4956 @ SV433 ) @ SY4957 @ SV433 )
= ( c_Orderings_Oord__class_Omax @ SV1177 @ ( c_Orderings_Oord__class_Omax @ SY4956 @ SY4957 @ SV433 ) @ SV433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3788,plain,
! [SV1178: $i,SV434: $i] :
( ( ! [SY4958: $i,SY4959: $i] :
( ~ ( class_Orderings_Olinorder @ SV434 )
| ( ( c_Orderings_Oord__class_Omax @ SV1178 @ ( c_Orderings_Oord__class_Omax @ SY4958 @ SY4959 @ SV434 ) @ SV434 )
= ( c_Orderings_Oord__class_Omax @ SY4958 @ ( c_Orderings_Oord__class_Omax @ SV1178 @ SY4959 @ SV434 ) @ SV434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3789,plain,
! [SV435: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV435 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV435 ) @ ( c_HOL_Oone__class_Oone @ SV435 ) ) @ ( c_HOL_Oone__class_Oone @ SV435 ) ) @ SV435 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3027]) ).
thf(3790,plain,
! [SV1179: $i,SV437: $i] :
( ( ! [SY4960: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ SV437 @ SV1179 @ SY4960 ) @ SY4960 )
| ~ ( c_List_Odistinct @ SV1179 @ SY4960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3791,plain,
! [SV1180: $i,SV438: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV438 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1180 @ SV438 ) @ SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3792,plain,
! [SV1181: $i,SV439: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV439 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1181 @ SV439 ) @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3793,plain,
! [SV1182: $i,SV440: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV440 ) @ ( c_Lambda_OdB_OAbs @ SV1182 ) )
| ~ ( c_Lambda_Obeta @ SV440 @ SV1182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3794,plain,
! [SV1183: $i,SV441: $i] :
( ( ! [SY4961: $i] :
( ~ ( class_Orderings_Olinorder @ SV441 )
| ( ( c_Orderings_Oord__class_Omax @ SV1183 @ ( c_Orderings_Oord__class_Omax @ SV1183 @ SY4961 @ SV441 ) @ SV441 )
= ( c_Orderings_Oord__class_Omax @ SV1183 @ SY4961 @ SV441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3795,plain,
! [SV1184: $i,SV442: $i] :
( ( ! [SY4962: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV442 @ SV1184 @ SY4962 ) @ ( c_List_Olist_OCons @ SV1184 @ ( c_List_Olist_ONil @ SY4962 ) @ SY4962 ) @ SY4962 )
= ( c_List_Olist_OCons @ SV1184 @ ( c_List_Oreplicate @ SV442 @ SV1184 @ SY4962 ) @ SY4962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3796,plain,
! [SV1185: $i,SV444: $i] :
( ( ! [SY4963: $i,SY4964: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV444 ) @ SV1185 ) @ SY4963 @ SY4964 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV444 @ SY4963 @ SY4964 ) ) @ ( c_Lambda_Osubstn @ SV1185 @ SY4963 @ SY4964 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3797,plain,
! [SV1186: $i,SV445: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV445 ) @ SV1186 ) @ SV1186 @ tc_nat )
= SV445 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3798,plain,
! [SV1187: $i,SV446: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV446 ) @ SV1187 ) @ SV446 @ tc_nat )
= SV1187 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3799,plain,
! [SV1188: $i,SV447: $i] :
( ( ! [SY4965: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV447 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1188 ) @ SY4965 ) @ SY4965 @ SV447 )
= SV1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3800,plain,
! [SV1189: $i,SV448: $i] :
( ( ! [SY4966: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV448 @ SV1189 @ SY4966 ) @ SY4966 )
= ( c_List_Oappend @ ( c_List_Orev @ SV1189 @ SY4966 ) @ ( c_List_Orev @ SV448 @ SY4966 ) @ SY4966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3801,plain,
! [SV1190: $i,SV449: $i] :
( ( ! [SY4967: $i,SY4968: $i,SY4969: $i,SY4970: $i] :
( ( c_List_Ofoldl @ SV449 @ SV1190 @ ( c_List_Oappend @ SY4967 @ SY4968 @ SY4969 ) @ SY4970 @ SY4969 )
= ( c_List_Ofoldl @ SV449 @ ( c_List_Ofoldl @ SV449 @ SV1190 @ SY4967 @ SY4970 @ SY4969 ) @ SY4968 @ SY4970 @ SY4969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3802,plain,
! [SV1191: $i,SV450: $i] :
( ( ! [SY4971: $i,SY4972: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV450 )
| ( c_lessequals @ SV1191 @ SY4971 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY4972 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SY4972 @ SY4971 @ SV450 ) @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SY4972 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3803,plain,
! [SV1192: $i,SV451: $i] :
( ( ! [SY4973: $i,SY4974: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV451 )
| ( c_lessequals @ SV1192 @ SY4973 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY4974 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SY4974 @ SY4973 @ SV451 ) @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SY4974 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(3804,plain,
! [SV1193: $i,SV452: $i] :
( ( ! [SY4975: $i,SY4976: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV452 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SY4975 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SY4976 @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ SY4975 @ SY4976 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3805,plain,
! [SV1194: $i,SV453: $i] :
( ( ! [SY4977: $i,SY4978: $i] :
( ( c_List_Orotate @ SV453 @ ( c_List_Orotate @ SV1194 @ SY4977 @ SY4978 ) @ SY4978 )
= ( c_List_Orotate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV453 ) @ SV1194 ) @ SY4977 @ SY4978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3806,plain,
! [SV1195: $i,SV454: $i] :
( ( ! [SY4979: $i,SY4980: $i] :
( ( c_Type_Otype_Otype__case @ SV454 @ SV1195 @ ( c_Type_Otype_OAtom @ SY4979 ) @ SY4980 )
= ( hAPP @ SV454 @ SY4979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3807,plain,
! [SV455: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV455 ) @ ( tc_List_Olist @ SV455 ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3808,plain,
! [SV1196: $i,SV456: $i] :
( ( ! [SY4981: $i] :
( ( c_List_Odistinct @ SV456 @ SV1196 )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ SY4981 @ SV456 @ SV1196 ) @ SV1196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3809,plain,
! [SV1197: $i,SV457: $i] :
( ( ! [SY4982: $i,SY4983: $i,SY4984: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SY4982 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY4983 ) @ SY4984 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SY4982 @ SY4984 @ SV457 )
| ~ ( c_lessequals @ SV1197 @ SY4983 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3810,plain,
! [SV1198: $i,SV458: $i] :
( ( ! [SY4985: $i,SY4986: $i,SY4987: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SY4985 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SY4986 ) @ SY4987 ) @ SV458 )
| ~ ( c_lessequals @ SY4985 @ SY4987 @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SY4986 @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3811,plain,
! [SV1199: $i,SV459: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV459 ) @ ( c_Suc @ SV1199 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV459 @ SV1199 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3812,plain,
! [SV1200: $i,SV460: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV460 @ SV1200 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV460 ) @ ( c_Suc @ SV1200 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3813,plain,
! [SV1201: $i,SV461: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV461 ) @ ( c_Suc @ SV1201 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV1201 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3814,plain,
! [SV1202: $i,SV462: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV462 ) @ SV1202 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1202 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3815,plain,
! [SV1203: $i,SV463: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV463 ) @ SV1203 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3816,plain,
! [SV1204: $i,SV464: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV464 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ SV1204 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV464 ) @ SV1204 ) @ SV1204 ) @ SV464 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3817,plain,
! [SV1205: $i,SV465: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV465 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV465 ) @ SV1205 ) @ SV1205 ) @ SV465 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1205 @ SV465 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3818,plain,
! [SV1206: $i,SV466: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV466 )
| ~ ( class_Int_Onumber__ring @ SV466 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1206 @ SV1206 @ SV466 )
= ( c_HOL_Ozero__class_Ozero @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3819,plain,
! [SV1207: $i,SV467: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV467 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1207 @ SV1207 @ SV467 )
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3820,plain,
! [SV1208: $i,SV468: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV468 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1208 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
= SV1208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3821,plain,
! [SV1209: $i,SV469: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV469 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1209 @ SV1209 @ SV469 )
= ( c_HOL_Ozero__class_Ozero @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3822,plain,
! [SV1210: $i,SV470: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV470 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1210 @ SV1210 @ SV470 )
= ( c_HOL_Ozero__class_Ozero @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3823,plain,
! [SV471: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV471 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3063]) ).
thf(3824,plain,
! [SV1211: $i,SV472: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV472 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) ) @ SV1211 )
= SV1211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3825,plain,
! [SV1212: $i,SV473: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV473 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV473 ) @ ( c_HOL_Ozero__class_Ozero @ SV473 ) ) @ SV1212 )
= SV1212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3826,plain,
! [SV1213: $i,SV474: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV474 )
| ~ ( class_Int_Onumber__ring @ SV474 )
| ( SV1213
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV474 ) @ SV1213 ) @ ( c_HOL_Ozero__class_Ozero @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3827,plain,
! [SV1214: $i,SV475: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV475 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV475 ) @ SV1214 ) @ ( c_HOL_Ozero__class_Ozero @ SV475 ) )
= SV1214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3828,plain,
! [SV1215: $i,SV476: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV476 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV476 ) @ ( c_HOL_Ozero__class_Ozero @ SV476 ) ) @ SV1215 )
= SV1215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3829,plain,
! [SV1216: $i,SV477: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV477 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV477 ) @ SV1216 ) @ ( c_HOL_Ozero__class_Ozero @ SV477 ) )
= SV1216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3830,plain,
! [SV1217: $i,SV478: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV478 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV478 ) @ SV1217 ) @ ( c_HOL_Ozero__class_Ozero @ SV478 ) )
= SV1217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3831,plain,
! [SV1218: $i,SV479: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV479 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV479 ) @ ( c_HOL_Ozero__class_Ozero @ SV479 ) ) @ SV1218 )
= SV1218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3832,plain,
! [SV480: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV480 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV480 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV480 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV480 )
= ( c_HOL_Oone__class_Oone @ SV480 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3833,plain,
! [SV1219: $i,SV481: $i] :
( ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV481 @ SV1219 )
= SV481 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3834,plain,
! [SV482: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV482 @ tc_nat )
= $true )
| ( ( SV482
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3075]) ).
thf(3835,plain,
! [SV483: $i] :
( ( ( SV483
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV483 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3836,plain,
! [SV1220: $i,SV486: $i] :
( ( ! [SY4988: $i,SY4989: $i,SY4990: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SV1220 @ SY4988 @ SY4989 ) @ SY4989 ) @ ( c_Nat_Osize__class_Osize @ SV486 @ ( tc_List_Olist @ SY4989 ) ) @ SY4990 @ SY4989 )
= ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SY4990 @ SY4988 @ SY4989 ) @ SY4989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3837,plain,
! [SV1221: $i,SV487: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV487 ) @ SV1221 ) @ SV487 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(3838,plain,
! [SV1222: $i,SV488: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV488 ) @ SV1222 ) @ SV1222 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3839,plain,
! [SV1223: $i,SV489: $i] :
( ( ! [SY4991: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV489 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1223 @ SY4991 @ tc_nat ) @ SV489 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1223 @ SV489 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4991 @ SV489 ) @ SV489 ) )
| ~ ( c_lessequals @ SY4991 @ SV1223 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3840,plain,
! [SV1224: $i,SV490: $i] :
( ( ! [SY4992: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV490 ) @ ( c_List_Olist_OCons @ SV1224 @ SY4992 @ SV490 ) @ SV490 )
= ( c_List_Olist_OCons @ SV1224 @ SY4992 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3841,plain,
! [SV1225: $i,SV491: $i] :
( ( ! [SY4993: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV491 ) @ SV1225 ) @ SY4993 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV491 @ ( c_HOL_Ominus__class_Ominus @ SY4993 @ SV1225 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3842,plain,
! [SV1226: $i,SV492: $i] :
( ( ! [SY4994: $i] :
( ( c_HOL_Oord__class_Oless @ SV492 @ ( c_HOL_Ominus__class_Ominus @ SV1226 @ SY4994 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SY4994 ) @ SV1226 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3843,plain,
! [SV1227: $i,SV493: $i] :
( ( ! [SY4995: $i,SY4996: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV493 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV1227 ) @ SY4995 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SY4996 ) @ SY4995 ) @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SY4996 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3844,plain,
! [SV1228: $i,SV494: $i] :
( ( ! [SY4997: $i,SY4998: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV494 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV1228 ) @ SY4997 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SY4998 ) @ SY4997 ) @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SY4998 @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3845,plain,
! [SV1229: $i,SV495: $i] :
( ( ! [SY4999: $i,SY5000: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV495 )
| ( c_HOL_Oord__class_Oless @ SV1229 @ SY4999 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1229 ) @ SY5000 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SY4999 ) @ SY5000 ) @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3846,plain,
! [SV1230: $i,SV496: $i] :
( ( ! [SY5001: $i,SY5002: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV496 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SY5001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SY5002 ) @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SY5001 @ SY5002 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3847,plain,
! [SV1231: $i,SV497: $i] :
( ( ! [SY5003: $i,SY5004: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV497 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SY5003 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SY5004 ) @ SV497 )
| ~ ( c_HOL_Oord__class_Oless @ SY5003 @ SY5004 @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3848,plain,
! [SV1232: $i,SV498: $i] :
( ( ! [SY5005: $i,SY5006: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV498 )
| ( c_HOL_Oord__class_Oless @ SV1232 @ SY5005 @ SV498 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SY5006 ) @ SV1232 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SY5006 ) @ SY5005 ) @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3849,plain,
! [SV1233: $i,SV499: $i] :
( ( ! [SY5007: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV499 ) @ SV1233 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5007 ) @ SV1233 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV499 @ SY5007 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3850,plain,
! [SV1234: $i,SV500: $i] :
( ( ! [SY5008: $i] :
( ( c_HOL_Oord__class_Oless @ SV500 @ SV1234 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5008 ) @ SV500 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5008 ) @ SV1234 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3851,plain,
! [SV1235: $i,SV501: $i] :
( ( ! [SY5009: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SV1235 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SY5009 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1235 @ SY5009 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3852,plain,
! [SV1236: $i,SV502: $i] :
( ( ! [SY5010: $i,SY5011: $i] :
( ~ ( class_Orderings_Oorder @ SV502 )
| ( c_lessequals @ SV1236 @ SY5010 @ SV502 )
| ~ ( c_lessequals @ SV1236 @ SY5011 @ SV502 )
| ~ ( c_lessequals @ SY5011 @ SY5010 @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3853,plain,
! [SV1237: $i,SV503: $i] :
( ( ! [SY5012: $i,SY5013: $i] :
( ~ ( class_Orderings_Oorder @ SV503 )
| ( c_HOL_Oord__class_Oless @ SV1237 @ SY5012 @ SV503 )
| ~ ( c_lessequals @ SV1237 @ SY5013 @ SV503 )
| ~ ( c_HOL_Oord__class_Oless @ SY5013 @ SY5012 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3854,plain,
! [SV1238: $i,SV504: $i] :
( ( ! [SY5014: $i,SY5015: $i] :
( ~ ( class_Orderings_Oorder @ SV504 )
| ( c_HOL_Oord__class_Oless @ SV1238 @ SY5014 @ SV504 )
| ~ ( c_HOL_Oord__class_Oless @ SV1238 @ SY5015 @ SV504 )
| ~ ( c_lessequals @ SY5015 @ SY5014 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3855,plain,
! [SV1239: $i,SV505: $i] :
( ( ! [SY5016: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SV1239 ) @ SY5016 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SY5016 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SV1239 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3856,plain,
! [SV1240: $i,SV506: $i] :
( ( ! [SY5017: $i,SY5018: $i] :
( ~ ( class_Orderings_Opreorder @ SV506 )
| ( c_lessequals @ SV1240 @ SY5017 @ SV506 )
| ~ ( c_lessequals @ SY5018 @ SY5017 @ SV506 )
| ~ ( c_lessequals @ SV1240 @ SY5018 @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3857,plain,
! [SV1241: $i,SV508: $i] :
( ( ! [SY5019: $i] :
( ( c_lessequals @ SV508 @ SV1241 @ tc_nat )
| ~ ( c_lessequals @ SY5019 @ SV1241 @ tc_nat )
| ~ ( c_lessequals @ SV508 @ SY5019 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3858,plain,
! [SV1242: $i,SV510: $i] :
( ( ~ ( class_Orderings_Oorder @ SV510 )
| ( c_lessequals @ SV1242 @ SV1242 @ SV510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3859,plain,
! [SV1243: $i,SV511: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV511 )
| ( c_lessequals @ SV1243 @ SV1243 @ SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3860,plain,
! [SV1244: $i,SV512: $i] :
( ( ! [SY5020: $i,SY5021: $i] :
( ~ ( class_Orderings_Opreorder @ SV512 )
| ( c_HOL_Oord__class_Oless @ SV1244 @ SY5020 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SY5021 @ SY5020 @ SV512 )
| ~ ( c_lessequals @ SV1244 @ SY5021 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3861,plain,
! [SV1245: $i,SV513: $i] :
( ( ! [SY5022: $i,SY5023: $i] :
( ~ ( class_Orderings_Opreorder @ SV513 )
| ( c_HOL_Oord__class_Oless @ SV1245 @ SY5022 @ SV513 )
| ~ ( c_lessequals @ SY5023 @ SY5022 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ SV1245 @ SY5023 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3862,plain,
! [SV1246: $i,SV514: $i] :
( ( ! [SY5024: $i,SY5025: $i,SY5026: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
| ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SY5024 ) @ SY5025 ) @ SV514 )
| ~ ( c_lessequals @ SY5026 @ SY5025 @ SV514 )
| ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SY5024 ) @ SY5026 ) @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3863,plain,
! [SV1247: $i,SV515: $i] :
( ( ! [SY5027: $i,SY5028: $i] :
( ( c_Type_Otyping @ SV515 @ SV1247 @ SY5027 )
| ~ ( c_Lambda_Obeta @ SY5028 @ SV1247 )
| ~ ( c_Type_Otyping @ SV515 @ SY5028 @ SY5027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3864,plain,
! [SV1248: $i,SV516: $i] :
( ( ! [SY5029: $i] :
( ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SY5029 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ominus__class_Ominus @ SV1248 @ SY5029 @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3865,plain,
! [SV1249: $i,SV517: $i] :
( ( ! [SY5030: $i,SY5031: $i,SY5032: $i,SY5033: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV1249 @ SY5030 @ SY5031 ) @ SY5032 @ SY5033 @ SY5031 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SY5032 @ SY5033 @ SY5031 ) @ SV1249 @ SY5030 @ SY5031 ) )
| ( SV1249 = SY5032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3866,plain,
! [SV1250: $i,SV518: $i] :
( ( ( SV518 = SV1250 )
| ~ ( c_HOL_Oord__class_Oless @ SV518 @ ( c_Suc @ SV1250 ) @ tc_nat )
| ~ ( c_lessequals @ SV1250 @ SV518 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3867,plain,
! [SV1251: $i,SV519: $i] :
( ( ! [SY5034: $i,SY5035: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV519 @ SV1251 @ SY5034 ) @ ( c_List_Olist_OCons @ SV1251 @ SY5035 @ SY5034 ) @ SY5034 )
= ( c_List_Olist_OCons @ SV1251 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV519 @ SV1251 @ SY5034 ) @ SY5035 @ SY5034 ) @ SY5034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3868,plain,
! [SV1252: $i,SV521: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV521 @ SV1252 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1252 @ SV521 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3114]) ).
thf(3869,plain,
! [SV1253: $i,SV522: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV522 @ SV1253 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1253 @ SV522 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3870,plain,
! [SV1254: $i,SV523: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV523 @ SV1254 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV523 ) @ SV1254 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3871,plain,
! [SV1255: $i,SV524: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV524 @ ( c_Suc @ SV1255 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV524 @ SV1255 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3872,plain,
! [SV1256: $i,SV525: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV525 @ SV1256 ) @ ( tc_List_Olist @ SV1256 ) )
= ( c_Nat_Osize__class_Osize @ SV525 @ ( tc_List_Olist @ SV1256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3873,plain,
! [SV526: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV526 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV526 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV526 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3119]) ).
thf(3874,plain,
! [SV1257: $i,SV527: $i] :
( ( ! [SY5036: $i,SY5037: $i,SY5038: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV527 @ SV1257 @ SY5036 ) @ ( c_Suc @ SY5037 ) @ SY5038 @ SY5036 )
= ( c_List_Olist_OCons @ SV527 @ ( c_List_Olist__update @ SV1257 @ SY5037 @ SY5038 @ SY5036 ) @ SY5036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3875,plain,
! [SV1258: $i,SV528: $i] :
( ( ! [SY5039: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV528 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1258 ) @ SY5039 ) @ SV528 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV528 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1258 @ SV528 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY5039 @ SV528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3876,plain,
! [SV1259: $i,SV529: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1259 @ tc_nat ) @ SV529 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV529 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1259 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3877,plain,
! [SV1260: $i,SV530: $i] :
( ( ! [SY5040: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV530 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1260 @ SY5040 @ SV530 ) @ SV530 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV530 ) @ ( c_List_Olistsum @ SV1260 @ SV530 ) ) @ ( c_List_Olistsum @ SY5040 @ SV530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3878,plain,
! [SV1261: $i,SV531: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV531 ) @ ( c_HOL_Ominus__class_Ominus @ SV1261 @ SV531 @ tc_nat ) )
= SV1261 )
| ( c_HOL_Oord__class_Oless @ SV1261 @ SV531 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3879,plain,
! [SV1262: $i,SV532: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV532 @ ( c_Suc @ SV1262 ) @ tc_nat ) @ SV532 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV532 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3880,plain,
! [SV1263: $i,SV533: $i] :
( ( ! [SY5041: $i] :
( ~ ( class_Orderings_Oorder @ SV533 )
| ( c_HOL_Oord__class_Oless @ SV1263 @ SY5041 @ SV533 )
| ( SY5041 = SV1263 )
| ~ ( c_lessequals @ SV1263 @ SY5041 @ SV533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3881,plain,
! [SV1264: $i,SV534: $i] :
( ( ! [SY5042: $i] :
( ~ ( class_Orderings_Oorder @ SV534 )
| ( c_HOL_Oord__class_Oless @ SV1264 @ SY5042 @ SV534 )
| ~ ( c_lessequals @ SV1264 @ SY5042 @ SV534 )
| ( SY5042 = SV1264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3882,plain,
! [SV1265: $i,SV535: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV535 @ SV1265 @ tc_nat )
| ( SV535 = SV1265 )
| ~ ( c_lessequals @ SV535 @ SV1265 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3883,plain,
! [SV1266: $i,SV536: $i] :
( ( ( SV536 = SV1266 )
| ( c_HOL_Oord__class_Oless @ SV536 @ SV1266 @ tc_nat )
| ~ ( c_lessequals @ SV536 @ SV1266 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3884,plain,
! [SV1267: $i,SV537: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV537 @ SV1267 @ tc_nat )
| ( SV537 = SV1267 )
| ~ ( c_lessequals @ SV537 @ SV1267 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3885,plain,
! [SV1268: $i,SV538: $i] :
( ( ! [SY5043: $i] :
( ~ ( class_Orderings_Oorder @ SV538 )
| ( SV1268 = SY5043 )
| ( c_HOL_Oord__class_Oless @ SV1268 @ SY5043 @ SV538 )
| ~ ( c_lessequals @ SV1268 @ SY5043 @ SV538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3886,plain,
! [SV1269: $i,SV539: $i] :
( ( ! [SY5044: $i] :
( ~ ( class_Orderings_Oorder @ SV539 )
| ( c_HOL_Oord__class_Oless @ SV1269 @ SY5044 @ SV539 )
| ( SV1269 = SY5044 )
| ~ ( c_lessequals @ SV1269 @ SY5044 @ SV539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3887,plain,
! [SV1270: $i,SV540: $i] :
( ( ! [SY5045: $i] :
( ~ ( class_Orderings_Oorder @ SV540 )
| ( c_HOL_Oord__class_Oless @ SV1270 @ SY5045 @ SV540 )
| ( SV1270 = SY5045 )
| ~ ( c_lessequals @ SV1270 @ SY5045 @ SV540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(3888,plain,
! [SV1271: $i,SV541: $i] :
( ( ! [SY5046: $i] :
( ~ ( class_Orderings_Oorder @ SV541 )
| ( c_HOL_Oord__class_Oless @ SV1271 @ SY5046 @ SV541 )
| ~ ( c_lessequals @ SV1271 @ SY5046 @ SV541 )
| ( SV1271 = SY5046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3889,plain,
! [SV1272: $i,SV542: $i] :
( ( ! [SY5047: $i] :
( ~ ( class_Orderings_Olinorder @ SV542 )
| ( SV1272 = SY5047 )
| ~ ( c_lessequals @ SV1272 @ SY5047 @ SV542 )
| ( c_HOL_Oord__class_Oless @ SV1272 @ SY5047 @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3890,plain,
! [SV1273: $i,SV543: $i] :
( ( ! [SY5048: $i] :
( ~ ( class_Orderings_Olinorder @ SV543 )
| ( SV1273 = SY5048 )
| ( c_HOL_Oord__class_Oless @ SV1273 @ SY5048 @ SV543 )
| ~ ( c_lessequals @ SV1273 @ SY5048 @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3891,plain,
! [SV1274: $i,SV545: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ SV545 ) ) @ SV1274 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV545 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1274 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3892,plain,
! [SV1275: $i,SV546: $i] :
( ( ! [SY5049: $i,SY5050: $i,SY5051: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV546 @ SV1275 @ SY5049 @ SY5050 ) @ SV1275 @ SY5051 @ SY5050 )
= ( c_List_Olist__update @ SV546 @ SV1275 @ SY5051 @ SY5050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3893,plain,
! [SV1276: $i,SV547: $i] :
( ( ( c_lessequals @ SV547 @ SV1276 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV547 ) @ ( c_Suc @ SV1276 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3894,plain,
! [SV1277: $i,SV548: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV548 ) @ ( c_Suc @ SV1277 ) @ tc_nat )
| ~ ( c_lessequals @ SV548 @ SV1277 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3895,plain,
! [SV1278: $i,SV549: $i] :
( ( ! [SY5052: $i,SY5053: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV549 @ SV1278 @ SY5052 ) @ SY5053 @ SY5052 )
= ( c_List_Oappend @ SV549 @ ( c_List_Oappend @ SV1278 @ SY5053 @ SY5052 ) @ SY5052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(3896,plain,
! [SV1279: $i,SV550: $i] :
( ( ! [SY5054: $i,SY5055: $i] :
( ( c_List_Oappend @ SV550 @ ( c_List_Oappend @ SV1279 @ SY5054 @ SY5055 ) @ SY5055 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV550 @ SV1279 @ SY5055 ) @ SY5054 @ SY5055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3897,plain,
! [SV1280: $i,SV551: $i] :
( ( ! [SY5056: $i,SY5057: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV551 @ SV1280 @ SY5056 ) @ SY5057 @ SY5056 )
= ( c_List_Oappend @ SV551 @ ( c_List_Oappend @ SV1280 @ SY5057 @ SY5056 ) @ SY5056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3898,plain,
! [SV1281: $i,SV552: $i] :
( ( ! [SY5058: $i,SY5059: $i] :
( ( c_List_Oappend @ SV552 @ ( c_List_Oappend @ SV1281 @ SY5058 @ SY5059 ) @ SY5059 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV552 @ SV1281 @ SY5059 ) @ SY5058 @ SY5059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3899,plain,
! [SV1282: $i,SV553: $i] :
( ( ! [SY5060: $i] :
( ~ ( class_Orderings_Oorder @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV1282 @ SY5060 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SY5060 @ SV1282 @ SV553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3900,plain,
! [SV1283: $i,SV554: $i] :
( ( ! [SY5061: $i] :
( ~ ( class_Orderings_Olinorder @ SV554 )
| ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SY5061 @ SV554 )
| ~ ( c_HOL_Oord__class_Oless @ SY5061 @ SV1283 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3901,plain,
! [SV1284: $i,SV555: $i] :
( ( ( c_lessequals @ SV555 @ SV1284 @ tc_nat )
| ( c_lessequals @ SV1284 @ SV555 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3902,plain,
! [SV1285: $i,SV556: $i] :
( ( ! [SY5062: $i] :
( ~ ( class_Orderings_Olinorder @ SV556 )
| ( c_lessequals @ SV1285 @ SY5062 @ SV556 )
| ( c_lessequals @ SY5062 @ SV1285 @ SV556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3903,plain,
! [SV1286: $i,SV557: $i] :
( ( ! [SY5063: $i] :
( ~ ( class_Orderings_Opreorder @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ SV1286 @ SY5063 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ SY5063 @ SV1286 @ SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3904,plain,
! [SV1287: $i,SV558: $i] :
( ( ! [SY5064: $i] :
( ~ ( class_Orderings_Opreorder @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ SV1287 @ SY5064 @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ SY5064 @ SV1287 @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3905,plain,
! [SV1288: $i,SV559: $i] :
( ( ( hBOOL @ ( hAPP @ SV559 @ SV1288 ) )
| ( hBOOL @ ( hAPP @ SV559 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV559 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV559 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3906,plain,
! [SV560: $i] :
( ( c_HOL_Oord__class_Oless @ SV560 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3907,plain,
! [SV561: $i] :
( ( c_HOL_Oord__class_Oless @ SV561 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3154]) ).
thf(3908,plain,
! [SV1289: $i,SV562: $i] :
( ( ( hBOOL @ ( hAPP @ SV562 @ SV1289 ) )
| ( hBOOL @ ( hAPP @ SV562 @ ( v_sko__List__Xupt__Xinduct__1 @ SV562 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV562 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3909,plain,
! [SV1290: $i,SV563: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV563 @ SV1290 )
= SV563 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3910,plain,
! [SV1291: $i,SV565: $i] :
( ( ( hBOOL @ ( hAPP @ SV565 @ SV1291 ) )
| ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV565 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3911,plain,
! [SV1292: $i,SV568: $i] :
( ( ! [SY5065: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV568 @ SV1292 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5065 @ SV1292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3912,plain,
! [SV1293: $i,SV574: $i] :
( ( ! [SY5066: $i,SY5067: $i,SY5068: $i,SY5069: $i,SY5070: $i] :
( ( ( hAPP @ ( hAPP @ SV574 @ SV1293 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SY5066 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5067 @ SY5068 @ SV574 @ SY5069 @ SY5066 @ SY5070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3913,plain,
! [SV1294: $i,SV575: $i] :
( ( ! [SY5071: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV575 )
| ( ( c_List_Olistsum @ ( c_List_Omap @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV575 @ SV1294 ) @ SY5071 @ SV1294 @ SV575 ) @ SV575 )
= ( c_HOL_Ozero__class_Ozero @ SV575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3914,plain,
! [SV1295: $i,SV576: $i] :
( ( ! [SY5072: $i] :
( ( c_Lambda_Osubstn @ SV576 @ SV1295 @ SY5072 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV576 ) @ ( c_Lambda_Oliftn @ SY5072 @ SV1295 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SY5072 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3915,plain,
! [SV1296: $i,SV577: $i] :
( ( ! [SY5073: $i,SY5074: $i,SY5075: $i] :
( ( c_List_Odrop @ SV577 @ ( c_List_Omap @ SV1296 @ SY5073 @ SY5074 @ SY5075 ) @ SY5075 )
= ( c_List_Omap @ SV1296 @ ( c_List_Odrop @ SV577 @ SY5073 @ SY5074 ) @ SY5074 @ SY5075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3916,plain,
! [SV1297: $i,SV578: $i] :
( ( ! [SY5076: $i,SY5077: $i] :
( ( c_List_Odistinct @ SV578 @ SV1297 )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ SY5076 @ SV578 @ SV1297 @ SY5077 ) @ SY5077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3917,plain,
! [SV1298: $i,SV579: $i] :
( ( ! [SY5078: $i,SY5079: $i,SY5080: $i] :
( ( c_List_Omap @ SV579 @ ( c_List_Oappend @ SV1298 @ SY5078 @ SY5079 ) @ SY5079 @ SY5080 )
= ( c_List_Oappend @ ( c_List_Omap @ SV579 @ SV1298 @ SY5079 @ SY5080 ) @ ( c_List_Omap @ SV579 @ SY5078 @ SY5079 @ SY5080 ) @ SY5080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(3918,plain,
! [SV1299: $i,SV580: $i] :
( ( ! [SY5081: $i,SY5082: $i,SY5083: $i] :
( ( c_List_Omap @ SV580 @ ( c_List_Oreplicate @ SV1299 @ SY5081 @ SY5082 ) @ SY5082 @ SY5083 )
= ( c_List_Oreplicate @ SV1299 @ ( hAPP @ SV580 @ SY5081 ) @ SY5083 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3919,plain,
! [SV1300: $i,SV581: $i] :
( ( ! [SY5084: $i,SY5085: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV581 @ SV1300 @ SY5084 @ SY5085 ) @ ( tc_List_Olist @ SY5085 ) )
= ( c_Nat_Osize__class_Osize @ SV1300 @ ( tc_List_Olist @ SY5084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3920,plain,
! [SV1301: $i,SV582: $i] :
( ( ! [SY5086: $i,SY5087: $i,SY5088: $i] :
( ( c_List_Orotate @ SV582 @ ( c_List_Omap @ SV1301 @ SY5086 @ SY5087 @ SY5088 ) @ SY5088 )
= ( c_List_Omap @ SV1301 @ ( c_List_Orotate @ SV582 @ SY5086 @ SY5087 ) @ SY5087 @ SY5088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3921,plain,
! [SV1302: $i,SV583: $i] :
( ( ! [SY5089: $i,SY5090: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV583 @ SV1302 @ SY5089 @ SY5090 ) @ SY5090 )
= ( c_List_Omap @ SV583 @ ( c_List_Orev @ SV1302 @ SY5089 ) @ SY5089 @ SY5090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3922,plain,
! [SV1303: $i,SV584: $i] :
( ( ! [SY5091: $i,SY5092: $i,SY5093: $i] :
( ( c_List_Otake @ SV584 @ ( c_List_Omap @ SV1303 @ SY5091 @ SY5092 @ SY5093 ) @ SY5093 )
= ( c_List_Omap @ SV1303 @ ( c_List_Otake @ SV584 @ SY5091 @ SY5092 ) @ SY5092 @ SY5093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3923,plain,
! [SV1304: $i,SV585: $i] :
( ( ! [SY5094: $i] :
( ( c_List_Omap @ SV585 @ ( c_List_Olist_ONil @ SV1304 ) @ SV1304 @ SY5094 )
= ( c_List_Olist_ONil @ SY5094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3924,plain,
! [SV1305: $i,SV586: $i] :
( ( ! [SY5095: $i,SY5096: $i,SY5097: $i,SY5098: $i] :
( ( c_List_Omap @ SV586 @ ( c_List_Omap @ SV1305 @ SY5095 @ SY5096 @ SY5097 ) @ SY5097 @ SY5098 )
= ( c_List_Omap @ ( c_Fun_Ocomp @ SV586 @ SV1305 @ SY5097 @ SY5098 @ SY5096 ) @ SY5095 @ SY5096 @ SY5098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3925,plain,
! [SV1306: $i,SV587: $i] :
( ( ! [SY5099: $i,SY5100: $i,SY5101: $i] :
( ( c_List_Omap @ SV587 @ ( c_List_Olist_OCons @ SV1306 @ SY5099 @ SY5100 ) @ SY5100 @ SY5101 )
= ( c_List_Olist_OCons @ ( hAPP @ SV587 @ SV1306 ) @ ( c_List_Omap @ SV587 @ SY5099 @ SY5100 @ SY5101 ) @ SY5101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3926,plain,
! [SV1307: $i,SV588: $i] :
( ( ! [SY5102: $i,SY5103: $i,SY5104: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV588 @ SV1307 ) @ ( c_List_Omap @ SV588 @ SY5102 @ SY5103 @ SY5104 ) @ SY5104 )
= ( c_List_Omap @ SV588 @ ( c_List_Olist_OCons @ SV1307 @ SY5102 @ SY5103 ) @ SY5103 @ SY5104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3927,plain,
! [SV1308: $i,SV589: $i] :
( ( ! [SY5105: $i,SY5106: $i,SY5107: $i] :
( ( c_List_Omap @ SV589 @ ( c_List_Olist_OCons @ SV1308 @ SY5105 @ SY5106 ) @ SY5106 @ SY5107 )
= ( c_List_Olist_OCons @ ( hAPP @ SV589 @ SV1308 ) @ ( c_List_Omap @ SV589 @ SY5105 @ SY5106 @ SY5107 ) @ SY5107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3928,plain,
! [SV1309: $i,SV590: $i] :
( ( ! [SY5108: $i,SY5109: $i,SY5110: $i,SY5111: $i] :
( ( c_List_Omap @ SV590 @ ( c_List_Olist__update @ SV1309 @ SY5108 @ SY5109 @ SY5110 ) @ SY5110 @ SY5111 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV590 @ SV1309 @ SY5110 @ SY5111 ) @ SY5108 @ ( hAPP @ SV590 @ SY5109 ) @ SY5111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3929,plain,
! [SV1310: $i,SV591: $i] :
( ( ! [SY5112: $i] :
( ( c_List_Olist_ONil @ SV591 )
= ( c_List_Omap @ SV1310 @ ( c_List_Olist_ONil @ SY5112 ) @ SY5112 @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3930,plain,
! [SV1311: $i,SV592: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV592 )
| ( ( c_List_Olistsum @ SV1311 @ SV592 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV592 ) @ SV1311 @ ( c_HOL_Ozero__class_Ozero @ SV592 ) @ SV592 @ SV592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3931,plain,
! [SV1312: $i,SV593: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV593 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV593 ) @ ( c_HOL_Ozero__class_Ozero @ SV593 ) @ SV1312 @ SV593 @ SV593 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV593 ) @ SV1312 @ ( c_HOL_Ozero__class_Ozero @ SV593 ) @ SV593 @ SV593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3932,plain,
! [SV1313: $i,SV594: $i] :
( ( ! [SY5113: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV594 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1313 @ SY5113 @ SV594 @ SV594 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1313 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SY5113 @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV594 @ SV594 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3933,plain,
! [SV1314: $i,SV595: $i] :
( ( ! [SY5114: $i,SY5115: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV595 ) @ SV1314 ) ) @ SY5114 ) @ SY5115 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV595 ) @ SY5114 ) @ SY5115 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1314 ) @ SY5114 ) @ SY5115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3934,plain,
! [SV1315: $i,SV596: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV596 ) ) @ SV1315 ) @ SV596 )
= SV1315 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3935,plain,
! [SV1316: $i,SV597: $i] :
( ( ! [SY5116: $i,SY5117: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV597 ) @ SV1316 ) @ SY5116 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY5117 ) @ SV1316 ) @ SY5116 ) )
| ~ ( c_Lambda_Obeta @ SV597 @ SY5117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3936,plain,
! [SV1317: $i,SV598: $i] :
( ( ! [SY5118: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV598 ) ) @ SV1317 ) @ SY5118 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV598 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1317 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5118 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3937,plain,
! [SV1318: $i,SV599: $i] :
( ( ! [SY5119: $i,SY5120: $i,SY5121: $i] :
( ( c_List_Ofoldr @ SV599 @ SV1318 @ SY5119 @ SY5120 @ SY5121 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV599 @ SY5120 @ SY5121 @ SY5121 ) @ SY5119 @ ( c_List_Orev @ SV1318 @ SY5120 ) @ SY5121 @ SY5120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3938,plain,
! [SV1319: $i,SV600: $i] :
( ( ! [SY5122: $i,SY5123: $i,SY5124: $i] :
( ( c_List_Ofoldl @ SV600 @ SV1319 @ SY5122 @ SY5123 @ SY5124 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV600 @ SY5123 @ SY5124 @ SY5123 ) @ ( c_List_Orev @ SY5122 @ SY5124 ) @ SV1319 @ SY5124 @ SY5123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3939,plain,
! [SV1320: $i,SV601: $i] :
( ( ! [SY5125: $i,SY5126: $i,SY5127: $i] :
( ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5125 ) @ SY5126 ) @ SY5127 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV1320 @ SY5125 ) @ SY5126 ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ SY5125 @ SY5127 ) ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ SY5126 @ SY5127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3194]) ).
thf(3940,plain,
! [SV1321: $i,SV602: $i] :
( ( ! [SY5128: $i,SY5129: $i,SY5130: $i] :
( ( c_Type_Otype_Otype__case @ SV602 @ SV1321 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5128 ) @ SY5129 ) @ SY5130 )
= ( hAPP @ ( hAPP @ SV1321 @ SY5128 ) @ SY5129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3941,plain,
! [SV1322: $i,SV603: $i] :
( ( ! [SY5131: $i,SY5132: $i,SY5133: $i] :
( ~ ( hBOOL @ ( hAPP @ SV603 @ ( c_Type_Otype_Otype__case @ SV1322 @ SY5131 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5132 ) @ SY5133 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV603 @ ( hAPP @ ( hAPP @ SY5131 @ SY5132 ) @ SY5133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(3942,plain,
! [SV1323: $i,SV604: $i] :
( ( ! [SY5134: $i,SY5135: $i,SY5136: $i] :
( ~ ( hBOOL @ ( hAPP @ SV604 @ ( c_Type_Otype_Otype__case @ SV1323 @ SY5134 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5135 ) @ SY5136 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV604 @ ( hAPP @ ( hAPP @ SY5134 @ SY5135 ) @ SY5136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3943,plain,
! [SV1324: $i,SV605: $i] :
( ( ! [SY5137: $i,SY5138: $i,SY5139: $i,SY5140: $i] :
( ( c_List_Ofoldr @ SV605 @ ( c_List_Olist_OCons @ SV1324 @ SY5137 @ SY5138 ) @ SY5139 @ SY5138 @ SY5140 )
= ( hAPP @ ( hAPP @ SV605 @ SV1324 ) @ ( c_List_Ofoldr @ SV605 @ SY5137 @ SY5139 @ SY5138 @ SY5140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3944,plain,
! [SV1325: $i,SV606: $i] :
( ( ! [SY5141: $i,SY5142: $i,SY5143: $i,SY5144: $i] :
( ( c_List_Ofoldr @ SV606 @ ( c_List_Oappend @ SV1325 @ SY5141 @ SY5142 ) @ SY5143 @ SY5142 @ SY5144 )
= ( c_List_Ofoldr @ SV606 @ SV1325 @ ( c_List_Ofoldr @ SV606 @ SY5141 @ SY5143 @ SY5142 @ SY5144 ) @ SY5142 @ SY5144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3945,plain,
! [SV1326: $i,SV607: $i] :
( ( ! [SY5145: $i,SY5146: $i] :
( ( c_List_Ofoldr @ SV607 @ ( c_List_Olist_ONil @ SV1326 ) @ SY5145 @ SV1326 @ SY5146 )
= SY5145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3946,plain,
! [SV1327: $i,SV608: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV608 ) @ SV1327 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3947,plain,
! [SV1328: $i,SV609: $i] :
( ( ! [SY5147: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SV1328 ) ) @ SY5147 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV609 ) @ SY5147 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1328 ) @ SY5147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3948,plain,
! [SV1329: $i,SV610: $i] :
( ( ! [SY5148: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV610 ) @ SV1329 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY5148 ) @ SV1329 ) )
| ~ ( c_Lambda_Obeta @ SV610 @ SY5148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3949,plain,
! [SV1330: $i,SV611: $i] :
( ( ! [SY5149: $i,SY5150: $i,SY5151: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV611 @ SV1330 @ SY5149 @ SY5150 ) @ SY5151 )
= ( hAPP @ SV611 @ SY5151 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5151 @ SV1330 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(3950,plain,
! [SV1331: $i,SV612: $i] :
( ( ! [SY5152: $i,SY5153: $i,SY5154: $i] :
( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1331 @ SY5152 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5153 )
| ~ ( c_Type_Otypings @ SV612 @ SY5152 @ SY5154 )
| ~ ( c_Type_Otyping @ SV612 @ SV1331 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY5154 @ SY5153 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(3951,plain,
! [SV1332: $i,SV613: $i] :
( ( ! [SY5155: $i,SY5156: $i] :
( ( c_Type_Otyping @ SV613 @ ( c_Lambda_OdB_OAbs @ SV1332 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5155 ) @ SY5156 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV613 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5155 @ tc_Type_Otype ) @ SV1332 @ SY5156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3952,plain,
! [SV1333: $i,SV614: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV614 )
| ~ ( class_Power_Opower @ SV614 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3953,plain,
! [SV1334: $i,SV615: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV615 )
| ~ ( class_Power_Opower @ SV615 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV615 ) @ SV1334 @ SV615 )
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
| ( SV1334
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3954,plain,
! [SV616: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV616 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
= ( c_HOL_Ozero__class_Ozero @ SV616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3209]) ).
thf(3955,plain,
! [SV1335: $i,SV617: $i] :
( ( ( c_Lambda_Osubstn @ SV617 @ SV1335 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV617 ) @ SV1335 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3956,plain,
! [SV1336: $i,SV618: $i] :
( ( ! [SY5157: $i,SY5158: $i,SY5159: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ SV1336 @ SY5157 @ SY5158 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5159 @ SY5158 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5159 @ SY5158 ) @ ( c_Suc @ SV1336 ) @ SY5157 @ SY5158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3957,plain,
! [SV1337: $i,SV619: $i] :
( ( ! [SY5160: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV619 @ SV1337 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY5160 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV619 ) @ SY5160 ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY5160 ) @ SV1337 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3958,plain,
! [SV1338: $i,SV620: $i] :
( ( ! [SY5161: $i,SY5162: $i,SY5163: $i,SY5164: $i,SY5165: $i] :
( ( c_List_Ofoldr @ SV620 @ ( c_List_Omap @ SV1338 @ SY5161 @ SY5162 @ SY5163 ) @ SY5164 @ SY5163 @ SY5165 )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ SV620 @ SV1338 @ SY5163 @ ( tc_fun @ SY5165 @ SY5165 ) @ SY5162 ) @ SY5161 @ SY5164 @ SY5162 @ SY5165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3959,plain,
! [SV1339: $i,SV621: $i] :
( ( ! [SY5166: $i,SY5167: $i,SY5168: $i,SY5169: $i] :
( ~ ( c_Type_Otyping @ SV621 @ SV1339 @ SY5166 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SY5167 @ SY5166 @ tc_Type_Otype ) @ SY5168 @ SY5169 )
| ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY5168 ) @ SV1339 ) @ SY5167 ) @ SY5169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3960,plain,
! [SV1340: $i,SV622: $i] :
( ( ! [SY5170: $i,SY5171: $i,SY5172: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV622 @ SV1340 @ SY5170 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY5171 ) @ SV1340 ) @ SY5172 )
| ~ ( c_Type_Otyping @ SV622 @ SY5171 @ SY5172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3961,plain,
! [SV623: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV623 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV623 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3962,plain,
! [SV1341: $i,SV624: $i] :
( ( ! [SY5173: $i,SY5174: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV624 @ SV1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY5173 ) @ SY5174 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV624 ) @ SY5173 ) @ SY5174 ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY5173 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY5174 ) @ SV1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3963,plain,
! [SV1342: $i,SV625: $i] :
( ( ! [SY5175: $i,SY5176: $i,SY5177: $i,SY5178: $i] :
( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY5175 ) @ SY5176 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5177 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SY5175 @ SY5178 @ tc_Type_Otype ) @ SY5176 @ SY5177 )
| ~ ( c_Type_Otyping @ SV625 @ SV1342 @ SY5178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3964,plain,
! [SV1343: $i,SV626: $i] :
( ( ! [SY5179: $i,SY5180: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV626 @ SV1343 @ SY5179 @ SY5180 ) @ SV1343 )
= SY5179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3965,plain,
! [SV1344: $i,SV627: $i] :
( ( ! [SY5181: $i,SY5182: $i,SY5183: $i,SY5184: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV627 @ SV1344 @ SY5181 @ SY5182 ) @ SY5183 ) @ SY5184 )
= ( hAPP @ ( hAPP @ SV627 @ SY5184 ) @ SY5183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3966,plain,
! [SV1345: $i,SV628: $i] :
( ( ! [SY5185: $i,SY5186: $i,SY5187: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV628 @ SV1345 @ SY5185 @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1345 ) @ SY5186 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5187 )
| ~ ( c_Type_Otypings @ SV628 @ SY5186 @ SY5187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3967,plain,
! [SV1346: $i,SV629: $i] :
( ( ! [SY5188: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV629 ) @ SV1346 ) ) @ SY5188 ) @ SV1346 )
= SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3968,plain,
! [SV1347: $i,SV630: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV630 @ SV1347 ) )
| ~ ( class_Orderings_Opreorder @ SV1347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3969,plain,
! [SV1348: $i,SV631: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV631 @ SV1348 ) )
| ~ ( class_Orderings_Oorder @ SV1348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3970,plain,
! [SV1349: $i,SV632: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV632 @ SV1349 ) )
| ~ ( class_Orderings_Obot @ SV1349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3971,plain,
! [SV1350: $i,SV633: $i] :
( ( ! [SY5189: $i,SY5190: $i,SY5191: $i,SY5192: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV633 @ SV1350 @ SY5189 @ SY5190 ) @ SY5191 ) @ SY5192 )
= ( hAPP @ ( hAPP @ SV633 @ SY5192 ) @ SY5191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3972,plain,
! [SV1351: $i,SV634: $i] :
( ( ! [SY5193: $i,SY5194: $i,SY5195: $i,SY5196: $i] :
( ( c_COMBB @ SV634 @ SV1351 @ SY5193 @ SY5194 @ SY5195 @ SY5196 )
= ( hAPP @ SV634 @ ( hAPP @ SV1351 @ SY5193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3973,plain,
! [SV1352: $i,SV635: $i] :
( ( c_fequal @ SV635 @ SV635 @ SV1352 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3974,plain,
! [SV1353: $i,SV636: $i] :
( ( ! [SY5197: $i] :
( ( SV636 = SV1353 )
| ~ ( c_fequal @ SV636 @ SV1353 @ SY5197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(3975,plain,
! [SV1354: $i,SV637: $i] :
( ( ! [SY5198: $i,SY5199: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV637 )
| ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SY5198 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SY5199 ) )
| ( SY5198 = SY5199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3976,plain,
! [SV1355: $i,SV638: $i] :
( ( ! [SY5200: $i] :
( ( SV638
!= ( c_List_Oappend @ SV638 @ SV1355 @ SY5200 ) )
| ( SV1355
= ( c_List_Olist_ONil @ SY5200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3977,plain,
! [SV1356: $i,SV639: $i] :
( ( ! [SY5201: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV639 )
| ( ( c_Power_Opower__class_Opower @ SV1356 @ SY5201 @ SV639 )
!= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
| ( SV1356
= ( c_HOL_Ozero__class_Ozero @ SV639 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3978,plain,
! [SV1357: $i,SV640: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV640 @ SV1357 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV640 @ SV1357 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3979,plain,
! [SV1358: $i,SV641: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV641 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV641 ) @ SV1358 ) @ SV1358 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1358
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3980,plain,
! [SV1359: $i,SV642: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV642 @ ( tc_List_Olist @ SV1359 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV642
= ( c_List_Olist_ONil @ SV1359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3981,plain,
! [SV1360: $i,SV643: $i] :
( ( ! [SY5202: $i,SY5203: $i,SY5204: $i] :
( ( ( c_List_Omap @ SV643 @ SV1360 @ SY5202 @ SY5203 )
!= ( c_List_Omap @ SV643 @ SY5204 @ SY5202 @ SY5203 ) )
| ( ( c_Nat_Osize__class_Osize @ SV1360 @ ( tc_List_Olist @ SY5202 ) )
= ( c_Nat_Osize__class_Osize @ SY5204 @ ( tc_List_Olist @ SY5202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3982,plain,
! [SV1361: $i,SV644: $i] :
( ( ! [SY5205: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SY5205 )
!= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SY5205 @ SV644 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
| ( SY5205
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3983,plain,
! [SV1362: $i,SV645: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV645 @ SV1362 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV1362 @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1362 = SV645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3984,plain,
! [SV1363: $i,SV646: $i] :
( ( ! [SY5206: $i,SY5207: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV646 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SY5206 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SY5207 ) )
| ( SY5206 = SY5207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3985,plain,
! [SV1364: $i,SV647: $i] :
( ( ! [SY5208: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV647 )
| ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SV1364 @ SY5208 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3986,plain,
! [SV1365: $i,SV648: $i] :
( ( ! [SY5209: $i,SY5210: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV648 ) @ SV1365 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY5209 ) @ SY5210 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV648 = SY5209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3987,plain,
! [SV1366: $i,SV649: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV649 ) @ SV1366 )
!= SV649 )
| ( SV1366
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3988,plain,
! [SV1367: $i,SV650: $i] :
( ( ! [SY5211: $i] :
( ( ( c_List_Oappend @ SV650 @ SV1367 @ SY5211 )
!= SV650 )
| ( SV1367
= ( c_List_Olist_ONil @ SY5211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3989,plain,
! [SV1368: $i,SV651: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV651 ) @ SV1368 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV651
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV651
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3990,plain,
! [SV1369: $i,SV652: $i] :
( ( ! [SY5212: $i,SY5213: $i] :
( ( ( c_List_Olist_ONil @ SV652 )
!= ( c_List_Omap @ SV1369 @ SY5212 @ SY5213 @ SV652 ) )
| ( SY5212
= ( c_List_Olist_ONil @ SY5213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3991,plain,
! [SV1370: $i,SV653: $i] :
( ( ! [SY5214: $i,SY5215: $i,SY5216: $i] :
( ( ( c_List_Oappend @ SV653 @ SV1370 @ SY5214 )
!= ( c_List_Oappend @ SY5215 @ SY5216 @ SY5214 ) )
| ( SV1370
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SY5214 ) ) @ SY5215 @ SY5214 ) @ SY5216 @ SY5214 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SY5214 ) ) @ ( c_Nat_Osize__class_Osize @ SY5215 @ ( tc_List_Olist @ SY5214 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3992,plain,
! [SV1371: $i,SV654: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV654 ) @ SV1371 ) )
| ( SV1371
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV654
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3993,plain,
! [SV1372: $i,SV655: $i] :
( ( ! [SY5217: $i,SY5218: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SY5217 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY5217 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SY5218 @ SV1372 ) @ SV1372 )
!= SY5218 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SY5217 @ SV1372 )
!= SV655 )
| ( SY5217
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY5217 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
| ( ( c_List_Oappend @ SY5217 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY5217 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SY5218 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SY5218 @ SV1372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3994,plain,
! [SV1373: $i,SV656: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV656 ) @ SV1373 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV656
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1373
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3995,plain,
! [SV1374: $i,SV657: $i] :
( ( ! [SY5219: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV657 @ SV1374 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY5219 @ SV1374 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV657 = SY5219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(3996,plain,
! [SV658: $i] :
( ( SV658
= ( c_Suc @ SV658 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3997,plain,
! [SV1375: $i,SV659: $i] :
( ( ! [SY5220: $i,SY5221: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV659 )
| ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SY5220 ) @ SV659 )
!= ( c_Power_Opower__class_Opower @ SY5221 @ ( c_Suc @ SY5220 ) @ SV659 ) )
| ( SV1375 = SY5221 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SY5221 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(3998,plain,
! [SV1376: $i,SV660: $i] :
( ( ! [SY5222: $i,SY5223: $i,SY5224: $i,SY5225: $i,SY5226: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY5222 ) @ SY5223 ) @ SY5224 ) ) )
| ~ ( c_Type_Otyping @ SY5225 @ SY5223 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY5223 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY5225 @ SY5224 @ SV1376 @ tc_Type_Otype ) @ SY5222 @ SY5226 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY5222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(3999,plain,
! [SV1377: $i,SV661: $i] :
( ( ( SV661
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV661 ) @ SV1377 ) )
| ( SV1377
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(4000,plain,
! [SV1378: $i,SV662: $i] :
( ( ! [SY5227: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV662 ) @ SV1378 )
!= ( c_Lambda_OdB_OVar @ SY5227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(4001,plain,
! [SV1379: $i,SV663: $i] :
( ( ! [SY5228: $i] :
( ( c_Lambda_OdB_OVar @ SV663 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1379 ) @ SY5228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3257]) ).
thf(4002,plain,
! [SV1380: $i,SV664: $i] :
( ( ! [SY5229: $i] :
( ( ( c_List_Olist_ONil @ SV664 )
!= ( c_List_Oreplicate @ SV1380 @ SY5229 @ SV664 ) )
| ( SV1380
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3258]) ).
thf(4003,plain,
! [SV1381: $i,SV665: $i] :
( ( ! [SY5230: $i,SY5231: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV665 )
| ( ( c_Power_Opower__class_Opower @ SV1381 @ SY5230 @ SV665 )
!= ( c_Power_Opower__class_Opower @ SV1381 @ SY5231 @ SV665 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 )
| ( SY5230 = SY5231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(4004,plain,
! [SV1382: $i,SV666: $i] :
( ( ! [SY5232: $i] :
( ( ( hAPP @ SV666 @ ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SV1382 @ SY5232 ) )
!= ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SV1382 @ SY5232 ) )
| ( ( c_List_Omap @ SV666 @ SV1382 @ SY5232 @ SY5232 )
= SV1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3260]) ).
thf(4005,plain,
! [SV1383: $i,SV667: $i] :
( ( ! [SY5233: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV667 ) @ SV1383 )
!= ( c_Lambda_OdB_OAbs @ SY5233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3261]) ).
thf(4006,plain,
! [SV1384: $i,SV668: $i] :
( ( ! [SY5234: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV668 )
| ~ ( class_Int_Onumber__ring @ SV668 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1384 @ SY5234 @ SV668 )
!= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
| ( SV1384 = SY5234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(4007,plain,
! [SV1385: $i,SV669: $i] :
( ( ! [SY5235: $i] :
( ( c_Type_Otype_OAtom @ SV669 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1385 ) @ SY5235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(4008,plain,
! [SV1386: $i,SV670: $i] :
( ( ! [SY5236: $i,SY5237: $i,SY5238: $i] :
( ( ( c_List_Oappend @ SV670 @ SV1386 @ SY5236 )
!= ( c_List_Oappend @ SY5237 @ SY5238 @ SY5236 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY5237 @ ( tc_List_Olist @ SY5236 ) ) @ SV670 @ SY5236 )
= SY5237 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV670 @ ( tc_List_Olist @ SY5236 ) ) @ ( c_Nat_Osize__class_Osize @ SY5237 @ ( tc_List_Olist @ SY5236 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(4009,plain,
! [SV671: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV671 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV671 )
!= ( c_HOL_Ozero__class_Ozero @ SV671 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(4010,plain,
! [SV1387: $i,SV672: $i] :
( ( ! [SY5239: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV672 ) @ SV1387 )
!= ( c_Type_Otype_OAtom @ SY5239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(4011,plain,
! [SV1388: $i,SV673: $i] :
( ( ! [SY5240: $i,SY5241: $i,SY5242: $i,SY5243: $i,SY5244: $i,SY5245: $i,SY5246: $i,SY5247: $i,SY5248: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SY5240 ) )
!= ( hAPP @ SY5241 @ ( hAPP @ SY5242 @ SY5243 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SY5244 @ SY5245 @ SY5246 ) @ SY5240 )
= ( hAPP @ ( c_Fun_Ocomp @ SY5241 @ SY5242 @ SY5247 @ SY5245 @ SY5248 ) @ SY5243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(4012,plain,
! [SV1389: $i,SV674: $i] :
( ( ! [SY5249: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV674 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1389 @ SV674 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY5249 @ SV674 ) )
| ( SV1389 = SY5249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(4013,plain,
! [SV1390: $i,SV675: $i] :
( ( ( ( c_List_Olist_ONil @ SV675 )
!= ( c_List_Orev @ SV1390 @ SV675 ) )
| ( SV1390
= ( c_List_Olist_ONil @ SV675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(4014,plain,
! [SV1391: $i,SV676: $i] :
( ( ! [SY5250: $i,SY5251: $i] :
( ( ( c_List_Oappend @ SV676 @ SV1391 @ SY5250 )
!= ( c_List_Oappend @ SV676 @ SY5251 @ SY5250 ) )
| ( SV1391 = SY5251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(4015,plain,
! [SV1392: $i,SV677: $i] :
( ( ! [SY5252: $i] :
( ( ( c_List_Otake @ SV677 @ SV1392 @ SY5252 )
!= ( c_List_Olist_ONil @ SY5252 ) )
| ( SV1392
= ( c_List_Olist_ONil @ SY5252 ) )
| ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(4016,plain,
! [SV1393: $i,SV678: $i] :
( ( ! [SY5253: $i,SY5254: $i,SY5255: $i,SY5256: $i,SY5257: $i,SY5258: $i,SY5259: $i] :
( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SY5253 @ SY5254 @ SY5255 )
!= ( c_Fun_Ocomp @ SY5256 @ SY5257 @ SY5258 @ SY5254 @ SY5255 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SY5259 ) )
= ( hAPP @ SY5256 @ ( hAPP @ SY5257 @ SY5259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(4017,plain,
! [SV1394: $i,SV679: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV679 ) @ SV1394 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1394
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1394
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(4018,plain,
! [SV1395: $i,SV680: $i] :
( ( ! [SY5260: $i] :
( ( SV680
!= ( c_List_Oappend @ SV1395 @ SV680 @ SY5260 ) )
| ( SV1395
= ( c_List_Olist_ONil @ SY5260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(4019,plain,
! [SV1396: $i,SV681: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV681 ) @ SV1396 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1396
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(4020,plain,
! [SV1397: $i,SV682: $i] :
( ( ! [SY5261: $i] :
( ( c_List_Olist_OCons @ SV682 @ SV1397 @ SY5261 )
!= ( c_List_Olist_ONil @ SY5261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(4021,plain,
! [SV1398: $i,SV683: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV683 ) @ SV1398 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1398
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV683
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(4022,plain,
! [SV1399: $i,SV684: $i] :
( ( ! [SY5262: $i,SY5263: $i,SY5264: $i] :
( ( ( hAPP @ SV684 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SY5262 @ SY5263 @ SY5264 ) )
!= ( hAPP @ SV1399 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SY5262 @ SY5263 @ SY5264 ) ) )
| ( ( c_List_Omap @ SV684 @ SY5262 @ SY5263 @ SY5264 )
= ( c_List_Omap @ SV1399 @ SY5262 @ SY5263 @ SY5264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(4023,plain,
! [SV1400: $i,SV685: $i] :
( ( ! [SY5265: $i] :
( ( ( c_List_Oappend @ SV685 @ SV1400 @ SY5265 )
!= ( c_List_Olist_ONil @ SY5265 ) )
| ( SV685
= ( c_List_Olist_ONil @ SY5265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(4024,plain,
! [SV1401: $i,SV686: $i] :
( ( ! [SY5266: $i,SY5267: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV686 ) @ SV1401 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY5266 ) @ SY5267 ) )
| ( SV1401 = SY5267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(4025,plain,
! [SV1402: $i,SV687: $i] :
( ( ! [SY5268: $i,SY5269: $i,SY5270: $i] :
( ( ( c_List_Oappend @ SV687 @ ( c_List_Olist_OCons @ SV1402 @ ( c_List_Olist_ONil @ SY5268 ) @ SY5268 ) @ SY5268 )
!= ( c_List_Oappend @ SY5269 @ ( c_List_Olist_OCons @ SY5270 @ ( c_List_Olist_ONil @ SY5268 ) @ SY5268 ) @ SY5268 ) )
| ( SV1402 = SY5270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(4026,plain,
! [SV1403: $i,SV688: $i] :
( ( ! [SY5271: $i,SY5272: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV688 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SY5271 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SY5272 ) )
| ( SY5271 = SY5272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(4027,plain,
! [SV1404: $i,SV689: $i] :
( ( ! [SY5273: $i,SY5274: $i,SY5275: $i] :
( ( ( c_List_Oreplicate @ SV689 @ SV1404 @ SY5273 )
!= ( c_List_Oreplicate @ SY5274 @ SY5275 @ SY5273 ) )
| ( SV689 = SY5274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(4028,plain,
! [SV1405: $i,SV690: $i] :
( ( ! [SY5276: $i,SY5277: $i,SY5278: $i] :
( ( ( hAPP @ SV690 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SY5276 @ SY5277 @ SY5278 ) )
!= ( hAPP @ SV1405 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SY5276 @ SY5277 @ SY5278 ) ) )
| ( ( c_List_Omap @ SV690 @ SY5276 @ SY5277 @ SY5278 )
= ( c_List_Omap @ SV1405 @ SY5276 @ SY5277 @ SY5278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(4029,plain,
! [SV1406: $i,SV691: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV691 )
!= ( c_Lambda_OdB_OAbs @ SV1406 ) )
| ( SV691 = SV1406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(4030,plain,
! [SV1407: $i,SV692: $i] :
( ( ! [SY5279: $i] :
( ( c_Lambda_OdB_OAbs @ SV692 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1407 ) @ SY5279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(4031,plain,
! [SV1408: $i,SV693: $i] :
( ( ! [SY5280: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV693 ) @ SV1408 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5280 ) @ SV1408 ) )
| ( SV693 = SY5280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(4032,plain,
! [SV1409: $i,SV694: $i] :
( ( ! [SY5281: $i,SY5282: $i,SY5283: $i] :
( ( ( c_List_Oappend @ SV694 @ SV1409 @ SY5281 )
!= ( c_List_Oappend @ SY5282 @ SY5283 @ SY5281 ) )
| ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SY5281 ) ) @ SY5282 @ SY5281 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SY5281 ) ) @ ( c_Nat_Osize__class_Osize @ SY5282 @ ( tc_List_Olist @ SY5281 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(4033,plain,
! [SV1410: $i,SV695: $i] :
( ( ! [SY5284: $i] :
( ( ( c_List_Oappend @ SV695 @ SV1410 @ SY5284 )
!= ( c_List_Olist_ONil @ SY5284 ) )
| ( SV1410
= ( c_List_Olist_ONil @ SY5284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(4034,plain,
! [SV1411: $i,SV696: $i] :
( ( ! [SY5285: $i,SY5286: $i,SY5287: $i] :
( ( ( c_List_Olist_OCons @ SV696 @ SV1411 @ SY5285 )
!= ( c_List_Olist_OCons @ SY5286 @ SY5287 @ SY5285 ) )
| ( SV696 = SY5286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(4035,plain,
! [SV1412: $i,SV697: $i] :
( ( ! [SY5288: $i,SY5289: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SY5288 @ SV1412 )
!= SV697 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY5288 @ ( tc_List_Olist @ SV1412 ) ) @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SY5288 @ SY5289 @ SV1412 )
= ( c_List_Oappend @ SV697 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SY5288 @ SV1412 ) @ SY5289 @ SV1412 ) @ SV1412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3291]) ).
thf(4036,plain,
! [SV1413: $i,SV698: $i] :
( ( ! [SY5290: $i] :
( ( ( c_List_Olist_ONil @ SV698 )
!= ( c_List_Oappend @ SV1413 @ SY5290 @ SV698 ) )
| ( SV1413
= ( c_List_Olist_ONil @ SV698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(4037,plain,
! [SV1414: $i,SV699: $i] :
( ( ! [SY5291: $i,SY5292: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV699 ) @ SV1414 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY5291 ) @ SY5292 ) )
| ( SV699 = SY5291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3293]) ).
thf(4038,plain,
! [SV1415: $i,SV700: $i] :
( ( ! [SY5293: $i,SY5294: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV700 ) @ SV1415 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY5293 ) @ SY5294 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1415 = SY5294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(4039,plain,
! [SV1416: $i,SV701: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV701 ) @ SV1416 ) )
| ( SV701
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV701
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3295]) ).
thf(4040,plain,
! [SV1417: $i,SV702: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV702 )
!= ( c_Lambda_OdB_OVar @ SV1417 ) )
| ( SV702 = SV1417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(4041,plain,
! [SV1418: $i,SV703: $i] :
( ( ! [SY5295: $i] :
( SV703
!= ( c_List_Olist_OCons @ SV1418 @ SV703 @ SY5295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(4042,plain,
! [SV1419: $i,SV704: $i] :
( ( ! [SY5296: $i,SY5297: $i,SY5298: $i] :
( ( ( c_List_Oreplicate @ SV704 @ SV1419 @ SY5296 )
!= ( c_List_Oreplicate @ SY5297 @ SY5298 @ SY5296 ) )
| ( SV1419 = SY5298 )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(4043,plain,
! [SV705: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV705 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(4044,plain,
! [SV1420: $i,SV706: $i] :
( ( ! [SY5299: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SV1420 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY5299 @ SV1420 @ tc_nat ) )
| ~ ( c_lessequals @ SV1420 @ SY5299 @ tc_nat )
| ~ ( c_lessequals @ SV1420 @ SV706 @ tc_nat )
| ( SV706 = SY5299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(4045,plain,
! [SV1421: $i,SV707: $i] :
( ( ! [SY5300: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV707 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1421 @ SY5300 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV707 )
= SV1421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(4046,plain,
! [SV1422: $i,SV708: $i] :
( ( ! [SY5301: $i,SY5302: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV708 ) @ SV1422 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5301 ) @ SY5302 ) )
| ( SV708 = SY5301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(4047,plain,
! [SV1423: $i,SV709: $i] :
( ( ! [SY5303: $i] :
( ( ( c_List_Orotate @ SV709 @ SV1423 @ SY5303 )
!= ( c_List_Olist_ONil @ SY5303 ) )
| ( SV1423
= ( c_List_Olist_ONil @ SY5303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(4048,plain,
! [SV710: $i] :
( ( ( c_Suc @ SV710 )
= SV710 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(4049,plain,
! [SV1424: $i,SV711: $i] :
( ( ! [SY5304: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV711 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1424 @ SY5304 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SV1424 = SY5304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(4050,plain,
! [SV1425: $i,SV712: $i] :
( ( ! [SY5305: $i,SY5306: $i,SY5307: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SY5305 @ SV712 )
!= ( c_HOL_Ominus__class_Ominus @ SY5306 @ SY5307 @ SV712 ) )
| ( c_HOL_Oord__class_Oless @ SY5306 @ SY5307 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SY5305 @ SV712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(4051,plain,
! [SV1426: $i,SV713: $i] :
( ( ! [SY5308: $i,SY5309: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV713 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1426 ) @ SY5308 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SY5309 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SY5308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(4052,plain,
! [SV1427: $i,SV714: $i] :
( ( ! [SY5310: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV714 )
| ~ ( class_Int_Onumber__ring @ SV714 )
| ( SV1427
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SV1427 ) @ SY5310 ) )
| ( SY5310
= ( c_HOL_Ozero__class_Ozero @ SV714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(4053,plain,
! [SV1428: $i,SV715: $i] :
( ( ! [SY5311: $i] :
( ( ( c_List_Orev @ SV715 @ SV1428 )
!= ( c_List_Orev @ SY5311 @ SV1428 ) )
| ( SV715 = SY5311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(4054,plain,
! [SV1429: $i,SV716: $i] :
( ( ! [SY5312: $i] :
( ( ( c_List_Olist_ONil @ SV716 )
!= ( c_List_Oappend @ SV1429 @ SY5312 @ SV716 ) )
| ( SY5312
= ( c_List_Olist_ONil @ SV716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(4055,plain,
! [SV1430: $i,SV717: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV717 ) @ SV1430 ) )
| ( SV717
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1430
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(4056,plain,
! [SV1431: $i,SV718: $i] :
( ( ! [SY5313: $i,SY5314: $i] :
( ( ( c_List_Omap @ SV718 @ SV1431 @ SY5313 @ SY5314 )
!= ( c_List_Olist_ONil @ SY5314 ) )
| ( SV1431
= ( c_List_Olist_ONil @ SY5313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(4057,plain,
! [SV1432: $i,SV719: $i] :
( ( ! [SY5315: $i,SY5316: $i] :
( ( ( c_List_Orev @ SV719 @ SV1432 )
!= ( c_List_Olist_OCons @ SY5315 @ SY5316 @ SV1432 ) )
| ( SV719
= ( c_List_Oappend @ ( c_List_Orev @ SY5316 @ SV1432 ) @ ( c_List_Olist_OCons @ SY5315 @ ( c_List_Olist_ONil @ SV1432 ) @ SV1432 ) @ SV1432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(4058,plain,
! [SV1433: $i,SV720: $i] :
( ( ! [SY5317: $i,SY5318: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV720 ) @ SV1433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY5317 ) @ SY5318 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(4059,plain,
! [SV1434: $i,SV721: $i] :
( ( ! [SY5319: $i,SY5320: $i,SY5321: $i] :
( ( ( c_List_Olist_OCons @ SV721 @ SV1434 @ SY5319 )
!= ( c_List_Olist_OCons @ SY5320 @ SY5321 @ SY5319 ) )
| ( SV1434 = SY5321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(4060,plain,
! [SV1435: $i,SV722: $i] :
( ( ! [SY5322: $i,SY5323: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV722 ) @ SV1435 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5322 ) @ SY5323 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5322 @ SV1435 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV722 @ SY5323 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(4061,plain,
! [SV1436: $i,SV723: $i] :
( ( ! [SY5324: $i,SY5325: $i] :
( ( ( c_List_Olist__update @ SV723 @ SV1436 @ SY5324 @ SY5325 )
!= ( c_List_Olist_ONil @ SY5325 ) )
| ( SV723
= ( c_List_Olist_ONil @ SY5325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(4062,plain,
! [SV1437: $i,SV724: $i] :
( ( ( ( c_List_Orev @ SV724 @ SV1437 )
!= ( c_List_Olist_ONil @ SV1437 ) )
| ( SV724
= ( c_List_Olist_ONil @ SV1437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(4063,plain,
! [SV1438: $i,SV725: $i] :
( ( ! [SY5326: $i,SY5327: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV725 ) @ SV1438 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY5326 ) @ SY5327 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV725 = SY5326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(4064,plain,
! [SV1439: $i,SV726: $i] :
( ( ! [SY5328: $i,SY5329: $i,SY5330: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SY5328 @ SV726 )
!= ( c_HOL_Ominus__class_Ominus @ SY5329 @ SY5330 @ SV726 ) )
| ( c_lessequals @ SY5330 @ SY5329 @ SV726 )
| ~ ( c_lessequals @ SY5328 @ SV1439 @ SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(4065,plain,
! [SV1440: $i,SV727: $i] :
( ( ! [SY5331: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SV1440 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SY5331 ) )
| ( SV1440 = SY5331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(4066,plain,
! [SV1441: $i,SV728: $i] :
( ( ! [SY5332: $i,SY5333: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV728 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1441 @ SV1441 @ SV728 )
!= ( c_HOL_Ominus__class_Ominus @ SY5332 @ SY5333 @ SV728 ) )
| ( SY5332 = SY5333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(4067,plain,
! [SV1442: $i,SV729: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV729 )
| ~ ( class_Power_Opower @ SV729 )
| ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(4068,plain,
! [SV1443: $i,SV730: $i] :
( ( ! [SY5334: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SY5334 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SY5334 @ SV730 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(4069,plain,
! [SV1444: $i,SV731: $i] :
( ( ! [SY5335: $i] :
( ( ( c_List_Oreplicate @ SV731 @ SV1444 @ SY5335 )
!= ( c_List_Olist_ONil @ SY5335 ) )
| ( SV731
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(4070,plain,
! [SV732: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV732 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV732 )
!= ( c_HOL_Oone__class_Oone @ SV732 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3326]) ).
thf(4071,plain,
! [SV1445: $i,SV733: $i] :
( ( ( ( c_Suc @ SV733 )
!= ( c_Suc @ SV1445 ) )
| ( SV733 = SV1445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3327]) ).
thf(4072,plain,
! [SV1446: $i,SV734: $i] :
( ( ! [SY5336: $i,SY5337: $i,SY5338: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV734 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SY5336 ) @ SY5337 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SY5336 ) @ SY5338 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ SY5337 )
= SY5338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3328]) ).
thf(4073,plain,
! [SV1447: $i,SV735: $i] :
( ( ! [SY5339: $i] :
( ( ( c_List_Orev @ SV735 @ SV1447 )
!= ( c_List_Olist_OCons @ SY5339 @ ( c_List_Olist_ONil @ SV1447 ) @ SV1447 ) )
| ( SV735
= ( c_List_Olist_OCons @ SY5339 @ ( c_List_Olist_ONil @ SV1447 ) @ SV1447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(4074,plain,
! [SV1448: $i,SV736: $i] :
( ( ! [SY5340: $i] :
( ( ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SV1448 ) @ SV1448 )
!= ( c_List_Orev @ SY5340 @ SV1448 ) )
| ( SY5340
= ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SV1448 ) @ SV1448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(4075,plain,
! [SV1449: $i,SV737: $i] :
( ( ( ( c_Suc @ SV737 )
!= ( c_Suc @ SV1449 ) )
| ( SV737 = SV1449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(4076,plain,
! [SV1450: $i,SV738: $i] :
( ( ! [SY5341: $i] :
( ( SV738
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SV1450 ) ) @ SY5341 @ SV1450 ) )
| ( ( c_List_Oappend @ SV738 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SV1450 ) ) @ SY5341 @ SV1450 ) @ SV1450 )
= SY5341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(4077,plain,
! [SV739: $i] :
( ( ( c_Suc @ SV739 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(4078,plain,
! [SV1451: $i,SV740: $i] :
( ( ! [SY5342: $i,SY5343: $i,SY5344: $i] :
( ( ( hAPP @ SV740 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SY5342 @ SY5343 @ SY5344 ) )
!= ( hAPP @ SV1451 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SY5342 @ SY5343 @ SY5344 ) ) )
| ( ( c_List_Omap @ SV740 @ SY5342 @ SY5343 @ SY5344 )
= ( c_List_Omap @ SV1451 @ SY5342 @ SY5343 @ SY5344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(4079,plain,
! [SV1452: $i,SV741: $i] :
( ( ! [SY5345: $i,SY5346: $i] :
( ( SV741
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SY5345 @ SV1452 ) )
| ( ( c_List_Oappend @ SV741 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SY5345 @ SV1452 ) @ SY5346 @ SV1452 ) @ SV1452 )
= ( c_List_Oappend @ SY5345 @ SY5346 @ SV1452 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ ( c_Nat_Osize__class_Osize @ SY5345 @ ( tc_List_Olist @ SV1452 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(4080,plain,
! [SV1453: $i,SV742: $i] :
( ( ! [SY5347: $i,SY5348: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV742 ) ) @ SV1453 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY5347 ) @ SY5348 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(4081,plain,
! [SV743: $i] :
( ( ( c_Suc @ SV743 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(4082,plain,
! [SV1454: $i,SV744: $i] :
( ( ! [SY5349: $i,SY5350: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV744 ) @ SV1454 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY5349 ) @ SY5350 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1454 = SY5350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(4083,plain,
! [SV1455: $i,SV745: $i] :
( ( ! [SY5351: $i] :
( ( c_List_Olist_OCons @ SV745 @ SV1455 @ SY5351 )
!= SV1455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(4084,plain,
! [SV1456: $i,SV746: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV746 )
!= ( c_Type_Otype_OAtom @ SV1456 ) )
| ( SV746 = SV1456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3340]) ).
thf(4085,plain,
! [SV1457: $i,SV747: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV747 ) @ SV1457 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV747
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(4086,plain,
! [SV748: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV748 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3342]) ).
thf(4087,plain,
! [SV1458: $i,SV749: $i] :
( ( ! [SY5352: $i,SY5353: $i,SY5354: $i] :
( ( ( c_List_Oappend @ SV749 @ SV1458 @ SY5352 )
!= ( c_List_Oappend @ SY5353 @ SY5354 @ SY5352 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY5353 @ ( tc_List_Olist @ SY5352 ) ) @ SV749 @ SY5352 ) @ SV1458 @ SY5352 )
= SY5354 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV749 @ ( tc_List_Olist @ SY5352 ) ) @ ( c_Nat_Osize__class_Osize @ SY5353 @ ( tc_List_Olist @ SY5352 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(4088,plain,
! [SV1459: $i,SV750: $i] :
( ( ! [SY5355: $i,SY5356: $i,SY5357: $i,SY5358: $i,SY5359: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY5355 ) @ SY5356 ) @ SY5357 ) ) )
| ~ ( c_Type_Otyping @ SY5358 @ SY5356 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY5356 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY5358 @ SY5357 @ SV750 @ tc_Type_Otype ) @ SY5355 @ SY5359 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY5355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(4089,plain,
! [SV1460: $i,SV751: $i] :
( ( ! [SY5360: $i] :
( ( ( c_List_Oappend @ SV751 @ SV1460 @ SY5360 )
!= SV1460 )
| ( SV751
= ( c_List_Olist_ONil @ SY5360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(4090,plain,
! [SV1461: $i,SV752: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV752 )
!= ( c_Lambda_OdB_OVar @ SV1461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(4091,plain,
! [SV1462: $i,SV753: $i] :
( ( ! [SY5361: $i] :
( ( c_List_Olist_ONil @ SV753 )
!= ( c_List_Olist_OCons @ SV1462 @ SY5361 @ SV753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(4092,plain,
! [SV1463: $i,SV754: $i] :
( ( ! [SY5362: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SV1463 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SY5362 ) )
| ( SV1463 = SY5362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(4093,plain,
! [SV1464: $i,SV755: $i] :
( ( ! [SY5363: $i,SY5364: $i,SY5365: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SY5363 @ SV755 )
!= ( c_HOL_Ominus__class_Ominus @ SY5364 @ SY5365 @ SV755 ) )
| ( c_HOL_Oord__class_Oless @ SV1464 @ SY5363 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SY5364 @ SY5365 @ SV755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(4094,plain,
! [SV1465: $i,SV756: $i] :
( ( ! [SY5366: $i] :
( ~ ( class_Orderings_Olinorder @ SV756 )
| ( ( c_Orderings_Oord__class_Omax @ SV1465 @ SY5366 @ SV756 )
!= SY5366 )
| ( c_lessequals @ SV1465 @ SY5366 @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(4095,plain,
! [SV1466: $i,SV757: $i] :
( ( ! [SY5367: $i,SY5368: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV757 )
| ( ( c_Power_Opower__class_Opower @ SV1466 @ SY5367 @ SV757 )
!= ( c_Power_Opower__class_Opower @ SY5368 @ SY5367 @ SV757 ) )
| ( SV1466 = SY5368 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5367 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SY5368 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(4096,plain,
! [SV1467: $i,SV758: $i] :
( ( ! [SY5369: $i] :
( ( ( c_List_Odrop @ SV758 @ SV1467 @ SY5369 )
!= ( c_List_Olist_ONil @ SY5369 ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1467 @ ( tc_List_Olist @ SY5369 ) ) @ SV758 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(4097,plain,
! [SV1468: $i,SV759: $i] :
( ( ! [SY5370: $i,SY5371: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1468 ) @ SY5370 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY5371 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV1468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(4098,plain,
! [SV1469: $i,SV760: $i] :
( ( ! [SY5372: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV760 @ SV1469 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY5372 ) )
| ( SV760
= ( c_Lambda_OdB_OAbs @ SY5372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(4099,plain,
! [SV1470: $i,SV761: $i] :
( ( ! [SY5373: $i] :
( ( ( c_Lambda_OdB_OVar @ SV761 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1470 @ SY5373 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV761 )
= SV1470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(4100,plain,
! [SV1471: $i,SV762: $i] :
( ( ! [SY5374: $i,SY5375: $i] :
( ( ( c_List_Oappend @ SV762 @ SV1471 @ SY5374 )
!= ( c_List_Oappend @ SY5375 @ SV1471 @ SY5374 ) )
| ( SV762 = SY5375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(4101,plain,
! [SV1472: $i,SV763: $i] :
( ( ! [SY5376: $i] :
( ( c_List_Olist_OCons @ SV763 @ SV1472 @ SY5376 )
!= ( c_List_Olist_ONil @ SY5376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(4102,plain,
! [SV1473: $i,SV764: $i] :
( ( ! [SY5377: $i,SY5378: $i,SY5379: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SY5377 @ SV764 )
!= ( c_HOL_Ominus__class_Ominus @ SY5378 @ SY5379 @ SV764 ) )
| ( c_lessequals @ SY5377 @ SV1473 @ SV764 )
| ~ ( c_lessequals @ SY5379 @ SY5378 @ SV764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(4103,plain,
! [SV1474: $i,SV765: $i] :
( ( ! [SY5380: $i,SY5381: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV765 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1474 @ SY5380 @ SV765 )
!= ( c_HOL_Ominus__class_Ominus @ SY5381 @ SY5381 @ SV765 ) )
| ( SV1474 = SY5380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(4104,plain,
! [SV1475: $i,SV766: $i] :
( ( ( c_Lambda_OdB_OVar @ SV766 )
!= ( c_Lambda_OdB_OAbs @ SV1475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(4105,plain,
! [SV1476: $i,SV767: $i] :
( ( ! [SY5382: $i,SY5383: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV767 ) @ SV1476 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5382 ) @ SY5383 ) )
| ( SV1476 = SY5383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(4106,plain,
! [SV1477: $i,SV768: $i] :
( ( ! [SY5384: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV768 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1477 @ SY5384 @ SV768 )
!= ( c_HOL_Ozero__class_Ozero @ SV768 ) )
| ( SV1477 = SY5384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(4107,plain,
! [SV1478: $i,SV769: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV769 ) @ SV1478 ) )
| ( SV1478
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1478
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(4108,plain,
! [SV1479: $i,SV770: $i] :
( ( ! [SY5385: $i,SY5386: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV770 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV1479 ) @ SY5385 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SY5386 ) @ SY5385 ) )
| ( SV1479 = SY5386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(4109,plain,
! [SV1480: $i,SV771: $i] :
( ( ! [SY5387: $i,SY5388: $i,SY5389: $i] :
( ( ( c_List_Oappend @ SV771 @ ( c_List_Olist_OCons @ SV1480 @ ( c_List_Olist_ONil @ SY5387 ) @ SY5387 ) @ SY5387 )
!= ( c_List_Oappend @ SY5388 @ ( c_List_Olist_OCons @ SY5389 @ ( c_List_Olist_ONil @ SY5387 ) @ SY5387 ) @ SY5387 ) )
| ( SV771 = SY5388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(4110,plain,
! [SV772: $i,SV1: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV1 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ SV772 ) @ SV772 ) @ SV1 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV772 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3366]) ).
thf(4111,plain,
! [SV773: $i,SV2: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV2 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV773 @ SV2 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV773 ) @ SV773 ) @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3367]) ).
thf(4112,plain,
! [SV3: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV3 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV3
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(4113,plain,
! [SV1481: $i,SV775: $i,SV7: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV7 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV7 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1481 @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV775 @ SV1481 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(4114,plain,
! [SV1482: $i,SV776: $i,SV8: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV8 )
| ( c_lessequals @ SV776 @ SV1482 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV776 @ SV8 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1482 @ SV8 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(4115,plain,
! [SV1483: $i,SV777: $i,SV9: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV9 @ SV777 @ SV1483 ) @ ( tc_List_Olist @ SV1483 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV777 @ ( tc_List_Olist @ SV1483 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(4116,plain,
! [SV1484: $i,SV778: $i,SV10: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV10 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV778 ) @ SV1484 ) @ tc_nat )
| ~ ( c_lessequals @ SV10 @ SV778 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1484 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(4117,plain,
! [SV1485: $i,SV779: $i,SV11: $i] :
( ( ! [SY5390: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SY5390 ) @ SV11 )
| ~ ( c_lessequals @ SV779 @ SY5390 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(4118,plain,
! [SV1486: $i,SV781: $i,SV13: $i] :
( ( ! [SY5391: $i] :
( ( c_List_Odrop @ SV13 @ ( c_List_Oappend @ SV781 @ SV1486 @ SY5391 ) @ SY5391 )
= ( c_List_Oappend @ ( c_List_Odrop @ SV13 @ SV781 @ SY5391 ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Nat_Osize__class_Osize @ SV781 @ ( tc_List_Olist @ SY5391 ) ) @ tc_nat ) @ SV1486 @ SY5391 ) @ SY5391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(4119,plain,
! [SV1487: $i,SV782: $i,SV14: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV14 @ SV782 @ tc_nat ) ) @ SV1487 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV782 ) @ SV1487 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV782 @ SV14 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(4120,plain,
! [SV1488: $i,SV783: $i,SV15: $i] :
( ( ! [SY5392: $i] :
( ~ ( class_Orderings_Olinorder @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SV1488 @ SV15 ) @ SY5392 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV1488 @ SY5392 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV783 @ SY5392 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(4121,plain,
! [SV784: $i,SV16: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV16 @ SV784 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV16 @ SV784 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(4122,plain,
! [SV1489: $i,SV785: $i,SV17: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV17 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV785 @ SV1489 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV785 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(4123,plain,
! [SV786: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ SV786 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV18 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(4124,plain,
! [SV1490: $i,SV788: $i,SV20: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV788 @ SV1490 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ SV788 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(4125,plain,
! [SV789: $i,SV21: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV21 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV21 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ ( c_Suc @ SV789 ) @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(4126,plain,
! [SV1491: $i,SV792: $i,SV24: $i] :
( ( ! [SY5393: $i] :
( ( ( c_List_Orev @ ( c_List_Olist__update @ SV24 @ SV792 @ SV1491 @ SY5393 ) @ SY5393 )
= ( c_List_Olist__update @ ( c_List_Orev @ SV24 @ SY5393 ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SY5393 ) ) @ SV792 @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1491 @ SY5393 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV792 @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SY5393 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(4127,plain,
! [SV1492: $i,SV793: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ SV793 ) )
| ( hBOOL @ ( hAPP @ SV25 @ SV1492 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1492 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV25 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(4128,plain,
! [SV1493: $i,SV797: $i,SV29: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV797 ) @ SV1493 @ tc_nat )
| ~ ( c_lessequals @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ SV797 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV797 @ SV1493 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(4129,plain,
! [SV1494: $i,SV798: $i,SV30: $i] :
( ( ( c_lessequals @ SV30 @ ( c_HOL_Ominus__class_Ominus @ SV798 @ SV1494 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV30 ) @ SV1494 ) @ SV798 @ tc_nat )
| ~ ( c_lessequals @ SV1494 @ SV798 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(4130,plain,
! [SV1495: $i,SV799: $i,SV31: $i] :
( ( ! [SY5394: $i] :
( ~ ( class_Orderings_Olinorder @ SV31 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SV1495 @ SV31 ) @ SY5394 @ SV31 )
| ~ ( c_lessequals @ SV1495 @ SY5394 @ SV31 )
| ~ ( c_lessequals @ SV799 @ SY5394 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(4131,plain,
! [SV1496: $i,SV800: $i,SV32: $i] :
( ( ! [SY5395: $i] :
( ~ ( class_Orderings_Olinorder @ SV32 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SV1496 @ SV32 ) @ SY5395 @ SV32 )
| ~ ( c_lessequals @ SV1496 @ SY5395 @ SV32 )
| ~ ( c_lessequals @ SV800 @ SY5395 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(4132,plain,
! [SV1497: $i,SV801: $i,SV33: $i] :
( ( ! [SY5396: $i] :
( ~ ( class_Orderings_Olinorder @ SV33 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SV1497 @ SV33 ) @ SY5396 @ SV33 )
| ~ ( c_lessequals @ SV1497 @ SY5396 @ SV33 )
| ~ ( c_lessequals @ SV801 @ SY5396 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(4133,plain,
! [SV1498: $i,SV802: $i,SV34: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV34 )
| ( c_lessequals @ SV802 @ ( c_Orderings_Oord__class_Omax @ SV802 @ SV1498 @ SV34 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(4134,plain,
! [SV1499: $i,SV803: $i,SV35: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV35 )
| ( c_lessequals @ SV803 @ ( c_Orderings_Oord__class_Omax @ SV1499 @ SV803 @ SV35 ) @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(4135,plain,
! [SV809: $i,SV41: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV41 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV41 ) @ SV809 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3404]) ).
thf(4136,plain,
! [SV1500: $i,SV810: $i,SV42: $i] :
( ( ( c_List_Odistinct @ SV42 @ SV810 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV42 @ SV1500 @ SV810 ) @ SV810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(4137,plain,
! [SV1501: $i,SV811: $i,SV43: $i] :
( ( ( c_List_Odistinct @ SV43 @ SV811 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV1501 @ SV43 @ SV811 ) @ SV811 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(4138,plain,
! [SV1502: $i,SV815: $i,SV47: $i] :
( ( ! [SY5397: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV47 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SY5397 @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SY5397 @ SV1502 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(4139,plain,
! [SV1503: $i,SV816: $i,SV48: $i] :
( ( SV48
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV48 @ ( tc_List_Olist @ SV816 ) ) @ ( c_List_Oappend @ SV48 @ SV1503 @ SV816 ) @ SV816 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(4140,plain,
! [SV1504: $i,SV817: $i,SV49: $i] :
( ( ! [SY5398: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
| ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SY5398 ) @ SV49 )
| ~ ( c_lessequals @ SV817 @ SY5398 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(4141,plain,
! [SV1505: $i,SV818: $i,SV50: $i] :
( ( ! [SY5399: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SY5399 ) @ SV50 )
| ~ ( c_lessequals @ SV818 @ SV1505 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SY5399 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(4142,plain,
! [SV819: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ SV51 @ SV819 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV51 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3414]) ).
thf(4143,plain,
! [SV820: $i,SV52: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV52 ) @ SV820 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV52 @ SV820 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3415]) ).
thf(4144,plain,
! [SV821: $i,SV53: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV53 @ SV821 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV53 ) @ SV821 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3416]) ).
thf(4145,plain,
! [SV822: $i,SV54: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV54 ) @ SV822 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV822 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3417]) ).
thf(4146,plain,
! [SV823: $i,SV55: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV55 @ SV823 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV55 ) @ SV823 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3418]) ).
thf(4147,plain,
! [SV1506: $i,SV824: $i,SV56: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV56 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV824 ) @ SV1506 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ SV824 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(4148,plain,
! [SV1507: $i,SV825: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV57 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV825 ) @ SV1507 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV1507 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(4149,plain,
! [SV1508: $i,SV826: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV58 @ SV826 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SV1508 ) @ SV826 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4150,plain,
! [SV1509: $i,SV827: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV59 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV827 ) @ SV1509 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV59 @ SV827 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(4151,plain,
! [SV1510: $i,SV828: $i,SV60: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV60 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV828 ) @ SV1510 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV60 @ SV1510 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(4152,plain,
! [SV1511: $i,SV829: $i,SV61: $i] :
( ( ! [SY5400: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV61 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SY5400 @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
| ~ ( c_lessequals @ SY5400 @ SV1511 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(4153,plain,
! [SV830: $i,SV63: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV63 ) @ SV830 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV63 @ SV830 @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV830 @ SV63 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3425]) ).
thf(4154,plain,
! [SV1512: $i,SV831: $i,SV64: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV64 ) @ SV831 @ SV1512 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV64 @ SV831 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1512 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(4155,plain,
! [SV1513: $i,SV832: $i,SV65: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV832 ) @ SV1513 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV1513 ) @ SV832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(4156,plain,
! [SV1514: $i,SV833: $i,SV66: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV66 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SV833 ) @ SV1514 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SV1514 ) @ SV833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(4157,plain,
! [SV1515: $i,SV835: $i,SV68: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV835 ) @ SV1515 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV1515 ) @ SV835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(4158,plain,
! [SV1516: $i,SV836: $i,SV69: $i] :
( ( ! [SY5401: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV69 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ SV1516 ) @ SY5401 @ SV69 @ SV69 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1516 @ SY5401 @ SV69 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(4159,plain,
! [SV1517: $i,SV837: $i,SV70: $i] :
( ( ( c_List_Orev @ ( c_List_Oreplicate @ SV70 @ SV837 @ SV1517 ) @ SV1517 )
= ( c_List_Oreplicate @ SV70 @ SV837 @ SV1517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(4160,plain,
! [SV1518: $i,SV838: $i,SV71: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV838 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV1518 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV71 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV838 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(4161,plain,
! [SV1519: $i,SV839: $i,SV72: $i] :
( ( ( ( hAPP @ SV72 @ SV839 )
= SV1519 )
| ~ ( c_Type_Otyping @ SV72 @ ( c_Lambda_OdB_OVar @ SV839 ) @ SV1519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(4162,plain,
! [SV1520: $i,SV840: $i,SV73: $i] :
( ( ! [SY5402: $i] :
( ( c_List_Otake @ ( c_Suc @ SV73 ) @ ( c_List_Olist_OCons @ SV840 @ SV1520 @ SY5402 ) @ SY5402 )
= ( c_List_Olist_OCons @ SV840 @ ( c_List_Otake @ SV73 @ SV1520 @ SY5402 ) @ SY5402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(4163,plain,
! [SV1521: $i,SV841: $i,SV74: $i] :
( ( ! [SY5403: $i] :
( ~ ( class_Orderings_Olinorder @ SV74 )
| ( c_lessequals @ SV841 @ SV1521 @ SV74 )
| ( c_lessequals @ SV841 @ SY5403 @ SV74 )
| ~ ( c_lessequals @ SV841 @ ( c_Orderings_Oord__class_Omax @ SY5403 @ SV1521 @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(4164,plain,
! [SV1522: $i,SV842: $i,SV75: $i] :
( ( ! [SY5404: $i] :
( ( c_List_Olistsp @ SV75 @ SV842 @ SV1522 )
| ~ ( c_List_Olistsp @ SV75 @ ( c_List_Oappend @ SY5404 @ SV842 @ SV1522 ) @ SV1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(4165,plain,
! [SV1523: $i,SV843: $i,SV76: $i] :
( ( ! [SY5405: $i] :
( ( c_List_Olistsp @ SV76 @ SV843 @ SV1523 )
| ~ ( c_List_Olistsp @ SV76 @ ( c_List_Oappend @ SV843 @ SY5405 @ SV1523 ) @ SV1523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(4166,plain,
! [SV1524: $i,SV844: $i,SV77: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV77 ) ) @ SV844 ) @ SV1524 )
= ( c_Lambda_OdB_OVar @ SV77 ) )
| ( SV77 = SV1524 )
| ( c_HOL_Oord__class_Oless @ SV1524 @ SV77 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(4167,plain,
! [SV1525: $i,SV845: $i,SV78: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV78 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ ( c_HOL_Ominus__class_Ominus @ SV845 @ SV1525 @ SV78 ) ) @ SV1525 )
= SV845 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(4168,plain,
! [SV1526: $i,SV846: $i,SV79: $i] :
( ( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV79 @ ( tc_List_Olist @ SV846 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV1526 @ SV79 @ SV846 ) @ ( tc_List_Olist @ SV846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(4169,plain,
! [SV1527: $i,SV847: $i,SV80: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV847 ) @ SV1527 ) @ SV847 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV80 @ SV1527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(4170,plain,
! [SV1528: $i,SV848: $i,SV81: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV81 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV848 ) @ SV1528 ) @ SV848 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV81 @ SV1528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(4171,plain,
! [SV1529: $i,SV849: $i,SV82: $i] :
( ( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV82 @ SV849 @ SV1529 ) @ SV1529 )
= ( c_List_Olist_OCons @ SV82 @ ( c_List_Olist_ONil @ SV1529 ) @ SV1529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3444]) ).
thf(4172,plain,
! [SV1530: $i,SV850: $i,SV83: $i] :
( ( ! [SY5406: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV83 ) @ SV850 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1530 ) @ SY5406 ) @ tc_nat )
| ~ ( c_lessequals @ SV850 @ SY5406 @ tc_nat )
| ~ ( c_lessequals @ SV83 @ SV1530 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(4173,plain,
! [SV1531: $i,SV851: $i,SV84: $i] :
( ( ! [SY5407: $i,SY5408: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SY5407 ) @ SY5408 ) @ SV84 )
| ~ ( c_lessequals @ SV1531 @ SY5408 @ SV84 )
| ~ ( c_lessequals @ SV851 @ SY5407 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3446]) ).
thf(4174,plain,
! [SV1532: $i,SV852: $i,SV85: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV85 @ SV852 @ SV1532 ) @ ( tc_List_Olist @ SV1532 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV852 @ ( tc_List_Olist @ SV1532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(4175,plain,
! [SV1533: $i,SV853: $i,SV86: $i] :
( ( ! [SY5409: $i,SY5410: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV86 @ SV853 @ SV1533 ) @ SY5409 @ SY5410 @ SV1533 )
= ( c_List_Oappend @ SV86 @ ( c_List_Olist__update @ SV853 @ ( c_HOL_Ominus__class_Ominus @ SY5409 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SV1533 ) ) @ tc_nat ) @ SY5410 @ SV1533 ) @ SV1533 ) )
| ( c_HOL_Oord__class_Oless @ SY5409 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SV1533 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(4176,plain,
! [SV1534: $i,SV854: $i,SV87: $i] :
( ( ( ( c_List_Otake @ SV87 @ SV854 @ SV1534 )
= SV854 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV854 @ ( tc_List_Olist @ SV1534 ) ) @ SV87 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(4177,plain,
! [SV855: $i,SV88: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SV855 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV88 @ SV855 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(4178,plain,
! [SV856: $i,SV89: $i] :
( ( ( c_lessequals @ SV89 @ SV856 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV89 @ ( c_Suc @ SV856 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3451]) ).
thf(4179,plain,
! [SV90: $i] :
( ( ( c_lessequals @ SV90 @ SV90 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ ( c_Suc @ SV90 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(4180,plain,
! [SV857: $i,SV91: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV91 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV857 @ SV91 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV857 @ SV91 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3453]) ).
thf(4181,plain,
! [SV92: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV92 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(4182,plain,
! [SV1535: $i,SV859: $i,SV94: $i] :
( ( ! [SY5411: $i] :
( ( c_List_Odrop @ SV94 @ ( c_List_Otake @ SV859 @ SV1535 @ SY5411 ) @ SY5411 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV859 @ SV94 @ tc_nat ) @ ( c_List_Odrop @ SV94 @ SV1535 @ SY5411 ) @ SY5411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(4183,plain,
! [SV1536: $i,SV860: $i,SV95: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV860 ) @ SV1536 ) @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1536 @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV860 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(4184,plain,
! [SV1537: $i,SV861: $i,SV96: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV96 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV861 @ ( c_Suc @ SV1537 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV861 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(4185,plain,
! [SV1538: $i,SV862: $i,SV97: $i] :
( ( ! [SY5412: $i] :
( ~ ( class_Orderings_Opreorder @ SV97 )
| ( c_HOL_Oord__class_Oless @ SV862 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SY5412 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV862 @ SY5412 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(4186,plain,
! [SV1539: $i,SV863: $i,SV98: $i] :
( ( ! [SY5413: $i] :
( ~ ( class_Orderings_Oorder @ SV98 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SV1539 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SY5413 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY5413 @ SV1539 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(4187,plain,
! [SV1540: $i,SV864: $i,SV99: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV99 )
| ( ( c_Orderings_Oord__class_Omax @ SV864 @ SV1540 @ SV99 )
= SV1540 )
| ~ ( c_lessequals @ SV864 @ SV1540 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(4188,plain,
! [SV1541: $i,SV865: $i,SV100: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV100 )
| ( ( c_Orderings_Oord__class_Omax @ SV865 @ SV1541 @ SV100 )
= SV865 )
| ~ ( c_lessequals @ SV1541 @ SV865 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(4189,plain,
! [SV1542: $i,SV866: $i,SV101: $i] :
( ( ! [SY5414: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV1542 ) @ SY5414 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ SV1542 ) ) @ SY5414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(4190,plain,
! [SV1543: $i,SV867: $i,SV102: $i] :
( ( ! [SY5415: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV102 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV1543 ) @ SY5415 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV1543 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ SY5415 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(4191,plain,
! [SV1544: $i,SV868: $i,SV103: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV868 ) @ SV1544 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV868 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ SV1544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(4192,plain,
! [SV1545: $i,SV869: $i,SV104: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV104 ) @ SV869 ) ) @ SV1545 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV104 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV869 ) @ SV1545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(4193,plain,
! [SV1546: $i,SV870: $i,SV105: $i] :
( ( ! [SY5416: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ SV1546 ) ) @ SY5416 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV1546 ) @ SY5416 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(4194,plain,
! [SV1547: $i,SV871: $i,SV106: $i] :
( ( ! [SY5417: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV106 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV1547 ) @ SY5417 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV1547 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ SY5417 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(4195,plain,
! [SV1548: $i,SV872: $i,SV107: $i] :
( ( ! [SY5418: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV107 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ SV1548 ) ) @ SY5418 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV1548 ) @ SY5418 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(4196,plain,
! [SV1549: $i,SV873: $i,SV108: $i] :
( ( ! [SY5419: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV108 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV1549 ) @ SY5419 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ SV1549 ) ) @ SY5419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(4197,plain,
! [SV1550: $i,SV874: $i,SV109: $i] :
( ( ! [SY5420: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV109 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SV1550 ) ) @ SY5420 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SY5420 ) ) @ SV1550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(4198,plain,
! [SV1551: $i,SV875: $i,SV110: $i] :
( ( ! [SY5421: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV1551 ) @ SY5421 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ SY5421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(4199,plain,
! [SV1552: $i,SV876: $i,SV111: $i] :
( ( ! [SY5422: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ SV1552 ) ) @ SY5422 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV1552 ) @ SY5422 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(4200,plain,
! [SV877: $i,SV112: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV112 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV877 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV877 ) @ SV112 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3474]) ).
thf(4201,plain,
! [SV1553: $i,SV878: $i,SV113: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV113 @ SV878 @ SV1553 ) @ SV1553 )
= ( c_List_Olist_OCons @ SV113 @ SV878 @ SV1553 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(4202,plain,
! [SV1554: $i,SV879: $i,SV114: $i] :
( ( ! [SY5423: $i] :
( ( c_List_Otake @ SV114 @ ( c_List_Odrop @ SV879 @ SV1554 @ SY5423 ) @ SY5423 )
= ( c_List_Odrop @ SV879 @ ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV114 ) @ SV879 ) @ SV1554 @ SY5423 ) @ SY5423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4203,plain,
! [SV1555: $i,SV880: $i,SV115: $i] :
( ( ( c_List_Oreplicate @ ( c_Suc @ SV115 ) @ SV880 @ SV1555 )
= ( c_List_Olist_OCons @ SV880 @ ( c_List_Oreplicate @ SV115 @ SV880 @ SV1555 ) @ SV1555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(4204,plain,
! [SV1556: $i,SV881: $i,SV116: $i] :
( ( ( c_lessequals @ SV116 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV881 ) @ SV1556 ) @ tc_nat )
| ~ ( c_lessequals @ SV116 @ SV1556 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(4205,plain,
! [SV1557: $i,SV882: $i,SV117: $i] :
( ( ( c_lessequals @ SV117 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV882 ) @ SV1557 ) @ tc_nat )
| ~ ( c_lessequals @ SV117 @ SV882 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(4206,plain,
! [SV1558: $i,SV883: $i,SV118: $i] :
( ( ( c_lessequals @ SV118 @ SV883 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1558 ) @ SV118 ) @ SV883 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(4207,plain,
! [SV1559: $i,SV884: $i,SV119: $i] :
( ( ( c_lessequals @ SV119 @ SV884 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV119 ) @ SV1559 ) @ SV884 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(4208,plain,
! [SV1560: $i,SV885: $i,SV120: $i] :
( ( ( c_lessequals @ SV120 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV885 ) @ SV1560 ) @ tc_nat )
| ~ ( c_lessequals @ SV120 @ SV1560 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(4209,plain,
! [SV1561: $i,SV886: $i,SV121: $i] :
( ( ( c_lessequals @ SV121 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV886 ) @ SV1561 ) @ tc_nat )
| ~ ( c_lessequals @ SV121 @ SV886 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(4210,plain,
! [SV1562: $i,SV887: $i,SV122: $i] :
( ( ( c_List_Orev @ ( c_List_Otake @ SV122 @ SV887 @ SV1562 ) @ SV1562 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV887 @ ( tc_List_Olist @ SV1562 ) ) @ SV122 @ tc_nat ) @ ( c_List_Orev @ SV887 @ SV1562 ) @ SV1562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(4211,plain,
! [SV888: $i,SV123: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV123 ) ) @ SV888 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV123 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV123 @ SV888 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3485]) ).
thf(4212,plain,
! [SV889: $i,SV124: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV124 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV124 ) @ SV889 @ SV124 )
= ( c_HOL_Oone__class_Oone @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3486]) ).
thf(4213,plain,
! [SV1563: $i,SV890: $i,SV125: $i] :
( ( ! [SY5424: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV125 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV890 @ SV1563 @ SV125 ) @ SY5424 @ SV125 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SY5424 @ SV125 ) @ ( c_HOL_Ominus__class_Ominus @ SV1563 @ SY5424 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(4214,plain,
! [SV1564: $i,SV891: $i,SV126: $i] :
( ( ! [SY5425: $i] :
( ( hAPP @ ( c_COMBK @ SV126 @ SV891 @ SV1564 ) @ SY5425 )
= SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(4215,plain,
! [SV1565: $i,SV892: $i,SV127: $i] :
( ( ( c_List_Orev @ ( c_List_Odrop @ SV127 @ SV892 @ SV1565 ) @ SV1565 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV892 @ ( tc_List_Olist @ SV1565 ) ) @ SV127 @ tc_nat ) @ ( c_List_Orev @ SV892 @ SV1565 ) @ SV1565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(4216,plain,
! [SV1566: $i,SV893: $i,SV128: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SV893 @ SV1566 @ SV128 )
| ( c_lessequals @ SV1566 @ SV893 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(4217,plain,
! [SV894: $i,SV129: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV129 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV894 @ SV894 @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV894 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3491]) ).
thf(4218,plain,
! [SV895: $i,SV130: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV130 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV895 @ SV895 @ SV130 )
| ( c_lessequals @ SV895 @ SV895 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(4219,plain,
! [SV1567: $i,SV896: $i,SV131: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SV896 @ SV1567 @ SV131 )
| ~ ( c_lessequals @ SV1567 @ SV896 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(4220,plain,
! [SV1568: $i,SV897: $i,SV132: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV132 )
| ( c_lessequals @ SV897 @ SV1568 @ SV132 )
| ( c_HOL_Oord__class_Oless @ SV1568 @ SV897 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(4221,plain,
! [SV1569: $i,SV898: $i,SV133: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV133 )
| ~ ( c_lessequals @ SV898 @ SV1569 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SV1569 @ SV898 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(4222,plain,
! [SV1570: $i,SV899: $i,SV134: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV134 )
| ( c_HOL_Oord__class_Oless @ SV899 @ SV1570 @ SV134 )
| ( c_lessequals @ SV1570 @ SV899 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4223,plain,
! [SV1571: $i,SV900: $i,SV135: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV135 )
| ~ ( c_lessequals @ SV900 @ SV1571 @ SV135 )
| ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV900 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4224,plain,
! [SV901: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ SV136 @ SV901 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV136 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3498]) ).
thf(4225,plain,
! [SV902: $i,SV137: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV137 @ SV137 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV137 ) ) @ SV902 ) @ SV137 )
= SV902 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3499]) ).
thf(4226,plain,
! [SV903: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ SV138 @ SV903 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV138 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV138 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(4227,plain,
! [SV1572: $i,SV904: $i,SV139: $i] :
( ( ! [SY5426: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
| ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SY5426 ) @ SV139 )
| ~ ( c_HOL_Oord__class_Oless @ SV904 @ SY5426 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4228,plain,
! [SV1573: $i,SV905: $i,SV140: $i] :
( ( ! [SY5427: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV140 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SV1573 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SY5427 @ SV140 ) @ SV140 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 )
| ~ ( c_lessequals @ SV1573 @ SY5427 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(4229,plain,
! [SV1574: $i,SV906: $i,SV141: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV906 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV1574 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1574 @ SV906 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(4230,plain,
! [SV1575: $i,SV907: $i,SV142: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV142 @ SV907 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1575 @ SV907 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV142 @ SV1575 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(4231,plain,
! [SV1576: $i,SV908: $i,SV143: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SV908 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV908 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV143 @ SV1576 @ tc_nat )
| ~ ( c_lessequals @ SV908 @ SV1576 @ tc_nat )
| ~ ( c_lessequals @ SV908 @ SV143 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(4232,plain,
! [SV1577: $i,SV909: $i,SV144: $i] :
( ( ( c_lessequals @ SV144 @ SV909 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SV1577 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV909 @ SV1577 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1577 @ SV909 @ tc_nat )
| ~ ( c_lessequals @ SV1577 @ SV144 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(4233,plain,
! [SV1578: $i,SV911: $i,SV146: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV146 @ SV911 @ tc_nat ) @ SV1578 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV146 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV911 ) @ SV1578 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(4234,plain,
! [SV1579: $i,SV912: $i,SV147: $i] :
( ( ! [SY5428: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV147 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SV1579 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SY5428 @ SV1579 @ SV147 ) @ SV147 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 )
| ~ ( c_lessequals @ SV912 @ SY5428 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(4235,plain,
! [SV148: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV148 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV148 )
= ( c_HOL_Oone__class_Oone @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(4236,plain,
! [SV1580: $i,SV913: $i,SV149: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV149 @ SV913 @ SV1580 ) @ SV1580 )
= ( c_List_Oappend @ ( c_List_Orev @ SV913 @ SV1580 ) @ ( c_List_Olist_OCons @ SV149 @ ( c_List_Olist_ONil @ SV1580 ) @ SV1580 ) @ SV1580 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3511]) ).
thf(4237,plain,
! [SV914: $i,SV150: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV150 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV914 ) @ SV150 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ ( c_HOL_Oone__class_Oone @ SV150 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV914 @ SV150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(4238,plain,
! [SV1581: $i,SV915: $i,SV151: $i] :
( ( ! [SY5429: $i,SY5430: $i,SY5431: $i] :
( ( c_List_Ofoldl @ SV151 @ SV915 @ ( c_List_Olist_OCons @ SV1581 @ SY5429 @ SY5430 ) @ SY5431 @ SY5430 )
= ( c_List_Ofoldl @ SV151 @ ( hAPP @ ( hAPP @ SV151 @ SV915 ) @ SV1581 ) @ SY5429 @ SY5431 @ SY5430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(4239,plain,
! [SV1582: $i,SV917: $i,SV153: $i] :
( ( ! [SY5432: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV153 ) @ ( c_List_Olist_OCons @ SV917 @ SV1582 @ SY5432 ) @ SY5432 )
= ( c_List_Odrop @ SV153 @ SV1582 @ SY5432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(4240,plain,
! [SV1583: $i,SV918: $i,SV154: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ SV918 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1583 ) @ SV918 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV154 @ SV1583 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3516]) ).
thf(4241,plain,
! [SV1584: $i,SV919: $i,SV155: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SV919 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SV1584 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV919 @ SV1584 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4242,plain,
! [SV1585: $i,SV921: $i,SV159: $i] :
( ( ! [SY5433: $i] :
( ~ ( class_Orderings_Olinorder @ SV159 )
| ( c_HOL_Oord__class_Oless @ SV921 @ ( c_Orderings_Oord__class_Omax @ SV1585 @ SY5433 @ SV159 ) @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV921 @ SV1585 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(4243,plain,
! [SV1586: $i,SV922: $i,SV160: $i] :
( ( ! [SY5434: $i] :
( ~ ( class_Orderings_Olinorder @ SV160 )
| ( c_HOL_Oord__class_Oless @ SV922 @ ( c_Orderings_Oord__class_Omax @ SV1586 @ SY5434 @ SV160 ) @ SV160 )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SY5434 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(4244,plain,
! [SV1587: $i,SV923: $i,SV161: $i] :
( ( ! [SY5435: $i] :
( ~ ( class_Orderings_Olinorder @ SV161 )
| ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Orderings_Oord__class_Omax @ SV1587 @ SY5435 @ SV161 ) @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV923 @ SV1587 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4245,plain,
! [SV1588: $i,SV924: $i,SV162: $i] :
( ( ! [SY5436: $i] :
( ~ ( class_Orderings_Olinorder @ SV162 )
| ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Orderings_Oord__class_Omax @ SV1588 @ SY5436 @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SY5436 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4246,plain,
! [SV1589: $i,SV925: $i,SV163: $i] :
( ( ! [SY5437: $i] :
( ~ ( class_Orderings_Olinorder @ SV163 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SV1589 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV925 @ SY5437 @ SV163 ) @ SV1589 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(4247,plain,
! [SV1590: $i,SV927: $i,SV165: $i] :
( ( ! [SY5438: $i,SY5439: $i,SY5440: $i,SY5441: $i,SY5442: $i,SY5443: $i] :
( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SY5438 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SY5439 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5438 ) @ SY5439 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5440 @ SV165 @ SV927 @ SY5441 @ SY5442 @ SY5443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4248,plain,
! [SV1591: $i,SV928: $i,SV166: $i] :
( ( ( c_Lambda_Oliftn @ ( c_Suc @ SV166 ) @ SV928 @ SV1591 )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV166 @ SV928 @ SV1591 ) ) @ SV1591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(4249,plain,
! [SV1592: $i,SV929: $i,SV168: $i] :
( ( ! [SY5444: $i,SY5445: $i,SY5446: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV168 @ SV929 @ SV1592 @ SY5444 @ SY5445 ) @ SY5446 )
= ( hAPP @ SV168 @ ( hAPP @ SV929 @ SY5446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(4250,plain,
! [SV1593: $i,SV930: $i,SV169: $i] :
( ( ! [SY5447: $i,SY5448: $i,SY5449: $i] :
( ( hAPP @ SV169 @ ( hAPP @ SV930 @ SV1593 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV169 @ SV930 @ SY5447 @ SY5448 @ SY5449 ) @ SV1593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(4251,plain,
! [SV1594: $i,SV931: $i,SV170: $i] :
( ( ! [SY5450: $i] :
( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ SV1594 @ SY5450 )
= ( c_List_Oappend @ ( c_List_Otake @ SV170 @ SV1594 @ SY5450 ) @ ( c_List_Otake @ SV931 @ ( c_List_Odrop @ SV170 @ SV1594 @ SY5450 ) @ SY5450 ) @ SY5450 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ ( c_Nat_Osize__class_Osize @ SV1594 @ ( tc_List_Olist @ SY5450 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4252,plain,
! [SV1595: $i,SV932: $i,SV171: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV171 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SV932 @ SV1595 @ SV171 @ SV171 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SV1595 @ SV932 @ SV171 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(4253,plain,
! [SV933: $i,SV172: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV172 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV933 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV172 )
= SV933 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3531]) ).
thf(4254,plain,
! [SV934: $i,SV173: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV173 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV934 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV173 )
= SV934 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(4255,plain,
! [SV935: $i,SV174: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV174 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ SV935 ) @ SV935 ) @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3533]) ).
thf(4256,plain,
! [SV936: $i,SV175: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV175 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV936 @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV936 ) @ SV936 ) @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3534]) ).
thf(4257,plain,
! [SV937: $i,SV176: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV176 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV937 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV937 ) @ SV937 ) @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3535]) ).
thf(4258,plain,
! [SV938: $i,SV177: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV177 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV177 ) @ SV938 ) @ SV938 ) @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ SV938 @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3536]) ).
thf(4259,plain,
! [SV1596: $i,SV939: $i,SV178: $i] :
( ( ! [SY5451: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV178 )
| ( c_HOL_Oord__class_Oless @ SV939 @ SV1596 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SV1596 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SY5451 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SV1596 @ SY5451 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4260,plain,
! [SV1597: $i,SV940: $i,SV179: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV179 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV940 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV1597 @ SV179 @ SV179 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV940 @ SV1597 @ SV179 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(4261,plain,
! [SV1598: $i,SV941: $i,SV180: $i] :
( ( ! [SY5452: $i] :
( ~ ( class_Orderings_Olinorder @ SV180 )
| ( c_lessequals @ SV941 @ SV1598 @ SV180 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY5452 @ SV941 @ SV180 ) @ SV1598 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4262,plain,
! [SV1599: $i,SV942: $i,SV181: $i] :
( ( ! [SY5453: $i] :
( ~ ( class_Orderings_Olinorder @ SV181 )
| ( c_lessequals @ SV942 @ SV1599 @ SV181 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV942 @ SY5453 @ SV181 ) @ SV1599 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(4263,plain,
! [SV1600: $i,SV943: $i,SV182: $i] :
( ( ! [SY5454: $i] :
( ~ ( class_Orderings_Olinorder @ SV182 )
| ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1600 @ SY5454 @ SV182 ) @ SV182 )
| ~ ( c_lessequals @ SV943 @ SY5454 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(4264,plain,
! [SV1601: $i,SV944: $i,SV183: $i] :
( ( ! [SY5455: $i] :
( ~ ( class_Orderings_Olinorder @ SV183 )
| ( c_lessequals @ SV944 @ ( c_Orderings_Oord__class_Omax @ SV1601 @ SY5455 @ SV183 ) @ SV183 )
| ~ ( c_lessequals @ SV944 @ SV1601 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(4265,plain,
! [SV1602: $i,SV945: $i,SV184: $i] :
( ( ! [SY5456: $i] :
( ~ ( class_Orderings_Olinorder @ SV184 )
| ( c_lessequals @ SV945 @ ( c_Orderings_Oord__class_Omax @ SV1602 @ SY5456 @ SV184 ) @ SV184 )
| ~ ( c_lessequals @ SV945 @ SY5456 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(4266,plain,
! [SV1603: $i,SV946: $i,SV185: $i] :
( ( ! [SY5457: $i] :
( ~ ( class_Orderings_Olinorder @ SV185 )
| ( c_lessequals @ SV946 @ ( c_Orderings_Oord__class_Omax @ SV1603 @ SY5457 @ SV185 ) @ SV185 )
| ~ ( c_lessequals @ SV946 @ SV1603 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(4267,plain,
! [SV1604: $i,SV947: $i,SV186: $i] :
( ( ! [SY5458: $i] :
( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_lessequals @ SV947 @ SV1604 @ SV186 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY5458 @ SV947 @ SV186 ) @ SV1604 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(4268,plain,
! [SV1605: $i,SV948: $i,SV187: $i] :
( ( ! [SY5459: $i] :
( ~ ( class_Orderings_Olinorder @ SV187 )
| ( c_lessequals @ SV948 @ SV1605 @ SV187 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV948 @ SY5459 @ SV187 ) @ SV1605 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(4269,plain,
! [SV1606: $i,SV949: $i,SV188: $i] :
( ( ( c_lessequals @ SV188 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SV1606 ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV188 @ SV1606 @ tc_nat ) @ SV949 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(4270,plain,
! [SV1607: $i,SV950: $i,SV189: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV189 @ SV950 @ tc_nat ) @ SV1607 @ tc_nat )
| ~ ( c_lessequals @ SV189 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1607 ) @ SV950 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(4271,plain,
! [SV1608: $i,SV951: $i,SV190: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV190 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ ( c_Power_Opower__class_Opower @ SV951 @ SV1608 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV951 @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(4272,plain,
! [SV1609: $i,SV952: $i,SV191: $i] :
( ( ! [SY5460: $i] :
( ~ ( class_Orderings_Olinorder @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV952 @ SV1609 @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV952 @ SY5460 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV952 @ ( c_Orderings_Oord__class_Omax @ SY5460 @ SV1609 @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(4273,plain,
! [SV1610: $i,SV953: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SV953 ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV953 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(4274,plain,
! [SV1611: $i,SV954: $i,SV193: $i] :
( ( ! [SY5461: $i] :
( ( c_List_Ofoldl @ SV193 @ SV954 @ ( c_List_Olist_ONil @ SV1611 ) @ SY5461 @ SV1611 )
= SV954 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(4275,plain,
! [SV1612: $i,SV955: $i,SV194: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV194 ) @ SV955 @ SV1612 )
= ( c_Lambda_OdB_OVar @ SV194 ) )
| ( SV194 = SV1612 )
| ( c_HOL_Oord__class_Oless @ SV1612 @ SV194 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(4276,plain,
! [SV195: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV195 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV195 ) @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3554]) ).
thf(4277,plain,
! [SV1613: $i,SV956: $i,SV196: $i] :
( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV196 @ SV956 @ SV1613 ) @ ( tc_List_Olist @ SV1613 ) ) @ ( c_Nat_Osize__class_Osize @ SV956 @ ( tc_List_Olist @ SV1613 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3555]) ).
thf(4278,plain,
! [SV1614: $i,SV958: $i,SV199: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV958 ) @ SV1614 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SV1614 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ SV958 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(4279,plain,
! [SV1615: $i,SV959: $i,SV200: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SV959 ) @ SV1615 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_lessequals @ SV1615 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SV959 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(4280,plain,
! [SV960: $i,SV201: $i] :
( ( ( SV201 = SV960 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV201 @ SV960 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV201 @ ( c_Suc @ SV960 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(4281,plain,
! [SV961: $i,SV202: $i] :
( ( ( SV202 = SV961 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV961 @ ( c_Suc @ SV202 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV961 @ SV202 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(4282,plain,
! [SV962: $i,SV203: $i] :
( ( ( SV203 = SV962 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV203 @ ( c_Suc @ SV962 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV203 @ SV962 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3561]) ).
thf(4283,plain,
! [SV1616: $i,SV963: $i,SV204: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ SV963 ) @ SV1616 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SV1616 @ tc_nat ) ) )
| ~ ( c_lessequals @ SV1616 @ SV963 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(4284,plain,
! [SV1617: $i,SV964: $i,SV205: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV964 ) @ SV1617 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV205 @ SV1617 @ tc_nat ) ) @ SV964 ) )
| ~ ( c_lessequals @ SV1617 @ SV205 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(4285,plain,
! [SV206: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV206 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ ( c_HOL_Oone__class_Oone @ SV206 ) @ SV206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3564]) ).
thf(4286,plain,
! [SV1618: $i,SV965: $i,SV207: $i] :
( ( ! [SY5462: $i,SY5463: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV207 @ SV965 @ SV1618 ) @ SY5462 @ SY5463 @ SV1618 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV207 @ SY5462 @ SY5463 @ SV1618 ) @ SV965 @ SV1618 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5462 @ ( c_Nat_Osize__class_Osize @ SV207 @ ( tc_List_Olist @ SV1618 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(4287,plain,
! [SV1619: $i,SV966: $i,SV208: $i] :
( ( ! [SY5464: $i,SY5465: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV208 @ SV966 @ SV1619 ) @ SY5464 @ SY5465 @ SV1619 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV208 @ SY5464 @ SY5465 @ SV1619 ) @ SV966 @ SV1619 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5464 @ ( c_Nat_Osize__class_Osize @ SV208 @ ( tc_List_Olist @ SV1619 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3566]) ).
thf(4288,plain,
! [SV1620: $i,SV967: $i,SV209: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV209 @ ( c_HOL_Ominus__class_Ominus @ SV967 @ SV1620 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV209 ) @ SV1620 ) @ SV967 @ tc_nat ) )
| ~ ( c_lessequals @ SV1620 @ SV967 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(4289,plain,
! [SV968: $i,SV210: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV210 ) @ SV968 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV210 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ SV968 ) ) )
= $true )
| ( ( SV210
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3568]) ).
thf(4290,plain,
! [SV1621: $i,SV969: $i,SV211: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV211 @ SV969 @ tc_nat ) @ SV1621 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV211 @ SV1621 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(4291,plain,
! [SV1622: $i,SV970: $i,SV212: $i] :
( ( ! [SY5466: $i] :
( ( c_Type_Otype_Otype__rec @ SV212 @ SV970 @ ( c_Type_Otype_OAtom @ SV1622 ) @ SY5466 )
= ( hAPP @ SV212 @ SV1622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(4292,plain,
! [SV1623: $i,SV971: $i,SV213: $i] :
( ( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1623 @ SV971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ SV213 @ SV1623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(4293,plain,
! [SV1624: $i,SV972: $i,SV214: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ SV214 @ SV972 @ SV1624 ) @ ( tc_List_Olist @ SV1624 ) )
= ( c_Nat_Osize__class_Osize @ SV972 @ ( tc_List_Olist @ SV1624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3572]) ).
thf(4294,plain,
! [SV1625: $i,SV974: $i,SV216: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV216 )
| ( c_HOL_Oord__class_Oless @ SV974 @ SV1625 @ SV216 )
| ( c_lessequals @ SV1625 @ SV974 @ SV216 )
| ~ ( c_lessequals @ SV974 @ SV1625 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(4295,plain,
! [SV975: $i,SV219: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV219 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV975 @ SV975 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3577]) ).
thf(4296,plain,
! [SV976: $i,SV220: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV220 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV976 @ SV976 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3578]) ).
thf(4297,plain,
! [SV977: $i,SV221: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV221 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV977 @ SV977 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3579]) ).
thf(4298,plain,
! [SV978: $i,SV222: $i] :
( ( ( ~ ( c_lessequals @ SV222 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV978 ) @ SV222 ) @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV978 ) @ SV222 ) @ SV222 @ tc_nat )
= SV978 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(4299,plain,
! [SV1626: $i,SV979: $i,SV223: $i] :
( ( ( ( c_Lambda_Oliftn @ SV223 @ ( c_Lambda_OdB_OVar @ SV979 ) @ SV1626 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV979 ) @ SV223 ) ) )
| ( c_HOL_Oord__class_Oless @ SV979 @ SV1626 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(4300,plain,
! [SV1627: $i,SV981: $i,SV225: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oappend @ SV225 @ SV981 @ SV1627 ) @ ( tc_List_Olist @ SV1627 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV225 @ ( tc_List_Olist @ SV1627 ) ) ) @ ( c_Nat_Osize__class_Osize @ SV981 @ ( tc_List_Olist @ SV1627 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3583]) ).
thf(4301,plain,
! [SV1628: $i,SV982: $i,SV226: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ SV226 @ SV982 @ SV1628 ) @ ( tc_List_Olist @ SV1628 ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV982 @ ( tc_List_Olist @ SV1628 ) ) @ SV226 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(4302,plain,
! [SV1629: $i,SV983: $i,SV227: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SV983 ) @ SV1629 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV1629 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV983 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(4303,plain,
! [SV1630: $i,SV988: $i,SV232: $i] :
( ( ! [SY5467: $i] :
( ( ( c_List_Otake @ SV232 @ ( c_List_Olist_OCons @ SV988 @ SV1630 @ SY5467 ) @ SY5467 )
= ( c_List_Olist_OCons @ SV988 @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV232 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1630 @ SY5467 ) @ SY5467 ) )
| ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4304,plain,
! [SV233: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV233 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV233 ) @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(4305,plain,
! [SV1631: $i,SV989: $i,SV234: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV234 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV989 @ SV1631 @ SV234 ) @ SV234 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV989 ) @ ( c_List_Olistsum @ SV1631 @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(4306,plain,
! [SV1632: $i,SV990: $i,SV235: $i] :
( ( ( c_Lambda_Oliftn @ SV235 @ ( c_Lambda_OdB_OAbs @ SV990 ) @ SV1632 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV235 @ SV990 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1632 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(4307,plain,
! [SV1633: $i,SV991: $i,SV236: $i] :
( ( ! [SY5468: $i,SY5469: $i,SY5470: $i,SY5471: $i] :
( ( ( hAPP @ ( hAPP @ SV236 @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV991 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SY5468 @ SV236 @ SY5469 @ SY5470 @ SY5471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3594]) ).
thf(4308,plain,
! [SV1634: $i,SV992: $i,SV237: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV237 )
| ( c_HOL_Oord__class_Oless @ SV992 @ SV1634 @ SV237 )
| ( c_HOL_Oord__class_Oless @ SV1634 @ SV992 @ SV237 )
| ( SV1634 = SV992 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3595]) ).
thf(4309,plain,
! [SV1635: $i,SV993: $i,SV238: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV238 )
| ( SV993 = SV1635 )
| ( c_HOL_Oord__class_Oless @ SV1635 @ SV993 @ SV238 )
| ( c_HOL_Oord__class_Oless @ SV993 @ SV1635 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(4310,plain,
! [SV994: $i,SV239: $i] :
( ( ( SV239 = SV994 )
= $true )
| ( ( ~ ( c_lessequals @ SV994 @ SV239 @ tc_nat )
| ~ ( c_lessequals @ SV239 @ SV994 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(4311,plain,
! [SV995: $i,SV240: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV240 @ SV995 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV995 @ SV240 @ tc_nat )
| ( SV995 = SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(4312,plain,
! [SV1636: $i,SV996: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV241 @ SV996 ) @ SV1636 ) )
| ( c_HOL_Oord__class_Oless @ SV996 @ SV1636 @ tc_nat )
| ( SV1636 = SV996 )
| ( c_HOL_Oord__class_Oless @ SV1636 @ SV996 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4313,plain,
! [SV1637: $i,SV997: $i,SV242: $i] :
( ( ! [SY5472: $i,SY5473: $i] :
( ( SV242 = SV997 )
| ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY5472 ) @ SY5473 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV997 )
| ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY5472 ) @ SY5473 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3600]) ).
thf(4314,plain,
! [SV1638: $i,SV998: $i,SV243: $i] :
( ( ! [SY5474: $i] :
( ~ ( class_Orderings_Olinorder @ SV243 )
| ( c_HOL_Oord__class_Oless @ SV998 @ SV1638 @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY5474 @ SV998 @ SV243 ) @ SV1638 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4315,plain,
! [SV244: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV244 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV244 ) @ SV244 )
= ( c_HOL_Ozero__class_Ozero @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3602]) ).
thf(4316,plain,
! [SV1639: $i,SV999: $i,SV245: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV245 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SV999 @ SV1639 @ SV245 ) @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1639 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SV999 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4317,plain,
! [SV1640: $i,SV1000: $i,SV246: $i] :
( ( ( ( c_List_Orotate @ SV246 @ SV1000 @ SV1640 )
= SV1000 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1000 @ ( tc_List_Olist @ SV1640 ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(4318,plain,
! [SV1641: $i,SV1001: $i,SV247: $i] :
( ( ! [SY5475: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV247 ) @ SV1001 ) @ SV1641 ) ) @ SY5475 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV247 ) @ SY5475 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1001 ) @ SY5475 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1641 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5475 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1641 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(4319,plain,
! [SV1642: $i,SV1004: $i,SV250: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SV1004 ) @ SV1642 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SV1642 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SV1004 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4320,plain,
! [SV1643: $i,SV1005: $i,SV251: $i] :
( ( ! [SY5476: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV251 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SY5476 @ SV1643 @ SV251 ) @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SY5476 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4321,plain,
! [SV1644: $i,SV1006: $i,SV252: $i] :
( ( ! [SY5477: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV252 @ SV1006 @ SV1644 ) @ SY5477 @ SV1644 )
= ( c_List_Olist_OCons @ SV252 @ ( c_List_Oappend @ SV1006 @ SY5477 @ SV1644 ) @ SV1644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4322,plain,
! [SV1645: $i,SV1007: $i,SV253: $i] :
( ( ! [SY5478: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV253 @ SV1007 @ SV1645 ) @ SY5478 @ SV1645 )
= ( c_List_Olist_OCons @ SV253 @ ( c_List_Oappend @ SV1007 @ SY5478 @ SV1645 ) @ SV1645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4323,plain,
! [SV1646: $i,SV1008: $i,SV254: $i] :
( ( SV254
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1008 @ ( tc_List_Olist @ SV1646 ) ) @ ( c_List_Oappend @ SV1008 @ SV254 @ SV1646 ) @ SV1646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(4324,plain,
! [SV1647: $i,SV1009: $i,SV255: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1009 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1647 @ SV1009 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1647 @ tc_nat ) )
| ~ ( c_lessequals @ SV1009 @ SV1647 @ tc_nat )
| ~ ( c_lessequals @ SV1009 @ SV255 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(4325,plain,
! [SV1648: $i,SV1010: $i,SV256: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SV1010 @ tc_nat ) @ SV1648 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SV1648 @ tc_nat ) @ SV1010 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3614]) ).
thf(4326,plain,
! [SV1649: $i,SV1011: $i,SV257: $i] :
( ( ! [SY5479: $i] :
( ( c_List_Omap @ ( c_COMBK @ SV257 @ SV1011 @ SV1649 ) @ SY5479 @ SV1649 @ SV1011 )
= ( c_List_Oreplicate @ ( c_Nat_Osize__class_Osize @ SY5479 @ ( tc_List_Olist @ SV1649 ) ) @ SV257 @ SV1011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(4327,plain,
! [SV1650: $i,SV1012: $i,SV258: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV1012 ) @ SV1650 ) @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1650 @ SV258 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1012 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(4328,plain,
! [SV1651: $i,SV1013: $i,SV259: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV1013 ) @ SV1651 ) @ SV259 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1651 @ SV259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1013 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4329,plain,
! [SV1652: $i,SV1014: $i,SV260: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV260 ) @ SV1014 @ SV1652 @ SV260 )
= ( c_List_Olist_ONil @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4330,plain,
! [SV1653: $i,SV1015: $i,SV261: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV261 ) @ SV1015 @ SV1653 @ SV261 )
= ( c_List_Olist_ONil @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(4331,plain,
! [SV1654: $i,SV1016: $i,SV262: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV262 ) @ SV1016 @ SV1654 @ SV262 )
= ( c_List_Olist_ONil @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(4332,plain,
! [SV1655: $i,SV1017: $i,SV263: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV263 @ SV1017 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1017 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1017 @ SV263 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV263 @ SV1655 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4333,plain,
! [SV1018: $i,SV264: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV264 ) @ SV1018 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV264 )
= SV1018 )
| ~ ( c_HOL_Oord__class_Oless @ SV264 @ SV1018 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3622]) ).
thf(4334,plain,
! [SV1019: $i,SV265: $i] :
( ( ( ~ ( c_lessequals @ SV265 @ SV1019 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV1019 ) @ SV265 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3623]) ).
thf(4335,plain,
! [SV1020: $i,SV266: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV266 ) @ SV1020 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV1020 @ SV266 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3624]) ).
thf(4336,plain,
! [SV1656: $i,SV1021: $i,SV267: $i] :
( ( ! [SY5480: $i] :
( ( c_List_Olist_OCons @ SV267 @ ( c_List_Oappend @ SV1021 @ SV1656 @ SY5480 ) @ SY5480 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV267 @ SV1021 @ SY5480 ) @ SV1656 @ SY5480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(4337,plain,
! [SV1657: $i,SV1022: $i,SV268: $i] :
( ( ! [SY5481: $i] :
( ( c_List_Olist_OCons @ SV268 @ ( c_List_Oappend @ SV1022 @ SV1657 @ SY5481 ) @ SY5481 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV268 @ SV1022 @ SY5481 ) @ SV1657 @ SY5481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(4338,plain,
! [SV1658: $i,SV1023: $i,SV269: $i] :
( ( ( c_lessequals @ SV269 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1023 ) @ SV269 ) @ SV1658 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1658 @ SV1023 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(4339,plain,
! [SV1024: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV270 @ ( tc_List_Olist @ SV1024 ) ) @ tc_nat )
= $true )
| ( ( SV270
= ( c_List_Olist_ONil @ SV1024 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3628]) ).
thf(4340,plain,
! [SV1659: $i,SV1025: $i,SV271: $i] :
( ( ! [SY5482: $i,SY5483: $i,SY5484: $i,SY5485: $i,SY5486: $i,SY5487: $i] :
( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SY5482 ) ) @ SY5483 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SY5483 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SY5482 ) @ SY5483 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5484 @ SV1025 @ SV271 @ SY5485 @ SY5486 @ SY5487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(4341,plain,
! [SV1660: $i,SV1026: $i,SV272: $i] :
( ( ! [SY5488: $i,SY5489: $i,SY5490: $i,SY5491: $i,SY5492: $i,SY5493: $i] :
( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SY5488 ) @ SY5489 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SY5488 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SY5489 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SY5490 @ SY5491 @ SY5492 @ SY5493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(4342,plain,
! [SV1661: $i,SV1027: $i,SV273: $i] :
( ( ! [SY5494: $i,SY5495: $i,SY5496: $i,SY5497: $i,SY5498: $i] :
( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SV1661 )
= ( hAPP @ ( hAPP @ SV273 @ SV1661 ) @ SV1027 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5494 @ SV273 @ SY5495 @ SY5496 @ SY5497 @ SY5498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3631]) ).
thf(4343,plain,
! [SV1662: $i,SV1028: $i,SV274: $i] :
( ( ! [SY5499: $i,SY5500: $i,SY5501: $i,SY5502: $i,SY5503: $i,SY5504: $i] :
( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SY5499 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SY5499 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5500 @ SV274 @ SY5501 @ SY5502 @ SY5503 @ SY5504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4344,plain,
! [SV1663: $i,SV1029: $i,SV275: $i] :
( ( ! [SY5505: $i,SY5506: $i,SY5507: $i,SY5508: $i] :
( ( ( hAPP @ ( hAPP @ SV275 @ SV1029 ) @ SV1663 )
= SV1663 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5505 @ SV275 @ SY5506 @ SY5507 @ SV1029 @ SY5508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(4345,plain,
! [SV1664: $i,SV1030: $i,SV276: $i] :
( ( ! [SY5509: $i,SY5510: $i,SY5511: $i,SY5512: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SV1030 ) @ SV1664 )
= SV1030 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5509 @ SV276 @ SY5510 @ SV1030 @ SY5511 @ SY5512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(4346,plain,
! [SV1665: $i,SV1031: $i,SV277: $i] :
( ( ! [SY5513: $i,SY5514: $i,SY5515: $i,SY5516: $i,SY5517: $i] :
( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SV1665 )
= ( hAPP @ ( hAPP @ SV277 @ SV1665 ) @ SV1031 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SY5513 @ SY5514 @ SY5515 @ SY5516 @ SY5517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(4347,plain,
! [SV1666: $i,SV1032: $i,SV278: $i] :
( ( ! [SY5518: $i,SY5519: $i,SY5520: $i,SY5521: $i,SY5522: $i,SY5523: $i] :
( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SY5518 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SY5518 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SY5519 @ SY5520 @ SY5521 @ SY5522 @ SY5523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3636]) ).
thf(4348,plain,
! [SV1667: $i,SV1033: $i,SV279: $i] :
( ( ! [SY5524: $i,SY5525: $i,SY5526: $i,SY5527: $i] :
( ( ( hAPP @ ( hAPP @ SV279 @ SV1033 ) @ SV1667 )
= SV1667 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SY5524 @ SY5525 @ SV1033 @ SY5526 @ SY5527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(4349,plain,
! [SV1668: $i,SV1034: $i,SV280: $i] :
( ( ! [SY5528: $i,SY5529: $i,SY5530: $i,SY5531: $i,SY5532: $i,SY5533: $i] :
( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SY5528 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SY5528 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SY5529 @ SY5530 @ SY5531 @ SY5532 @ SY5533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4350,plain,
! [SV1669: $i,SV1035: $i,SV281: $i] :
( ( ! [SY5534: $i,SY5535: $i,SY5536: $i,SY5537: $i,SY5538: $i] :
( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SV1669 )
= ( hAPP @ ( hAPP @ SV281 @ SV1669 ) @ SV1035 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SY5534 @ SY5535 @ SY5536 @ SY5537 @ SY5538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(4351,plain,
! [SV1670: $i,SV1036: $i,SV282: $i] :
( ( ! [SY5539: $i,SY5540: $i,SY5541: $i,SY5542: $i,SY5543: $i,SY5544: $i] :
( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SY5539 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SY5539 ) ) @ SV1670 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SY5540 @ SY5541 @ SY5542 @ SY5543 @ SY5544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(4352,plain,
! [SV1671: $i,SV1037: $i,SV283: $i] :
( ( ! [SY5545: $i,SY5546: $i,SY5547: $i,SY5548: $i,SY5549: $i,SY5550: $i] :
( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SY5545 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SY5545 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SY5546 @ SY5547 @ SY5548 @ SY5549 @ SY5550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(4353,plain,
! [SV1672: $i,SV1038: $i,SV284: $i] :
( ( ! [SY5551: $i,SY5552: $i,SY5553: $i,SY5554: $i,SY5555: $i,SY5556: $i] :
( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SY5551 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SY5551 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SY5552 @ SY5553 @ SY5554 @ SY5555 @ SY5556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3642]) ).
thf(4354,plain,
! [SV1673: $i,SV1039: $i,SV285: $i] :
( ( ! [SY5557: $i,SY5558: $i,SY5559: $i,SY5560: $i,SY5561: $i,SY5562: $i,SY5563: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SY5557 ) @ SY5558 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SY5557 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SY5558 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SY5559 @ SY5560 @ SY5561 @ SY5562 @ SY5563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(4355,plain,
! [SV1674: $i,SV1040: $i,SV286: $i] :
( ( ! [SY5564: $i,SY5565: $i,SY5566: $i,SY5567: $i,SY5568: $i,SY5569: $i] :
( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SY5564 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SY5564 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5565 @ SV286 @ SY5566 @ SY5567 @ SY5568 @ SY5569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(4356,plain,
! [SV1675: $i,SV1041: $i,SV287: $i] :
( ( ! [SY5570: $i,SY5571: $i,SY5572: $i,SY5573: $i,SY5574: $i,SY5575: $i] :
( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SY5570 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SY5570 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5571 @ SV287 @ SY5572 @ SY5573 @ SY5574 @ SY5575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(4357,plain,
! [SV1676: $i,SV1042: $i,SV288: $i] :
( ( ! [SY5576: $i,SY5577: $i,SY5578: $i,SY5579: $i,SY5580: $i,SY5581: $i] :
( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SY5576 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SY5576 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5577 @ SV288 @ SY5578 @ SY5579 @ SY5580 @ SY5581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(4358,plain,
! [SV1677: $i,SV1043: $i,SV289: $i] :
( ( ! [SY5582: $i,SY5583: $i,SY5584: $i,SY5585: $i,SY5586: $i,SY5587: $i] :
( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SY5582 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SY5582 ) ) @ SV1677 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5583 @ SV289 @ SY5584 @ SY5585 @ SY5586 @ SY5587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(4359,plain,
! [SV1678: $i,SV1044: $i,SV290: $i] :
( ( ! [SY5588: $i,SY5589: $i,SY5590: $i,SY5591: $i,SY5592: $i,SY5593: $i,SY5594: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SY5588 ) @ SY5589 ) )
= ( hAPP @ ( hAPP @ SV290 @ SY5588 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SY5589 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5590 @ SV290 @ SY5591 @ SY5592 @ SY5593 @ SY5594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3648]) ).
thf(4360,plain,
! [SV1679: $i,SV1045: $i,SV291: $i] :
( ( ! [SY5595: $i,SY5596: $i,SY5597: $i,SY5598: $i,SY5599: $i,SY5600: $i,SY5601: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SY5595 ) @ SY5596 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SY5595 ) @ SY5596 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5597 @ SV291 @ SY5598 @ SY5599 @ SY5600 @ SY5601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3649]) ).
thf(4361,plain,
! [SV1680: $i,SV1046: $i,SV292: $i] :
( ( ! [SY5602: $i,SY5603: $i,SY5604: $i,SY5605: $i,SY5606: $i,SY5607: $i,SY5608: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SY5602 ) @ SY5603 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SY5602 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SY5603 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5604 @ SV292 @ SY5605 @ SY5606 @ SY5607 @ SY5608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3650]) ).
thf(4362,plain,
! [SV1681: $i,SV1047: $i,SV293: $i] :
( ( ! [SY5609: $i,SY5610: $i,SY5611: $i,SY5612: $i] :
( ( ( hAPP @ ( hAPP @ SV293 @ SV1047 ) @ SV1681 )
= SV1047 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5609 @ SV293 @ SY5610 @ SY5611 @ SV1681 @ SY5612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3651]) ).
thf(4363,plain,
! [SV1682: $i,SV1048: $i,SV294: $i] :
( ( ! [SY5613: $i,SY5614: $i,SY5615: $i,SY5616: $i] :
( ( ( hAPP @ ( hAPP @ SV294 @ SV1048 ) @ SV1682 )
= SV1682 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5613 @ SV294 @ SY5614 @ SY5615 @ SV1048 @ SY5616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(4364,plain,
! [SV1683: $i,SV1049: $i,SV295: $i] :
( ( ! [SY5617: $i,SY5618: $i,SY5619: $i,SY5620: $i] :
( ( ( hAPP @ ( hAPP @ SV295 @ SV1049 ) @ SV1683 )
= SV1683 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5617 @ SV295 @ SY5618 @ SV1683 @ SY5619 @ SY5620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4365,plain,
! [SV1684: $i,SV1050: $i,SV296: $i] :
( ( ! [SY5621: $i,SY5622: $i,SY5623: $i,SY5624: $i] :
( ( ( hAPP @ ( hAPP @ SV296 @ SV1050 ) @ SV1684 )
= SV1050 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5621 @ SV296 @ SY5622 @ SV1050 @ SY5623 @ SY5624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(4366,plain,
! [SV1685: $i,SV1051: $i,SV297: $i] :
( ( ! [SY5625: $i,SY5626: $i,SY5627: $i,SY5628: $i,SY5629: $i,SY5630: $i] :
( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SY5625 ) ) @ SY5626 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SY5626 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SY5625 ) @ SY5626 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SY5627 @ SY5628 @ SY5629 @ SY5630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3655]) ).
thf(4367,plain,
! [SV1686: $i,SV1052: $i,SV298: $i] :
( ( ! [SY5631: $i,SY5632: $i,SY5633: $i,SY5634: $i,SY5635: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SV1686 )
= ( hAPP @ ( hAPP @ SV298 @ SV1686 ) @ SV1052 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5631 @ SV298 @ SY5632 @ SY5633 @ SY5634 @ SY5635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3656]) ).
thf(4368,plain,
! [SV1687: $i,SV1053: $i,SV299: $i] :
( ( ! [SY5636: $i,SY5637: $i,SY5638: $i,SY5639: $i] :
( ( ( hAPP @ ( hAPP @ SV299 @ SV1053 ) @ SV1687 )
= SV1053 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SY5636 @ SY5637 @ SV1687 @ SY5638 @ SY5639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3657]) ).
thf(4369,plain,
! [SV1688: $i,SV1054: $i,SV300: $i] :
( ( ! [SY5640: $i,SY5641: $i,SY5642: $i,SY5643: $i] :
( ( ( hAPP @ ( hAPP @ SV300 @ SV1054 ) @ SV1688 )
= SV1688 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SY5640 @ SY5641 @ SV1054 @ SY5642 @ SY5643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(4370,plain,
! [SV1689: $i,SV1055: $i,SV301: $i] :
( ( ! [SY5644: $i,SY5645: $i,SY5646: $i,SY5647: $i] :
( ( ( hAPP @ ( hAPP @ SV301 @ SV1055 ) @ SV1055 )
= ( hAPP @ ( hAPP @ SV1689 @ ( hAPP @ ( hAPP @ SV301 @ SY5644 ) @ SY5644 ) ) @ SV1055 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SV1689 @ SY5645 @ SY5646 @ SY5644 @ SY5647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(4371,plain,
! [SV1690: $i,SV1056: $i,SV302: $i] :
( ( ! [SY5648: $i,SY5649: $i,SY5650: $i,SY5651: $i,SY5652: $i] :
( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SV1690 @ SY5648 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SV1690 @ ( hAPP @ ( hAPP @ SV302 @ SY5648 ) @ SY5649 ) ) @ SV1056 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SV1690 @ SY5650 @ SY5651 @ SY5649 @ SY5652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3660]) ).
thf(4372,plain,
! [SV1691: $i,SV1057: $i,SV303: $i] :
( ( ! [SY5653: $i,SY5654: $i,SY5655: $i,SY5656: $i,SY5657: $i] :
( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SV1691 ) @ SY5653 ) ) @ SY5653 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SV1691 ) @ SY5654 ) ) @ SY5653 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SY5655 @ SY5656 @ SY5654 @ SY5657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(4373,plain,
! [SV1692: $i,SV1058: $i,SV304: $i] :
( ( ! [SY5658: $i,SY5659: $i,SY5660: $i,SY5661: $i,SY5662: $i,SY5663: $i] :
( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SY5658 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SY5659 ) @ SY5658 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SY5659 ) ) @ SY5658 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SY5660 @ SY5661 @ SY5662 @ SY5663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(4374,plain,
! [SV1693: $i,SV1059: $i,SV305: $i] :
( ( ! [SY5664: $i] :
( ~ ( hBOOL @ ( hAPP @ SV305 @ ( c_Type_Otype_Otype__case @ SV1059 @ SV1693 @ ( c_Type_Otype_OAtom @ SY5664 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV305 @ ( hAPP @ SV1059 @ SY5664 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3663]) ).
thf(4375,plain,
! [SV1694: $i,SV1060: $i,SV306: $i] :
( ( ! [SY5665: $i] :
( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_Type_Otype_Otype__case @ SV1060 @ SV1694 @ ( c_Type_Otype_OAtom @ SY5665 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV306 @ ( hAPP @ SV1060 @ SY5665 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(4376,plain,
! [SV1695: $i,SV1061: $i,SV307: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ SV307 @ SV1061 @ SV1695 ) @ SV1695 )
= SV1061 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(4377,plain,
! [SV1696: $i,SV1062: $i,SV308: $i] :
( ( ! [SY5666: $i,SY5667: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1062 ) @ SV1696 ) ) @ ( c_Suc @ SY5666 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY5667 ) @ SV1062 ) @ SY5666 ) ) @ SV1696 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ SY5667 ) @ SV1696 ) ) @ SV1062 ) @ SY5666 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1696 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5666 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3666]) ).
thf(4378,plain,
! [SV1697: $i,SV1063: $i,SV309: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ SV309 @ SV1063 @ SV1697 ) @ ( c_List_Odrop @ SV309 @ SV1063 @ SV1697 ) @ SV1697 )
= SV1063 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(4379,plain,
! [SV1698: $i,SV1064: $i,SV310: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV310 ) @ SV1064 @ tc_nat ) @ ( c_Suc @ SV1698 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV310 @ SV1064 @ tc_nat ) @ SV1698 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3668]) ).
thf(4380,plain,
! [SV312: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV312 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV312 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(4381,plain,
! [SV1699: $i,SV1066: $i,SV313: $i] :
( ( ! [SY5668: $i,SY5669: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV1699 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SY5668 ) @ SY5669 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SY5668 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1699 ) @ SY5669 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(4382,plain,
! [SV1700: $i,SV1067: $i,SV314: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV1067 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV1700 ) )
| ~ ( c_Lambda_Obeta @ SV1067 @ SV1700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(4383,plain,
! [SV1701: $i,SV1068: $i,SV315: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV315 ) @ SV1068 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1701 ) @ SV1068 ) )
| ~ ( c_Lambda_Obeta @ SV315 @ SV1701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(4384,plain,
! [SV1702: $i,SV1069: $i,SV316: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV316 @ SV1069 ) @ ( c_List_Olist_OCons @ SV1702 @ ( c_List_Olist_ONil @ SV1069 ) @ SV1069 ) @ SV1069 ) @ SV1069 )
= ( c_List_Olist_OCons @ SV1702 @ SV316 @ SV1069 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(4385,plain,
! [SV1070: $i,SV317: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV317 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1070 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3675]) ).
thf(4386,plain,
! [SV1703: $i,SV1071: $i,SV318: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV318 ) @ SV1071 @ SV1703 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV318 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1703 @ SV318 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(4387,plain,
! [SV1704: $i,SV1072: $i,SV319: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV319 )
| ( ( c_Orderings_Oord__class_Omax @ SV1072 @ SV1704 @ SV319 )
= ( c_Orderings_Oord__class_Omax @ SV1704 @ SV1072 @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3677]) ).
thf(4388,plain,
! [SV1705: $i,SV1073: $i,SV320: $i] :
( ( ( ( c_Lambda_Oliftn @ SV320 @ ( c_Lambda_OdB_OVar @ SV1073 ) @ SV1705 )
= ( c_Lambda_OdB_OVar @ SV1073 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1073 @ SV1705 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3678]) ).
thf(4389,plain,
! [SV1706: $i,SV1074: $i,SV321: $i] :
( ( ( ( c_List_Odrop @ SV321 @ SV1074 @ SV1706 )
= ( c_List_Olist_ONil @ SV1706 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1074 @ ( tc_List_Olist @ SV1706 ) ) @ SV321 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(4390,plain,
! [SV1707: $i,SV1075: $i,SV323: $i] :
( ( ( c_List_Odistinct @ ( c_List_Odrop @ SV323 @ SV1075 @ SV1707 ) @ SV1707 )
| ~ ( c_List_Odistinct @ SV1075 @ SV1707 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3680]) ).
thf(4391,plain,
! [SV1076: $i,SV324: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orev @ SV324 @ SV1076 ) @ SV1076 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV324 @ SV1076 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(4392,plain,
! [SV1077: $i,SV325: $i] :
( ( ( c_List_Odistinct @ SV325 @ SV1077 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Orev @ SV325 @ SV1077 ) @ SV1077 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(4393,plain,
! [SV1708: $i,SV1078: $i,SV326: $i] :
( ( ! [SY5670: $i] :
( ( c_List_Odrop @ SV326 @ ( c_List_Oreplicate @ SV1078 @ SV1708 @ SY5670 ) @ SY5670 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV1078 @ SV326 @ tc_nat ) @ SV1708 @ SY5670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(4394,plain,
! [SV1079: $i,SV327: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV327 @ SV1079 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1079 @ SV327 @ tc_nat )
| ( SV1079 = SV327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3684]) ).
thf(4395,plain,
! [SV1709: $i,SV1080: $i,SV328: $i] :
( ( ~ ( class_Orderings_Oorder @ SV328 )
| ( SV1080 = SV1709 )
| ~ ( c_lessequals @ SV1709 @ SV1080 @ SV328 )
| ~ ( c_lessequals @ SV1080 @ SV1709 @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(4396,plain,
! [SV1710: $i,SV1081: $i,SV329: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV329 )
| ( c_HOL_Oord__class_Oless @ SV1081 @ SV1710 @ SV329 )
| ( c_HOL_Oord__class_Oless @ SV1710 @ SV1081 @ SV329 )
| ( SV1710 = SV1081 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3686]) ).
thf(4397,plain,
! [SV1711: $i,SV1082: $i,SV330: $i] :
( ( ~ ( class_Orderings_Oorder @ SV330 )
| ( SV1082 = SV1711 )
| ~ ( c_lessequals @ SV1711 @ SV1082 @ SV330 )
| ~ ( c_lessequals @ SV1082 @ SV1711 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(4398,plain,
! [SV1712: $i,SV1083: $i,SV331: $i] :
( ( ~ ( class_Orderings_Oorder @ SV331 )
| ( SV1083 = SV1712 )
| ~ ( c_lessequals @ SV1083 @ SV1712 @ SV331 )
| ~ ( c_lessequals @ SV1712 @ SV1083 @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(4399,plain,
! [SV1713: $i,SV1084: $i,SV332: $i] :
( ( ! [SY5671: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV332 @ SV1084 @ SV1713 ) @ ( c_List_Oreplicate @ SY5671 @ SV1084 @ SV1713 ) @ SV1713 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY5671 @ SV1084 @ SV1713 ) @ ( c_List_Oreplicate @ SV332 @ SV1084 @ SV1713 ) @ SV1713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(4400,plain,
! [SV1714: $i,SV1085: $i,SV333: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV333 )
| ( c_HOL_Oord__class_Oless @ SV1085 @ SV1714 @ SV333 )
| ( SV1714 = SV1085 )
| ( c_HOL_Oord__class_Oless @ SV1714 @ SV1085 @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3690]) ).
thf(4401,plain,
! [SV1715: $i,SV1086: $i,SV334: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV334 )
| ( SV1086 = SV1715 )
| ( c_HOL_Oord__class_Oless @ SV1086 @ SV1715 @ SV334 )
| ( c_HOL_Oord__class_Oless @ SV1715 @ SV1086 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(4402,plain,
! [SV1716: $i,SV1087: $i,SV335: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV335 )
| ( c_lessequals @ SV1087 @ SV1716 @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SV1716 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(4403,plain,
! [SV1717: $i,SV1088: $i,SV336: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV336 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV1717 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ SV1088 @ SV1717 @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(4404,plain,
! [SV337: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV337 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV337 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(4405,plain,
! [SV338: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV338 @ tc_nat )
= $false )
| ( ( SV338
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV338 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3695]) ).
thf(4406,plain,
! [SV1089: $i,SV339: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV339 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1089 @ SV1089 @ SV339 )
= SV1089 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3696]) ).
thf(4407,plain,
! [SV1718: $i,SV1090: $i,SV340: $i] :
( ( ! [SY5672: $i,SY5673: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SY5672 ) @ SY5673 ) @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1718 @ SY5673 @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SY5672 @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(4408,plain,
! [SV1719: $i,SV1091: $i,SV341: $i] :
( ( ! [SY5674: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV341 ) @ SV1091 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1719 ) @ SY5674 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1091 @ SY5674 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV341 @ SV1719 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(4409,plain,
! [SV1092: $i,SV342: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV342 ) @ SV1092 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV1092 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3699]) ).
thf(4410,plain,
! [SV1093: $i,SV343: $i] :
( ( ( c_lessequals @ SV343 @ SV1093 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV343 @ SV1093 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3700]) ).
thf(4411,plain,
! [SV1094: $i,SV344: $i] :
( ( ( c_lessequals @ SV344 @ SV1094 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV344 @ SV1094 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(4412,plain,
! [SV1720: $i,SV1095: $i,SV345: $i] :
( ( ~ ( class_Orderings_Oorder @ SV345 )
| ( c_lessequals @ SV1095 @ SV1720 @ SV345 )
| ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SV1720 @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3702]) ).
thf(4413,plain,
! [SV1721: $i,SV1096: $i,SV346: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV346 )
| ( c_lessequals @ SV1096 @ SV1721 @ SV346 )
| ~ ( c_HOL_Oord__class_Oless @ SV1096 @ SV1721 @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(4414,plain,
! [SV1722: $i,SV1097: $i,SV347: $i] :
( ( ! [SY5675: $i,SY5676: $i] :
( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1097 ) @ SV1722 ) @ SY5675 )
| ~ ( c_Type_Otyping @ SV347 @ SV1722 @ SY5676 )
| ~ ( c_Type_Otyping @ SV347 @ SV1097 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5676 ) @ SY5675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(4415,plain,
! [SV1723: $i,SV1098: $i,SV349: $i] :
( ( ! [SY5677: $i] :
( ( ( c_List_Olist__update @ SV349 @ SV1098 @ SV1723 @ SY5677 )
= ( c_List_Oappend @ ( c_List_Otake @ SV1098 @ SV349 @ SY5677 ) @ ( c_List_Olist_OCons @ SV1723 @ ( c_List_Odrop @ ( c_Suc @ SV1098 ) @ SV349 @ SY5677 ) @ SY5677 ) @ SY5677 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1098 @ ( c_Nat_Osize__class_Osize @ SV349 @ ( tc_List_Olist @ SY5677 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3705]) ).
thf(4416,plain,
! [SV1724: $i,SV1099: $i,SV350: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV350 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ ( c_Power_Opower__class_Opower @ SV1099 @ ( c_Suc @ SV1724 ) @ SV350 ) @ SV350 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ SV1099 @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(4417,plain,
! [SV1100: $i,SV351: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV351 ) @ SV1100 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(4418,plain,
! [SV1725: $i,SV1101: $i,SV352: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1725 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV352 ) @ SV1725 ) @ ( c_Suc @ SV1101 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV1725 @ SV1101 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3708]) ).
thf(4419,plain,
! [SV1726: $i,SV1102: $i,SV353: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV353 )
| ( c_HOL_Oord__class_Oless @ SV1102 @ SV1726 @ SV353 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1102 @ SV1726 @ SV353 ) @ ( c_HOL_Ozero__class_Ozero @ SV353 ) @ SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3709]) ).
thf(4420,plain,
! [SV1727: $i,SV1103: $i,SV354: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV354 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1103 @ SV1727 @ SV354 ) @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV354 )
| ~ ( c_HOL_Oord__class_Oless @ SV1103 @ SV1727 @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(4421,plain,
! [SV1728: $i,SV1104: $i,SV355: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV355 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1104 @ SV355 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1728 @ SV355 ) @ SV355 )
| ~ ( c_HOL_Oord__class_Oless @ SV1104 @ SV1728 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(4422,plain,
! [SV1729: $i,SV1105: $i,SV356: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV356 )
| ( c_HOL_Oord__class_Oless @ SV1105 @ SV1729 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1105 @ SV356 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1729 @ SV356 ) @ SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(4423,plain,
! [SV1730: $i,SV1106: $i,SV359: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV359 ) @ SV1106 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1730 @ SV1106 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV359 @ SV1730 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(4424,plain,
! [SV1731: $i,SV1107: $i,SV360: $i] :
( ( ! [SY5678: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV360 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV1107 ) @ SV1731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SY5678 ) @ SV1731 ) @ SV360 )
| ~ ( c_lessequals @ SV1107 @ SY5678 @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3714]) ).
thf(4425,plain,
! [SV1732: $i,SV1108: $i,SV361: $i] :
( ( ! [SY5679: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV361 )
| ( c_lessequals @ SV1108 @ SV1732 @ SV361 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1108 ) @ SY5679 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1732 ) @ SY5679 ) @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3715]) ).
thf(4426,plain,
! [SV1733: $i,SV1109: $i,SV362: $i] :
( ( ! [SY5680: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV362 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV1733 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SY5680 ) @ SV362 )
| ~ ( c_lessequals @ SV1733 @ SY5680 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3716]) ).
thf(4427,plain,
! [SV1734: $i,SV1110: $i,SV363: $i] :
( ( ! [SY5681: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV363 )
| ( c_lessequals @ SV1110 @ SV1734 @ SV363 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SY5681 ) @ SV1110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SY5681 ) @ SV1734 ) @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(4428,plain,
! [SV1735: $i,SV1111: $i,SV364: $i] :
( ( ! [SY5682: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV364 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV1111 ) @ SV1735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SY5682 ) @ SV1735 ) @ SV364 )
| ~ ( c_lessequals @ SV1111 @ SY5682 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(4429,plain,
! [SV1736: $i,SV1112: $i,SV365: $i] :
( ( ! [SY5683: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV365 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV1736 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SY5683 ) @ SV365 )
| ~ ( c_lessequals @ SV1736 @ SY5683 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3719]) ).
thf(4430,plain,
! [SV1737: $i,SV1113: $i,SV366: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV366 ) @ SV1113 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1737 ) @ SV1113 ) @ tc_nat )
| ~ ( c_lessequals @ SV366 @ SV1737 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(4431,plain,
! [SV1738: $i,SV1114: $i,SV367: $i] :
( ( ( c_lessequals @ SV367 @ SV1114 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1738 ) @ SV367 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1738 ) @ SV1114 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(4432,plain,
! [SV1739: $i,SV1115: $i,SV368: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SV1739 ) @ tc_nat )
| ~ ( c_lessequals @ SV1115 @ SV1739 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3722]) ).
thf(4433,plain,
! [SV369: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV369 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV369 ) @ ( c_HOL_Oone__class_Oone @ SV369 ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3723]) ).
thf(4434,plain,
! [SV1740: $i,SV1116: $i,SV370: $i] :
( ( ! [SY5684: $i] :
( ( ( c_List_Olist__update @ SV370 @ SV1116 @ SV1740 @ SY5684 )
= SV370 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SY5684 ) ) @ SV1116 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3724]) ).
thf(4435,plain,
! [SV1117: $i,SV371: $i] :
( ( ( ~ ( c_lessequals @ SV371 @ SV1117 @ tc_nat ) )
= $true )
| ( ( SV1117
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1117 @ SV371 @ tc_nat ) ) @ SV371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3725]) ).
thf(4436,plain,
! [SV1118: $i,SV372: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV372 ) @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV372 @ tc_nat ) )
= SV1118 )
= $true )
| ( ( ~ ( c_lessequals @ SV372 @ SV1118 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3726]) ).
thf(4437,plain,
! [SV1119: $i,SV373: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV373 @ SV1119 @ tc_nat ) ) @ SV1119 )
= SV373 )
= $true )
| ( ( ~ ( c_lessequals @ SV1119 @ SV373 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3727]) ).
thf(4438,plain,
! [SV1741: $i,SV1120: $i,SV374: $i] :
( ( ! [SY5685: $i,SY5686: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV374 @ SV1120 @ SV1741 @ SY5685 ) @ SY5686 )
= ( hAPP @ SV374 @ ( c_HOL_Ominus__class_Ominus @ SY5686 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1120 @ SY5686 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(4439,plain,
! [SV1742: $i,SV1121: $i,SV375: $i] :
( ( ! [SY5687: $i,SY5688: $i,SY5689: $i,SY5690: $i,SY5691: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ SY5687 ) )
= ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ ( c_Suc @ SY5687 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5688 @ SV375 @ SV1742 @ SY5689 @ SY5690 @ SY5691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(4440,plain,
! [SV1743: $i,SV1122: $i,SV376: $i] :
( ( ! [SY5692: $i,SY5693: $i,SY5694: $i,SY5695: $i,SY5696: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ SY5692 ) ) @ SV1743 )
= ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ ( c_Suc @ SY5692 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5693 @ SV376 @ SV1122 @ SY5694 @ SY5695 @ SY5696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(4441,plain,
! [SV1744: $i,SV1123: $i,SV377: $i] :
( ( ! [SY5697: $i,SY5698: $i,SY5699: $i,SY5700: $i,SY5701: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SV1744 ) )
= ( hAPP @ ( hAPP @ SY5697 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SV1744 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5698 @ SY5697 @ SV377 @ SY5699 @ SY5700 @ SY5701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(4442,plain,
! [SV1745: $i,SV1124: $i,SV378: $i] :
( ( ! [SY5702: $i,SY5703: $i,SY5704: $i,SY5705: $i,SY5706: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SV1745 ) )
= ( hAPP @ ( hAPP @ SY5702 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SV1745 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5703 @ SY5702 @ SV378 @ SY5704 @ SY5705 @ SY5706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(4443,plain,
! [SV1125: $i,SV379: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV379 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1125 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV1125 ) @ ( c_HOL_Oone__class_Oone @ SV379 ) ) @ SV379 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3733]) ).
thf(4444,plain,
! [SV1746: $i,SV1126: $i,SV380: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ ( c_HOL_Ominus__class_Ominus @ SV1126 @ SV1746 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ SV1126 ) @ SV1746 @ tc_nat ) )
| ~ ( c_lessequals @ SV1746 @ SV1126 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(4445,plain,
! [SV1747: $i,SV1127: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV381 @ SV1127 @ tc_nat ) ) @ SV1747 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV381 ) @ SV1747 ) @ SV1127 @ tc_nat ) )
| ~ ( c_lessequals @ SV1127 @ SV381 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(4446,plain,
! [SV1748: $i,SV1128: $i,SV382: $i] :
( ( ! [SY5707: $i] :
( ( c_List_Odrop @ SV382 @ ( c_List_Odrop @ SV1128 @ SV1748 @ SY5707 ) @ SY5707 )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV382 ) @ SV1128 ) @ SV1748 @ SY5707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(4447,plain,
! [SV1749: $i,SV1129: $i,SV383: $i] :
( ( ! [SY5708: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV383 )
| ( c_lessequals @ SV1129 @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SY5708 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SV1749 @ ( c_Suc @ SY5708 ) @ SV383 ) @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(4448,plain,
! [SV1750: $i,SV1130: $i,SV384: $i] :
( ( ! [SY5709: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV384 ) @ SV1130 ) @ SV1750 @ SY5709 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV384 @ SV1750 @ SY5709 ) @ ( c_List_Oreplicate @ SV1130 @ SV1750 @ SY5709 ) @ SY5709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(4449,plain,
! [SV1751: $i,SV1132: $i,SV386: $i] :
( ( ! [SY5710: $i] :
( ( c_List_Otake @ SV386 @ ( c_List_Oappend @ SV1132 @ SV1751 @ SY5710 ) @ SY5710 )
= ( c_List_Oappend @ ( c_List_Otake @ SV386 @ SV1132 @ SY5710 ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV386 @ ( c_Nat_Osize__class_Osize @ SV1132 @ ( tc_List_Olist @ SY5710 ) ) @ tc_nat ) @ SV1751 @ SY5710 ) @ SY5710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3740]) ).
thf(4450,plain,
! [SV1133: $i,SV387: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV387 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV387 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1133 @ SV387 ) @ SV387 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1133 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3741]) ).
thf(4451,plain,
! [SV1134: $i,SV388: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV388 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1134 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV388 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1134 @ SV388 ) @ SV388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(4452,plain,
! [SV1752: $i,SV1135: $i,SV389: $i] :
( ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV389 @ SV1135 @ SV1752 ) @ SV1752 )
= ( c_List_Olist_ONil @ SV1752 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3743]) ).
thf(4453,plain,
! [SV1136: $i,SV390: $i] :
( ( ( ~ ( class_Power_Opower @ SV390 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1136 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV390 )
= ( c_HOL_Oone__class_Oone @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(4454,plain,
! [SV1137: $i,SV391: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV391 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1137 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV391 )
= ( c_HOL_Oone__class_Oone @ SV391 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(4455,plain,
! [SV1753: $i,SV1138: $i,SV392: $i] :
( ( ( c_List_Odistinct @ SV392 @ SV1138 )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ SV1753 @ SV392 @ SV1138 ) @ SV1138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(4456,plain,
! [SV1754: $i,SV1139: $i,SV393: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate @ SV393 @ SV1139 @ SV1754 ) @ SV1754 )
| ~ ( c_List_Odistinct @ SV1139 @ SV1754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(4457,plain,
! [SV1140: $i,SV394: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV394 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Orev @ SV1140 @ SV394 ) @ SV394 )
= ( c_List_Olistsum @ SV1140 @ SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3748]) ).
thf(4458,plain,
! [SV1755: $i,SV1141: $i,SV395: $i] :
( ( ! [SY5711: $i] :
( ( c_List_Olistsp @ SV395 @ ( c_List_Oappend @ SV1141 @ SV1755 @ SY5711 ) @ SY5711 )
| ~ ( c_List_Olistsp @ SV395 @ SV1755 @ SY5711 )
| ~ ( c_List_Olistsp @ SV395 @ SV1141 @ SY5711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3749]) ).
thf(4459,plain,
! [SV1756: $i,SV1142: $i,SV396: $i] :
( ( ! [SY5712: $i,SY5713: $i,SY5714: $i,SY5715: $i] :
( ( c_Fun_Ocomp @ SV396 @ ( c_Fun_Ocomp @ SV1142 @ SV1756 @ SY5712 @ SY5713 @ SY5714 ) @ SY5713 @ SY5715 @ SY5714 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV396 @ SV1142 @ SY5713 @ SY5715 @ SY5712 ) @ SV1756 @ SY5712 @ SY5715 @ SY5714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3750]) ).
thf(4460,plain,
! [SV1757: $i,SV1143: $i,SV397: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV397 ) ) @ SV1143 ) @ SV1757 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV397 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV397 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3751]) ).
thf(4461,plain,
! [SV1758: $i,SV1144: $i,SV398: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV398 ) ) @ SV1144 ) @ SV1758 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV398 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1758 @ SV398 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3752]) ).
thf(4462,plain,
! [SV1759: $i,SV1145: $i,SV399: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV399 @ SV1145 @ SV1759 ) @ ( tc_List_Olist @ SV1759 ) )
= SV399 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(4463,plain,
! [SV1146: $i,SV400: $i] :
( ( ( c_lessequals @ SV400 @ SV1146 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV400 ) @ SV1146 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3754]) ).
thf(4464,plain,
! [SV1147: $i,SV401: $i] :
( ( ( c_lessequals @ SV401 @ ( c_Suc @ SV1147 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV401 @ SV1147 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3755]) ).
thf(4465,plain,
! [SV1760: $i,SV1148: $i,SV403: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV403 @ SV1148 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV1760 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1148 @ SV1760 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV1148 @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV403 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3757]) ).
thf(4466,plain,
! [SV1761: $i,SV1149: $i,SV404: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SV1149 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1761 @ SV1149 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV404 @ SV1761 @ tc_nat )
| ~ ( c_lessequals @ SV1149 @ SV1761 @ tc_nat )
| ~ ( c_lessequals @ SV1149 @ SV404 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3758]) ).
thf(4467,plain,
! [SV1762: $i,SV1150: $i,SV405: $i] :
( ( ! [SY5716: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV405 )
| ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1762 ) @ SY5716 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SY5716 @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1762 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3759]) ).
thf(4468,plain,
! [SV1763: $i,SV1151: $i,SV406: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV406 ) ) @ SV1151 ) @ SV1763 )
= ( c_Lambda_OdB_OVar @ SV406 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV406 @ SV1763 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(4469,plain,
! [SV1764: $i,SV1152: $i,SV407: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV407 ) @ ( c_Lambda_OdB_OVar @ SV1152 ) ) @ SV1764 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(4470,plain,
! [SV1153: $i,SV408: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV408 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV408 ) @ SV1153 ) @ SV1153 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_lessequals @ SV1153 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3762]) ).
thf(4471,plain,
! [SV1154: $i,SV409: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV409 ) )
= $true )
| ( ( ( c_lessequals @ SV1154 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV409 ) @ SV1154 ) @ SV1154 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(4472,plain,
! [SV1765: $i,SV1155: $i,SV410: $i] :
( ( ! [SY5717: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SV1765 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SY5717 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SY5717 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(4473,plain,
! [SV1766: $i,SV1156: $i,SV411: $i] :
( ( ! [SY5718: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV411 )
| ( c_HOL_Oord__class_Oless @ SV1156 @ SV1766 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY5718 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SY5718 @ SV1766 @ SV411 ) @ SV411 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SY5718 @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3765]) ).
thf(4474,plain,
! [SV1767: $i,SV1157: $i,SV412: $i] :
( ( ! [SY5719: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SV1767 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SY5719 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1767 @ SY5719 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3766]) ).
thf(4475,plain,
! [SV1768: $i,SV1158: $i,SV413: $i] :
( ( ! [SY5720: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV413 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1768 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY5720 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SY5720 @ SV1768 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SY5720 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(4476,plain,
! [SV1769: $i,SV1159: $i,SV414: $i] :
( ( ! [SY5721: $i] :
( ( c_Lambda_Oliftn @ SV414 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1159 ) @ SV1769 ) @ SY5721 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV414 @ SV1159 @ SY5721 ) ) @ ( c_Lambda_Oliftn @ SV414 @ SV1769 @ SY5721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3768]) ).
thf(4477,plain,
! [SV1770: $i,SV1161: $i,SV416: $i] :
( ( ! [SY5722: $i] :
( ( ( c_List_Odrop @ SV416 @ ( c_List_Olist_OCons @ SV1161 @ SV1770 @ SY5722 ) @ SY5722 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1770 @ SY5722 ) )
| ( SV416
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3770]) ).
thf(4478,plain,
! [SV1162: $i,SV417: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV417 @ ( c_HOL_Ominus__class_Ominus @ SV417 @ SV1162 @ tc_nat ) @ tc_nat )
= SV1162 )
= $true )
| ( ( ~ ( c_lessequals @ SV1162 @ SV417 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3771]) ).
thf(4479,plain,
! [SV1163: $i,SV418: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV418 ) ) @ SV1163 )
= ( c_Lambda_OdB_OVar @ SV418 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV418 @ SV1163 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3772]) ).
thf(4480,plain,
! [SV1771: $i,SV1165: $i,SV420: $i] :
( ( ! [SY5723: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV420 @ SV1165 @ SV1771 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5723 @ SV1771 )
= ( c_List_Olist_OCons @ SY5723 @ SV1165 @ SV1771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(4481,plain,
! [SV1166: $i,SV421: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV421 @ SV421 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV421 ) @ SV1166 @ SV421 )
= ( c_Lambda_Oliftn @ SV421 @ SV1166 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3775]) ).
thf(4482,plain,
! [SV1772: $i,SV1167: $i,SV422: $i] :
( ( ! [SY5724: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV422 @ SV1167 @ SV1772 @ SY5724 ) @ ( tc_List_Olist @ SY5724 ) )
= ( c_Nat_Osize__class_Osize @ SV422 @ ( tc_List_Olist @ SY5724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(4483,plain,
! [SV1168: $i,SV423: $i] :
( ( ( SV423
= ( c_Suc @ SV1168 ) )
= $true )
| ( ( ( c_lessequals @ SV423 @ SV1168 @ tc_nat )
| ~ ( c_lessequals @ SV423 @ ( c_Suc @ SV1168 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3777]) ).
thf(4484,plain,
! [SV1169: $i,SV425: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV425 @ SV1169 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1169 @ ( c_Suc @ SV425 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3779]) ).
thf(4485,plain,
! [SV1170: $i,SV426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV426 @ ( c_Suc @ SV1170 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1170 @ SV426 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3780]) ).
thf(4486,plain,
! [SV1773: $i,SV1171: $i,SV427: $i] :
( ( ! [SY5725: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV427 ) @ SV1171 ) @ SV1773 ) ) @ SY5725 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV427 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5725 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1171 ) @ SY5725 ) ) @ SV1773 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1773 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5725 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(4487,plain,
! [SV1774: $i,SV1172: $i,SV428: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SV1172 ) ) @ ( c_Suc @ SV1774 ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SV1774 ) ) @ SV1172 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1172 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1774 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(4488,plain,
! [SV1775: $i,SV1173: $i,SV429: $i] :
( ( ( c_List_Olist_OCons @ SV429 @ SV1173 @ SV1775 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV1775 ) @ ( c_List_Olist_OCons @ SV429 @ SV1173 @ SV1775 ) @ SV1775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3783]) ).
thf(4489,plain,
! [SV1776: $i,SV1175: $i,SV431: $i] :
( ( ! [SY5726: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV431 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ ( c_Orderings_Oord__class_Omax @ SV1175 @ SV1776 @ SV431 ) ) @ SY5726 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1175 ) @ SY5726 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1776 ) @ SY5726 ) @ SV431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(4490,plain,
! [SV1176: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV432 ) @ ( c_Lambda_OdB_OVar @ SV1176 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3786]) ).
thf(4491,plain,
! [SV1777: $i,SV1177: $i,SV433: $i] :
( ( ! [SY5727: $i] :
( ~ ( class_Orderings_Olinorder @ SV433 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1177 @ SV1777 @ SV433 ) @ SY5727 @ SV433 )
= ( c_Orderings_Oord__class_Omax @ SV1177 @ ( c_Orderings_Oord__class_Omax @ SV1777 @ SY5727 @ SV433 ) @ SV433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3787]) ).
thf(4492,plain,
! [SV1778: $i,SV1178: $i,SV434: $i] :
( ( ! [SY5728: $i] :
( ~ ( class_Orderings_Olinorder @ SV434 )
| ( ( c_Orderings_Oord__class_Omax @ SV1178 @ ( c_Orderings_Oord__class_Omax @ SV1778 @ SY5728 @ SV434 ) @ SV434 )
= ( c_Orderings_Oord__class_Omax @ SV1778 @ ( c_Orderings_Oord__class_Omax @ SV1178 @ SY5728 @ SV434 ) @ SV434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(4493,plain,
! [SV435: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV435 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV435 ) @ ( c_HOL_Oone__class_Oone @ SV435 ) ) @ ( c_HOL_Oone__class_Oone @ SV435 ) ) @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(4494,plain,
! [SV1779: $i,SV1179: $i,SV437: $i] :
( ( ( c_List_Odistinct @ ( c_List_Otake @ SV437 @ SV1179 @ SV1779 ) @ SV1779 )
| ~ ( c_List_Odistinct @ SV1179 @ SV1779 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(4495,plain,
! [SV1180: $i,SV438: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV438 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1180 @ SV438 ) @ SV438 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(4496,plain,
! [SV1181: $i,SV439: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV439 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1181 @ SV439 ) @ SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(4497,plain,
! [SV1182: $i,SV440: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV440 ) @ ( c_Lambda_OdB_OAbs @ SV1182 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV440 @ SV1182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3793]) ).
thf(4498,plain,
! [SV1780: $i,SV1183: $i,SV441: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV441 )
| ( ( c_Orderings_Oord__class_Omax @ SV1183 @ ( c_Orderings_Oord__class_Omax @ SV1183 @ SV1780 @ SV441 ) @ SV441 )
= ( c_Orderings_Oord__class_Omax @ SV1183 @ SV1780 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(4499,plain,
! [SV1781: $i,SV1184: $i,SV442: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV442 @ SV1184 @ SV1781 ) @ ( c_List_Olist_OCons @ SV1184 @ ( c_List_Olist_ONil @ SV1781 ) @ SV1781 ) @ SV1781 )
= ( c_List_Olist_OCons @ SV1184 @ ( c_List_Oreplicate @ SV442 @ SV1184 @ SV1781 ) @ SV1781 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(4500,plain,
! [SV1782: $i,SV1185: $i,SV444: $i] :
( ( ! [SY5729: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV444 ) @ SV1185 ) @ SV1782 @ SY5729 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV444 @ SV1782 @ SY5729 ) ) @ ( c_Lambda_Osubstn @ SV1185 @ SV1782 @ SY5729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(4501,plain,
! [SV1783: $i,SV1188: $i,SV447: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV447 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1188 ) @ SV1783 ) @ SV1783 @ SV447 )
= SV1188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3799]) ).
thf(4502,plain,
! [SV1784: $i,SV1189: $i,SV448: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ SV448 @ SV1189 @ SV1784 ) @ SV1784 )
= ( c_List_Oappend @ ( c_List_Orev @ SV1189 @ SV1784 ) @ ( c_List_Orev @ SV448 @ SV1784 ) @ SV1784 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(4503,plain,
! [SV1785: $i,SV1190: $i,SV449: $i] :
( ( ! [SY5730: $i,SY5731: $i,SY5732: $i] :
( ( c_List_Ofoldl @ SV449 @ SV1190 @ ( c_List_Oappend @ SV1785 @ SY5730 @ SY5731 ) @ SY5732 @ SY5731 )
= ( c_List_Ofoldl @ SV449 @ ( c_List_Ofoldl @ SV449 @ SV1190 @ SV1785 @ SY5732 @ SY5731 ) @ SY5730 @ SY5732 @ SY5731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3801]) ).
thf(4504,plain,
! [SV1786: $i,SV1191: $i,SV450: $i] :
( ( ! [SY5733: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV450 )
| ( c_lessequals @ SV1191 @ SV1786 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY5733 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SY5733 @ SV1786 @ SV450 ) @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SY5733 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3802]) ).
thf(4505,plain,
! [SV1787: $i,SV1192: $i,SV451: $i] :
( ( ! [SY5734: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV451 )
| ( c_lessequals @ SV1192 @ SV1787 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY5734 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SY5734 @ SV1787 @ SV451 ) @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SY5734 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3803]) ).
thf(4506,plain,
! [SV1788: $i,SV1193: $i,SV452: $i] :
( ( ! [SY5735: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV452 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SV1788 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SY5735 @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ SV1788 @ SY5735 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3804]) ).
thf(4507,plain,
! [SV1789: $i,SV1194: $i,SV453: $i] :
( ( ! [SY5736: $i] :
( ( c_List_Orotate @ SV453 @ ( c_List_Orotate @ SV1194 @ SV1789 @ SY5736 ) @ SY5736 )
= ( c_List_Orotate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV453 ) @ SV1194 ) @ SV1789 @ SY5736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3805]) ).
thf(4508,plain,
! [SV1790: $i,SV1195: $i,SV454: $i] :
( ( ! [SY5737: $i] :
( ( c_Type_Otype_Otype__case @ SV454 @ SV1195 @ ( c_Type_Otype_OAtom @ SV1790 ) @ SY5737 )
= ( hAPP @ SV454 @ SV1790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3806]) ).
thf(4509,plain,
! [SV1791: $i,SV1196: $i,SV456: $i] :
( ( ( c_List_Odistinct @ SV456 @ SV1196 )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ SV1791 @ SV456 @ SV1196 ) @ SV1196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(4510,plain,
! [SV1792: $i,SV1197: $i,SV457: $i] :
( ( ! [SY5738: $i,SY5739: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY5738 ) @ SY5739 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1792 @ SY5739 @ SV457 )
| ~ ( c_lessequals @ SV1197 @ SY5738 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3809]) ).
thf(4511,plain,
! [SV1793: $i,SV1198: $i,SV458: $i] :
( ( ! [SY5740: $i,SY5741: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SY5740 ) @ SY5741 ) @ SV458 )
| ~ ( c_lessequals @ SV1793 @ SY5741 @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SY5740 @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(4512,plain,
! [SV1199: $i,SV459: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV459 ) @ ( c_Suc @ SV1199 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV459 @ SV1199 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3811]) ).
thf(4513,plain,
! [SV1200: $i,SV460: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV460 @ SV1200 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV460 ) @ ( c_Suc @ SV1200 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3812]) ).
thf(4514,plain,
! [SV1201: $i,SV461: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV461 ) @ ( c_Suc @ SV1201 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV1201 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3813]) ).
thf(4515,plain,
! [SV1202: $i,SV462: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV462 ) @ SV1202 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1202 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3814]) ).
thf(4516,plain,
! [SV1203: $i,SV463: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV463 ) @ SV1203 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(4517,plain,
! [SV1204: $i,SV464: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV464 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ SV1204 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV464 ) @ SV1204 ) @ SV1204 ) @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3816]) ).
thf(4518,plain,
! [SV1205: $i,SV465: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV465 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV465 ) @ SV1205 ) @ SV1205 ) @ SV465 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1205 @ SV465 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(4519,plain,
! [SV1206: $i,SV466: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV466 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV466 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1206 @ SV1206 @ SV466 )
= ( c_HOL_Ozero__class_Ozero @ SV466 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3818]) ).
thf(4520,plain,
! [SV1207: $i,SV467: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV467 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1207 @ SV1207 @ SV467 )
= ( c_HOL_Ozero__class_Ozero @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(4521,plain,
! [SV1208: $i,SV468: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV468 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1208 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
= SV1208 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3820]) ).
thf(4522,plain,
! [SV1209: $i,SV469: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV469 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1209 @ SV1209 @ SV469 )
= ( c_HOL_Ozero__class_Ozero @ SV469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(4523,plain,
! [SV1210: $i,SV470: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV470 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1210 @ SV1210 @ SV470 )
= ( c_HOL_Ozero__class_Ozero @ SV470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3822]) ).
thf(4524,plain,
! [SV471: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV471 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(4525,plain,
! [SV1211: $i,SV472: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV472 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) ) @ SV1211 )
= SV1211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(4526,plain,
! [SV1212: $i,SV473: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV473 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV473 ) @ ( c_HOL_Ozero__class_Ozero @ SV473 ) ) @ SV1212 )
= SV1212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(4527,plain,
! [SV1213: $i,SV474: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV474 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV474 )
| ( SV1213
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV474 ) @ SV1213 ) @ ( c_HOL_Ozero__class_Ozero @ SV474 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3826]) ).
thf(4528,plain,
! [SV1214: $i,SV475: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV475 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV475 ) @ SV1214 ) @ ( c_HOL_Ozero__class_Ozero @ SV475 ) )
= SV1214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(4529,plain,
! [SV1215: $i,SV476: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV476 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV476 ) @ ( c_HOL_Ozero__class_Ozero @ SV476 ) ) @ SV1215 )
= SV1215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3828]) ).
thf(4530,plain,
! [SV1216: $i,SV477: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV477 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV477 ) @ SV1216 ) @ ( c_HOL_Ozero__class_Ozero @ SV477 ) )
= SV1216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3829]) ).
thf(4531,plain,
! [SV1217: $i,SV478: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV478 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV478 ) @ SV1217 ) @ ( c_HOL_Ozero__class_Ozero @ SV478 ) )
= SV1217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3830]) ).
thf(4532,plain,
! [SV1218: $i,SV479: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV479 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV479 ) @ ( c_HOL_Ozero__class_Ozero @ SV479 ) ) @ SV1218 )
= SV1218 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3831]) ).
thf(4533,plain,
! [SV480: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV480 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV480 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV480 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV480 )
= ( c_HOL_Oone__class_Oone @ SV480 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3832]) ).
thf(4534,plain,
! [SV483: $i] :
( ( ( c_lessequals @ SV483 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false )
| ( ( SV483
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3835]) ).
thf(4535,plain,
! [SV1794: $i,SV1220: $i,SV486: $i] :
( ( ! [SY5742: $i,SY5743: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SV1220 @ SV1794 @ SY5742 ) @ SY5742 ) @ ( c_Nat_Osize__class_Osize @ SV486 @ ( tc_List_Olist @ SY5742 ) ) @ SY5743 @ SY5742 )
= ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SY5743 @ SV1794 @ SY5742 ) @ SY5742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(4536,plain,
! [SV1221: $i,SV487: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV487 ) @ SV1221 ) @ SV487 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(4537,plain,
! [SV1222: $i,SV488: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV488 ) @ SV1222 ) @ SV1222 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(4538,plain,
! [SV1795: $i,SV1223: $i,SV489: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV489 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1795 @ tc_nat ) @ SV489 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1223 @ SV489 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1795 @ SV489 ) @ SV489 ) )
| ~ ( c_lessequals @ SV1795 @ SV1223 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4539,plain,
! [SV1796: $i,SV1224: $i,SV490: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV490 ) @ ( c_List_Olist_OCons @ SV1224 @ SV1796 @ SV490 ) @ SV490 )
= ( c_List_Olist_OCons @ SV1224 @ SV1796 @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3840]) ).
thf(4540,plain,
! [SV1797: $i,SV1225: $i,SV491: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV491 ) @ SV1225 ) @ SV1797 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV491 @ ( c_HOL_Ominus__class_Ominus @ SV1797 @ SV1225 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(4541,plain,
! [SV1798: $i,SV1226: $i,SV492: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV492 @ ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1798 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV1798 ) @ SV1226 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(4542,plain,
! [SV1799: $i,SV1227: $i,SV493: $i] :
( ( ! [SY5744: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV493 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV1227 ) @ SV1799 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SY5744 ) @ SV1799 ) @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SY5744 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3843]) ).
thf(4543,plain,
! [SV1800: $i,SV1228: $i,SV494: $i] :
( ( ! [SY5745: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV494 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV1228 ) @ SV1800 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SY5745 ) @ SV1800 ) @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SY5745 @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(4544,plain,
! [SV1801: $i,SV1229: $i,SV495: $i] :
( ( ! [SY5746: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV495 )
| ( c_HOL_Oord__class_Oless @ SV1229 @ SV1801 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1229 ) @ SY5746 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1801 ) @ SY5746 ) @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3845]) ).
thf(4545,plain,
! [SV1802: $i,SV1230: $i,SV496: $i] :
( ( ! [SY5747: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV496 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV1802 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SY5747 ) @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1802 @ SY5747 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3846]) ).
thf(4546,plain,
! [SV1803: $i,SV1231: $i,SV497: $i] :
( ( ! [SY5748: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV497 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV1803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SY5748 ) @ SV497 )
| ~ ( c_HOL_Oord__class_Oless @ SV1803 @ SY5748 @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3847]) ).
thf(4547,plain,
! [SV1804: $i,SV1232: $i,SV498: $i] :
( ( ! [SY5749: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV498 )
| ( c_HOL_Oord__class_Oless @ SV1232 @ SV1804 @ SV498 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SY5749 ) @ SV1232 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SY5749 ) @ SV1804 ) @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3848]) ).
thf(4548,plain,
! [SV1805: $i,SV1233: $i,SV499: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV499 ) @ SV1233 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1805 ) @ SV1233 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV499 @ SV1805 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3849]) ).
thf(4549,plain,
! [SV1806: $i,SV1234: $i,SV500: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV500 @ SV1234 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1806 ) @ SV500 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1806 ) @ SV1234 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(4550,plain,
! [SV1807: $i,SV1235: $i,SV501: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SV1235 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SV1807 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1235 @ SV1807 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3851]) ).
thf(4551,plain,
! [SV1808: $i,SV1236: $i,SV502: $i] :
( ( ! [SY5750: $i] :
( ~ ( class_Orderings_Oorder @ SV502 )
| ( c_lessequals @ SV1236 @ SV1808 @ SV502 )
| ~ ( c_lessequals @ SV1236 @ SY5750 @ SV502 )
| ~ ( c_lessequals @ SY5750 @ SV1808 @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3852]) ).
thf(4552,plain,
! [SV1809: $i,SV1237: $i,SV503: $i] :
( ( ! [SY5751: $i] :
( ~ ( class_Orderings_Oorder @ SV503 )
| ( c_HOL_Oord__class_Oless @ SV1237 @ SV1809 @ SV503 )
| ~ ( c_lessequals @ SV1237 @ SY5751 @ SV503 )
| ~ ( c_HOL_Oord__class_Oless @ SY5751 @ SV1809 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(4553,plain,
! [SV1810: $i,SV1238: $i,SV504: $i] :
( ( ! [SY5752: $i] :
( ~ ( class_Orderings_Oorder @ SV504 )
| ( c_HOL_Oord__class_Oless @ SV1238 @ SV1810 @ SV504 )
| ~ ( c_HOL_Oord__class_Oless @ SV1238 @ SY5752 @ SV504 )
| ~ ( c_lessequals @ SY5752 @ SV1810 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4554,plain,
! [SV1811: $i,SV1239: $i,SV505: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SV1239 ) @ SV1811 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SV1811 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SV1239 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3855]) ).
thf(4555,plain,
! [SV1812: $i,SV1240: $i,SV506: $i] :
( ( ! [SY5753: $i] :
( ~ ( class_Orderings_Opreorder @ SV506 )
| ( c_lessequals @ SV1240 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SY5753 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SV1240 @ SY5753 @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3856]) ).
thf(4556,plain,
! [SV1813: $i,SV1241: $i,SV508: $i] :
( ( ( c_lessequals @ SV508 @ SV1241 @ tc_nat )
| ~ ( c_lessequals @ SV1813 @ SV1241 @ tc_nat )
| ~ ( c_lessequals @ SV508 @ SV1813 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4557,plain,
! [SV1242: $i,SV510: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV510 ) )
= $true )
| ( ( c_lessequals @ SV1242 @ SV1242 @ SV510 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(4558,plain,
! [SV1243: $i,SV511: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV511 ) )
= $true )
| ( ( c_lessequals @ SV1243 @ SV1243 @ SV511 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3859]) ).
thf(4559,plain,
! [SV1814: $i,SV1244: $i,SV512: $i] :
( ( ! [SY5754: $i] :
( ~ ( class_Orderings_Opreorder @ SV512 )
| ( c_HOL_Oord__class_Oless @ SV1244 @ SV1814 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SY5754 @ SV1814 @ SV512 )
| ~ ( c_lessequals @ SV1244 @ SY5754 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3860]) ).
thf(4560,plain,
! [SV1815: $i,SV1245: $i,SV513: $i] :
( ( ! [SY5755: $i] :
( ~ ( class_Orderings_Opreorder @ SV513 )
| ( c_HOL_Oord__class_Oless @ SV1245 @ SV1815 @ SV513 )
| ~ ( c_lessequals @ SY5755 @ SV1815 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ SV1245 @ SY5755 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3861]) ).
thf(4561,plain,
! [SV1816: $i,SV1246: $i,SV514: $i] :
( ( ! [SY5756: $i,SY5757: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
| ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SY5756 ) @ SV514 )
| ~ ( c_lessequals @ SY5757 @ SY5756 @ SV514 )
| ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SY5757 ) @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3862]) ).
thf(4562,plain,
! [SV1817: $i,SV1247: $i,SV515: $i] :
( ( ! [SY5758: $i] :
( ( c_Type_Otyping @ SV515 @ SV1247 @ SV1817 )
| ~ ( c_Lambda_Obeta @ SY5758 @ SV1247 )
| ~ ( c_Type_Otyping @ SV515 @ SY5758 @ SV1817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(4563,plain,
! [SV1818: $i,SV1248: $i,SV516: $i] :
( ( ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SV1818 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ominus__class_Ominus @ SV1248 @ SV1818 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3864]) ).
thf(4564,plain,
! [SV1819: $i,SV1249: $i,SV517: $i] :
( ( ! [SY5759: $i,SY5760: $i,SY5761: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV1249 @ SV1819 @ SY5759 ) @ SY5760 @ SY5761 @ SY5759 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SY5760 @ SY5761 @ SY5759 ) @ SV1249 @ SV1819 @ SY5759 ) )
| ( SV1249 = SY5760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3865]) ).
thf(4565,plain,
! [SV1250: $i,SV518: $i] :
( ( ( SV518 = SV1250 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV518 @ ( c_Suc @ SV1250 ) @ tc_nat )
| ~ ( c_lessequals @ SV1250 @ SV518 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3866]) ).
thf(4566,plain,
! [SV1820: $i,SV1251: $i,SV519: $i] :
( ( ! [SY5762: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV519 @ SV1251 @ SV1820 ) @ ( c_List_Olist_OCons @ SV1251 @ SY5762 @ SV1820 ) @ SV1820 )
= ( c_List_Olist_OCons @ SV1251 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV519 @ SV1251 @ SV1820 ) @ SY5762 @ SV1820 ) @ SV1820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(4567,plain,
! [SV1252: $i,SV521: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV521 @ SV1252 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1252 @ SV521 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3868]) ).
thf(4568,plain,
! [SV1253: $i,SV522: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV522 @ SV1253 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1253 @ SV522 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3869]) ).
thf(4569,plain,
! [SV1254: $i,SV523: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV523 @ SV1254 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV523 ) @ SV1254 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3870]) ).
thf(4570,plain,
! [SV1255: $i,SV524: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV524 @ ( c_Suc @ SV1255 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV524 @ SV1255 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3871]) ).
thf(4571,plain,
! [SV526: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV526 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV526 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV526 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(4572,plain,
! [SV1821: $i,SV1257: $i,SV527: $i] :
( ( ! [SY5763: $i,SY5764: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV527 @ SV1257 @ SV1821 ) @ ( c_Suc @ SY5763 ) @ SY5764 @ SV1821 )
= ( c_List_Olist_OCons @ SV527 @ ( c_List_Olist__update @ SV1257 @ SY5763 @ SY5764 @ SV1821 ) @ SV1821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(4573,plain,
! [SV1822: $i,SV1258: $i,SV528: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV528 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1258 ) @ SV1822 ) @ SV528 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV528 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1258 @ SV528 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1822 @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3875]) ).
thf(4574,plain,
! [SV1259: $i,SV529: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1259 @ tc_nat ) @ SV529 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV529 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1259 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3876]) ).
thf(4575,plain,
! [SV1823: $i,SV1260: $i,SV530: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV530 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1260 @ SV1823 @ SV530 ) @ SV530 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV530 ) @ ( c_List_Olistsum @ SV1260 @ SV530 ) ) @ ( c_List_Olistsum @ SV1823 @ SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3877]) ).
thf(4576,plain,
! [SV1261: $i,SV531: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV531 ) @ ( c_HOL_Ominus__class_Ominus @ SV1261 @ SV531 @ tc_nat ) )
= SV1261 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1261 @ SV531 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3878]) ).
thf(4577,plain,
! [SV1262: $i,SV532: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV532 @ ( c_Suc @ SV1262 ) @ tc_nat ) @ SV532 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV532 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3879]) ).
thf(4578,plain,
! [SV1824: $i,SV1263: $i,SV533: $i] :
( ( ~ ( class_Orderings_Oorder @ SV533 )
| ( c_HOL_Oord__class_Oless @ SV1263 @ SV1824 @ SV533 )
| ( SV1824 = SV1263 )
| ~ ( c_lessequals @ SV1263 @ SV1824 @ SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3880]) ).
thf(4579,plain,
! [SV1825: $i,SV1264: $i,SV534: $i] :
( ( ~ ( class_Orderings_Oorder @ SV534 )
| ( c_HOL_Oord__class_Oless @ SV1264 @ SV1825 @ SV534 )
| ~ ( c_lessequals @ SV1264 @ SV1825 @ SV534 )
| ( SV1825 = SV1264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3881]) ).
thf(4580,plain,
! [SV1265: $i,SV535: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV535 @ SV1265 @ tc_nat )
= $true )
| ( ( ( SV535 = SV1265 )
| ~ ( c_lessequals @ SV535 @ SV1265 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3882]) ).
thf(4581,plain,
! [SV1266: $i,SV536: $i] :
( ( ( SV536 = SV1266 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV536 @ SV1266 @ tc_nat )
| ~ ( c_lessequals @ SV536 @ SV1266 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3883]) ).
thf(4582,plain,
! [SV1267: $i,SV537: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV537 @ SV1267 @ tc_nat )
= $true )
| ( ( ( SV537 = SV1267 )
| ~ ( c_lessequals @ SV537 @ SV1267 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3884]) ).
thf(4583,plain,
! [SV1826: $i,SV1268: $i,SV538: $i] :
( ( ~ ( class_Orderings_Oorder @ SV538 )
| ( SV1268 = SV1826 )
| ( c_HOL_Oord__class_Oless @ SV1268 @ SV1826 @ SV538 )
| ~ ( c_lessequals @ SV1268 @ SV1826 @ SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3885]) ).
thf(4584,plain,
! [SV1827: $i,SV1269: $i,SV539: $i] :
( ( ~ ( class_Orderings_Oorder @ SV539 )
| ( c_HOL_Oord__class_Oless @ SV1269 @ SV1827 @ SV539 )
| ( SV1269 = SV1827 )
| ~ ( c_lessequals @ SV1269 @ SV1827 @ SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3886]) ).
thf(4585,plain,
! [SV1828: $i,SV1270: $i,SV540: $i] :
( ( ~ ( class_Orderings_Oorder @ SV540 )
| ( c_HOL_Oord__class_Oless @ SV1270 @ SV1828 @ SV540 )
| ( SV1270 = SV1828 )
| ~ ( c_lessequals @ SV1270 @ SV1828 @ SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3887]) ).
thf(4586,plain,
! [SV1829: $i,SV1271: $i,SV541: $i] :
( ( ~ ( class_Orderings_Oorder @ SV541 )
| ( c_HOL_Oord__class_Oless @ SV1271 @ SV1829 @ SV541 )
| ~ ( c_lessequals @ SV1271 @ SV1829 @ SV541 )
| ( SV1271 = SV1829 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3888]) ).
thf(4587,plain,
! [SV1830: $i,SV1272: $i,SV542: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV542 )
| ( SV1272 = SV1830 )
| ~ ( c_lessequals @ SV1272 @ SV1830 @ SV542 )
| ( c_HOL_Oord__class_Oless @ SV1272 @ SV1830 @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3889]) ).
thf(4588,plain,
! [SV1831: $i,SV1273: $i,SV543: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV543 )
| ( SV1273 = SV1831 )
| ( c_HOL_Oord__class_Oless @ SV1273 @ SV1831 @ SV543 )
| ~ ( c_lessequals @ SV1273 @ SV1831 @ SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3890]) ).
thf(4589,plain,
! [SV1832: $i,SV1275: $i,SV546: $i] :
( ( ! [SY5765: $i,SY5766: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV546 @ SV1275 @ SV1832 @ SY5765 ) @ SV1275 @ SY5766 @ SY5765 )
= ( c_List_Olist__update @ SV546 @ SV1275 @ SY5766 @ SY5765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3892]) ).
thf(4590,plain,
! [SV1276: $i,SV547: $i] :
( ( ( c_lessequals @ SV547 @ SV1276 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV547 ) @ ( c_Suc @ SV1276 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3893]) ).
thf(4591,plain,
! [SV1277: $i,SV548: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV548 ) @ ( c_Suc @ SV1277 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV548 @ SV1277 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3894]) ).
thf(4592,plain,
! [SV1833: $i,SV1278: $i,SV549: $i] :
( ( ! [SY5767: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV549 @ SV1278 @ SV1833 ) @ SY5767 @ SV1833 )
= ( c_List_Oappend @ SV549 @ ( c_List_Oappend @ SV1278 @ SY5767 @ SV1833 ) @ SV1833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4593,plain,
! [SV1834: $i,SV1279: $i,SV550: $i] :
( ( ! [SY5768: $i] :
( ( c_List_Oappend @ SV550 @ ( c_List_Oappend @ SV1279 @ SV1834 @ SY5768 ) @ SY5768 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV550 @ SV1279 @ SY5768 ) @ SV1834 @ SY5768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4594,plain,
! [SV1835: $i,SV1280: $i,SV551: $i] :
( ( ! [SY5769: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV551 @ SV1280 @ SV1835 ) @ SY5769 @ SV1835 )
= ( c_List_Oappend @ SV551 @ ( c_List_Oappend @ SV1280 @ SY5769 @ SV1835 ) @ SV1835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(4595,plain,
! [SV1836: $i,SV1281: $i,SV552: $i] :
( ( ! [SY5770: $i] :
( ( c_List_Oappend @ SV552 @ ( c_List_Oappend @ SV1281 @ SV1836 @ SY5770 ) @ SY5770 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV552 @ SV1281 @ SY5770 ) @ SV1836 @ SY5770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(4596,plain,
! [SV1837: $i,SV1282: $i,SV553: $i] :
( ( ~ ( class_Orderings_Oorder @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV1282 @ SV1837 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV1837 @ SV1282 @ SV553 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3899]) ).
thf(4597,plain,
! [SV1838: $i,SV1283: $i,SV554: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV554 )
| ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1838 @ SV554 )
| ~ ( c_HOL_Oord__class_Oless @ SV1838 @ SV1283 @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4598,plain,
! [SV1284: $i,SV555: $i] :
( ( ( c_lessequals @ SV555 @ SV1284 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV1284 @ SV555 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3901]) ).
thf(4599,plain,
! [SV1839: $i,SV1285: $i,SV556: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV556 )
| ( c_lessequals @ SV1285 @ SV1839 @ SV556 )
| ( c_lessequals @ SV1839 @ SV1285 @ SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3902]) ).
thf(4600,plain,
! [SV1840: $i,SV1286: $i,SV557: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ SV1286 @ SV1840 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ SV1840 @ SV1286 @ SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(4601,plain,
! [SV1841: $i,SV1287: $i,SV558: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ SV1287 @ SV1841 @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ SV1841 @ SV1287 @ SV558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3904]) ).
thf(4602,plain,
! [SV1288: $i,SV559: $i] :
( ( ( hBOOL @ ( hAPP @ SV559 @ SV1288 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV559 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV559 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV559 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4603,plain,
! [SV1289: $i,SV562: $i] :
( ( ( hBOOL @ ( hAPP @ SV562 @ SV1289 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV562 @ ( v_sko__List__Xupt__Xinduct__1 @ SV562 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV562 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3908]) ).
thf(4604,plain,
! [SV1291: $i,SV565: $i] :
( ( ( hBOOL @ ( hAPP @ SV565 @ SV1291 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV565 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3910]) ).
thf(4605,plain,
! [SV1842: $i,SV1292: $i,SV568: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV568 @ SV1292 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1842 @ SV1292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4606,plain,
! [SV1843: $i,SV1293: $i,SV574: $i] :
( ( ! [SY5771: $i,SY5772: $i,SY5773: $i,SY5774: $i] :
( ( ( hAPP @ ( hAPP @ SV574 @ SV1293 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1843 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5771 @ SY5772 @ SV574 @ SY5773 @ SV1843 @ SY5774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(4607,plain,
! [SV1844: $i,SV1294: $i,SV575: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV575 )
| ( ( c_List_Olistsum @ ( c_List_Omap @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV575 @ SV1294 ) @ SV1844 @ SV1294 @ SV575 ) @ SV575 )
= ( c_HOL_Ozero__class_Ozero @ SV575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4608,plain,
! [SV1845: $i,SV1295: $i,SV576: $i] :
( ( ( c_Lambda_Osubstn @ SV576 @ SV1295 @ SV1845 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV576 ) @ ( c_Lambda_Oliftn @ SV1845 @ SV1295 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SV1845 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(4609,plain,
! [SV1846: $i,SV1296: $i,SV577: $i] :
( ( ! [SY5775: $i,SY5776: $i] :
( ( c_List_Odrop @ SV577 @ ( c_List_Omap @ SV1296 @ SV1846 @ SY5775 @ SY5776 ) @ SY5776 )
= ( c_List_Omap @ SV1296 @ ( c_List_Odrop @ SV577 @ SV1846 @ SY5775 ) @ SY5775 @ SY5776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4610,plain,
! [SV1847: $i,SV1297: $i,SV578: $i] :
( ( ! [SY5777: $i] :
( ( c_List_Odistinct @ SV578 @ SV1297 )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ SV1847 @ SV578 @ SV1297 @ SY5777 ) @ SY5777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4611,plain,
! [SV1848: $i,SV1298: $i,SV579: $i] :
( ( ! [SY5778: $i,SY5779: $i] :
( ( c_List_Omap @ SV579 @ ( c_List_Oappend @ SV1298 @ SV1848 @ SY5778 ) @ SY5778 @ SY5779 )
= ( c_List_Oappend @ ( c_List_Omap @ SV579 @ SV1298 @ SY5778 @ SY5779 ) @ ( c_List_Omap @ SV579 @ SV1848 @ SY5778 @ SY5779 ) @ SY5779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3917]) ).
thf(4612,plain,
! [SV1849: $i,SV1299: $i,SV580: $i] :
( ( ! [SY5780: $i,SY5781: $i] :
( ( c_List_Omap @ SV580 @ ( c_List_Oreplicate @ SV1299 @ SV1849 @ SY5780 ) @ SY5780 @ SY5781 )
= ( c_List_Oreplicate @ SV1299 @ ( hAPP @ SV580 @ SV1849 ) @ SY5781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(4613,plain,
! [SV1850: $i,SV1300: $i,SV581: $i] :
( ( ! [SY5782: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV581 @ SV1300 @ SV1850 @ SY5782 ) @ ( tc_List_Olist @ SY5782 ) )
= ( c_Nat_Osize__class_Osize @ SV1300 @ ( tc_List_Olist @ SV1850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3919]) ).
thf(4614,plain,
! [SV1851: $i,SV1301: $i,SV582: $i] :
( ( ! [SY5783: $i,SY5784: $i] :
( ( c_List_Orotate @ SV582 @ ( c_List_Omap @ SV1301 @ SV1851 @ SY5783 @ SY5784 ) @ SY5784 )
= ( c_List_Omap @ SV1301 @ ( c_List_Orotate @ SV582 @ SV1851 @ SY5783 ) @ SY5783 @ SY5784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3920]) ).
thf(4615,plain,
! [SV1852: $i,SV1302: $i,SV583: $i] :
( ( ! [SY5785: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV583 @ SV1302 @ SV1852 @ SY5785 ) @ SY5785 )
= ( c_List_Omap @ SV583 @ ( c_List_Orev @ SV1302 @ SV1852 ) @ SV1852 @ SY5785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3921]) ).
thf(4616,plain,
! [SV1853: $i,SV1303: $i,SV584: $i] :
( ( ! [SY5786: $i,SY5787: $i] :
( ( c_List_Otake @ SV584 @ ( c_List_Omap @ SV1303 @ SV1853 @ SY5786 @ SY5787 ) @ SY5787 )
= ( c_List_Omap @ SV1303 @ ( c_List_Otake @ SV584 @ SV1853 @ SY5786 ) @ SY5786 @ SY5787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4617,plain,
! [SV1854: $i,SV1304: $i,SV585: $i] :
( ( ( c_List_Omap @ SV585 @ ( c_List_Olist_ONil @ SV1304 ) @ SV1304 @ SV1854 )
= ( c_List_Olist_ONil @ SV1854 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4618,plain,
! [SV1855: $i,SV1305: $i,SV586: $i] :
( ( ! [SY5788: $i,SY5789: $i,SY5790: $i] :
( ( c_List_Omap @ SV586 @ ( c_List_Omap @ SV1305 @ SV1855 @ SY5788 @ SY5789 ) @ SY5789 @ SY5790 )
= ( c_List_Omap @ ( c_Fun_Ocomp @ SV586 @ SV1305 @ SY5789 @ SY5790 @ SY5788 ) @ SV1855 @ SY5788 @ SY5790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(4619,plain,
! [SV1856: $i,SV1306: $i,SV587: $i] :
( ( ! [SY5791: $i,SY5792: $i] :
( ( c_List_Omap @ SV587 @ ( c_List_Olist_OCons @ SV1306 @ SV1856 @ SY5791 ) @ SY5791 @ SY5792 )
= ( c_List_Olist_OCons @ ( hAPP @ SV587 @ SV1306 ) @ ( c_List_Omap @ SV587 @ SV1856 @ SY5791 @ SY5792 ) @ SY5792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3925]) ).
thf(4620,plain,
! [SV1857: $i,SV1307: $i,SV588: $i] :
( ( ! [SY5793: $i,SY5794: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV588 @ SV1307 ) @ ( c_List_Omap @ SV588 @ SV1857 @ SY5793 @ SY5794 ) @ SY5794 )
= ( c_List_Omap @ SV588 @ ( c_List_Olist_OCons @ SV1307 @ SV1857 @ SY5793 ) @ SY5793 @ SY5794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3926]) ).
thf(4621,plain,
! [SV1858: $i,SV1308: $i,SV589: $i] :
( ( ! [SY5795: $i,SY5796: $i] :
( ( c_List_Omap @ SV589 @ ( c_List_Olist_OCons @ SV1308 @ SV1858 @ SY5795 ) @ SY5795 @ SY5796 )
= ( c_List_Olist_OCons @ ( hAPP @ SV589 @ SV1308 ) @ ( c_List_Omap @ SV589 @ SV1858 @ SY5795 @ SY5796 ) @ SY5796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3927]) ).
thf(4622,plain,
! [SV1859: $i,SV1309: $i,SV590: $i] :
( ( ! [SY5797: $i,SY5798: $i,SY5799: $i] :
( ( c_List_Omap @ SV590 @ ( c_List_Olist__update @ SV1309 @ SV1859 @ SY5797 @ SY5798 ) @ SY5798 @ SY5799 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV590 @ SV1309 @ SY5798 @ SY5799 ) @ SV1859 @ ( hAPP @ SV590 @ SY5797 ) @ SY5799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3928]) ).
thf(4623,plain,
! [SV1860: $i,SV1310: $i,SV591: $i] :
( ( ( c_List_Olist_ONil @ SV591 )
= ( c_List_Omap @ SV1310 @ ( c_List_Olist_ONil @ SV1860 ) @ SV1860 @ SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3929]) ).
thf(4624,plain,
! [SV1311: $i,SV592: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV592 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV1311 @ SV592 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV592 ) @ SV1311 @ ( c_HOL_Ozero__class_Ozero @ SV592 ) @ SV592 @ SV592 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3930]) ).
thf(4625,plain,
! [SV1312: $i,SV593: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV593 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV593 ) @ ( c_HOL_Ozero__class_Ozero @ SV593 ) @ SV1312 @ SV593 @ SV593 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV593 ) @ SV1312 @ ( c_HOL_Ozero__class_Ozero @ SV593 ) @ SV593 @ SV593 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3931]) ).
thf(4626,plain,
! [SV1861: $i,SV1313: $i,SV594: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV594 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1313 @ SV1861 @ SV594 @ SV594 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1313 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1861 @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV594 @ SV594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3932]) ).
thf(4627,plain,
! [SV1862: $i,SV1314: $i,SV595: $i] :
( ( ! [SY5800: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV595 ) @ SV1314 ) ) @ SV1862 ) @ SY5800 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV595 ) @ SV1862 ) @ SY5800 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1314 ) @ SV1862 ) @ SY5800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4628,plain,
! [SV1863: $i,SV1316: $i,SV597: $i] :
( ( ! [SY5801: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV597 ) @ SV1316 ) @ SV1863 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY5801 ) @ SV1316 ) @ SV1863 ) )
| ~ ( c_Lambda_Obeta @ SV597 @ SY5801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4629,plain,
! [SV1864: $i,SV1317: $i,SV598: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV598 ) ) @ SV1317 ) @ SV1864 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV598 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1317 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1864 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4630,plain,
! [SV1865: $i,SV1318: $i,SV599: $i] :
( ( ! [SY5802: $i,SY5803: $i] :
( ( c_List_Ofoldr @ SV599 @ SV1318 @ SV1865 @ SY5802 @ SY5803 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV599 @ SY5802 @ SY5803 @ SY5803 ) @ SV1865 @ ( c_List_Orev @ SV1318 @ SY5802 ) @ SY5803 @ SY5802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3937]) ).
thf(4631,plain,
! [SV1866: $i,SV1319: $i,SV600: $i] :
( ( ! [SY5804: $i,SY5805: $i] :
( ( c_List_Ofoldl @ SV600 @ SV1319 @ SV1866 @ SY5804 @ SY5805 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV600 @ SY5804 @ SY5805 @ SY5804 ) @ ( c_List_Orev @ SV1866 @ SY5805 ) @ SV1319 @ SY5805 @ SY5804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4632,plain,
! [SV1867: $i,SV1320: $i,SV601: $i] :
( ( ! [SY5806: $i,SY5807: $i] :
( ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1867 ) @ SY5806 ) @ SY5807 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV1320 @ SV1867 ) @ SY5806 ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ SV1867 @ SY5807 ) ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ SY5806 @ SY5807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4633,plain,
! [SV1868: $i,SV1321: $i,SV602: $i] :
( ( ! [SY5808: $i,SY5809: $i] :
( ( c_Type_Otype_Otype__case @ SV602 @ SV1321 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1868 ) @ SY5808 ) @ SY5809 )
= ( hAPP @ ( hAPP @ SV1321 @ SV1868 ) @ SY5808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(4634,plain,
! [SV1869: $i,SV1322: $i,SV603: $i] :
( ( ! [SY5810: $i,SY5811: $i] :
( ~ ( hBOOL @ ( hAPP @ SV603 @ ( c_Type_Otype_Otype__case @ SV1322 @ SV1869 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5810 ) @ SY5811 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV603 @ ( hAPP @ ( hAPP @ SV1869 @ SY5810 ) @ SY5811 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3941]) ).
thf(4635,plain,
! [SV1870: $i,SV1323: $i,SV604: $i] :
( ( ! [SY5812: $i,SY5813: $i] :
( ~ ( hBOOL @ ( hAPP @ SV604 @ ( c_Type_Otype_Otype__case @ SV1323 @ SV1870 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5812 ) @ SY5813 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV604 @ ( hAPP @ ( hAPP @ SV1870 @ SY5812 ) @ SY5813 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3942]) ).
thf(4636,plain,
! [SV1871: $i,SV1324: $i,SV605: $i] :
( ( ! [SY5814: $i,SY5815: $i,SY5816: $i] :
( ( c_List_Ofoldr @ SV605 @ ( c_List_Olist_OCons @ SV1324 @ SV1871 @ SY5814 ) @ SY5815 @ SY5814 @ SY5816 )
= ( hAPP @ ( hAPP @ SV605 @ SV1324 ) @ ( c_List_Ofoldr @ SV605 @ SV1871 @ SY5815 @ SY5814 @ SY5816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(4637,plain,
! [SV1872: $i,SV1325: $i,SV606: $i] :
( ( ! [SY5817: $i,SY5818: $i,SY5819: $i] :
( ( c_List_Ofoldr @ SV606 @ ( c_List_Oappend @ SV1325 @ SV1872 @ SY5817 ) @ SY5818 @ SY5817 @ SY5819 )
= ( c_List_Ofoldr @ SV606 @ SV1325 @ ( c_List_Ofoldr @ SV606 @ SV1872 @ SY5818 @ SY5817 @ SY5819 ) @ SY5817 @ SY5819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4638,plain,
! [SV1873: $i,SV1326: $i,SV607: $i] :
( ( ! [SY5820: $i] :
( ( c_List_Ofoldr @ SV607 @ ( c_List_Olist_ONil @ SV1326 ) @ SV1873 @ SV1326 @ SY5820 )
= SV1873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(4639,plain,
! [SV1327: $i,SV608: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV608 ) @ SV1327 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV608 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3946]) ).
thf(4640,plain,
! [SV1874: $i,SV1328: $i,SV609: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SV1328 ) ) @ SV1874 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV609 ) @ SV1874 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1328 ) @ SV1874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3947]) ).
thf(4641,plain,
! [SV1875: $i,SV1329: $i,SV610: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV610 ) @ SV1329 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1875 ) @ SV1329 ) )
| ~ ( c_Lambda_Obeta @ SV610 @ SV1875 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3948]) ).
thf(4642,plain,
! [SV1876: $i,SV1330: $i,SV611: $i] :
( ( ! [SY5821: $i,SY5822: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV611 @ SV1330 @ SV1876 @ SY5821 ) @ SY5822 )
= ( hAPP @ SV611 @ SY5822 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5822 @ SV1330 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3949]) ).
thf(4643,plain,
! [SV1877: $i,SV1331: $i,SV612: $i] :
( ( ! [SY5823: $i,SY5824: $i] :
( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1331 @ SV1877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5823 )
| ~ ( c_Type_Otypings @ SV612 @ SV1877 @ SY5824 )
| ~ ( c_Type_Otyping @ SV612 @ SV1331 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY5824 @ SY5823 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3950]) ).
thf(4644,plain,
! [SV1878: $i,SV1332: $i,SV613: $i] :
( ( ! [SY5825: $i] :
( ( c_Type_Otyping @ SV613 @ ( c_Lambda_OdB_OAbs @ SV1332 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1878 ) @ SY5825 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV613 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1878 @ tc_Type_Otype ) @ SV1332 @ SY5825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3951]) ).
thf(4645,plain,
! [SV1333: $i,SV614: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV614 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV614 )
| ~ ( class_Power_Opower @ SV614 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(4646,plain,
! [SV1334: $i,SV615: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV615 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV615 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV615 ) @ SV1334 @ SV615 )
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
| ( SV1334
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3953]) ).
thf(4647,plain,
! [SV616: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV616 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
= ( c_HOL_Ozero__class_Ozero @ SV616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3954]) ).
thf(4648,plain,
! [SV1879: $i,SV1336: $i,SV618: $i] :
( ( ! [SY5826: $i,SY5827: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ SV1336 @ SV1879 @ SY5826 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5827 @ SY5826 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5827 @ SY5826 ) @ ( c_Suc @ SV1336 ) @ SV1879 @ SY5826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3956]) ).
thf(4649,plain,
! [SV1880: $i,SV1337: $i,SV619: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV619 @ SV1337 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1880 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV619 ) @ SV1880 ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1880 ) @ SV1337 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3957]) ).
thf(4650,plain,
! [SV1881: $i,SV1338: $i,SV620: $i] :
( ( ! [SY5828: $i,SY5829: $i,SY5830: $i,SY5831: $i] :
( ( c_List_Ofoldr @ SV620 @ ( c_List_Omap @ SV1338 @ SV1881 @ SY5828 @ SY5829 ) @ SY5830 @ SY5829 @ SY5831 )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ SV620 @ SV1338 @ SY5829 @ ( tc_fun @ SY5831 @ SY5831 ) @ SY5828 ) @ SV1881 @ SY5830 @ SY5828 @ SY5831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3958]) ).
thf(4651,plain,
! [SV1882: $i,SV1339: $i,SV621: $i] :
( ( ! [SY5832: $i,SY5833: $i,SY5834: $i] :
( ~ ( c_Type_Otyping @ SV621 @ SV1339 @ SV1882 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SY5832 @ SV1882 @ tc_Type_Otype ) @ SY5833 @ SY5834 )
| ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY5833 ) @ SV1339 ) @ SY5832 ) @ SY5834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3959]) ).
thf(4652,plain,
! [SV1883: $i,SV1340: $i,SV622: $i] :
( ( ! [SY5835: $i,SY5836: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV622 @ SV1340 @ SV1883 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY5835 ) @ SV1340 ) @ SY5836 )
| ~ ( c_Type_Otyping @ SV622 @ SY5835 @ SY5836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3960]) ).
thf(4653,plain,
! [SV623: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV623 @ tc_Lambda_OdB )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV623 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3961]) ).
thf(4654,plain,
! [SV1884: $i,SV1341: $i,SV624: $i] :
( ( ! [SY5837: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV624 @ SV1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1884 ) @ SY5837 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV624 ) @ SV1884 ) @ SY5837 ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1884 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY5837 ) @ SV1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3962]) ).
thf(4655,plain,
! [SV1885: $i,SV1342: $i,SV625: $i] :
( ( ! [SY5838: $i,SY5839: $i,SY5840: $i] :
( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1885 ) @ SY5838 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5839 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SV1885 @ SY5840 @ tc_Type_Otype ) @ SY5838 @ SY5839 )
| ~ ( c_Type_Otyping @ SV625 @ SV1342 @ SY5840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3963]) ).
thf(4656,plain,
! [SV1886: $i,SV1343: $i,SV626: $i] :
( ( ! [SY5841: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV626 @ SV1343 @ SV1886 @ SY5841 ) @ SV1343 )
= SV1886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4657,plain,
! [SV1887: $i,SV1344: $i,SV627: $i] :
( ( ! [SY5842: $i,SY5843: $i,SY5844: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV627 @ SV1344 @ SV1887 @ SY5842 ) @ SY5843 ) @ SY5844 )
= ( hAPP @ ( hAPP @ SV627 @ SY5844 ) @ SY5843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3965]) ).
thf(4658,plain,
! [SV1888: $i,SV1345: $i,SV628: $i] :
( ( ! [SY5845: $i,SY5846: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV628 @ SV1345 @ SV1888 @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1345 ) @ SY5845 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5846 )
| ~ ( c_Type_Otypings @ SV628 @ SY5845 @ SY5846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3966]) ).
thf(4659,plain,
! [SV1889: $i,SV1346: $i,SV629: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV629 ) @ SV1346 ) ) @ SV1889 ) @ SV1346 )
= SV629 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3967]) ).
thf(4660,plain,
! [SV1347: $i,SV630: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV630 @ SV1347 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV1347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4661,plain,
! [SV1348: $i,SV631: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV631 @ SV1348 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV1348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3969]) ).
thf(4662,plain,
! [SV1349: $i,SV632: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV632 @ SV1349 ) )
= $true )
| ( ( ~ ( class_Orderings_Obot @ SV1349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4663,plain,
! [SV1890: $i,SV1350: $i,SV633: $i] :
( ( ! [SY5847: $i,SY5848: $i,SY5849: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV633 @ SV1350 @ SV1890 @ SY5847 ) @ SY5848 ) @ SY5849 )
= ( hAPP @ ( hAPP @ SV633 @ SY5849 ) @ SY5848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4664,plain,
! [SV1891: $i,SV1351: $i,SV634: $i] :
( ( ! [SY5850: $i,SY5851: $i,SY5852: $i] :
( ( c_COMBB @ SV634 @ SV1351 @ SV1891 @ SY5850 @ SY5851 @ SY5852 )
= ( hAPP @ SV634 @ ( hAPP @ SV1351 @ SV1891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3972]) ).
thf(4665,plain,
! [SV1892: $i,SV1353: $i,SV636: $i] :
( ( ( SV636 = SV1353 )
| ~ ( c_fequal @ SV636 @ SV1353 @ SV1892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3974]) ).
thf(4666,plain,
! [SV1893: $i,SV1354: $i,SV637: $i] :
( ( ! [SY5853: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV637 )
| ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV1893 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SY5853 ) )
| ( SV1893 = SY5853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3975]) ).
thf(4667,plain,
! [SV1894: $i,SV1355: $i,SV638: $i] :
( ( ( SV638
!= ( c_List_Oappend @ SV638 @ SV1355 @ SV1894 ) )
| ( SV1355
= ( c_List_Olist_ONil @ SV1894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4668,plain,
! [SV1895: $i,SV1356: $i,SV639: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV639 )
| ( ( c_Power_Opower__class_Opower @ SV1356 @ SV1895 @ SV639 )
!= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
| ( SV1356
= ( c_HOL_Ozero__class_Ozero @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3977]) ).
thf(4669,plain,
! [SV1357: $i,SV640: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV640 @ SV1357 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV640 @ SV1357 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3978]) ).
thf(4670,plain,
! [SV1358: $i,SV641: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV641 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV641 ) @ SV1358 ) @ SV1358 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1358
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3979]) ).
thf(4671,plain,
! [SV1359: $i,SV642: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV642 @ ( tc_List_Olist @ SV1359 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV642
= ( c_List_Olist_ONil @ SV1359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3980]) ).
thf(4672,plain,
! [SV1896: $i,SV1360: $i,SV643: $i] :
( ( ! [SY5854: $i,SY5855: $i] :
( ( ( c_List_Omap @ SV643 @ SV1360 @ SV1896 @ SY5854 )
!= ( c_List_Omap @ SV643 @ SY5855 @ SV1896 @ SY5854 ) )
| ( ( c_Nat_Osize__class_Osize @ SV1360 @ ( tc_List_Olist @ SV1896 ) )
= ( c_Nat_Osize__class_Osize @ SY5855 @ ( tc_List_Olist @ SV1896 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3981]) ).
thf(4673,plain,
! [SV1897: $i,SV1361: $i,SV644: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
!= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
| ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3982]) ).
thf(4674,plain,
! [SV1362: $i,SV645: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV645 @ SV1362 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1362 @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1362 = SV645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3983]) ).
thf(4675,plain,
! [SV1898: $i,SV1363: $i,SV646: $i] :
( ( ! [SY5856: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV646 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV1898 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SY5856 ) )
| ( SV1898 = SY5856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3984]) ).
thf(4676,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV647 )
| ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3985]) ).
thf(4677,plain,
! [SV1900: $i,SV1365: $i,SV648: $i] :
( ( ! [SY5857: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV648 ) @ SV1365 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1900 ) @ SY5857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV648 = SV1900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3986]) ).
thf(4678,plain,
! [SV1366: $i,SV649: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV649 ) @ SV1366 )
!= SV649 )
= $true )
| ( ( SV1366
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3987]) ).
thf(4679,plain,
! [SV1901: $i,SV1367: $i,SV650: $i] :
( ( ( ( c_List_Oappend @ SV650 @ SV1367 @ SV1901 )
!= SV650 )
| ( SV1367
= ( c_List_Olist_ONil @ SV1901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4680,plain,
! [SV1368: $i,SV651: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV651 ) @ SV1368 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV651
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV651
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3989]) ).
thf(4681,plain,
! [SV1902: $i,SV1369: $i,SV652: $i] :
( ( ! [SY5858: $i] :
( ( ( c_List_Olist_ONil @ SV652 )
!= ( c_List_Omap @ SV1369 @ SV1902 @ SY5858 @ SV652 ) )
| ( SV1902
= ( c_List_Olist_ONil @ SY5858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3990]) ).
thf(4682,plain,
! [SV1903: $i,SV1370: $i,SV653: $i] :
( ( ! [SY5859: $i,SY5860: $i] :
( ( ( c_List_Oappend @ SV653 @ SV1370 @ SV1903 )
!= ( c_List_Oappend @ SY5859 @ SY5860 @ SV1903 ) )
| ( SV1370
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ SY5859 @ SV1903 ) @ SY5860 @ SV1903 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ ( c_Nat_Osize__class_Osize @ SY5859 @ ( tc_List_Olist @ SV1903 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3991]) ).
thf(4683,plain,
! [SV1371: $i,SV654: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV654 ) @ SV1371 ) )
= $true )
| ( ( ( SV1371
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV654
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3992]) ).
thf(4684,plain,
! [SV1904: $i,SV1372: $i,SV655: $i] :
( ( ! [SY5861: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SY5861 @ SV1372 ) @ SV1372 )
!= SY5861 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 )
!= SV655 )
| ( SV1904
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
| ( ( c_List_Oappend @ SV1904 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SY5861 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SY5861 @ SV1372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3993]) ).
thf(4685,plain,
! [SV1373: $i,SV656: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV656 ) @ SV1373 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV656
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1373
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4686,plain,
! [SV1905: $i,SV1374: $i,SV657: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV657 @ SV1374 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1905 @ SV1374 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV657 = SV1905 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3995]) ).
thf(4687,plain,
! [SV1906: $i,SV1375: $i,SV659: $i] :
( ( ! [SY5862: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV659 )
| ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
!= ( c_Power_Opower__class_Opower @ SY5862 @ ( c_Suc @ SV1906 ) @ SV659 ) )
| ( SV1375 = SY5862 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SY5862 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4688,plain,
! [SV1907: $i,SV1376: $i,SV660: $i] :
( ( ! [SY5863: $i,SY5864: $i,SY5865: $i,SY5866: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SY5863 ) @ SY5864 ) ) )
| ~ ( c_Type_Otyping @ SY5865 @ SY5863 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY5863 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY5865 @ SY5864 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SY5866 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4689,plain,
! [SV1377: $i,SV661: $i] :
( ( ( SV661
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV661 ) @ SV1377 ) )
= $true )
| ( ( SV1377
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3999]) ).
thf(4690,plain,
! [SV1908: $i,SV1378: $i,SV662: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV662 ) @ SV1378 )
!= ( c_Lambda_OdB_OVar @ SV1908 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(4691,plain,
! [SV1909: $i,SV1379: $i,SV663: $i] :
( ( ( c_Lambda_OdB_OVar @ SV663 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1379 ) @ SV1909 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4001]) ).
thf(4692,plain,
! [SV1910: $i,SV1380: $i,SV664: $i] :
( ( ( ( c_List_Olist_ONil @ SV664 )
!= ( c_List_Oreplicate @ SV1380 @ SV1910 @ SV664 ) )
| ( SV1380
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4002]) ).
thf(4693,plain,
! [SV1911: $i,SV1381: $i,SV665: $i] :
( ( ! [SY5867: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV665 )
| ( ( c_Power_Opower__class_Opower @ SV1381 @ SV1911 @ SV665 )
!= ( c_Power_Opower__class_Opower @ SV1381 @ SY5867 @ SV665 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 )
| ( SV1911 = SY5867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4694,plain,
! [SV1912: $i,SV1382: $i,SV666: $i] :
( ( ( ( hAPP @ SV666 @ ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SV1382 @ SV1912 ) )
!= ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SV1382 @ SV1912 ) )
| ( ( c_List_Omap @ SV666 @ SV1382 @ SV1912 @ SV1912 )
= SV1382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4695,plain,
! [SV1913: $i,SV1383: $i,SV667: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV667 ) @ SV1383 )
!= ( c_Lambda_OdB_OAbs @ SV1913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4696,plain,
! [SV1914: $i,SV1384: $i,SV668: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV668 )
| ~ ( class_Int_Onumber__ring @ SV668 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1384 @ SV1914 @ SV668 )
!= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
| ( SV1384 = SV1914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(4697,plain,
! [SV1915: $i,SV1385: $i,SV669: $i] :
( ( ( c_Type_Otype_OAtom @ SV669 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1385 ) @ SV1915 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(4698,plain,
! [SV1916: $i,SV1386: $i,SV670: $i] :
( ( ! [SY5868: $i,SY5869: $i] :
( ( ( c_List_Oappend @ SV670 @ SV1386 @ SV1916 )
!= ( c_List_Oappend @ SY5868 @ SY5869 @ SV1916 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY5868 @ ( tc_List_Olist @ SV1916 ) ) @ SV670 @ SV1916 )
= SY5868 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV670 @ ( tc_List_Olist @ SV1916 ) ) @ ( c_Nat_Osize__class_Osize @ SY5868 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4008]) ).
thf(4699,plain,
! [SV671: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV671 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV671 )
!= ( c_HOL_Ozero__class_Ozero @ SV671 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4009]) ).
thf(4700,plain,
! [SV1917: $i,SV1387: $i,SV672: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV672 ) @ SV1387 )
!= ( c_Type_Otype_OAtom @ SV1917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4010]) ).
thf(4701,plain,
! [SV1918: $i,SV1388: $i,SV673: $i] :
( ( ! [SY5870: $i,SY5871: $i,SY5872: $i,SY5873: $i,SY5874: $i,SY5875: $i,SY5876: $i,SY5877: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SY5870 @ ( hAPP @ SY5871 @ SY5872 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SY5873 @ SY5874 @ SY5875 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SY5870 @ SY5871 @ SY5876 @ SY5874 @ SY5877 ) @ SY5872 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4702,plain,
! [SV1919: $i,SV1389: $i,SV674: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV674 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1389 @ SV674 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1919 @ SV674 ) )
| ( SV1389 = SV1919 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4012]) ).
thf(4703,plain,
! [SV1390: $i,SV675: $i] :
( ( ( ( c_List_Olist_ONil @ SV675 )
!= ( c_List_Orev @ SV1390 @ SV675 ) )
= $true )
| ( ( SV1390
= ( c_List_Olist_ONil @ SV675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4704,plain,
! [SV1920: $i,SV1391: $i,SV676: $i] :
( ( ! [SY5878: $i] :
( ( ( c_List_Oappend @ SV676 @ SV1391 @ SV1920 )
!= ( c_List_Oappend @ SV676 @ SY5878 @ SV1920 ) )
| ( SV1391 = SY5878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4014]) ).
thf(4705,plain,
! [SV1921: $i,SV1392: $i,SV677: $i] :
( ( ( ( c_List_Otake @ SV677 @ SV1392 @ SV1921 )
!= ( c_List_Olist_ONil @ SV1921 ) )
| ( SV1392
= ( c_List_Olist_ONil @ SV1921 ) )
| ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4015]) ).
thf(4706,plain,
! [SV1922: $i,SV1393: $i,SV678: $i] :
( ( ! [SY5879: $i,SY5880: $i,SY5881: $i,SY5882: $i,SY5883: $i,SY5884: $i] :
( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SY5879 @ SY5880 )
!= ( c_Fun_Ocomp @ SY5881 @ SY5882 @ SY5883 @ SY5879 @ SY5880 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SY5884 ) )
= ( hAPP @ SY5881 @ ( hAPP @ SY5882 @ SY5884 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4016]) ).
thf(4707,plain,
! [SV1394: $i,SV679: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV679 ) @ SV1394 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV1394
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1394
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4017]) ).
thf(4708,plain,
! [SV1923: $i,SV1395: $i,SV680: $i] :
( ( ( SV680
!= ( c_List_Oappend @ SV1395 @ SV680 @ SV1923 ) )
| ( SV1395
= ( c_List_Olist_ONil @ SV1923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4018]) ).
thf(4709,plain,
! [SV1396: $i,SV681: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV681 ) @ SV1396 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1396
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4710,plain,
! [SV1924: $i,SV1397: $i,SV682: $i] :
( ( ( c_List_Olist_OCons @ SV682 @ SV1397 @ SV1924 )
!= ( c_List_Olist_ONil @ SV1924 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(4711,plain,
! [SV1398: $i,SV683: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV683 ) @ SV1398 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV1398
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV683
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4021]) ).
thf(4712,plain,
! [SV1925: $i,SV1399: $i,SV684: $i] :
( ( ! [SY5885: $i,SY5886: $i] :
( ( ( hAPP @ SV684 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SY5885 @ SY5886 ) )
!= ( hAPP @ SV1399 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SY5885 @ SY5886 ) ) )
| ( ( c_List_Omap @ SV684 @ SV1925 @ SY5885 @ SY5886 )
= ( c_List_Omap @ SV1399 @ SV1925 @ SY5885 @ SY5886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4022]) ).
thf(4713,plain,
! [SV1926: $i,SV1400: $i,SV685: $i] :
( ( ( ( c_List_Oappend @ SV685 @ SV1400 @ SV1926 )
!= ( c_List_Olist_ONil @ SV1926 ) )
| ( SV685
= ( c_List_Olist_ONil @ SV1926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4023]) ).
thf(4714,plain,
! [SV1927: $i,SV1401: $i,SV686: $i] :
( ( ! [SY5887: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV686 ) @ SV1401 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1927 ) @ SY5887 ) )
| ( SV1401 = SY5887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4024]) ).
thf(4715,plain,
! [SV1928: $i,SV1402: $i,SV687: $i] :
( ( ! [SY5888: $i,SY5889: $i] :
( ( ( c_List_Oappend @ SV687 @ ( c_List_Olist_OCons @ SV1402 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 )
!= ( c_List_Oappend @ SY5888 @ ( c_List_Olist_OCons @ SY5889 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 ) )
| ( SV1402 = SY5889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(4716,plain,
! [SV1929: $i,SV1403: $i,SV688: $i] :
( ( ! [SY5890: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV688 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV1929 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SY5890 ) )
| ( SV1929 = SY5890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4026]) ).
thf(4717,plain,
! [SV1930: $i,SV1404: $i,SV689: $i] :
( ( ! [SY5891: $i,SY5892: $i] :
( ( ( c_List_Oreplicate @ SV689 @ SV1404 @ SV1930 )
!= ( c_List_Oreplicate @ SY5891 @ SY5892 @ SV1930 ) )
| ( SV689 = SY5891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4027]) ).
thf(4718,plain,
! [SV1931: $i,SV1405: $i,SV690: $i] :
( ( ! [SY5893: $i,SY5894: $i] :
( ( ( hAPP @ SV690 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SY5893 @ SY5894 ) )
!= ( hAPP @ SV1405 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SY5893 @ SY5894 ) ) )
| ( ( c_List_Omap @ SV690 @ SV1931 @ SY5893 @ SY5894 )
= ( c_List_Omap @ SV1405 @ SV1931 @ SY5893 @ SY5894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4028]) ).
thf(4719,plain,
! [SV1406: $i,SV691: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV691 )
!= ( c_Lambda_OdB_OAbs @ SV1406 ) )
= $true )
| ( ( SV691 = SV1406 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4029]) ).
thf(4720,plain,
! [SV1932: $i,SV1407: $i,SV692: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV692 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1407 ) @ SV1932 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4030]) ).
thf(4721,plain,
! [SV1933: $i,SV1408: $i,SV693: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV693 ) @ SV1408 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1933 ) @ SV1408 ) )
| ( SV693 = SV1933 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4031]) ).
thf(4722,plain,
! [SV1934: $i,SV1409: $i,SV694: $i] :
( ( ! [SY5895: $i,SY5896: $i] :
( ( ( c_List_Oappend @ SV694 @ SV1409 @ SV1934 )
!= ( c_List_Oappend @ SY5895 @ SY5896 @ SV1934 ) )
| ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ SY5895 @ SV1934 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ ( c_Nat_Osize__class_Osize @ SY5895 @ ( tc_List_Olist @ SV1934 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4032]) ).
thf(4723,plain,
! [SV1935: $i,SV1410: $i,SV695: $i] :
( ( ( ( c_List_Oappend @ SV695 @ SV1410 @ SV1935 )
!= ( c_List_Olist_ONil @ SV1935 ) )
| ( SV1410
= ( c_List_Olist_ONil @ SV1935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4033]) ).
thf(4724,plain,
! [SV1936: $i,SV1411: $i,SV696: $i] :
( ( ! [SY5897: $i,SY5898: $i] :
( ( ( c_List_Olist_OCons @ SV696 @ SV1411 @ SV1936 )
!= ( c_List_Olist_OCons @ SY5897 @ SY5898 @ SV1936 ) )
| ( SV696 = SY5897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4034]) ).
thf(4725,plain,
! [SV1937: $i,SV1412: $i,SV697: $i] :
( ( ! [SY5899: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 )
!= SV697 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1937 @ ( tc_List_Olist @ SV1412 ) ) @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SV1937 @ SY5899 @ SV1412 )
= ( c_List_Oappend @ SV697 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 ) @ SY5899 @ SV1412 ) @ SV1412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4035]) ).
thf(4726,plain,
! [SV1938: $i,SV1413: $i,SV698: $i] :
( ( ( ( c_List_Olist_ONil @ SV698 )
!= ( c_List_Oappend @ SV1413 @ SV1938 @ SV698 ) )
| ( SV1413
= ( c_List_Olist_ONil @ SV698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4036]) ).
thf(4727,plain,
! [SV1939: $i,SV1414: $i,SV699: $i] :
( ( ! [SY5900: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV699 ) @ SV1414 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1939 ) @ SY5900 ) )
| ( SV699 = SV1939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4037]) ).
thf(4728,plain,
! [SV1940: $i,SV1415: $i,SV700: $i] :
( ( ! [SY5901: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV700 ) @ SV1415 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1940 ) @ SY5901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1415 = SY5901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4038]) ).
thf(4729,plain,
! [SV1416: $i,SV701: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV701 ) @ SV1416 ) )
= $true )
| ( ( ( SV701
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV701
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4039]) ).
thf(4730,plain,
! [SV1417: $i,SV702: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV702 )
!= ( c_Lambda_OdB_OVar @ SV1417 ) )
= $true )
| ( ( SV702 = SV1417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4731,plain,
! [SV1941: $i,SV1418: $i,SV703: $i] :
( ( SV703
!= ( c_List_Olist_OCons @ SV1418 @ SV703 @ SV1941 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4041]) ).
thf(4732,plain,
! [SV1942: $i,SV1419: $i,SV704: $i] :
( ( ! [SY5902: $i,SY5903: $i] :
( ( ( c_List_Oreplicate @ SV704 @ SV1419 @ SV1942 )
!= ( c_List_Oreplicate @ SY5902 @ SY5903 @ SV1942 ) )
| ( SV1419 = SY5903 )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(4733,plain,
! [SV1943: $i,SV1420: $i,SV706: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SV1420 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV1943 @ SV1420 @ tc_nat ) )
| ~ ( c_lessequals @ SV1420 @ SV1943 @ tc_nat )
| ~ ( c_lessequals @ SV1420 @ SV706 @ tc_nat )
| ( SV706 = SV1943 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4044]) ).
thf(4734,plain,
! [SV1944: $i,SV1421: $i,SV707: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV707 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1421 @ SV1944 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV707 )
= SV1421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4045]) ).
thf(4735,plain,
! [SV1945: $i,SV1422: $i,SV708: $i] :
( ( ! [SY5904: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV708 ) @ SV1422 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1945 ) @ SY5904 ) )
| ( SV708 = SV1945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4046]) ).
thf(4736,plain,
! [SV1946: $i,SV1423: $i,SV709: $i] :
( ( ( ( c_List_Orotate @ SV709 @ SV1423 @ SV1946 )
!= ( c_List_Olist_ONil @ SV1946 ) )
| ( SV1423
= ( c_List_Olist_ONil @ SV1946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4047]) ).
thf(4737,plain,
! [SV1947: $i,SV1424: $i,SV711: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV711 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1424 @ SV1947 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SV1424 = SV1947 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4049]) ).
thf(4738,plain,
! [SV1948: $i,SV1425: $i,SV712: $i] :
( ( ! [SY5905: $i,SY5906: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
!= ( c_HOL_Ominus__class_Ominus @ SY5905 @ SY5906 @ SV712 ) )
| ( c_HOL_Oord__class_Oless @ SY5905 @ SY5906 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4050]) ).
thf(4739,plain,
! [SV1949: $i,SV1426: $i,SV713: $i] :
( ( ! [SY5907: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV713 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1426 ) @ SV1949 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SY5907 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SV1949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4051]) ).
thf(4740,plain,
! [SV1950: $i,SV1427: $i,SV714: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV714 )
| ~ ( class_Int_Onumber__ring @ SV714 )
| ( SV1427
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SV1427 ) @ SV1950 ) )
| ( SV1950
= ( c_HOL_Ozero__class_Ozero @ SV714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4052]) ).
thf(4741,plain,
! [SV1951: $i,SV1428: $i,SV715: $i] :
( ( ( ( c_List_Orev @ SV715 @ SV1428 )
!= ( c_List_Orev @ SV1951 @ SV1428 ) )
| ( SV715 = SV1951 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4053]) ).
thf(4742,plain,
! [SV1952: $i,SV1429: $i,SV716: $i] :
( ( ( ( c_List_Olist_ONil @ SV716 )
!= ( c_List_Oappend @ SV1429 @ SV1952 @ SV716 ) )
| ( SV1952
= ( c_List_Olist_ONil @ SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4054]) ).
thf(4743,plain,
! [SV1430: $i,SV717: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV717 ) @ SV1430 ) )
= $true )
| ( ( ( SV717
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1430
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4055]) ).
thf(4744,plain,
! [SV1953: $i,SV1431: $i,SV718: $i] :
( ( ! [SY5908: $i] :
( ( ( c_List_Omap @ SV718 @ SV1431 @ SV1953 @ SY5908 )
!= ( c_List_Olist_ONil @ SY5908 ) )
| ( SV1431
= ( c_List_Olist_ONil @ SV1953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4056]) ).
thf(4745,plain,
! [SV1954: $i,SV1432: $i,SV719: $i] :
( ( ! [SY5909: $i] :
( ( ( c_List_Orev @ SV719 @ SV1432 )
!= ( c_List_Olist_OCons @ SV1954 @ SY5909 @ SV1432 ) )
| ( SV719
= ( c_List_Oappend @ ( c_List_Orev @ SY5909 @ SV1432 ) @ ( c_List_Olist_OCons @ SV1954 @ ( c_List_Olist_ONil @ SV1432 ) @ SV1432 ) @ SV1432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4057]) ).
thf(4746,plain,
! [SV1955: $i,SV1433: $i,SV720: $i] :
( ( ! [SY5910: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV720 ) @ SV1433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1955 ) @ SY5910 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4058]) ).
thf(4747,plain,
! [SV1956: $i,SV1434: $i,SV721: $i] :
( ( ! [SY5911: $i,SY5912: $i] :
( ( ( c_List_Olist_OCons @ SV721 @ SV1434 @ SV1956 )
!= ( c_List_Olist_OCons @ SY5911 @ SY5912 @ SV1956 ) )
| ( SV1434 = SY5912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4059]) ).
thf(4748,plain,
! [SV1957: $i,SV1435: $i,SV722: $i] :
( ( ! [SY5913: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV722 ) @ SV1435 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1957 ) @ SY5913 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1957 @ SV1435 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV722 @ SY5913 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4060]) ).
thf(4749,plain,
! [SV1958: $i,SV1436: $i,SV723: $i] :
( ( ! [SY5914: $i] :
( ( ( c_List_Olist__update @ SV723 @ SV1436 @ SV1958 @ SY5914 )
!= ( c_List_Olist_ONil @ SY5914 ) )
| ( SV723
= ( c_List_Olist_ONil @ SY5914 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4061]) ).
thf(4750,plain,
! [SV1437: $i,SV724: $i] :
( ( ( ( c_List_Orev @ SV724 @ SV1437 )
!= ( c_List_Olist_ONil @ SV1437 ) )
= $true )
| ( ( SV724
= ( c_List_Olist_ONil @ SV1437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4062]) ).
thf(4751,plain,
! [SV1959: $i,SV1438: $i,SV725: $i] :
( ( ! [SY5915: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV725 ) @ SV1438 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1959 ) @ SY5915 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV725 = SV1959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4063]) ).
thf(4752,plain,
! [SV1960: $i,SV1439: $i,SV726: $i] :
( ( ! [SY5916: $i,SY5917: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
!= ( c_HOL_Ominus__class_Ominus @ SY5916 @ SY5917 @ SV726 ) )
| ( c_lessequals @ SY5917 @ SY5916 @ SV726 )
| ~ ( c_lessequals @ SV1960 @ SV1439 @ SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(4753,plain,
! [SV1961: $i,SV1440: $i,SV727: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SV1440 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SV1961 ) )
| ( SV1440 = SV1961 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4754,plain,
! [SV1962: $i,SV1441: $i,SV728: $i] :
( ( ! [SY5918: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV728 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1441 @ SV1441 @ SV728 )
!= ( c_HOL_Ominus__class_Ominus @ SV1962 @ SY5918 @ SV728 ) )
| ( SV1962 = SY5918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4066]) ).
thf(4755,plain,
! [SV1442: $i,SV729: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV729 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV729 )
| ~ ( class_Power_Opower @ SV729 )
| ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4067]) ).
thf(4756,plain,
! [SV1963: $i,SV1443: $i,SV730: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4068]) ).
thf(4757,plain,
! [SV1964: $i,SV1444: $i,SV731: $i] :
( ( ( ( c_List_Oreplicate @ SV731 @ SV1444 @ SV1964 )
!= ( c_List_Olist_ONil @ SV1964 ) )
| ( SV731
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(4758,plain,
! [SV732: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV732 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV732 )
!= ( c_HOL_Oone__class_Oone @ SV732 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4070]) ).
thf(4759,plain,
! [SV1445: $i,SV733: $i] :
( ( ( ( c_Suc @ SV733 )
!= ( c_Suc @ SV1445 ) )
= $true )
| ( ( SV733 = SV1445 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4071]) ).
thf(4760,plain,
! [SV1965: $i,SV1446: $i,SV734: $i] :
( ( ! [SY5919: $i,SY5920: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV734 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SY5919 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SY5920 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ SY5919 )
= SY5920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4072]) ).
thf(4761,plain,
! [SV1966: $i,SV1447: $i,SV735: $i] :
( ( ( ( c_List_Orev @ SV735 @ SV1447 )
!= ( c_List_Olist_OCons @ SV1966 @ ( c_List_Olist_ONil @ SV1447 ) @ SV1447 ) )
| ( SV735
= ( c_List_Olist_OCons @ SV1966 @ ( c_List_Olist_ONil @ SV1447 ) @ SV1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4073]) ).
thf(4762,plain,
! [SV1967: $i,SV1448: $i,SV736: $i] :
( ( ( ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SV1448 ) @ SV1448 )
!= ( c_List_Orev @ SV1967 @ SV1448 ) )
| ( SV1967
= ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SV1448 ) @ SV1448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4074]) ).
thf(4763,plain,
! [SV1449: $i,SV737: $i] :
( ( ( ( c_Suc @ SV737 )
!= ( c_Suc @ SV1449 ) )
= $true )
| ( ( SV737 = SV1449 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4075]) ).
thf(4764,plain,
! [SV1968: $i,SV1450: $i,SV738: $i] :
( ( ( SV738
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SV1450 ) ) @ SV1968 @ SV1450 ) )
| ( ( c_List_Oappend @ SV738 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SV1450 ) ) @ SV1968 @ SV1450 ) @ SV1450 )
= SV1968 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4076]) ).
thf(4765,plain,
! [SV1969: $i,SV1451: $i,SV740: $i] :
( ( ! [SY5921: $i,SY5922: $i] :
( ( ( hAPP @ SV740 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SY5921 @ SY5922 ) )
!= ( hAPP @ SV1451 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SY5921 @ SY5922 ) ) )
| ( ( c_List_Omap @ SV740 @ SV1969 @ SY5921 @ SY5922 )
= ( c_List_Omap @ SV1451 @ SV1969 @ SY5921 @ SY5922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(4766,plain,
! [SV1970: $i,SV1452: $i,SV741: $i] :
( ( ! [SY5923: $i] :
( ( SV741
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) )
| ( ( c_List_Oappend @ SV741 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) @ SY5923 @ SV1452 ) @ SV1452 )
= ( c_List_Oappend @ SV1970 @ SY5923 @ SV1452 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ ( c_Nat_Osize__class_Osize @ SV1970 @ ( tc_List_Olist @ SV1452 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4079]) ).
thf(4767,plain,
! [SV1971: $i,SV1453: $i,SV742: $i] :
( ( ! [SY5924: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV742 ) ) @ SV1453 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1971 ) @ SY5924 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4768,plain,
! [SV1972: $i,SV1454: $i,SV744: $i] :
( ( ! [SY5925: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV744 ) @ SV1454 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1972 ) @ SY5925 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1454 = SY5925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4082]) ).
thf(4769,plain,
! [SV1973: $i,SV1455: $i,SV745: $i] :
( ( ( c_List_Olist_OCons @ SV745 @ SV1455 @ SV1973 )
!= SV1455 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4083]) ).
thf(4770,plain,
! [SV1456: $i,SV746: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV746 )
!= ( c_Type_Otype_OAtom @ SV1456 ) )
= $true )
| ( ( SV746 = SV1456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4771,plain,
! [SV1457: $i,SV747: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV747 ) @ SV1457 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV747
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4085]) ).
thf(4772,plain,
! [SV1974: $i,SV1458: $i,SV749: $i] :
( ( ! [SY5926: $i,SY5927: $i] :
( ( ( c_List_Oappend @ SV749 @ SV1458 @ SV1974 )
!= ( c_List_Oappend @ SY5926 @ SY5927 @ SV1974 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY5926 @ ( tc_List_Olist @ SV1974 ) ) @ SV749 @ SV1974 ) @ SV1458 @ SV1974 )
= SY5927 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV749 @ ( tc_List_Olist @ SV1974 ) ) @ ( c_Nat_Osize__class_Osize @ SY5926 @ ( tc_List_Olist @ SV1974 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4087]) ).
thf(4773,plain,
! [SV1975: $i,SV1459: $i,SV750: $i] :
( ( ! [SY5928: $i,SY5929: $i,SY5930: $i,SY5931: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SY5928 ) @ SY5929 ) ) )
| ~ ( c_Type_Otyping @ SY5930 @ SY5928 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY5928 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY5930 @ SY5929 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SY5931 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4088]) ).
thf(4774,plain,
! [SV1976: $i,SV1460: $i,SV751: $i] :
( ( ( ( c_List_Oappend @ SV751 @ SV1460 @ SV1976 )
!= SV1460 )
| ( SV751
= ( c_List_Olist_ONil @ SV1976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4089]) ).
thf(4775,plain,
! [SV1461: $i,SV752: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV752 )
= ( c_Lambda_OdB_OVar @ SV1461 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4090]) ).
thf(4776,plain,
! [SV1977: $i,SV1462: $i,SV753: $i] :
( ( ( c_List_Olist_ONil @ SV753 )
!= ( c_List_Olist_OCons @ SV1462 @ SV1977 @ SV753 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4091]) ).
thf(4777,plain,
! [SV1978: $i,SV1463: $i,SV754: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SV1463 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SV1978 ) )
| ( SV1463 = SV1978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4092]) ).
thf(4778,plain,
! [SV1979: $i,SV1464: $i,SV755: $i] :
( ( ! [SY5932: $i,SY5933: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
!= ( c_HOL_Ominus__class_Ominus @ SY5932 @ SY5933 @ SV755 ) )
| ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SY5932 @ SY5933 @ SV755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4779,plain,
! [SV1980: $i,SV1465: $i,SV756: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV756 )
| ( ( c_Orderings_Oord__class_Omax @ SV1465 @ SV1980 @ SV756 )
!= SV1980 )
| ( c_lessequals @ SV1465 @ SV1980 @ SV756 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4094]) ).
thf(4780,plain,
! [SV1981: $i,SV1466: $i,SV757: $i] :
( ( ! [SY5934: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV757 )
| ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
!= ( c_Power_Opower__class_Opower @ SY5934 @ SV1981 @ SV757 ) )
| ( SV1466 = SY5934 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SY5934 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4781,plain,
! [SV1982: $i,SV1467: $i,SV758: $i] :
( ( ( ( c_List_Odrop @ SV758 @ SV1467 @ SV1982 )
!= ( c_List_Olist_ONil @ SV1982 ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1467 @ ( tc_List_Olist @ SV1982 ) ) @ SV758 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(4782,plain,
! [SV1983: $i,SV1468: $i,SV759: $i] :
( ( ! [SY5935: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1468 ) @ SV1983 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY5935 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV1468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4097]) ).
thf(4783,plain,
! [SV1984: $i,SV1469: $i,SV760: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV760 @ SV1469 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1984 ) )
| ( SV760
= ( c_Lambda_OdB_OAbs @ SV1984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4784,plain,
! [SV1985: $i,SV1470: $i,SV761: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV761 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1470 @ SV1985 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV761 )
= SV1470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4785,plain,
! [SV1986: $i,SV1471: $i,SV762: $i] :
( ( ! [SY5936: $i] :
( ( ( c_List_Oappend @ SV762 @ SV1471 @ SV1986 )
!= ( c_List_Oappend @ SY5936 @ SV1471 @ SV1986 ) )
| ( SV762 = SY5936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4786,plain,
! [SV1987: $i,SV1472: $i,SV763: $i] :
( ( ( c_List_Olist_OCons @ SV763 @ SV1472 @ SV1987 )
!= ( c_List_Olist_ONil @ SV1987 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4787,plain,
! [SV1988: $i,SV1473: $i,SV764: $i] :
( ( ! [SY5937: $i,SY5938: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
!= ( c_HOL_Ominus__class_Ominus @ SY5937 @ SY5938 @ SV764 ) )
| ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
| ~ ( c_lessequals @ SY5938 @ SY5937 @ SV764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4102]) ).
thf(4788,plain,
! [SV1989: $i,SV1474: $i,SV765: $i] :
( ( ! [SY5939: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV765 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1474 @ SV1989 @ SV765 )
!= ( c_HOL_Ominus__class_Ominus @ SY5939 @ SY5939 @ SV765 ) )
| ( SV1474 = SV1989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4103]) ).
thf(4789,plain,
! [SV1475: $i,SV766: $i] :
( ( ( c_Lambda_OdB_OVar @ SV766 )
= ( c_Lambda_OdB_OAbs @ SV1475 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4104]) ).
thf(4790,plain,
! [SV1990: $i,SV1476: $i,SV767: $i] :
( ( ! [SY5940: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV767 ) @ SV1476 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1990 ) @ SY5940 ) )
| ( SV1476 = SY5940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(4791,plain,
! [SV1991: $i,SV1477: $i,SV768: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV768 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV1991 @ SV768 )
!= ( c_HOL_Ozero__class_Ozero @ SV768 ) )
| ( SV1477 = SV1991 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4106]) ).
thf(4792,plain,
! [SV1478: $i,SV769: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV769 ) @ SV1478 ) )
= $true )
| ( ( ( SV1478
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1478
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4107]) ).
thf(4793,plain,
! [SV1992: $i,SV1479: $i,SV770: $i] :
( ( ! [SY5941: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV770 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV1479 ) @ SV1992 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SY5941 ) @ SV1992 ) )
| ( SV1479 = SY5941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4108]) ).
thf(4794,plain,
! [SV1993: $i,SV1480: $i,SV771: $i] :
( ( ! [SY5942: $i,SY5943: $i] :
( ( ( c_List_Oappend @ SV771 @ ( c_List_Olist_OCons @ SV1480 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 )
!= ( c_List_Oappend @ SY5942 @ ( c_List_Olist_OCons @ SY5943 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 ) )
| ( SV771 = SY5942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4109]) ).
thf(4795,plain,
! [SV772: $i,SV1: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV1 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ SV772 ) @ SV772 ) @ SV1 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV772 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4110]) ).
thf(4796,plain,
! [SV773: $i,SV2: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV2 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV773 @ SV2 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV773 ) @ SV773 ) @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4111]) ).
thf(4797,plain,
! [SV1481: $i,SV775: $i,SV7: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV7 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV7 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1481 @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV775 @ SV1481 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4798,plain,
! [SV1482: $i,SV776: $i,SV8: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV8 ) )
= $true )
| ( ( ( c_lessequals @ SV776 @ SV1482 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV776 @ SV8 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1482 @ SV8 ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4799,plain,
! [SV1484: $i,SV778: $i,SV10: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV10 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV778 ) @ SV1484 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV10 @ SV778 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1484 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4116]) ).
thf(4800,plain,
! [SV1994: $i,SV1485: $i,SV779: $i,SV11: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
| ~ ( c_lessequals @ SV779 @ SV1994 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4117]) ).
thf(4801,plain,
! [SV1995: $i,SV1486: $i,SV781: $i,SV13: $i] :
( ( ( c_List_Odrop @ SV13 @ ( c_List_Oappend @ SV781 @ SV1486 @ SV1995 ) @ SV1995 )
= ( c_List_Oappend @ ( c_List_Odrop @ SV13 @ SV781 @ SV1995 ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Nat_Osize__class_Osize @ SV781 @ ( tc_List_Olist @ SV1995 ) ) @ tc_nat ) @ SV1486 @ SV1995 ) @ SV1995 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4118]) ).
thf(4802,plain,
! [SV1487: $i,SV782: $i,SV14: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV14 @ SV782 @ tc_nat ) ) @ SV1487 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV782 ) @ SV1487 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV782 @ SV14 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4119]) ).
thf(4803,plain,
! [SV1996: $i,SV1488: $i,SV783: $i,SV15: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SV1488 @ SV15 ) @ SV1996 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV1488 @ SV1996 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV1996 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4120]) ).
thf(4804,plain,
! [SV784: $i,SV16: $i] :
( ( ( c_lessequals @ SV16 @ SV784 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV16 @ SV784 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4121]) ).
thf(4805,plain,
! [SV1489: $i,SV785: $i,SV17: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV17 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV785 @ SV1489 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV785 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4806,plain,
! [SV786: $i,SV18: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV18 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV18 @ SV786 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4123]) ).
thf(4807,plain,
! [SV1490: $i,SV788: $i,SV20: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV788 @ SV1490 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ SV788 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4124]) ).
thf(4808,plain,
! [SV789: $i,SV21: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV21 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV21 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ ( c_Suc @ SV789 ) @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4125]) ).
thf(4809,plain,
! [SV1997: $i,SV1491: $i,SV792: $i,SV24: $i] :
( ( ( ( c_List_Orev @ ( c_List_Olist__update @ SV24 @ SV792 @ SV1491 @ SV1997 ) @ SV1997 )
= ( c_List_Olist__update @ ( c_List_Orev @ SV24 @ SV1997 ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV1997 ) ) @ SV792 @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1491 @ SV1997 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV792 @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV1997 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4126]) ).
thf(4810,plain,
! [SV1492: $i,SV793: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ SV793 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV25 @ SV1492 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1492 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV25 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4127]) ).
thf(4811,plain,
! [SV1493: $i,SV797: $i,SV29: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV797 ) @ SV1493 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ SV797 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV797 @ SV1493 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4812,plain,
! [SV1494: $i,SV798: $i,SV30: $i] :
( ( ( c_lessequals @ SV30 @ ( c_HOL_Ominus__class_Ominus @ SV798 @ SV1494 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV30 ) @ SV1494 ) @ SV798 @ tc_nat )
| ~ ( c_lessequals @ SV1494 @ SV798 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4129]) ).
thf(4813,plain,
! [SV1998: $i,SV1495: $i,SV799: $i,SV31: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV31 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SV1495 @ SV31 ) @ SV1998 @ SV31 )
| ~ ( c_lessequals @ SV1495 @ SV1998 @ SV31 )
| ~ ( c_lessequals @ SV799 @ SV1998 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4814,plain,
! [SV1999: $i,SV1496: $i,SV800: $i,SV32: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV32 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SV1496 @ SV32 ) @ SV1999 @ SV32 )
| ~ ( c_lessequals @ SV1496 @ SV1999 @ SV32 )
| ~ ( c_lessequals @ SV800 @ SV1999 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4815,plain,
! [SV2000: $i,SV1497: $i,SV801: $i,SV33: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV33 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SV1497 @ SV33 ) @ SV2000 @ SV33 )
| ~ ( c_lessequals @ SV1497 @ SV2000 @ SV33 )
| ~ ( c_lessequals @ SV801 @ SV2000 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4816,plain,
! [SV1498: $i,SV802: $i,SV34: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV34 ) )
= $true )
| ( ( c_lessequals @ SV802 @ ( c_Orderings_Oord__class_Omax @ SV802 @ SV1498 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4133]) ).
thf(4817,plain,
! [SV1499: $i,SV803: $i,SV35: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV35 ) )
= $true )
| ( ( c_lessequals @ SV803 @ ( c_Orderings_Oord__class_Omax @ SV1499 @ SV803 @ SV35 ) @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4134]) ).
thf(4818,plain,
! [SV809: $i,SV41: $i] :
( ( ( class_Orderings_Obot @ SV41 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV41 ) @ SV809 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4135]) ).
thf(4819,plain,
! [SV1500: $i,SV810: $i,SV42: $i] :
( ( ( c_List_Odistinct @ SV42 @ SV810 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV42 @ SV1500 @ SV810 ) @ SV810 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4820,plain,
! [SV1501: $i,SV811: $i,SV43: $i] :
( ( ( c_List_Odistinct @ SV43 @ SV811 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV1501 @ SV43 @ SV811 ) @ SV811 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4137]) ).
thf(4821,plain,
! [SV2001: $i,SV1502: $i,SV815: $i,SV47: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV47 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4822,plain,
! [SV2002: $i,SV1504: $i,SV817: $i,SV49: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
| ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
| ~ ( c_lessequals @ SV817 @ SV2002 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4140]) ).
thf(4823,plain,
! [SV2003: $i,SV1505: $i,SV818: $i,SV50: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
| ~ ( c_lessequals @ SV818 @ SV1505 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4824,plain,
! [SV819: $i,SV51: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV51 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV51 @ SV819 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4142]) ).
thf(4825,plain,
! [SV820: $i,SV52: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV52 @ SV820 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV52 ) @ SV820 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4143]) ).
thf(4826,plain,
! [SV821: $i,SV53: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV53 ) @ SV821 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV53 @ SV821 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4144]) ).
thf(4827,plain,
! [SV822: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV822 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV54 ) @ SV822 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4145]) ).
thf(4828,plain,
! [SV823: $i,SV55: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV55 ) @ SV823 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ SV823 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4146]) ).
thf(4829,plain,
! [SV1506: $i,SV824: $i,SV56: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV56 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV824 ) @ SV1506 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV56 @ SV824 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4147]) ).
thf(4830,plain,
! [SV1507: $i,SV825: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV57 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV825 ) @ SV1507 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV1507 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4148]) ).
thf(4831,plain,
! [SV1508: $i,SV826: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV58 @ SV826 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SV1508 ) @ SV826 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4149]) ).
thf(4832,plain,
! [SV1509: $i,SV827: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV59 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV827 ) @ SV1509 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV59 @ SV827 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4833,plain,
! [SV1510: $i,SV828: $i,SV60: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV60 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV828 ) @ SV1510 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV60 @ SV1510 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4151]) ).
thf(4834,plain,
! [SV2004: $i,SV1511: $i,SV829: $i,SV61: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV61 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
| ~ ( c_lessequals @ SV2004 @ SV1511 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4152]) ).
thf(4835,plain,
! [SV63: $i,SV830: $i] :
( ( ( c_lessequals @ SV830 @ SV63 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV63 ) @ SV830 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV63 @ SV830 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4153]) ).
thf(4836,plain,
! [SV1513: $i,SV832: $i,SV65: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV832 ) @ SV1513 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV1513 ) @ SV832 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4837,plain,
! [SV1514: $i,SV833: $i,SV66: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV66 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SV833 ) @ SV1514 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SV1514 ) @ SV833 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4156]) ).
thf(4838,plain,
! [SV1515: $i,SV835: $i,SV68: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV835 ) @ SV1515 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV1515 ) @ SV835 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4157]) ).
thf(4839,plain,
! [SV2005: $i,SV1516: $i,SV836: $i,SV69: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV69 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ SV1516 ) @ SV2005 @ SV69 @ SV69 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1516 @ SV2005 @ SV69 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4158]) ).
thf(4840,plain,
! [SV1518: $i,SV838: $i,SV71: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV838 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV1518 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV71 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV838 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4160]) ).
thf(4841,plain,
! [SV1519: $i,SV839: $i,SV72: $i] :
( ( ( ( hAPP @ SV72 @ SV839 )
= SV1519 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV72 @ ( c_Lambda_OdB_OVar @ SV839 ) @ SV1519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4161]) ).
thf(4842,plain,
! [SV2006: $i,SV1520: $i,SV840: $i,SV73: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV73 ) @ ( c_List_Olist_OCons @ SV840 @ SV1520 @ SV2006 ) @ SV2006 )
= ( c_List_Olist_OCons @ SV840 @ ( c_List_Otake @ SV73 @ SV1520 @ SV2006 ) @ SV2006 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4162]) ).
thf(4843,plain,
! [SV2007: $i,SV1521: $i,SV841: $i,SV74: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV74 )
| ( c_lessequals @ SV841 @ SV1521 @ SV74 )
| ( c_lessequals @ SV841 @ SV2007 @ SV74 )
| ~ ( c_lessequals @ SV841 @ ( c_Orderings_Oord__class_Omax @ SV2007 @ SV1521 @ SV74 ) @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4163]) ).
thf(4844,plain,
! [SV2008: $i,SV1522: $i,SV842: $i,SV75: $i] :
( ( ( c_List_Olistsp @ SV75 @ SV842 @ SV1522 )
| ~ ( c_List_Olistsp @ SV75 @ ( c_List_Oappend @ SV2008 @ SV842 @ SV1522 ) @ SV1522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4164]) ).
thf(4845,plain,
! [SV2009: $i,SV1523: $i,SV843: $i,SV76: $i] :
( ( ( c_List_Olistsp @ SV76 @ SV843 @ SV1523 )
| ~ ( c_List_Olistsp @ SV76 @ ( c_List_Oappend @ SV843 @ SV2009 @ SV1523 ) @ SV1523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4165]) ).
thf(4846,plain,
! [SV1524: $i,SV844: $i,SV77: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV77 ) ) @ SV844 ) @ SV1524 )
= ( c_Lambda_OdB_OVar @ SV77 ) )
= $true )
| ( ( ( SV77 = SV1524 )
| ( c_HOL_Oord__class_Oless @ SV1524 @ SV77 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4166]) ).
thf(4847,plain,
! [SV1525: $i,SV845: $i,SV78: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV78 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ ( c_HOL_Ominus__class_Ominus @ SV845 @ SV1525 @ SV78 ) ) @ SV1525 )
= SV845 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4167]) ).
thf(4848,plain,
! [SV1527: $i,SV847: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV847 ) @ SV1527 ) @ SV847 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV80 @ SV1527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4169]) ).
thf(4849,plain,
! [SV1528: $i,SV848: $i,SV81: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV81 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV848 ) @ SV1528 ) @ SV848 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV81 @ SV1528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4170]) ).
thf(4850,plain,
! [SV2010: $i,SV1530: $i,SV850: $i,SV83: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV83 ) @ SV850 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1530 ) @ SV2010 ) @ tc_nat )
| ~ ( c_lessequals @ SV850 @ SV2010 @ tc_nat )
| ~ ( c_lessequals @ SV83 @ SV1530 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4851,plain,
! [SV2011: $i,SV1531: $i,SV851: $i,SV84: $i] :
( ( ! [SY5944: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV2011 ) @ SY5944 ) @ SV84 )
| ~ ( c_lessequals @ SV1531 @ SY5944 @ SV84 )
| ~ ( c_lessequals @ SV851 @ SV2011 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4173]) ).
thf(4852,plain,
! [SV2012: $i,SV1533: $i,SV853: $i,SV86: $i] :
( ( ! [SY5945: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV86 @ SV853 @ SV1533 ) @ SV2012 @ SY5945 @ SV1533 )
= ( c_List_Oappend @ SV86 @ ( c_List_Olist__update @ SV853 @ ( c_HOL_Ominus__class_Ominus @ SV2012 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SV1533 ) ) @ tc_nat ) @ SY5945 @ SV1533 ) @ SV1533 ) )
| ( c_HOL_Oord__class_Oless @ SV2012 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SV1533 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(4853,plain,
! [SV1534: $i,SV854: $i,SV87: $i] :
( ( ( ( c_List_Otake @ SV87 @ SV854 @ SV1534 )
= SV854 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV854 @ ( tc_List_Olist @ SV1534 ) ) @ SV87 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4176]) ).
thf(4854,plain,
! [SV855: $i,SV88: $i] :
( ( ( c_lessequals @ SV88 @ SV855 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV88 @ ( c_Suc @ SV855 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4177]) ).
thf(4855,plain,
! [SV856: $i,SV89: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV89 @ ( c_Suc @ SV856 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV89 @ SV856 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4856,plain,
! [SV857: $i,SV91: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV91 )
= $false )
| ( ( ( c_List_Olistsum @ SV857 @ SV91 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV857 @ SV91 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4180]) ).
thf(4857,plain,
! [SV92: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4181]) ).
thf(4858,plain,
! [SV2013: $i,SV1535: $i,SV859: $i,SV94: $i] :
( ( ( c_List_Odrop @ SV94 @ ( c_List_Otake @ SV859 @ SV1535 @ SV2013 ) @ SV2013 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV859 @ SV94 @ tc_nat ) @ ( c_List_Odrop @ SV94 @ SV1535 @ SV2013 ) @ SV2013 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4182]) ).
thf(4859,plain,
! [SV1536: $i,SV860: $i,SV95: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV860 ) @ SV1536 ) @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1536 @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV860 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4183]) ).
thf(4860,plain,
! [SV1537: $i,SV861: $i,SV96: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV96 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV861 @ ( c_Suc @ SV1537 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV861 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4184]) ).
thf(4861,plain,
! [SV2014: $i,SV1538: $i,SV862: $i,SV97: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV97 )
| ( c_HOL_Oord__class_Oless @ SV862 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV2014 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV862 @ SV2014 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4185]) ).
thf(4862,plain,
! [SV2015: $i,SV1539: $i,SV863: $i,SV98: $i] :
( ( ~ ( class_Orderings_Oorder @ SV98 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SV1539 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV2015 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV2015 @ SV1539 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4186]) ).
thf(4863,plain,
! [SV1540: $i,SV864: $i,SV99: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV99 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV864 @ SV1540 @ SV99 )
= SV1540 )
| ~ ( c_lessequals @ SV864 @ SV1540 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4187]) ).
thf(4864,plain,
! [SV1541: $i,SV865: $i,SV100: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV100 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV865 @ SV1541 @ SV100 )
= SV865 )
| ~ ( c_lessequals @ SV1541 @ SV865 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4188]) ).
thf(4865,plain,
! [SV2016: $i,SV1542: $i,SV866: $i,SV101: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV1542 ) @ SV2016 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ SV1542 ) ) @ SV2016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4189]) ).
thf(4866,plain,
! [SV2017: $i,SV1543: $i,SV867: $i,SV102: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV102 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV1543 ) @ SV2017 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV1543 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ SV2017 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4190]) ).
thf(4867,plain,
! [SV2018: $i,SV1546: $i,SV870: $i,SV105: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ SV1546 ) ) @ SV2018 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV1546 ) @ SV2018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4193]) ).
thf(4868,plain,
! [SV2019: $i,SV1547: $i,SV871: $i,SV106: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV106 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV1547 ) @ SV2019 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV1547 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ SV2019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4194]) ).
thf(4869,plain,
! [SV2020: $i,SV1548: $i,SV872: $i,SV107: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV107 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ SV1548 ) ) @ SV2020 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV1548 ) @ SV2020 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(4870,plain,
! [SV2021: $i,SV1549: $i,SV873: $i,SV108: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV108 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV1549 ) @ SV2021 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ SV1549 ) ) @ SV2021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(4871,plain,
! [SV2022: $i,SV1550: $i,SV874: $i,SV109: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV109 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SV1550 ) ) @ SV2022 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SV2022 ) ) @ SV1550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4197]) ).
thf(4872,plain,
! [SV2023: $i,SV1551: $i,SV875: $i,SV110: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV1551 ) @ SV2023 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ SV2023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4198]) ).
thf(4873,plain,
! [SV2024: $i,SV1552: $i,SV876: $i,SV111: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV111 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ SV1552 ) ) @ SV2024 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV1552 ) @ SV2024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4199]) ).
thf(4874,plain,
! [SV112: $i,SV877: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV877 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV877 ) @ SV112 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV112 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4200]) ).
thf(4875,plain,
! [SV2025: $i,SV1554: $i,SV879: $i,SV114: $i] :
( ( ( c_List_Otake @ SV114 @ ( c_List_Odrop @ SV879 @ SV1554 @ SV2025 ) @ SV2025 )
= ( c_List_Odrop @ SV879 @ ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV114 ) @ SV879 ) @ SV1554 @ SV2025 ) @ SV2025 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4202]) ).
thf(4876,plain,
! [SV1556: $i,SV881: $i,SV116: $i] :
( ( ( c_lessequals @ SV116 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV881 ) @ SV1556 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV116 @ SV1556 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4204]) ).
thf(4877,plain,
! [SV1557: $i,SV882: $i,SV117: $i] :
( ( ( c_lessequals @ SV117 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV882 ) @ SV1557 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV117 @ SV882 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4205]) ).
thf(4878,plain,
! [SV1558: $i,SV883: $i,SV118: $i] :
( ( ( c_lessequals @ SV118 @ SV883 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1558 ) @ SV118 ) @ SV883 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4206]) ).
thf(4879,plain,
! [SV1559: $i,SV884: $i,SV119: $i] :
( ( ( c_lessequals @ SV119 @ SV884 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV119 ) @ SV1559 ) @ SV884 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4207]) ).
thf(4880,plain,
! [SV1560: $i,SV885: $i,SV120: $i] :
( ( ( c_lessequals @ SV120 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV885 ) @ SV1560 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV120 @ SV1560 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4208]) ).
thf(4881,plain,
! [SV1561: $i,SV886: $i,SV121: $i] :
( ( ( c_lessequals @ SV121 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV886 ) @ SV1561 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV121 @ SV886 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4882,plain,
! [SV889: $i,SV124: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV124 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV124 ) @ SV889 @ SV124 )
= ( c_HOL_Oone__class_Oone @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4212]) ).
thf(4883,plain,
! [SV2026: $i,SV1563: $i,SV890: $i,SV125: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV125 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV890 @ SV1563 @ SV125 ) @ SV2026 @ SV125 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV2026 @ SV125 ) @ ( c_HOL_Ominus__class_Ominus @ SV1563 @ SV2026 @ SV125 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4213]) ).
thf(4884,plain,
! [SV2027: $i,SV1564: $i,SV891: $i,SV126: $i] :
( ( ( hAPP @ ( c_COMBK @ SV126 @ SV891 @ SV1564 ) @ SV2027 )
= SV126 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4214]) ).
thf(4885,plain,
! [SV1566: $i,SV893: $i,SV128: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV128 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV893 @ SV1566 @ SV128 )
| ( c_lessequals @ SV1566 @ SV893 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4216]) ).
thf(4886,plain,
! [SV894: $i,SV129: $i] :
( ( ( class_Orderings_Olinorder @ SV129 )
= $false )
| ( ( ~ ( c_lessequals @ SV894 @ SV894 @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV894 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4887,plain,
! [SV895: $i,SV130: $i] :
( ( ( class_Orderings_Olinorder @ SV130 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV895 @ SV895 @ SV130 )
| ( c_lessequals @ SV895 @ SV895 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4888,plain,
! [SV1567: $i,SV896: $i,SV131: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV131 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV896 @ SV1567 @ SV131 )
| ~ ( c_lessequals @ SV1567 @ SV896 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4219]) ).
thf(4889,plain,
! [SV1568: $i,SV897: $i,SV132: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV132 ) )
= $true )
| ( ( ( c_lessequals @ SV897 @ SV1568 @ SV132 )
| ( c_HOL_Oord__class_Oless @ SV1568 @ SV897 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4220]) ).
thf(4890,plain,
! [SV1569: $i,SV898: $i,SV133: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV133 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV898 @ SV1569 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SV1569 @ SV898 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4221]) ).
thf(4891,plain,
! [SV1570: $i,SV899: $i,SV134: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV134 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV899 @ SV1570 @ SV134 )
| ( c_lessequals @ SV1570 @ SV899 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4222]) ).
thf(4892,plain,
! [SV1571: $i,SV900: $i,SV135: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV135 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV900 @ SV1571 @ SV135 )
| ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV900 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4893,plain,
! [SV901: $i,SV136: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV136 ) @ tc_nat )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV901 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4224]) ).
thf(4894,plain,
! [SV903: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ SV138 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV138 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV138 @ SV903 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4226]) ).
thf(4895,plain,
! [SV2028: $i,SV1572: $i,SV904: $i,SV139: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
| ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
| ~ ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4227]) ).
thf(4896,plain,
! [SV2029: $i,SV1573: $i,SV905: $i,SV140: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV140 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SV1573 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SV2029 @ SV140 ) @ SV140 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 )
| ~ ( c_lessequals @ SV1573 @ SV2029 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(4897,plain,
! [SV1574: $i,SV906: $i,SV141: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV906 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV1574 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1574 @ SV906 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4229]) ).
thf(4898,plain,
! [SV1575: $i,SV907: $i,SV142: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV142 @ SV907 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1575 @ SV907 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV142 @ SV1575 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4230]) ).
thf(4899,plain,
! [SV1576: $i,SV908: $i,SV143: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SV908 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV908 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV143 @ SV1576 @ tc_nat )
| ~ ( c_lessequals @ SV908 @ SV1576 @ tc_nat )
| ~ ( c_lessequals @ SV908 @ SV143 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4231]) ).
thf(4900,plain,
! [SV1577: $i,SV909: $i,SV144: $i] :
( ( ( c_lessequals @ SV144 @ SV909 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SV1577 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV909 @ SV1577 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1577 @ SV909 @ tc_nat )
| ~ ( c_lessequals @ SV1577 @ SV144 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4232]) ).
thf(4901,plain,
! [SV2030: $i,SV1579: $i,SV912: $i,SV147: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV147 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SV1579 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SV2030 @ SV1579 @ SV147 ) @ SV147 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 )
| ~ ( c_lessequals @ SV912 @ SV2030 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4234]) ).
thf(4902,plain,
! [SV914: $i,SV150: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV150 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV914 ) @ SV150 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV150 ) @ ( c_HOL_Oone__class_Oone @ SV150 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV914 @ SV150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4237]) ).
thf(4903,plain,
! [SV2031: $i,SV1581: $i,SV915: $i,SV151: $i] :
( ( ! [SY5946: $i,SY5947: $i] :
( ( c_List_Ofoldl @ SV151 @ SV915 @ ( c_List_Olist_OCons @ SV1581 @ SV2031 @ SY5946 ) @ SY5947 @ SY5946 )
= ( c_List_Ofoldl @ SV151 @ ( hAPP @ ( hAPP @ SV151 @ SV915 ) @ SV1581 ) @ SV2031 @ SY5947 @ SY5946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4238]) ).
thf(4904,plain,
! [SV2032: $i,SV1582: $i,SV917: $i,SV153: $i] :
( ( ( c_List_Odrop @ ( c_Suc @ SV153 ) @ ( c_List_Olist_OCons @ SV917 @ SV1582 @ SV2032 ) @ SV2032 )
= ( c_List_Odrop @ SV153 @ SV1582 @ SV2032 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4239]) ).
thf(4905,plain,
! [SV2033: $i,SV1585: $i,SV921: $i,SV159: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV159 )
| ( c_HOL_Oord__class_Oless @ SV921 @ ( c_Orderings_Oord__class_Omax @ SV1585 @ SV2033 @ SV159 ) @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV921 @ SV1585 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4242]) ).
thf(4906,plain,
! [SV2034: $i,SV1586: $i,SV922: $i,SV160: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV160 )
| ( c_HOL_Oord__class_Oless @ SV922 @ ( c_Orderings_Oord__class_Omax @ SV1586 @ SV2034 @ SV160 ) @ SV160 )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV2034 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4243]) ).
thf(4907,plain,
! [SV2035: $i,SV1587: $i,SV923: $i,SV161: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV161 )
| ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Orderings_Oord__class_Omax @ SV1587 @ SV2035 @ SV161 ) @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV923 @ SV1587 @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4244]) ).
thf(4908,plain,
! [SV2036: $i,SV1588: $i,SV924: $i,SV162: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV162 )
| ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Orderings_Oord__class_Omax @ SV1588 @ SV2036 @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2036 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4245]) ).
thf(4909,plain,
! [SV2037: $i,SV1589: $i,SV925: $i,SV163: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV163 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SV1589 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV925 @ SV2037 @ SV163 ) @ SV1589 @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4246]) ).
thf(4910,plain,
! [SV2038: $i,SV1590: $i,SV927: $i,SV165: $i] :
( ( ! [SY5948: $i,SY5949: $i,SY5950: $i,SY5951: $i,SY5952: $i] :
( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2038 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SY5948 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2038 ) @ SY5948 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5949 @ SV165 @ SV927 @ SY5950 @ SY5951 @ SY5952 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4247]) ).
thf(4911,plain,
! [SV2039: $i,SV1592: $i,SV929: $i,SV168: $i] :
( ( ! [SY5953: $i,SY5954: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV168 @ SV929 @ SV1592 @ SV2039 @ SY5953 ) @ SY5954 )
= ( hAPP @ SV168 @ ( hAPP @ SV929 @ SY5954 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4249]) ).
thf(4912,plain,
! [SV2040: $i,SV1593: $i,SV930: $i,SV169: $i] :
( ( ! [SY5955: $i,SY5956: $i] :
( ( hAPP @ SV169 @ ( hAPP @ SV930 @ SV1593 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV169 @ SV930 @ SV2040 @ SY5955 @ SY5956 ) @ SV1593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4250]) ).
thf(4913,plain,
! [SV2041: $i,SV1594: $i,SV931: $i,SV170: $i] :
( ( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ SV1594 @ SV2041 )
= ( c_List_Oappend @ ( c_List_Otake @ SV170 @ SV1594 @ SV2041 ) @ ( c_List_Otake @ SV931 @ ( c_List_Odrop @ SV170 @ SV1594 @ SV2041 ) @ SV2041 ) @ SV2041 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ ( c_Nat_Osize__class_Osize @ SV1594 @ ( tc_List_Olist @ SV2041 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4251]) ).
thf(4914,plain,
! [SV1595: $i,SV932: $i,SV171: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV171 ) )
= $true )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SV932 @ SV1595 @ SV171 @ SV171 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SV1595 @ SV932 @ SV171 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4252]) ).
thf(4915,plain,
! [SV933: $i,SV172: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV172 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV933 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV172 )
= SV933 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4253]) ).
thf(4916,plain,
! [SV934: $i,SV173: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV173 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV934 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV173 )
= SV934 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4254]) ).
thf(4917,plain,
! [SV935: $i,SV174: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV174 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ SV935 ) @ SV935 ) @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4918,plain,
! [SV936: $i,SV175: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV175 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV936 @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV936 ) @ SV936 ) @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4256]) ).
thf(4919,plain,
! [SV937: $i,SV176: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV176 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV937 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV937 ) @ SV937 ) @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4257]) ).
thf(4920,plain,
! [SV938: $i,SV177: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV177 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV177 ) @ SV938 ) @ SV938 ) @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ SV938 @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4258]) ).
thf(4921,plain,
! [SV2042: $i,SV1596: $i,SV939: $i,SV178: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV178 )
| ( c_HOL_Oord__class_Oless @ SV939 @ SV1596 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SV1596 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SV2042 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SV1596 @ SV2042 @ SV178 ) @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4259]) ).
thf(4922,plain,
! [SV1597: $i,SV940: $i,SV179: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV179 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV940 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV1597 @ SV179 @ SV179 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV940 @ SV1597 @ SV179 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4260]) ).
thf(4923,plain,
! [SV2043: $i,SV1598: $i,SV941: $i,SV180: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV180 )
| ( c_lessequals @ SV941 @ SV1598 @ SV180 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2043 @ SV941 @ SV180 ) @ SV1598 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4261]) ).
thf(4924,plain,
! [SV2044: $i,SV1599: $i,SV942: $i,SV181: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV181 )
| ( c_lessequals @ SV942 @ SV1599 @ SV181 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV942 @ SV2044 @ SV181 ) @ SV1599 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4262]) ).
thf(4925,plain,
! [SV2045: $i,SV1600: $i,SV943: $i,SV182: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV182 )
| ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1600 @ SV2045 @ SV182 ) @ SV182 )
| ~ ( c_lessequals @ SV943 @ SV2045 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4263]) ).
thf(4926,plain,
! [SV2046: $i,SV1601: $i,SV944: $i,SV183: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV183 )
| ( c_lessequals @ SV944 @ ( c_Orderings_Oord__class_Omax @ SV1601 @ SV2046 @ SV183 ) @ SV183 )
| ~ ( c_lessequals @ SV944 @ SV1601 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4264]) ).
thf(4927,plain,
! [SV2047: $i,SV1602: $i,SV945: $i,SV184: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV184 )
| ( c_lessequals @ SV945 @ ( c_Orderings_Oord__class_Omax @ SV1602 @ SV2047 @ SV184 ) @ SV184 )
| ~ ( c_lessequals @ SV945 @ SV2047 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4265]) ).
thf(4928,plain,
! [SV2048: $i,SV1603: $i,SV946: $i,SV185: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV185 )
| ( c_lessequals @ SV946 @ ( c_Orderings_Oord__class_Omax @ SV1603 @ SV2048 @ SV185 ) @ SV185 )
| ~ ( c_lessequals @ SV946 @ SV1603 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4266]) ).
thf(4929,plain,
! [SV2049: $i,SV1604: $i,SV947: $i,SV186: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_lessequals @ SV947 @ SV1604 @ SV186 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2049 @ SV947 @ SV186 ) @ SV1604 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4267]) ).
thf(4930,plain,
! [SV2050: $i,SV1605: $i,SV948: $i,SV187: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV187 )
| ( c_lessequals @ SV948 @ SV1605 @ SV187 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV948 @ SV2050 @ SV187 ) @ SV1605 @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(4931,plain,
! [SV1606: $i,SV949: $i,SV188: $i] :
( ( ( c_lessequals @ SV188 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SV1606 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV188 @ SV1606 @ tc_nat ) @ SV949 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4269]) ).
thf(4932,plain,
! [SV1607: $i,SV950: $i,SV189: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV189 @ SV950 @ tc_nat ) @ SV1607 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV189 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1607 ) @ SV950 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4270]) ).
thf(4933,plain,
! [SV1608: $i,SV951: $i,SV190: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV190 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ ( c_Power_Opower__class_Opower @ SV951 @ SV1608 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV951 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4271]) ).
thf(4934,plain,
! [SV2051: $i,SV1609: $i,SV952: $i,SV191: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV952 @ SV1609 @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV952 @ SV2051 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV952 @ ( c_Orderings_Oord__class_Omax @ SV2051 @ SV1609 @ SV191 ) @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4272]) ).
thf(4935,plain,
! [SV1610: $i,SV953: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SV953 ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV953 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4273]) ).
thf(4936,plain,
! [SV2052: $i,SV1611: $i,SV954: $i,SV193: $i] :
( ( ( c_List_Ofoldl @ SV193 @ SV954 @ ( c_List_Olist_ONil @ SV1611 ) @ SV2052 @ SV1611 )
= SV954 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4274]) ).
thf(4937,plain,
! [SV1612: $i,SV955: $i,SV194: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV194 ) @ SV955 @ SV1612 )
= ( c_Lambda_OdB_OVar @ SV194 ) )
= $true )
| ( ( ( SV194 = SV1612 )
| ( c_HOL_Oord__class_Oless @ SV1612 @ SV194 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4275]) ).
thf(4938,plain,
! [SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV195 ) @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4276]) ).
thf(4939,plain,
! [SV1613: $i,SV956: $i,SV196: $i] :
( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV196 @ SV956 @ SV1613 ) @ ( tc_List_Olist @ SV1613 ) ) @ ( c_Nat_Osize__class_Osize @ SV956 @ ( tc_List_Olist @ SV1613 ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4277]) ).
thf(4940,plain,
! [SV1614: $i,SV958: $i,SV199: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV958 ) @ SV1614 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SV1614 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ SV958 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4278]) ).
thf(4941,plain,
! [SV1615: $i,SV959: $i,SV200: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SV959 ) @ SV1615 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_lessequals @ SV1615 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SV959 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4279]) ).
thf(4942,plain,
! [SV960: $i,SV201: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV201 @ SV960 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV201 @ ( c_Suc @ SV960 ) @ tc_nat ) )
= $true )
| ( ( SV201 = SV960 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4280]) ).
thf(4943,plain,
! [SV202: $i,SV961: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV961 @ ( c_Suc @ SV202 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV961 @ SV202 @ tc_nat )
= $true )
| ( ( SV202 = SV961 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4281]) ).
thf(4944,plain,
! [SV962: $i,SV203: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV203 @ ( c_Suc @ SV962 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV203 @ SV962 @ tc_nat )
= $true )
| ( ( SV203 = SV962 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4282]) ).
thf(4945,plain,
! [SV1616: $i,SV963: $i,SV204: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ SV963 ) @ SV1616 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SV1616 @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1616 @ SV963 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(4946,plain,
! [SV1617: $i,SV964: $i,SV205: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV964 ) @ SV1617 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV205 @ SV1617 @ tc_nat ) ) @ SV964 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1617 @ SV205 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4284]) ).
thf(4947,plain,
! [SV2053: $i,SV1618: $i,SV965: $i,SV207: $i] :
( ( ! [SY5957: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV207 @ SV965 @ SV1618 ) @ SV2053 @ SY5957 @ SV1618 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV207 @ SV2053 @ SY5957 @ SV1618 ) @ SV965 @ SV1618 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2053 @ ( c_Nat_Osize__class_Osize @ SV207 @ ( tc_List_Olist @ SV1618 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4286]) ).
thf(4948,plain,
! [SV2054: $i,SV1619: $i,SV966: $i,SV208: $i] :
( ( ! [SY5958: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV208 @ SV966 @ SV1619 ) @ SV2054 @ SY5958 @ SV1619 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV208 @ SV2054 @ SY5958 @ SV1619 ) @ SV966 @ SV1619 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2054 @ ( c_Nat_Osize__class_Osize @ SV208 @ ( tc_List_Olist @ SV1619 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4287]) ).
thf(4949,plain,
! [SV1620: $i,SV967: $i,SV209: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV209 @ ( c_HOL_Ominus__class_Ominus @ SV967 @ SV1620 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV209 ) @ SV1620 ) @ SV967 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1620 @ SV967 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4288]) ).
thf(4950,plain,
! [SV1621: $i,SV969: $i,SV211: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV211 @ SV969 @ tc_nat ) @ SV1621 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV211 @ SV1621 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4290]) ).
thf(4951,plain,
! [SV2055: $i,SV1622: $i,SV970: $i,SV212: $i] :
( ( ( c_Type_Otype_Otype__rec @ SV212 @ SV970 @ ( c_Type_Otype_OAtom @ SV1622 ) @ SV2055 )
= ( hAPP @ SV212 @ SV1622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4291]) ).
thf(4952,plain,
! [SV1623: $i,SV971: $i,SV213: $i] :
( ( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1623 @ SV971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV213 @ SV1623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4292]) ).
thf(4953,plain,
! [SV1625: $i,SV974: $i,SV216: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV216 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV974 @ SV1625 @ SV216 )
| ( c_lessequals @ SV1625 @ SV974 @ SV216 )
| ~ ( c_lessequals @ SV974 @ SV1625 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4294]) ).
thf(4954,plain,
! [SV975: $i,SV219: $i] :
( ( ( class_Orderings_Oorder @ SV219 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV975 @ SV975 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4295]) ).
thf(4955,plain,
! [SV976: $i,SV220: $i] :
( ( ( class_Orderings_Olinorder @ SV220 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV976 @ SV976 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4296]) ).
thf(4956,plain,
! [SV977: $i,SV221: $i] :
( ( ( class_Orderings_Opreorder @ SV221 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV977 @ SV977 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4957,plain,
! [SV978: $i,SV222: $i] :
( ( ( c_lessequals @ SV222 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV978 ) @ SV222 ) @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV978 ) @ SV222 ) @ SV222 @ tc_nat )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4958,plain,
! [SV1626: $i,SV979: $i,SV223: $i] :
( ( ( ( c_Lambda_Oliftn @ SV223 @ ( c_Lambda_OdB_OVar @ SV979 ) @ SV1626 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV979 ) @ SV223 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV979 @ SV1626 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4299]) ).
thf(4959,plain,
! [SV1629: $i,SV983: $i,SV227: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SV983 ) @ SV1629 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV1629 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV983 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4302]) ).
thf(4960,plain,
! [SV2056: $i,SV1630: $i,SV988: $i,SV232: $i] :
( ( ( ( c_List_Otake @ SV232 @ ( c_List_Olist_OCons @ SV988 @ SV1630 @ SV2056 ) @ SV2056 )
= ( c_List_Olist_OCons @ SV988 @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV232 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1630 @ SV2056 ) @ SV2056 ) )
| ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4303]) ).
thf(4961,plain,
! [SV233: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV233 ) @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4962,plain,
! [SV1631: $i,SV989: $i,SV234: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV234 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV989 @ SV1631 @ SV234 ) @ SV234 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV989 ) @ ( c_List_Olistsum @ SV1631 @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4305]) ).
thf(4963,plain,
! [SV2057: $i,SV1633: $i,SV991: $i,SV236: $i] :
( ( ! [SY5959: $i,SY5960: $i,SY5961: $i] :
( ( ( hAPP @ ( hAPP @ SV236 @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV991 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV2057 @ SV236 @ SY5959 @ SY5960 @ SY5961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4307]) ).
thf(4964,plain,
! [SV1634: $i,SV992: $i,SV237: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV237 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV992 @ SV1634 @ SV237 )
| ( c_HOL_Oord__class_Oless @ SV1634 @ SV992 @ SV237 )
| ( SV1634 = SV992 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4308]) ).
thf(4965,plain,
! [SV1635: $i,SV993: $i,SV238: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV238 ) )
= $true )
| ( ( ( SV993 = SV1635 )
| ( c_HOL_Oord__class_Oless @ SV1635 @ SV993 @ SV238 )
| ( c_HOL_Oord__class_Oless @ SV993 @ SV1635 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4966,plain,
! [SV239: $i,SV994: $i] :
( ( ( ~ ( c_lessequals @ SV994 @ SV239 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV239 @ SV994 @ tc_nat ) )
= $true )
| ( ( SV239 = SV994 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4310]) ).
thf(4967,plain,
! [SV240: $i,SV995: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV995 @ SV240 @ tc_nat )
= $true )
| ( ( SV995 = SV240 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV240 @ SV995 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4311]) ).
thf(4968,plain,
! [SV1636: $i,SV996: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV241 @ SV996 ) @ SV1636 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV996 @ SV1636 @ tc_nat )
| ( SV1636 = SV996 )
| ( c_HOL_Oord__class_Oless @ SV1636 @ SV996 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(4969,plain,
! [SV2058: $i,SV1637: $i,SV997: $i,SV242: $i] :
( ( ! [SY5962: $i] :
( ( SV242 = SV997 )
| ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SY5962 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV997 )
| ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SY5962 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4313]) ).
thf(4970,plain,
! [SV2059: $i,SV1638: $i,SV998: $i,SV243: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV243 )
| ( c_HOL_Oord__class_Oless @ SV998 @ SV1638 @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2059 @ SV998 @ SV243 ) @ SV1638 @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4314]) ).
thf(4971,plain,
! [SV1639: $i,SV999: $i,SV245: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV245 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SV999 @ SV1639 @ SV245 ) @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1639 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SV999 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4316]) ).
thf(4972,plain,
! [SV1640: $i,SV1000: $i,SV246: $i] :
( ( ( ( c_List_Orotate @ SV246 @ SV1000 @ SV1640 )
= SV1000 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1000 @ ( tc_List_Olist @ SV1640 ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4317]) ).
thf(4973,plain,
! [SV2060: $i,SV1641: $i,SV1001: $i,SV247: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV247 ) @ SV1001 ) @ SV1641 ) ) @ SV2060 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV247 ) @ SV2060 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1001 ) @ SV2060 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1641 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2060 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1641 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4974,plain,
! [SV1642: $i,SV1004: $i,SV250: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SV1004 ) @ SV1642 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SV1642 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SV1004 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4319]) ).
thf(4975,plain,
! [SV2061: $i,SV1643: $i,SV1005: $i,SV251: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV251 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4320]) ).
thf(4976,plain,
! [SV2062: $i,SV1644: $i,SV1006: $i,SV252: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV252 @ SV1006 @ SV1644 ) @ SV2062 @ SV1644 )
= ( c_List_Olist_OCons @ SV252 @ ( c_List_Oappend @ SV1006 @ SV2062 @ SV1644 ) @ SV1644 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4321]) ).
thf(4977,plain,
! [SV2063: $i,SV1645: $i,SV1007: $i,SV253: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV253 @ SV1007 @ SV1645 ) @ SV2063 @ SV1645 )
= ( c_List_Olist_OCons @ SV253 @ ( c_List_Oappend @ SV1007 @ SV2063 @ SV1645 ) @ SV1645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4322]) ).
thf(4978,plain,
! [SV1647: $i,SV1009: $i,SV255: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1009 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1647 @ SV1009 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1647 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1009 @ SV1647 @ tc_nat )
| ~ ( c_lessequals @ SV1009 @ SV255 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4324]) ).
thf(4979,plain,
! [SV2064: $i,SV1649: $i,SV1011: $i,SV257: $i] :
( ( ( c_List_Omap @ ( c_COMBK @ SV257 @ SV1011 @ SV1649 ) @ SV2064 @ SV1649 @ SV1011 )
= ( c_List_Oreplicate @ ( c_Nat_Osize__class_Osize @ SV2064 @ ( tc_List_Olist @ SV1649 ) ) @ SV257 @ SV1011 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(4980,plain,
! [SV1650: $i,SV1012: $i,SV258: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV1012 ) @ SV1650 ) @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1650 @ SV258 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1012 @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4327]) ).
thf(4981,plain,
! [SV1651: $i,SV1013: $i,SV259: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV1013 ) @ SV1651 ) @ SV259 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1651 @ SV259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1013 @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4328]) ).
thf(4982,plain,
! [SV1655: $i,SV1017: $i,SV263: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV263 @ SV1017 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1017 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1017 @ SV263 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV263 @ SV1655 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4332]) ).
thf(4983,plain,
! [SV1018: $i,SV264: $i] :
( ( ( ( c_Suc @ SV264 )
= SV1018 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV264 @ SV1018 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV264 ) @ SV1018 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4333]) ).
thf(4984,plain,
! [SV1019: $i,SV265: $i] :
( ( ( c_lessequals @ SV265 @ SV1019 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV1019 ) @ SV265 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4985,plain,
! [SV2065: $i,SV1656: $i,SV1021: $i,SV267: $i] :
( ( ( c_List_Olist_OCons @ SV267 @ ( c_List_Oappend @ SV1021 @ SV1656 @ SV2065 ) @ SV2065 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV267 @ SV1021 @ SV2065 ) @ SV1656 @ SV2065 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4336]) ).
thf(4986,plain,
! [SV2066: $i,SV1657: $i,SV1022: $i,SV268: $i] :
( ( ( c_List_Olist_OCons @ SV268 @ ( c_List_Oappend @ SV1022 @ SV1657 @ SV2066 ) @ SV2066 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV268 @ SV1022 @ SV2066 ) @ SV1657 @ SV2066 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4337]) ).
thf(4987,plain,
! [SV1658: $i,SV1023: $i,SV269: $i] :
( ( ( c_lessequals @ SV269 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1023 ) @ SV269 ) @ SV1658 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1658 @ SV1023 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4338]) ).
thf(4988,plain,
! [SV2067: $i,SV1659: $i,SV1025: $i,SV271: $i] :
( ( ! [SY5963: $i,SY5964: $i,SY5965: $i,SY5966: $i,SY5967: $i] :
( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SV2067 ) ) @ SY5963 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SY5963 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SV2067 ) @ SY5963 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5964 @ SV1025 @ SV271 @ SY5965 @ SY5966 @ SY5967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4340]) ).
thf(4989,plain,
! [SV2068: $i,SV1660: $i,SV1026: $i,SV272: $i] :
( ( ! [SY5968: $i,SY5969: $i,SY5970: $i,SY5971: $i,SY5972: $i] :
( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SV2068 ) @ SY5968 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2068 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SY5968 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SY5969 @ SY5970 @ SY5971 @ SY5972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4341]) ).
thf(4990,plain,
! [SV2069: $i,SV1661: $i,SV1027: $i,SV273: $i] :
( ( ! [SY5973: $i,SY5974: $i,SY5975: $i,SY5976: $i] :
( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SV1661 )
= ( hAPP @ ( hAPP @ SV273 @ SV1661 ) @ SV1027 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2069 @ SV273 @ SY5973 @ SY5974 @ SY5975 @ SY5976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4342]) ).
thf(4991,plain,
! [SV2070: $i,SV1662: $i,SV1028: $i,SV274: $i] :
( ( ! [SY5977: $i,SY5978: $i,SY5979: $i,SY5980: $i,SY5981: $i] :
( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SV2070 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SV2070 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5977 @ SV274 @ SY5978 @ SY5979 @ SY5980 @ SY5981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4343]) ).
thf(4992,plain,
! [SV2071: $i,SV1663: $i,SV1029: $i,SV275: $i] :
( ( ! [SY5982: $i,SY5983: $i,SY5984: $i] :
( ( ( hAPP @ ( hAPP @ SV275 @ SV1029 ) @ SV1663 )
= SV1663 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2071 @ SV275 @ SY5982 @ SY5983 @ SV1029 @ SY5984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(4993,plain,
! [SV2072: $i,SV1664: $i,SV1030: $i,SV276: $i] :
( ( ! [SY5985: $i,SY5986: $i,SY5987: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SV1030 ) @ SV1664 )
= SV1030 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2072 @ SV276 @ SY5985 @ SV1030 @ SY5986 @ SY5987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4345]) ).
thf(4994,plain,
! [SV2073: $i,SV1665: $i,SV1031: $i,SV277: $i] :
( ( ! [SY5988: $i,SY5989: $i,SY5990: $i,SY5991: $i] :
( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SV1665 )
= ( hAPP @ ( hAPP @ SV277 @ SV1665 ) @ SV1031 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SV2073 @ SY5988 @ SY5989 @ SY5990 @ SY5991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4346]) ).
thf(4995,plain,
! [SV2074: $i,SV1666: $i,SV1032: $i,SV278: $i] :
( ( ! [SY5992: $i,SY5993: $i,SY5994: $i,SY5995: $i,SY5996: $i] :
( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SV2074 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SV2074 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SY5992 @ SY5993 @ SY5994 @ SY5995 @ SY5996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(4996,plain,
! [SV2075: $i,SV1667: $i,SV1033: $i,SV279: $i] :
( ( ! [SY5997: $i,SY5998: $i,SY5999: $i] :
( ( ( hAPP @ ( hAPP @ SV279 @ SV1033 ) @ SV1667 )
= SV1667 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SV2075 @ SY5997 @ SV1033 @ SY5998 @ SY5999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4348]) ).
thf(4997,plain,
! [SV2076: $i,SV1668: $i,SV1034: $i,SV280: $i] :
( ( ! [SY6000: $i,SY6001: $i,SY6002: $i,SY6003: $i,SY6004: $i] :
( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SV2076 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SV2076 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SY6000 @ SY6001 @ SY6002 @ SY6003 @ SY6004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4349]) ).
thf(4998,plain,
! [SV2077: $i,SV1669: $i,SV1035: $i,SV281: $i] :
( ( ! [SY6005: $i,SY6006: $i,SY6007: $i,SY6008: $i] :
( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SV1669 )
= ( hAPP @ ( hAPP @ SV281 @ SV1669 ) @ SV1035 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SV2077 @ SY6005 @ SY6006 @ SY6007 @ SY6008 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4350]) ).
thf(4999,plain,
! [SV2078: $i,SV1670: $i,SV1036: $i,SV282: $i] :
( ( ! [SY6009: $i,SY6010: $i,SY6011: $i,SY6012: $i,SY6013: $i] :
( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SV2078 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV2078 ) ) @ SV1670 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SY6009 @ SY6010 @ SY6011 @ SY6012 @ SY6013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4351]) ).
thf(5000,plain,
! [SV2079: $i,SV1671: $i,SV1037: $i,SV283: $i] :
( ( ! [SY6014: $i,SY6015: $i,SY6016: $i,SY6017: $i,SY6018: $i] :
( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SV2079 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SV2079 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SY6014 @ SY6015 @ SY6016 @ SY6017 @ SY6018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4352]) ).
thf(5001,plain,
! [SV2080: $i,SV1672: $i,SV1038: $i,SV284: $i] :
( ( ! [SY6019: $i,SY6020: $i,SY6021: $i,SY6022: $i,SY6023: $i] :
( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SV2080 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SV2080 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SY6019 @ SY6020 @ SY6021 @ SY6022 @ SY6023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4353]) ).
thf(5002,plain,
! [SV2081: $i,SV1673: $i,SV1039: $i,SV285: $i] :
( ( ! [SY6024: $i,SY6025: $i,SY6026: $i,SY6027: $i,SY6028: $i,SY6029: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SY6024 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SY6024 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SY6025 @ SY6026 @ SY6027 @ SY6028 @ SY6029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4354]) ).
thf(5003,plain,
! [SV2082: $i,SV1674: $i,SV1040: $i,SV286: $i] :
( ( ! [SY6030: $i,SY6031: $i,SY6032: $i,SY6033: $i,SY6034: $i] :
( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SV2082 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SV2082 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6030 @ SV286 @ SY6031 @ SY6032 @ SY6033 @ SY6034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4355]) ).
thf(5004,plain,
! [SV2083: $i,SV1675: $i,SV1041: $i,SV287: $i] :
( ( ! [SY6035: $i,SY6036: $i,SY6037: $i,SY6038: $i,SY6039: $i] :
( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SV2083 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SV2083 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6035 @ SV287 @ SY6036 @ SY6037 @ SY6038 @ SY6039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4356]) ).
thf(5005,plain,
! [SV2084: $i,SV1676: $i,SV1042: $i,SV288: $i] :
( ( ! [SY6040: $i,SY6041: $i,SY6042: $i,SY6043: $i,SY6044: $i] :
( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SV2084 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SV2084 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6040 @ SV288 @ SY6041 @ SY6042 @ SY6043 @ SY6044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(5006,plain,
! [SV2085: $i,SV1677: $i,SV1043: $i,SV289: $i] :
( ( ! [SY6045: $i,SY6046: $i,SY6047: $i,SY6048: $i,SY6049: $i] :
( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SV2085 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV2085 ) ) @ SV1677 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6045 @ SV289 @ SY6046 @ SY6047 @ SY6048 @ SY6049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(5007,plain,
! [SV2086: $i,SV1678: $i,SV1044: $i,SV290: $i] :
( ( ! [SY6050: $i,SY6051: $i,SY6052: $i,SY6053: $i,SY6054: $i,SY6055: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SY6050 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SY6050 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6051 @ SV290 @ SY6052 @ SY6053 @ SY6054 @ SY6055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(5008,plain,
! [SV2087: $i,SV1679: $i,SV1045: $i,SV291: $i] :
( ( ! [SY6056: $i,SY6057: $i,SY6058: $i,SY6059: $i,SY6060: $i,SY6061: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SY6056 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SY6056 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6057 @ SV291 @ SY6058 @ SY6059 @ SY6060 @ SY6061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4360]) ).
thf(5009,plain,
! [SV2088: $i,SV1680: $i,SV1046: $i,SV292: $i] :
( ( ! [SY6062: $i,SY6063: $i,SY6064: $i,SY6065: $i,SY6066: $i,SY6067: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SY6062 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SY6062 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6063 @ SV292 @ SY6064 @ SY6065 @ SY6066 @ SY6067 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(5010,plain,
! [SV2089: $i,SV1681: $i,SV1047: $i,SV293: $i] :
( ( ! [SY6068: $i,SY6069: $i,SY6070: $i] :
( ( ( hAPP @ ( hAPP @ SV293 @ SV1047 ) @ SV1681 )
= SV1047 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2089 @ SV293 @ SY6068 @ SY6069 @ SV1681 @ SY6070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(5011,plain,
! [SV2090: $i,SV1682: $i,SV1048: $i,SV294: $i] :
( ( ! [SY6071: $i,SY6072: $i,SY6073: $i] :
( ( ( hAPP @ ( hAPP @ SV294 @ SV1048 ) @ SV1682 )
= SV1682 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2090 @ SV294 @ SY6071 @ SY6072 @ SV1048 @ SY6073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4363]) ).
thf(5012,plain,
! [SV2091: $i,SV1683: $i,SV1049: $i,SV295: $i] :
( ( ! [SY6074: $i,SY6075: $i,SY6076: $i] :
( ( ( hAPP @ ( hAPP @ SV295 @ SV1049 ) @ SV1683 )
= SV1683 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2091 @ SV295 @ SY6074 @ SV1683 @ SY6075 @ SY6076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4364]) ).
thf(5013,plain,
! [SV2092: $i,SV1684: $i,SV1050: $i,SV296: $i] :
( ( ! [SY6077: $i,SY6078: $i,SY6079: $i] :
( ( ( hAPP @ ( hAPP @ SV296 @ SV1050 ) @ SV1684 )
= SV1050 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2092 @ SV296 @ SY6077 @ SV1050 @ SY6078 @ SY6079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(5014,plain,
! [SV2093: $i,SV1685: $i,SV1051: $i,SV297: $i] :
( ( ! [SY6080: $i,SY6081: $i,SY6082: $i,SY6083: $i,SY6084: $i] :
( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SV2093 ) ) @ SY6080 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SY6080 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SV2093 ) @ SY6080 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SY6081 @ SY6082 @ SY6083 @ SY6084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4366]) ).
thf(5015,plain,
! [SV2094: $i,SV1686: $i,SV1052: $i,SV298: $i] :
( ( ! [SY6085: $i,SY6086: $i,SY6087: $i,SY6088: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SV1686 )
= ( hAPP @ ( hAPP @ SV298 @ SV1686 ) @ SV1052 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2094 @ SV298 @ SY6085 @ SY6086 @ SY6087 @ SY6088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4367]) ).
thf(5016,plain,
! [SV2095: $i,SV1687: $i,SV1053: $i,SV299: $i] :
( ( ! [SY6089: $i,SY6090: $i,SY6091: $i] :
( ( ( hAPP @ ( hAPP @ SV299 @ SV1053 ) @ SV1687 )
= SV1053 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SV2095 @ SY6089 @ SV1687 @ SY6090 @ SY6091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4368]) ).
thf(5017,plain,
! [SV2096: $i,SV1688: $i,SV1054: $i,SV300: $i] :
( ( ! [SY6092: $i,SY6093: $i,SY6094: $i] :
( ( ( hAPP @ ( hAPP @ SV300 @ SV1054 ) @ SV1688 )
= SV1688 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SV2096 @ SY6092 @ SV1054 @ SY6093 @ SY6094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4369]) ).
thf(5018,plain,
! [SV2097: $i,SV1689: $i,SV1055: $i,SV301: $i] :
( ( ! [SY6095: $i,SY6096: $i,SY6097: $i] :
( ( ( hAPP @ ( hAPP @ SV301 @ SV1055 ) @ SV1055 )
= ( hAPP @ ( hAPP @ SV1689 @ ( hAPP @ ( hAPP @ SV301 @ SV2097 ) @ SV2097 ) ) @ SV1055 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SV1689 @ SY6095 @ SY6096 @ SV2097 @ SY6097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4370]) ).
thf(5019,plain,
! [SV2098: $i,SV1690: $i,SV1056: $i,SV302: $i] :
( ( ! [SY6098: $i,SY6099: $i,SY6100: $i,SY6101: $i] :
( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SV1690 @ SV2098 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SV1690 @ ( hAPP @ ( hAPP @ SV302 @ SV2098 ) @ SY6098 ) ) @ SV1056 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SV1690 @ SY6099 @ SY6100 @ SY6098 @ SY6101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4371]) ).
thf(5020,plain,
! [SV2099: $i,SV1691: $i,SV1057: $i,SV303: $i] :
( ( ! [SY6102: $i,SY6103: $i,SY6104: $i,SY6105: $i] :
( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SV1691 ) @ SV2099 ) ) @ SV2099 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SV1691 ) @ SY6102 ) ) @ SV2099 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SY6103 @ SY6104 @ SY6102 @ SY6105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4372]) ).
thf(5021,plain,
! [SV2100: $i,SV1692: $i,SV1058: $i,SV304: $i] :
( ( ! [SY6106: $i,SY6107: $i,SY6108: $i,SY6109: $i,SY6110: $i] :
( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SV2100 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SY6106 ) @ SV2100 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SY6106 ) ) @ SV2100 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SY6107 @ SY6108 @ SY6109 @ SY6110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4373]) ).
thf(5022,plain,
! [SV2101: $i,SV1693: $i,SV1059: $i,SV305: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV305 @ ( c_Type_Otype_Otype__case @ SV1059 @ SV1693 @ ( c_Type_Otype_OAtom @ SV2101 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV305 @ ( hAPP @ SV1059 @ SV2101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(5023,plain,
! [SV2102: $i,SV1694: $i,SV1060: $i,SV306: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_Type_Otype_Otype__case @ SV1060 @ SV1694 @ ( c_Type_Otype_OAtom @ SV2102 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV306 @ ( hAPP @ SV1060 @ SV2102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4375]) ).
thf(5024,plain,
! [SV2103: $i,SV1696: $i,SV1062: $i,SV308: $i] :
( ( ! [SY6111: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1062 ) @ SV1696 ) ) @ ( c_Suc @ SV2103 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY6111 ) @ SV1062 ) @ SV2103 ) ) @ SV1696 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ SY6111 ) @ SV1696 ) ) @ SV1062 ) @ SV2103 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1696 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2103 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(5025,plain,
! [SV2104: $i,SV1699: $i,SV1066: $i,SV313: $i] :
( ( ! [SY6112: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV1699 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV2104 ) @ SY6112 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV2104 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1699 ) @ SY6112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4381]) ).
thf(5026,plain,
! [SV1700: $i,SV1067: $i,SV314: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV1067 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV1700 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV1067 @ SV1700 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4382]) ).
thf(5027,plain,
! [SV1701: $i,SV1068: $i,SV315: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV315 ) @ SV1068 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1701 ) @ SV1068 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV315 @ SV1701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4383]) ).
thf(5028,plain,
! [SV1070: $i,SV317: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV317 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1070 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4385]) ).
thf(5029,plain,
! [SV1703: $i,SV1071: $i,SV318: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV318 ) @ SV1071 @ SV1703 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV318 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1703 @ SV318 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4386]) ).
thf(5030,plain,
! [SV1704: $i,SV1072: $i,SV319: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV319 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1072 @ SV1704 @ SV319 )
= ( c_Orderings_Oord__class_Omax @ SV1704 @ SV1072 @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4387]) ).
thf(5031,plain,
! [SV1705: $i,SV1073: $i,SV320: $i] :
( ( ( ( c_Lambda_Oliftn @ SV320 @ ( c_Lambda_OdB_OVar @ SV1073 ) @ SV1705 )
= ( c_Lambda_OdB_OVar @ SV1073 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1073 @ SV1705 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4388]) ).
thf(5032,plain,
! [SV1706: $i,SV1074: $i,SV321: $i] :
( ( ( ( c_List_Odrop @ SV321 @ SV1074 @ SV1706 )
= ( c_List_Olist_ONil @ SV1706 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1074 @ ( tc_List_Olist @ SV1706 ) ) @ SV321 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4389]) ).
thf(5033,plain,
! [SV1707: $i,SV1075: $i,SV323: $i] :
( ( ( c_List_Odistinct @ ( c_List_Odrop @ SV323 @ SV1075 @ SV1707 ) @ SV1707 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV1075 @ SV1707 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(5034,plain,
! [SV1076: $i,SV324: $i] :
( ( ( c_List_Odistinct @ SV324 @ SV1076 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Orev @ SV324 @ SV1076 ) @ SV1076 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4391]) ).
thf(5035,plain,
! [SV1077: $i,SV325: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orev @ SV325 @ SV1077 ) @ SV1077 )
= $false )
| ( ( c_List_Odistinct @ SV325 @ SV1077 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4392]) ).
thf(5036,plain,
! [SV2105: $i,SV1708: $i,SV1078: $i,SV326: $i] :
( ( ( c_List_Odrop @ SV326 @ ( c_List_Oreplicate @ SV1078 @ SV1708 @ SV2105 ) @ SV2105 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV1078 @ SV326 @ tc_nat ) @ SV1708 @ SV2105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4393]) ).
thf(5037,plain,
! [SV327: $i,SV1079: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1079 @ SV327 @ tc_nat )
= $true )
| ( ( SV1079 = SV327 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV327 @ SV1079 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4394]) ).
thf(5038,plain,
! [SV1709: $i,SV1080: $i,SV328: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV328 ) )
= $true )
| ( ( ( SV1080 = SV1709 )
| ~ ( c_lessequals @ SV1709 @ SV1080 @ SV328 )
| ~ ( c_lessequals @ SV1080 @ SV1709 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4395]) ).
thf(5039,plain,
! [SV1710: $i,SV1081: $i,SV329: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV329 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1081 @ SV1710 @ SV329 )
| ( c_HOL_Oord__class_Oless @ SV1710 @ SV1081 @ SV329 )
| ( SV1710 = SV1081 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4396]) ).
thf(5040,plain,
! [SV1711: $i,SV1082: $i,SV330: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV330 ) )
= $true )
| ( ( ( SV1082 = SV1711 )
| ~ ( c_lessequals @ SV1711 @ SV1082 @ SV330 )
| ~ ( c_lessequals @ SV1082 @ SV1711 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4397]) ).
thf(5041,plain,
! [SV1712: $i,SV1083: $i,SV331: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV331 ) )
= $true )
| ( ( ( SV1083 = SV1712 )
| ~ ( c_lessequals @ SV1083 @ SV1712 @ SV331 )
| ~ ( c_lessequals @ SV1712 @ SV1083 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4398]) ).
thf(5042,plain,
! [SV2106: $i,SV1713: $i,SV1084: $i,SV332: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV332 @ SV1084 @ SV1713 ) @ ( c_List_Oreplicate @ SV2106 @ SV1084 @ SV1713 ) @ SV1713 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV2106 @ SV1084 @ SV1713 ) @ ( c_List_Oreplicate @ SV332 @ SV1084 @ SV1713 ) @ SV1713 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4399]) ).
thf(5043,plain,
! [SV1714: $i,SV1085: $i,SV333: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV333 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1085 @ SV1714 @ SV333 )
| ( SV1714 = SV1085 )
| ( c_HOL_Oord__class_Oless @ SV1714 @ SV1085 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4400]) ).
thf(5044,plain,
! [SV1715: $i,SV1086: $i,SV334: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV334 ) )
= $true )
| ( ( ( SV1086 = SV1715 )
| ( c_HOL_Oord__class_Oless @ SV1086 @ SV1715 @ SV334 )
| ( c_HOL_Oord__class_Oless @ SV1715 @ SV1086 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(5045,plain,
! [SV1716: $i,SV1087: $i,SV335: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV335 ) )
= $true )
| ( ( ( c_lessequals @ SV1087 @ SV1716 @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SV1716 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4402]) ).
thf(5046,plain,
! [SV1717: $i,SV1088: $i,SV336: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV336 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV1717 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ SV1088 @ SV1717 @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4403]) ).
thf(5047,plain,
! [SV1089: $i,SV339: $i] :
( ( ( class_Orderings_Olinorder @ SV339 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1089 @ SV1089 @ SV339 )
= SV1089 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4406]) ).
thf(5048,plain,
! [SV2107: $i,SV1718: $i,SV1090: $i,SV340: $i] :
( ( ! [SY6113: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV2107 ) @ SY6113 ) @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1718 @ SY6113 @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SV2107 @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4407]) ).
thf(5049,plain,
! [SV2108: $i,SV1719: $i,SV1091: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV341 ) @ SV1091 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1719 ) @ SV2108 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1091 @ SV2108 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV341 @ SV1719 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4408]) ).
thf(5050,plain,
! [SV342: $i,SV1092: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV1092 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV342 ) @ SV1092 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4409]) ).
thf(5051,plain,
! [SV1093: $i,SV343: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV343 @ SV1093 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV343 @ SV1093 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4410]) ).
thf(5052,plain,
! [SV1094: $i,SV344: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV344 @ SV1094 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV344 @ SV1094 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(5053,plain,
! [SV1720: $i,SV1095: $i,SV345: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV345 ) )
= $true )
| ( ( ( c_lessequals @ SV1095 @ SV1720 @ SV345 )
| ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SV1720 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4412]) ).
thf(5054,plain,
! [SV1721: $i,SV1096: $i,SV346: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV346 ) )
= $true )
| ( ( ( c_lessequals @ SV1096 @ SV1721 @ SV346 )
| ~ ( c_HOL_Oord__class_Oless @ SV1096 @ SV1721 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4413]) ).
thf(5055,plain,
! [SV2109: $i,SV1722: $i,SV1097: $i,SV347: $i] :
( ( ! [SY6114: $i] :
( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1097 ) @ SV1722 ) @ SV2109 )
| ~ ( c_Type_Otyping @ SV347 @ SV1722 @ SY6114 )
| ~ ( c_Type_Otyping @ SV347 @ SV1097 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY6114 ) @ SV2109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4414]) ).
thf(5056,plain,
! [SV2110: $i,SV1723: $i,SV1098: $i,SV349: $i] :
( ( ( ( c_List_Olist__update @ SV349 @ SV1098 @ SV1723 @ SV2110 )
= ( c_List_Oappend @ ( c_List_Otake @ SV1098 @ SV349 @ SV2110 ) @ ( c_List_Olist_OCons @ SV1723 @ ( c_List_Odrop @ ( c_Suc @ SV1098 ) @ SV349 @ SV2110 ) @ SV2110 ) @ SV2110 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1098 @ ( c_Nat_Osize__class_Osize @ SV349 @ ( tc_List_Olist @ SV2110 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4415]) ).
thf(5057,plain,
! [SV1724: $i,SV1099: $i,SV350: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV350 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ ( c_Power_Opower__class_Opower @ SV1099 @ ( c_Suc @ SV1724 ) @ SV350 ) @ SV350 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ SV1099 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(5058,plain,
! [SV1725: $i,SV1101: $i,SV352: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1725 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV352 ) @ SV1725 ) @ ( c_Suc @ SV1101 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1725 @ SV1101 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4418]) ).
thf(5059,plain,
! [SV1726: $i,SV1102: $i,SV353: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV353 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1102 @ SV1726 @ SV353 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1102 @ SV1726 @ SV353 ) @ ( c_HOL_Ozero__class_Ozero @ SV353 ) @ SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(5060,plain,
! [SV1727: $i,SV1103: $i,SV354: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV354 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1103 @ SV1727 @ SV354 ) @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV354 )
| ~ ( c_HOL_Oord__class_Oless @ SV1103 @ SV1727 @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(5061,plain,
! [SV1728: $i,SV1104: $i,SV355: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV355 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1104 @ SV355 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1728 @ SV355 ) @ SV355 )
| ~ ( c_HOL_Oord__class_Oless @ SV1104 @ SV1728 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(5062,plain,
! [SV1729: $i,SV1105: $i,SV356: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV356 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1105 @ SV1729 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1105 @ SV356 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1729 @ SV356 ) @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4422]) ).
thf(5063,plain,
! [SV1730: $i,SV1106: $i,SV359: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV359 ) @ SV1106 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1730 @ SV1106 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV359 @ SV1730 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4423]) ).
thf(5064,plain,
! [SV2111: $i,SV1731: $i,SV1107: $i,SV360: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV360 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV1107 ) @ SV1731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV2111 ) @ SV1731 ) @ SV360 )
| ~ ( c_lessequals @ SV1107 @ SV2111 @ SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4424]) ).
thf(5065,plain,
! [SV2112: $i,SV1732: $i,SV1108: $i,SV361: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV361 )
| ( c_lessequals @ SV1108 @ SV1732 @ SV361 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1108 ) @ SV2112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1732 ) @ SV2112 ) @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4425]) ).
thf(5066,plain,
! [SV2113: $i,SV1733: $i,SV1109: $i,SV362: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV362 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV1733 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV2113 ) @ SV362 )
| ~ ( c_lessequals @ SV1733 @ SV2113 @ SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4426]) ).
thf(5067,plain,
! [SV2114: $i,SV1734: $i,SV1110: $i,SV363: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV363 )
| ( c_lessequals @ SV1110 @ SV1734 @ SV363 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1734 ) @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4427]) ).
thf(5068,plain,
! [SV2115: $i,SV1735: $i,SV1111: $i,SV364: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV364 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV1111 ) @ SV1735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV2115 ) @ SV1735 ) @ SV364 )
| ~ ( c_lessequals @ SV1111 @ SV2115 @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4428]) ).
thf(5069,plain,
! [SV2116: $i,SV1736: $i,SV1112: $i,SV365: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV365 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV1736 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV2116 ) @ SV365 )
| ~ ( c_lessequals @ SV1736 @ SV2116 @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4429]) ).
thf(5070,plain,
! [SV1737: $i,SV1113: $i,SV366: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV366 ) @ SV1113 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1737 ) @ SV1113 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV366 @ SV1737 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(5071,plain,
! [SV1738: $i,SV1114: $i,SV367: $i] :
( ( ( c_lessequals @ SV367 @ SV1114 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1738 ) @ SV367 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1738 ) @ SV1114 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4431]) ).
thf(5072,plain,
! [SV1739: $i,SV1115: $i,SV368: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SV1739 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1115 @ SV1739 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4432]) ).
thf(5073,plain,
! [SV2117: $i,SV1740: $i,SV1116: $i,SV370: $i] :
( ( ( ( c_List_Olist__update @ SV370 @ SV1116 @ SV1740 @ SV2117 )
= SV370 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SV2117 ) ) @ SV1116 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4434]) ).
thf(5074,plain,
! [SV1117: $i,SV371: $i] :
( ( ( c_lessequals @ SV371 @ SV1117 @ tc_nat )
= $false )
| ( ( SV1117
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1117 @ SV371 @ tc_nat ) ) @ SV371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4435]) ).
thf(5075,plain,
! [SV1118: $i,SV372: $i] :
( ( ( c_lessequals @ SV372 @ SV1118 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV372 ) @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV372 @ tc_nat ) )
= SV1118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4436]) ).
thf(5076,plain,
! [SV373: $i,SV1119: $i] :
( ( ( c_lessequals @ SV1119 @ SV373 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV373 @ SV1119 @ tc_nat ) ) @ SV1119 )
= SV373 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4437]) ).
thf(5077,plain,
! [SV2118: $i,SV1741: $i,SV1120: $i,SV374: $i] :
( ( ! [SY6115: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV374 @ SV1120 @ SV1741 @ SV2118 ) @ SY6115 )
= ( hAPP @ SV374 @ ( c_HOL_Ominus__class_Ominus @ SY6115 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1120 @ SY6115 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4438]) ).
thf(5078,plain,
! [SV2119: $i,SV1742: $i,SV1121: $i,SV375: $i] :
( ( ! [SY6116: $i,SY6117: $i,SY6118: $i,SY6119: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ SV2119 ) )
= ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ ( c_Suc @ SV2119 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6116 @ SV375 @ SV1742 @ SY6117 @ SY6118 @ SY6119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4439]) ).
thf(5079,plain,
! [SV2120: $i,SV1743: $i,SV1122: $i,SV376: $i] :
( ( ! [SY6120: $i,SY6121: $i,SY6122: $i,SY6123: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ SV2120 ) ) @ SV1743 )
= ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ ( c_Suc @ SV2120 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6120 @ SV376 @ SV1122 @ SY6121 @ SY6122 @ SY6123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4440]) ).
thf(5080,plain,
! [SV2121: $i,SV1744: $i,SV1123: $i,SV377: $i] :
( ( ! [SY6124: $i,SY6125: $i,SY6126: $i,SY6127: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SV1744 ) )
= ( hAPP @ ( hAPP @ SV2121 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SV1744 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6124 @ SV2121 @ SV377 @ SY6125 @ SY6126 @ SY6127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4441]) ).
thf(5081,plain,
! [SV2122: $i,SV1745: $i,SV1124: $i,SV378: $i] :
( ( ! [SY6128: $i,SY6129: $i,SY6130: $i,SY6131: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SV1745 ) )
= ( hAPP @ ( hAPP @ SV2122 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SV1745 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6128 @ SV2122 @ SV378 @ SY6129 @ SY6130 @ SY6131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4442]) ).
thf(5082,plain,
! [SV1125: $i,SV379: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV379 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1125 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV379 ) @ SV1125 ) @ ( c_HOL_Oone__class_Oone @ SV379 ) ) @ SV379 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4443]) ).
thf(5083,plain,
! [SV1746: $i,SV1126: $i,SV380: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ ( c_HOL_Ominus__class_Ominus @ SV1126 @ SV1746 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ SV1126 ) @ SV1746 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1746 @ SV1126 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4444]) ).
thf(5084,plain,
! [SV1747: $i,SV1127: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV381 @ SV1127 @ tc_nat ) ) @ SV1747 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV381 ) @ SV1747 ) @ SV1127 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1127 @ SV381 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4445]) ).
thf(5085,plain,
! [SV2123: $i,SV1748: $i,SV1128: $i,SV382: $i] :
( ( ( c_List_Odrop @ SV382 @ ( c_List_Odrop @ SV1128 @ SV1748 @ SV2123 ) @ SV2123 )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV382 ) @ SV1128 ) @ SV1748 @ SV2123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4446]) ).
thf(5086,plain,
! [SV2124: $i,SV1749: $i,SV1129: $i,SV383: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV383 )
| ( c_lessequals @ SV1129 @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SV2124 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SV1749 @ ( c_Suc @ SV2124 ) @ SV383 ) @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4447]) ).
thf(5087,plain,
! [SV2125: $i,SV1750: $i,SV1130: $i,SV384: $i] :
( ( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV384 ) @ SV1130 ) @ SV1750 @ SV2125 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV384 @ SV1750 @ SV2125 ) @ ( c_List_Oreplicate @ SV1130 @ SV1750 @ SV2125 ) @ SV2125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4448]) ).
thf(5088,plain,
! [SV2126: $i,SV1751: $i,SV1132: $i,SV386: $i] :
( ( ( c_List_Otake @ SV386 @ ( c_List_Oappend @ SV1132 @ SV1751 @ SV2126 ) @ SV2126 )
= ( c_List_Oappend @ ( c_List_Otake @ SV386 @ SV1132 @ SV2126 ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV386 @ ( c_Nat_Osize__class_Osize @ SV1132 @ ( tc_List_Olist @ SV2126 ) ) @ tc_nat ) @ SV1751 @ SV2126 ) @ SV2126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4449]) ).
thf(5089,plain,
! [SV1133: $i,SV387: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV387 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV387 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1133 @ SV387 ) @ SV387 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1133 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4450]) ).
thf(5090,plain,
! [SV1134: $i,SV388: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV388 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1134 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV388 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1134 @ SV388 ) @ SV388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4451]) ).
thf(5091,plain,
! [SV1136: $i,SV390: $i] :
( ( ( class_Power_Opower @ SV390 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1136 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV390 )
= ( c_HOL_Oone__class_Oone @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4453]) ).
thf(5092,plain,
! [SV1137: $i,SV391: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV391 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1137 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV391 )
= ( c_HOL_Oone__class_Oone @ SV391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4454]) ).
thf(5093,plain,
! [SV1753: $i,SV1138: $i,SV392: $i] :
( ( ( c_List_Odistinct @ SV392 @ SV1138 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Orotate @ SV1753 @ SV392 @ SV1138 ) @ SV1138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(5094,plain,
! [SV1754: $i,SV1139: $i,SV393: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate @ SV393 @ SV1139 @ SV1754 ) @ SV1754 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV1139 @ SV1754 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4456]) ).
thf(5095,plain,
! [SV1140: $i,SV394: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV394 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Orev @ SV1140 @ SV394 ) @ SV394 )
= ( c_List_Olistsum @ SV1140 @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4457]) ).
thf(5096,plain,
! [SV2127: $i,SV1755: $i,SV1141: $i,SV395: $i] :
( ( ( c_List_Olistsp @ SV395 @ ( c_List_Oappend @ SV1141 @ SV1755 @ SV2127 ) @ SV2127 )
| ~ ( c_List_Olistsp @ SV395 @ SV1755 @ SV2127 )
| ~ ( c_List_Olistsp @ SV395 @ SV1141 @ SV2127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4458]) ).
thf(5097,plain,
! [SV2128: $i,SV1756: $i,SV1142: $i,SV396: $i] :
( ( ! [SY6132: $i,SY6133: $i,SY6134: $i] :
( ( c_Fun_Ocomp @ SV396 @ ( c_Fun_Ocomp @ SV1142 @ SV1756 @ SV2128 @ SY6132 @ SY6133 ) @ SY6132 @ SY6134 @ SY6133 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV396 @ SV1142 @ SY6132 @ SY6134 @ SV2128 ) @ SV1756 @ SV2128 @ SY6134 @ SY6133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4459]) ).
thf(5098,plain,
! [SV1757: $i,SV1143: $i,SV397: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV397 ) ) @ SV1143 ) @ SV1757 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV397 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV397 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4460]) ).
thf(5099,plain,
! [SV1758: $i,SV1144: $i,SV398: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV398 ) ) @ SV1144 ) @ SV1758 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV398 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1758 @ SV398 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4461]) ).
thf(5100,plain,
! [SV1146: $i,SV400: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV400 ) @ SV1146 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV400 @ SV1146 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4463]) ).
thf(5101,plain,
! [SV1147: $i,SV401: $i] :
( ( ( c_lessequals @ SV401 @ SV1147 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV401 @ ( c_Suc @ SV1147 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4464]) ).
thf(5102,plain,
! [SV1760: $i,SV1148: $i,SV403: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV403 @ SV1148 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV1760 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1148 @ SV1760 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV1148 @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV403 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(5103,plain,
! [SV1761: $i,SV1149: $i,SV404: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SV1149 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1761 @ SV1149 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV404 @ SV1761 @ tc_nat )
| ~ ( c_lessequals @ SV1149 @ SV1761 @ tc_nat )
| ~ ( c_lessequals @ SV1149 @ SV404 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4466]) ).
thf(5104,plain,
! [SV2129: $i,SV1762: $i,SV1150: $i,SV405: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV405 )
| ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1762 ) @ SV2129 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2129 @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1762 @ SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4467]) ).
thf(5105,plain,
! [SV1763: $i,SV1151: $i,SV406: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV406 ) ) @ SV1151 ) @ SV1763 )
= ( c_Lambda_OdB_OVar @ SV406 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV406 @ SV1763 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4468]) ).
thf(5106,plain,
! [SV1764: $i,SV1152: $i,SV407: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV407 ) @ ( c_Lambda_OdB_OVar @ SV1152 ) ) @ SV1764 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4469]) ).
thf(5107,plain,
! [SV1153: $i,SV408: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV408 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV408 ) @ SV1153 ) @ SV1153 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_lessequals @ SV1153 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4470]) ).
thf(5108,plain,
! [SV1154: $i,SV409: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV409 )
= $false )
| ( ( ( c_lessequals @ SV1154 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV409 ) @ SV1154 ) @ SV1154 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4471]) ).
thf(5109,plain,
! [SV2130: $i,SV1765: $i,SV1155: $i,SV410: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SV1765 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SV2130 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2130 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4472]) ).
thf(5110,plain,
! [SV2131: $i,SV1766: $i,SV1156: $i,SV411: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV411 )
| ( c_HOL_Oord__class_Oless @ SV1156 @ SV1766 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1766 @ SV411 ) @ SV411 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SV2131 @ SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4473]) ).
thf(5111,plain,
! [SV2132: $i,SV1767: $i,SV1157: $i,SV412: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SV1767 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SV2132 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1767 @ SV2132 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4474]) ).
thf(5112,plain,
! [SV2133: $i,SV1768: $i,SV1158: $i,SV413: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV413 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1768 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1768 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV2133 @ SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4475]) ).
thf(5113,plain,
! [SV2134: $i,SV1769: $i,SV1159: $i,SV414: $i] :
( ( ( c_Lambda_Oliftn @ SV414 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1159 ) @ SV1769 ) @ SV2134 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV414 @ SV1159 @ SV2134 ) ) @ ( c_Lambda_Oliftn @ SV414 @ SV1769 @ SV2134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4476]) ).
thf(5114,plain,
! [SV2135: $i,SV1770: $i,SV1161: $i,SV416: $i] :
( ( ( ( c_List_Odrop @ SV416 @ ( c_List_Olist_OCons @ SV1161 @ SV1770 @ SV2135 ) @ SV2135 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1770 @ SV2135 ) )
| ( SV416
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4477]) ).
thf(5115,plain,
! [SV417: $i,SV1162: $i] :
( ( ( c_lessequals @ SV1162 @ SV417 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV417 @ ( c_HOL_Ominus__class_Ominus @ SV417 @ SV1162 @ tc_nat ) @ tc_nat )
= SV1162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4478]) ).
thf(5116,plain,
! [SV1163: $i,SV418: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV418 @ SV1163 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV418 ) ) @ SV1163 )
= ( c_Lambda_OdB_OVar @ SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4479]) ).
thf(5117,plain,
! [SV2136: $i,SV1771: $i,SV1165: $i,SV420: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV420 @ SV1165 @ SV1771 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2136 @ SV1771 )
= ( c_List_Olist_OCons @ SV2136 @ SV1165 @ SV1771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4480]) ).
thf(5118,plain,
! [SV2137: $i,SV1772: $i,SV1167: $i,SV422: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV422 @ SV1167 @ SV1772 @ SV2137 ) @ ( tc_List_Olist @ SV2137 ) )
= ( c_Nat_Osize__class_Osize @ SV422 @ ( tc_List_Olist @ SV2137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4482]) ).
thf(5119,plain,
! [SV1168: $i,SV423: $i] :
( ( ( c_lessequals @ SV423 @ SV1168 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV423 @ ( c_Suc @ SV1168 ) @ tc_nat ) )
= $true )
| ( ( SV423
= ( c_Suc @ SV1168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4483]) ).
thf(5120,plain,
! [SV1169: $i,SV425: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV425 @ SV1169 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1169 @ ( c_Suc @ SV425 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(5121,plain,
! [SV2138: $i,SV1773: $i,SV1171: $i,SV427: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV427 ) @ SV1171 ) @ SV1773 ) ) @ SV2138 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV427 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2138 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1171 ) @ SV2138 ) ) @ SV1773 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1773 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2138 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4486]) ).
thf(5122,plain,
! [SV1774: $i,SV1172: $i,SV428: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SV1172 ) ) @ ( c_Suc @ SV1774 ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SV1774 ) ) @ SV1172 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1172 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1774 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4487]) ).
thf(5123,plain,
! [SV2139: $i,SV1776: $i,SV1175: $i,SV431: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV431 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ ( c_Orderings_Oord__class_Omax @ SV1175 @ SV1776 @ SV431 ) ) @ SV2139 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1175 ) @ SV2139 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1776 ) @ SV2139 ) @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4489]) ).
thf(5124,plain,
! [SV1176: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV432 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV432 ) @ ( c_Lambda_OdB_OVar @ SV1176 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4490]) ).
thf(5125,plain,
! [SV2140: $i,SV1777: $i,SV1177: $i,SV433: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV433 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1177 @ SV1777 @ SV433 ) @ SV2140 @ SV433 )
= ( c_Orderings_Oord__class_Omax @ SV1177 @ ( c_Orderings_Oord__class_Omax @ SV1777 @ SV2140 @ SV433 ) @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4491]) ).
thf(5126,plain,
! [SV2141: $i,SV1778: $i,SV1178: $i,SV434: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV434 )
| ( ( c_Orderings_Oord__class_Omax @ SV1178 @ ( c_Orderings_Oord__class_Omax @ SV1778 @ SV2141 @ SV434 ) @ SV434 )
= ( c_Orderings_Oord__class_Omax @ SV1778 @ ( c_Orderings_Oord__class_Omax @ SV1178 @ SV2141 @ SV434 ) @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4492]) ).
thf(5127,plain,
! [SV1779: $i,SV1179: $i,SV437: $i] :
( ( ( c_List_Odistinct @ ( c_List_Otake @ SV437 @ SV1179 @ SV1779 ) @ SV1779 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV1179 @ SV1779 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4494]) ).
thf(5128,plain,
! [SV1180: $i,SV438: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV438 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1180 @ SV438 ) @ SV438 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(5129,plain,
! [SV1181: $i,SV439: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV439 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1181 @ SV439 ) @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(5130,plain,
! [SV1182: $i,SV440: $i] :
( ( ( c_Lambda_Obeta @ SV440 @ SV1182 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV440 ) @ ( c_Lambda_OdB_OAbs @ SV1182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4497]) ).
thf(5131,plain,
! [SV1780: $i,SV1183: $i,SV441: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV441 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1183 @ ( c_Orderings_Oord__class_Omax @ SV1183 @ SV1780 @ SV441 ) @ SV441 )
= ( c_Orderings_Oord__class_Omax @ SV1183 @ SV1780 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4498]) ).
thf(5132,plain,
! [SV2142: $i,SV1782: $i,SV1185: $i,SV444: $i] :
( ( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV444 ) @ SV1185 ) @ SV1782 @ SV2142 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV444 @ SV1782 @ SV2142 ) ) @ ( c_Lambda_Osubstn @ SV1185 @ SV1782 @ SV2142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4500]) ).
thf(5133,plain,
! [SV1783: $i,SV1188: $i,SV447: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV447 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1188 ) @ SV1783 ) @ SV1783 @ SV447 )
= SV1188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(5134,plain,
! [SV2143: $i,SV1785: $i,SV1190: $i,SV449: $i] :
( ( ! [SY6135: $i,SY6136: $i] :
( ( c_List_Ofoldl @ SV449 @ SV1190 @ ( c_List_Oappend @ SV1785 @ SV2143 @ SY6135 ) @ SY6136 @ SY6135 )
= ( c_List_Ofoldl @ SV449 @ ( c_List_Ofoldl @ SV449 @ SV1190 @ SV1785 @ SY6136 @ SY6135 ) @ SV2143 @ SY6136 @ SY6135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4503]) ).
thf(5135,plain,
! [SV2144: $i,SV1786: $i,SV1191: $i,SV450: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV450 )
| ( c_lessequals @ SV1191 @ SV1786 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1786 @ SV450 ) @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SV2144 @ SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4504]) ).
thf(5136,plain,
! [SV2145: $i,SV1787: $i,SV1192: $i,SV451: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV451 )
| ( c_lessequals @ SV1192 @ SV1787 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1787 @ SV451 ) @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SV2145 @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4505]) ).
thf(5137,plain,
! [SV2146: $i,SV1788: $i,SV1193: $i,SV452: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV452 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SV1788 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SV2146 @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ SV1788 @ SV2146 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4506]) ).
thf(5138,plain,
! [SV2147: $i,SV1789: $i,SV1194: $i,SV453: $i] :
( ( ( c_List_Orotate @ SV453 @ ( c_List_Orotate @ SV1194 @ SV1789 @ SV2147 ) @ SV2147 )
= ( c_List_Orotate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV453 ) @ SV1194 ) @ SV1789 @ SV2147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4507]) ).
thf(5139,plain,
! [SV2148: $i,SV1790: $i,SV1195: $i,SV454: $i] :
( ( ( c_Type_Otype_Otype__case @ SV454 @ SV1195 @ ( c_Type_Otype_OAtom @ SV1790 ) @ SV2148 )
= ( hAPP @ SV454 @ SV1790 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4508]) ).
thf(5140,plain,
! [SV1791: $i,SV1196: $i,SV456: $i] :
( ( ( c_List_Odistinct @ SV456 @ SV1196 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ SV1791 @ SV456 @ SV1196 ) @ SV1196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(5141,plain,
! [SV2149: $i,SV1792: $i,SV1197: $i,SV457: $i] :
( ( ! [SY6137: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV2149 ) @ SY6137 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1792 @ SY6137 @ SV457 )
| ~ ( c_lessequals @ SV1197 @ SV2149 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4510]) ).
thf(5142,plain,
! [SV2150: $i,SV1793: $i,SV1198: $i,SV458: $i] :
( ( ! [SY6138: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV2150 ) @ SY6138 ) @ SV458 )
| ~ ( c_lessequals @ SV1793 @ SY6138 @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SV2150 @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4511]) ).
thf(5143,plain,
! [SV1199: $i,SV459: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV459 @ SV1199 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV459 ) @ ( c_Suc @ SV1199 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4512]) ).
thf(5144,plain,
! [SV1200: $i,SV460: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV460 ) @ ( c_Suc @ SV1200 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV460 @ SV1200 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4513]) ).
thf(5145,plain,
! [SV1201: $i,SV461: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV461 @ SV1201 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV461 ) @ ( c_Suc @ SV1201 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4514]) ).
thf(5146,plain,
! [SV462: $i,SV1202: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1202 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV462 ) @ SV1202 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4515]) ).
thf(5147,plain,
! [SV1203: $i,SV463: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV463 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV463 ) @ SV1203 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4516]) ).
thf(5148,plain,
! [SV1204: $i,SV464: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV464 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ SV1204 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV464 ) @ SV1204 ) @ SV1204 ) @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4517]) ).
thf(5149,plain,
! [SV1205: $i,SV465: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV465 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV465 ) @ SV1205 ) @ SV1205 ) @ SV465 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1205 @ SV465 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4518]) ).
thf(5150,plain,
! [SV1206: $i,SV466: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV466 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV466 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1206 @ SV1206 @ SV466 )
= ( c_HOL_Ozero__class_Ozero @ SV466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4519]) ).
thf(5151,plain,
! [SV1207: $i,SV467: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV467 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1207 @ SV1207 @ SV467 )
= ( c_HOL_Ozero__class_Ozero @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4520]) ).
thf(5152,plain,
! [SV1208: $i,SV468: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV468 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1208 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
= SV1208 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4521]) ).
thf(5153,plain,
! [SV1209: $i,SV469: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV469 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1209 @ SV1209 @ SV469 )
= ( c_HOL_Ozero__class_Ozero @ SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4522]) ).
thf(5154,plain,
! [SV1210: $i,SV470: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV470 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1210 @ SV1210 @ SV470 )
= ( c_HOL_Ozero__class_Ozero @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4523]) ).
thf(5155,plain,
! [SV1211: $i,SV472: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV472 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) ) @ SV1211 )
= SV1211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4525]) ).
thf(5156,plain,
! [SV1212: $i,SV473: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV473 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV473 ) @ ( c_HOL_Ozero__class_Ozero @ SV473 ) ) @ SV1212 )
= SV1212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4526]) ).
thf(5157,plain,
! [SV1213: $i,SV474: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV474 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV474 )
| ( SV1213
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV474 ) @ SV1213 ) @ ( c_HOL_Ozero__class_Ozero @ SV474 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4527]) ).
thf(5158,plain,
! [SV1214: $i,SV475: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV475 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV475 ) @ SV1214 ) @ ( c_HOL_Ozero__class_Ozero @ SV475 ) )
= SV1214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4528]) ).
thf(5159,plain,
! [SV1215: $i,SV476: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV476 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV476 ) @ ( c_HOL_Ozero__class_Ozero @ SV476 ) ) @ SV1215 )
= SV1215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4529]) ).
thf(5160,plain,
! [SV1216: $i,SV477: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV477 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV477 ) @ SV1216 ) @ ( c_HOL_Ozero__class_Ozero @ SV477 ) )
= SV1216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4530]) ).
thf(5161,plain,
! [SV1217: $i,SV478: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV478 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV478 ) @ SV1217 ) @ ( c_HOL_Ozero__class_Ozero @ SV478 ) )
= SV1217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4531]) ).
thf(5162,plain,
! [SV1218: $i,SV479: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV479 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV479 ) @ ( c_HOL_Ozero__class_Ozero @ SV479 ) ) @ SV1218 )
= SV1218 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4532]) ).
thf(5163,plain,
! [SV480: $i] :
( ( ( ~ ( class_Power_Opower @ SV480 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV480 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV480 )
= ( c_HOL_Oone__class_Oone @ SV480 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV480 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4533]) ).
thf(5164,plain,
! [SV2151: $i,SV1794: $i,SV1220: $i,SV486: $i] :
( ( ! [SY6139: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SV1220 @ SV1794 @ SV2151 ) @ SV2151 ) @ ( c_Nat_Osize__class_Osize @ SV486 @ ( tc_List_Olist @ SV2151 ) ) @ SY6139 @ SV2151 )
= ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SY6139 @ SV1794 @ SV2151 ) @ SV2151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4535]) ).
thf(5165,plain,
! [SV1795: $i,SV1223: $i,SV489: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV489 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1795 @ tc_nat ) @ SV489 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1223 @ SV489 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1795 @ SV489 ) @ SV489 ) )
| ~ ( c_lessequals @ SV1795 @ SV1223 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4538]) ).
thf(5166,plain,
! [SV1797: $i,SV1225: $i,SV491: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV491 ) @ SV1225 ) @ SV1797 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV491 @ ( c_HOL_Ominus__class_Ominus @ SV1797 @ SV1225 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4540]) ).
thf(5167,plain,
! [SV1798: $i,SV1226: $i,SV492: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV492 @ ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1798 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV1798 ) @ SV1226 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4541]) ).
thf(5168,plain,
! [SV2152: $i,SV1799: $i,SV1227: $i,SV493: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV493 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV1227 ) @ SV1799 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV2152 ) @ SV1799 ) @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SV2152 @ SV493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4542]) ).
thf(5169,plain,
! [SV2153: $i,SV1800: $i,SV1228: $i,SV494: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV494 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV1228 ) @ SV1800 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV2153 ) @ SV1800 ) @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SV2153 @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4543]) ).
thf(5170,plain,
! [SV2154: $i,SV1801: $i,SV1229: $i,SV495: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV495 )
| ( c_HOL_Oord__class_Oless @ SV1229 @ SV1801 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1229 ) @ SV2154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1801 ) @ SV2154 ) @ SV495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4544]) ).
thf(5171,plain,
! [SV2155: $i,SV1802: $i,SV1230: $i,SV496: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV496 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV1802 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV2155 ) @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1802 @ SV2155 @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4545]) ).
thf(5172,plain,
! [SV2156: $i,SV1803: $i,SV1231: $i,SV497: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV497 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV1803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV2156 ) @ SV497 )
| ~ ( c_HOL_Oord__class_Oless @ SV1803 @ SV2156 @ SV497 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4546]) ).
thf(5173,plain,
! [SV2157: $i,SV1804: $i,SV1232: $i,SV498: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV498 )
| ( c_HOL_Oord__class_Oless @ SV1232 @ SV1804 @ SV498 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1232 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1804 ) @ SV498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4547]) ).
thf(5174,plain,
! [SV1805: $i,SV1233: $i,SV499: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV499 ) @ SV1233 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1805 ) @ SV1233 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV499 @ SV1805 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(5175,plain,
! [SV1806: $i,SV1234: $i,SV500: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV500 @ SV1234 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1806 ) @ SV500 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1806 ) @ SV1234 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4549]) ).
thf(5176,plain,
! [SV1807: $i,SV1235: $i,SV501: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SV1235 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SV1807 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1235 @ SV1807 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4550]) ).
thf(5177,plain,
! [SV2158: $i,SV1808: $i,SV1236: $i,SV502: $i] :
( ( ~ ( class_Orderings_Oorder @ SV502 )
| ( c_lessequals @ SV1236 @ SV1808 @ SV502 )
| ~ ( c_lessequals @ SV1236 @ SV2158 @ SV502 )
| ~ ( c_lessequals @ SV2158 @ SV1808 @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4551]) ).
thf(5178,plain,
! [SV2159: $i,SV1809: $i,SV1237: $i,SV503: $i] :
( ( ~ ( class_Orderings_Oorder @ SV503 )
| ( c_HOL_Oord__class_Oless @ SV1237 @ SV1809 @ SV503 )
| ~ ( c_lessequals @ SV1237 @ SV2159 @ SV503 )
| ~ ( c_HOL_Oord__class_Oless @ SV2159 @ SV1809 @ SV503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4552]) ).
thf(5179,plain,
! [SV2160: $i,SV1810: $i,SV1238: $i,SV504: $i] :
( ( ~ ( class_Orderings_Oorder @ SV504 )
| ( c_HOL_Oord__class_Oless @ SV1238 @ SV1810 @ SV504 )
| ~ ( c_HOL_Oord__class_Oless @ SV1238 @ SV2160 @ SV504 )
| ~ ( c_lessequals @ SV2160 @ SV1810 @ SV504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4553]) ).
thf(5180,plain,
! [SV1811: $i,SV1239: $i,SV505: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SV1239 ) @ SV1811 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SV1811 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SV1239 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4554]) ).
thf(5181,plain,
! [SV2161: $i,SV1812: $i,SV1240: $i,SV506: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV506 )
| ( c_lessequals @ SV1240 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SV2161 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SV1240 @ SV2161 @ SV506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4555]) ).
thf(5182,plain,
! [SV1813: $i,SV1241: $i,SV508: $i] :
( ( ( c_lessequals @ SV508 @ SV1241 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1813 @ SV1241 @ tc_nat )
| ~ ( c_lessequals @ SV508 @ SV1813 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4556]) ).
thf(5183,plain,
! [SV1242: $i,SV510: $i] :
( ( ( class_Orderings_Oorder @ SV510 )
= $false )
| ( ( c_lessequals @ SV1242 @ SV1242 @ SV510 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(5184,plain,
! [SV1243: $i,SV511: $i] :
( ( ( class_Orderings_Opreorder @ SV511 )
= $false )
| ( ( c_lessequals @ SV1243 @ SV1243 @ SV511 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4558]) ).
thf(5185,plain,
! [SV2162: $i,SV1814: $i,SV1244: $i,SV512: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV512 )
| ( c_HOL_Oord__class_Oless @ SV1244 @ SV1814 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV2162 @ SV1814 @ SV512 )
| ~ ( c_lessequals @ SV1244 @ SV2162 @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4559]) ).
thf(5186,plain,
! [SV2163: $i,SV1815: $i,SV1245: $i,SV513: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV513 )
| ( c_HOL_Oord__class_Oless @ SV1245 @ SV1815 @ SV513 )
| ~ ( c_lessequals @ SV2163 @ SV1815 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ SV1245 @ SV2163 @ SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4560]) ).
thf(5187,plain,
! [SV2164: $i,SV1816: $i,SV1246: $i,SV514: $i] :
( ( ! [SY6140: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
| ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2164 ) @ SV514 )
| ~ ( c_lessequals @ SY6140 @ SV2164 @ SV514 )
| ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SY6140 ) @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4561]) ).
thf(5188,plain,
! [SV2165: $i,SV1817: $i,SV1247: $i,SV515: $i] :
( ( ( c_Type_Otyping @ SV515 @ SV1247 @ SV1817 )
| ~ ( c_Lambda_Obeta @ SV2165 @ SV1247 )
| ~ ( c_Type_Otyping @ SV515 @ SV2165 @ SV1817 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4562]) ).
thf(5189,plain,
! [SV1818: $i,SV1248: $i,SV516: $i] :
( ( ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SV1818 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ominus__class_Ominus @ SV1248 @ SV1818 @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(5190,plain,
! [SV2166: $i,SV1819: $i,SV1249: $i,SV517: $i] :
( ( ! [SY6141: $i,SY6142: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV1249 @ SV1819 @ SV2166 ) @ SY6141 @ SY6142 @ SV2166 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SY6141 @ SY6142 @ SV2166 ) @ SV1249 @ SV1819 @ SV2166 ) )
| ( SV1249 = SY6141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4564]) ).
thf(5191,plain,
! [SV1250: $i,SV518: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV518 @ ( c_Suc @ SV1250 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1250 @ SV518 @ tc_nat ) )
= $true )
| ( ( SV518 = SV1250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(5192,plain,
! [SV2167: $i,SV1820: $i,SV1251: $i,SV519: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV519 @ SV1251 @ SV1820 ) @ ( c_List_Olist_OCons @ SV1251 @ SV2167 @ SV1820 ) @ SV1820 )
= ( c_List_Olist_OCons @ SV1251 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV519 @ SV1251 @ SV1820 ) @ SV2167 @ SV1820 ) @ SV1820 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4566]) ).
thf(5193,plain,
! [SV521: $i,SV1252: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1252 @ SV521 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV521 @ SV1252 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4567]) ).
thf(5194,plain,
! [SV522: $i,SV1253: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1253 @ SV522 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV522 @ SV1253 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4568]) ).
thf(5195,plain,
! [SV1254: $i,SV523: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV523 ) @ SV1254 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV523 @ SV1254 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4569]) ).
thf(5196,plain,
! [SV1255: $i,SV524: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV524 @ SV1255 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV524 @ ( c_Suc @ SV1255 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4570]) ).
thf(5197,plain,
! [SV2168: $i,SV1821: $i,SV1257: $i,SV527: $i] :
( ( ! [SY6143: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV527 @ SV1257 @ SV1821 ) @ ( c_Suc @ SV2168 ) @ SY6143 @ SV1821 )
= ( c_List_Olist_OCons @ SV527 @ ( c_List_Olist__update @ SV1257 @ SV2168 @ SY6143 @ SV1821 ) @ SV1821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4572]) ).
thf(5198,plain,
! [SV1822: $i,SV1258: $i,SV528: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV528 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1258 ) @ SV1822 ) @ SV528 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV528 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1258 @ SV528 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1822 @ SV528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4573]) ).
thf(5199,plain,
! [SV1259: $i,SV529: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV529 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1259 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1259 @ tc_nat ) @ SV529 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4574]) ).
thf(5200,plain,
! [SV1823: $i,SV1260: $i,SV530: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV530 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1260 @ SV1823 @ SV530 ) @ SV530 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV530 ) @ ( c_List_Olistsum @ SV1260 @ SV530 ) ) @ ( c_List_Olistsum @ SV1823 @ SV530 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4575]) ).
thf(5201,plain,
! [SV1262: $i,SV532: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV532 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV532 @ ( c_Suc @ SV1262 ) @ tc_nat ) @ SV532 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4577]) ).
thf(5202,plain,
! [SV1824: $i,SV1263: $i,SV533: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV533 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1263 @ SV1824 @ SV533 )
| ( SV1824 = SV1263 )
| ~ ( c_lessequals @ SV1263 @ SV1824 @ SV533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4578]) ).
thf(5203,plain,
! [SV1825: $i,SV1264: $i,SV534: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV534 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1825 @ SV534 )
| ~ ( c_lessequals @ SV1264 @ SV1825 @ SV534 )
| ( SV1825 = SV1264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4579]) ).
thf(5204,plain,
! [SV1265: $i,SV535: $i] :
( ( ( SV535 = SV1265 )
= $true )
| ( ( ~ ( c_lessequals @ SV535 @ SV1265 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV535 @ SV1265 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4580]) ).
thf(5205,plain,
! [SV1266: $i,SV536: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV536 @ SV1266 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV536 @ SV1266 @ tc_nat ) )
= $true )
| ( ( SV536 = SV1266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(5206,plain,
! [SV1267: $i,SV537: $i] :
( ( ( SV537 = SV1267 )
= $true )
| ( ( ~ ( c_lessequals @ SV537 @ SV1267 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV537 @ SV1267 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4582]) ).
thf(5207,plain,
! [SV1826: $i,SV1268: $i,SV538: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV538 ) )
= $true )
| ( ( ( SV1268 = SV1826 )
| ( c_HOL_Oord__class_Oless @ SV1268 @ SV1826 @ SV538 )
| ~ ( c_lessequals @ SV1268 @ SV1826 @ SV538 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4583]) ).
thf(5208,plain,
! [SV1827: $i,SV1269: $i,SV539: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV539 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1269 @ SV1827 @ SV539 )
| ( SV1269 = SV1827 )
| ~ ( c_lessequals @ SV1269 @ SV1827 @ SV539 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4584]) ).
thf(5209,plain,
! [SV1828: $i,SV1270: $i,SV540: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV540 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1270 @ SV1828 @ SV540 )
| ( SV1270 = SV1828 )
| ~ ( c_lessequals @ SV1270 @ SV1828 @ SV540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4585]) ).
thf(5210,plain,
! [SV1829: $i,SV1271: $i,SV541: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV541 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1271 @ SV1829 @ SV541 )
| ~ ( c_lessequals @ SV1271 @ SV1829 @ SV541 )
| ( SV1271 = SV1829 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4586]) ).
thf(5211,plain,
! [SV1830: $i,SV1272: $i,SV542: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV542 ) )
= $true )
| ( ( ( SV1272 = SV1830 )
| ~ ( c_lessequals @ SV1272 @ SV1830 @ SV542 )
| ( c_HOL_Oord__class_Oless @ SV1272 @ SV1830 @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4587]) ).
thf(5212,plain,
! [SV1831: $i,SV1273: $i,SV543: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV543 ) )
= $true )
| ( ( ( SV1273 = SV1831 )
| ( c_HOL_Oord__class_Oless @ SV1273 @ SV1831 @ SV543 )
| ~ ( c_lessequals @ SV1273 @ SV1831 @ SV543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4588]) ).
thf(5213,plain,
! [SV2169: $i,SV1832: $i,SV1275: $i,SV546: $i] :
( ( ! [SY6144: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV546 @ SV1275 @ SV1832 @ SV2169 ) @ SV1275 @ SY6144 @ SV2169 )
= ( c_List_Olist__update @ SV546 @ SV1275 @ SY6144 @ SV2169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4589]) ).
thf(5214,plain,
! [SV1276: $i,SV547: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV547 ) @ ( c_Suc @ SV1276 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV547 @ SV1276 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4590]) ).
thf(5215,plain,
! [SV1277: $i,SV548: $i] :
( ( ( c_lessequals @ SV548 @ SV1277 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV548 ) @ ( c_Suc @ SV1277 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4591]) ).
thf(5216,plain,
! [SV2170: $i,SV1833: $i,SV1278: $i,SV549: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV549 @ SV1278 @ SV1833 ) @ SV2170 @ SV1833 )
= ( c_List_Oappend @ SV549 @ ( c_List_Oappend @ SV1278 @ SV2170 @ SV1833 ) @ SV1833 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4592]) ).
thf(5217,plain,
! [SV2171: $i,SV1834: $i,SV1279: $i,SV550: $i] :
( ( ( c_List_Oappend @ SV550 @ ( c_List_Oappend @ SV1279 @ SV1834 @ SV2171 ) @ SV2171 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV550 @ SV1279 @ SV2171 ) @ SV1834 @ SV2171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4593]) ).
thf(5218,plain,
! [SV2172: $i,SV1835: $i,SV1280: $i,SV551: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV551 @ SV1280 @ SV1835 ) @ SV2172 @ SV1835 )
= ( c_List_Oappend @ SV551 @ ( c_List_Oappend @ SV1280 @ SV2172 @ SV1835 ) @ SV1835 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4594]) ).
thf(5219,plain,
! [SV2173: $i,SV1836: $i,SV1281: $i,SV552: $i] :
( ( ( c_List_Oappend @ SV552 @ ( c_List_Oappend @ SV1281 @ SV1836 @ SV2173 ) @ SV2173 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV552 @ SV1281 @ SV2173 ) @ SV1836 @ SV2173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4595]) ).
thf(5220,plain,
! [SV1837: $i,SV1282: $i,SV553: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV553 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1282 @ SV1837 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV1837 @ SV1282 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4596]) ).
thf(5221,plain,
! [SV1838: $i,SV1283: $i,SV554: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV554 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1838 @ SV554 )
| ~ ( c_HOL_Oord__class_Oless @ SV1838 @ SV1283 @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4597]) ).
thf(5222,plain,
! [SV1839: $i,SV1285: $i,SV556: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV556 ) )
= $true )
| ( ( ( c_lessequals @ SV1285 @ SV1839 @ SV556 )
| ( c_lessequals @ SV1839 @ SV1285 @ SV556 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4599]) ).
thf(5223,plain,
! [SV1840: $i,SV1286: $i,SV557: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV557 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1286 @ SV1840 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ SV1840 @ SV1286 @ SV557 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4600]) ).
thf(5224,plain,
! [SV1841: $i,SV1287: $i,SV558: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV558 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1287 @ SV1841 @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ SV1841 @ SV1287 @ SV558 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4601]) ).
thf(5225,plain,
! [SV1288: $i,SV559: $i] :
( ( ( hBOOL @ ( hAPP @ SV559 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV559 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV559 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4602]) ).
thf(5226,plain,
! [SV1289: $i,SV562: $i] :
( ( ( hBOOL @ ( hAPP @ SV562 @ ( v_sko__List__Xupt__Xinduct__1 @ SV562 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV562 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV562 @ SV1289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4603]) ).
thf(5227,plain,
! [SV1291: $i,SV565: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV565 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV565 @ SV1291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4604]) ).
thf(5228,plain,
! [SV2174: $i,SV1843: $i,SV1293: $i,SV574: $i] :
( ( ! [SY6145: $i,SY6146: $i,SY6147: $i] :
( ( ( hAPP @ ( hAPP @ SV574 @ SV1293 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1843 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2174 @ SY6145 @ SV574 @ SY6146 @ SV1843 @ SY6147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4606]) ).
thf(5229,plain,
! [SV1844: $i,SV1294: $i,SV575: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV575 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Omap @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV575 @ SV1294 ) @ SV1844 @ SV1294 @ SV575 ) @ SV575 )
= ( c_HOL_Ozero__class_Ozero @ SV575 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4607]) ).
thf(5230,plain,
! [SV2175: $i,SV1846: $i,SV1296: $i,SV577: $i] :
( ( ! [SY6148: $i] :
( ( c_List_Odrop @ SV577 @ ( c_List_Omap @ SV1296 @ SV1846 @ SV2175 @ SY6148 ) @ SY6148 )
= ( c_List_Omap @ SV1296 @ ( c_List_Odrop @ SV577 @ SV1846 @ SV2175 ) @ SV2175 @ SY6148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4609]) ).
thf(5231,plain,
! [SV2176: $i,SV1847: $i,SV1297: $i,SV578: $i] :
( ( ( c_List_Odistinct @ SV578 @ SV1297 )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ SV1847 @ SV578 @ SV1297 @ SV2176 ) @ SV2176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4610]) ).
thf(5232,plain,
! [SV2177: $i,SV1848: $i,SV1298: $i,SV579: $i] :
( ( ! [SY6149: $i] :
( ( c_List_Omap @ SV579 @ ( c_List_Oappend @ SV1298 @ SV1848 @ SV2177 ) @ SV2177 @ SY6149 )
= ( c_List_Oappend @ ( c_List_Omap @ SV579 @ SV1298 @ SV2177 @ SY6149 ) @ ( c_List_Omap @ SV579 @ SV1848 @ SV2177 @ SY6149 ) @ SY6149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4611]) ).
thf(5233,plain,
! [SV2178: $i,SV1849: $i,SV1299: $i,SV580: $i] :
( ( ! [SY6150: $i] :
( ( c_List_Omap @ SV580 @ ( c_List_Oreplicate @ SV1299 @ SV1849 @ SV2178 ) @ SV2178 @ SY6150 )
= ( c_List_Oreplicate @ SV1299 @ ( hAPP @ SV580 @ SV1849 ) @ SY6150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4612]) ).
thf(5234,plain,
! [SV2179: $i,SV1850: $i,SV1300: $i,SV581: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV581 @ SV1300 @ SV1850 @ SV2179 ) @ ( tc_List_Olist @ SV2179 ) )
= ( c_Nat_Osize__class_Osize @ SV1300 @ ( tc_List_Olist @ SV1850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4613]) ).
thf(5235,plain,
! [SV2180: $i,SV1851: $i,SV1301: $i,SV582: $i] :
( ( ! [SY6151: $i] :
( ( c_List_Orotate @ SV582 @ ( c_List_Omap @ SV1301 @ SV1851 @ SV2180 @ SY6151 ) @ SY6151 )
= ( c_List_Omap @ SV1301 @ ( c_List_Orotate @ SV582 @ SV1851 @ SV2180 ) @ SV2180 @ SY6151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4614]) ).
thf(5236,plain,
! [SV2181: $i,SV1852: $i,SV1302: $i,SV583: $i] :
( ( ( c_List_Orev @ ( c_List_Omap @ SV583 @ SV1302 @ SV1852 @ SV2181 ) @ SV2181 )
= ( c_List_Omap @ SV583 @ ( c_List_Orev @ SV1302 @ SV1852 ) @ SV1852 @ SV2181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4615]) ).
thf(5237,plain,
! [SV2182: $i,SV1853: $i,SV1303: $i,SV584: $i] :
( ( ! [SY6152: $i] :
( ( c_List_Otake @ SV584 @ ( c_List_Omap @ SV1303 @ SV1853 @ SV2182 @ SY6152 ) @ SY6152 )
= ( c_List_Omap @ SV1303 @ ( c_List_Otake @ SV584 @ SV1853 @ SV2182 ) @ SV2182 @ SY6152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4616]) ).
thf(5238,plain,
! [SV2183: $i,SV1855: $i,SV1305: $i,SV586: $i] :
( ( ! [SY6153: $i,SY6154: $i] :
( ( c_List_Omap @ SV586 @ ( c_List_Omap @ SV1305 @ SV1855 @ SV2183 @ SY6153 ) @ SY6153 @ SY6154 )
= ( c_List_Omap @ ( c_Fun_Ocomp @ SV586 @ SV1305 @ SY6153 @ SY6154 @ SV2183 ) @ SV1855 @ SV2183 @ SY6154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4618]) ).
thf(5239,plain,
! [SV2184: $i,SV1856: $i,SV1306: $i,SV587: $i] :
( ( ! [SY6155: $i] :
( ( c_List_Omap @ SV587 @ ( c_List_Olist_OCons @ SV1306 @ SV1856 @ SV2184 ) @ SV2184 @ SY6155 )
= ( c_List_Olist_OCons @ ( hAPP @ SV587 @ SV1306 ) @ ( c_List_Omap @ SV587 @ SV1856 @ SV2184 @ SY6155 ) @ SY6155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4619]) ).
thf(5240,plain,
! [SV2185: $i,SV1857: $i,SV1307: $i,SV588: $i] :
( ( ! [SY6156: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV588 @ SV1307 ) @ ( c_List_Omap @ SV588 @ SV1857 @ SV2185 @ SY6156 ) @ SY6156 )
= ( c_List_Omap @ SV588 @ ( c_List_Olist_OCons @ SV1307 @ SV1857 @ SV2185 ) @ SV2185 @ SY6156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4620]) ).
thf(5241,plain,
! [SV2186: $i,SV1858: $i,SV1308: $i,SV589: $i] :
( ( ! [SY6157: $i] :
( ( c_List_Omap @ SV589 @ ( c_List_Olist_OCons @ SV1308 @ SV1858 @ SV2186 ) @ SV2186 @ SY6157 )
= ( c_List_Olist_OCons @ ( hAPP @ SV589 @ SV1308 ) @ ( c_List_Omap @ SV589 @ SV1858 @ SV2186 @ SY6157 ) @ SY6157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4621]) ).
thf(5242,plain,
! [SV2187: $i,SV1859: $i,SV1309: $i,SV590: $i] :
( ( ! [SY6158: $i,SY6159: $i] :
( ( c_List_Omap @ SV590 @ ( c_List_Olist__update @ SV1309 @ SV1859 @ SV2187 @ SY6158 ) @ SY6158 @ SY6159 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV590 @ SV1309 @ SY6158 @ SY6159 ) @ SV1859 @ ( hAPP @ SV590 @ SV2187 ) @ SY6159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4622]) ).
thf(5243,plain,
! [SV1311: $i,SV592: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV592 )
= $false )
| ( ( ( c_List_Olistsum @ SV1311 @ SV592 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV592 ) @ SV1311 @ ( c_HOL_Ozero__class_Ozero @ SV592 ) @ SV592 @ SV592 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4624]) ).
thf(5244,plain,
! [SV1312: $i,SV593: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV593 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV593 ) @ ( c_HOL_Ozero__class_Ozero @ SV593 ) @ SV1312 @ SV593 @ SV593 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV593 ) @ SV1312 @ ( c_HOL_Ozero__class_Ozero @ SV593 ) @ SV593 @ SV593 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4625]) ).
thf(5245,plain,
! [SV1861: $i,SV1313: $i,SV594: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV594 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1313 @ SV1861 @ SV594 @ SV594 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1313 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1861 @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV594 @ SV594 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4626]) ).
thf(5246,plain,
! [SV2188: $i,SV1862: $i,SV1314: $i,SV595: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV595 ) @ SV1314 ) ) @ SV1862 ) @ SV2188 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV595 ) @ SV1862 ) @ SV2188 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1314 ) @ SV1862 ) @ SV2188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4627]) ).
thf(5247,plain,
! [SV2189: $i,SV1863: $i,SV1316: $i,SV597: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV597 ) @ SV1316 ) @ SV1863 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2189 ) @ SV1316 ) @ SV1863 ) )
| ~ ( c_Lambda_Obeta @ SV597 @ SV2189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4628]) ).
thf(5248,plain,
! [SV2190: $i,SV1865: $i,SV1318: $i,SV599: $i] :
( ( ! [SY6160: $i] :
( ( c_List_Ofoldr @ SV599 @ SV1318 @ SV1865 @ SV2190 @ SY6160 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV599 @ SV2190 @ SY6160 @ SY6160 ) @ SV1865 @ ( c_List_Orev @ SV1318 @ SV2190 ) @ SY6160 @ SV2190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4630]) ).
thf(5249,plain,
! [SV2191: $i,SV1866: $i,SV1319: $i,SV600: $i] :
( ( ! [SY6161: $i] :
( ( c_List_Ofoldl @ SV600 @ SV1319 @ SV1866 @ SV2191 @ SY6161 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV600 @ SV2191 @ SY6161 @ SV2191 ) @ ( c_List_Orev @ SV1866 @ SY6161 ) @ SV1319 @ SY6161 @ SV2191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4631]) ).
thf(5250,plain,
! [SV2192: $i,SV1867: $i,SV1320: $i,SV601: $i] :
( ( ! [SY6162: $i] :
( ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1867 ) @ SV2192 ) @ SY6162 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV1320 @ SV1867 ) @ SV2192 ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ SV1867 @ SY6162 ) ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ SV2192 @ SY6162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4632]) ).
thf(5251,plain,
! [SV2193: $i,SV1868: $i,SV1321: $i,SV602: $i] :
( ( ! [SY6163: $i] :
( ( c_Type_Otype_Otype__case @ SV602 @ SV1321 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1868 ) @ SV2193 ) @ SY6163 )
= ( hAPP @ ( hAPP @ SV1321 @ SV1868 ) @ SV2193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4633]) ).
thf(5252,plain,
! [SV2194: $i,SV1869: $i,SV1322: $i,SV603: $i] :
( ( ! [SY6164: $i] :
( ~ ( hBOOL @ ( hAPP @ SV603 @ ( c_Type_Otype_Otype__case @ SV1322 @ SV1869 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2194 ) @ SY6164 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV603 @ ( hAPP @ ( hAPP @ SV1869 @ SV2194 ) @ SY6164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4634]) ).
thf(5253,plain,
! [SV2195: $i,SV1870: $i,SV1323: $i,SV604: $i] :
( ( ! [SY6165: $i] :
( ~ ( hBOOL @ ( hAPP @ SV604 @ ( c_Type_Otype_Otype__case @ SV1323 @ SV1870 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2195 ) @ SY6165 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV604 @ ( hAPP @ ( hAPP @ SV1870 @ SV2195 ) @ SY6165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4635]) ).
thf(5254,plain,
! [SV2196: $i,SV1871: $i,SV1324: $i,SV605: $i] :
( ( ! [SY6166: $i,SY6167: $i] :
( ( c_List_Ofoldr @ SV605 @ ( c_List_Olist_OCons @ SV1324 @ SV1871 @ SV2196 ) @ SY6166 @ SV2196 @ SY6167 )
= ( hAPP @ ( hAPP @ SV605 @ SV1324 ) @ ( c_List_Ofoldr @ SV605 @ SV1871 @ SY6166 @ SV2196 @ SY6167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4636]) ).
thf(5255,plain,
! [SV2197: $i,SV1872: $i,SV1325: $i,SV606: $i] :
( ( ! [SY6168: $i,SY6169: $i] :
( ( c_List_Ofoldr @ SV606 @ ( c_List_Oappend @ SV1325 @ SV1872 @ SV2197 ) @ SY6168 @ SV2197 @ SY6169 )
= ( c_List_Ofoldr @ SV606 @ SV1325 @ ( c_List_Ofoldr @ SV606 @ SV1872 @ SY6168 @ SV2197 @ SY6169 ) @ SV2197 @ SY6169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4637]) ).
thf(5256,plain,
! [SV2198: $i,SV1873: $i,SV1326: $i,SV607: $i] :
( ( ( c_List_Ofoldr @ SV607 @ ( c_List_Olist_ONil @ SV1326 ) @ SV1873 @ SV1326 @ SV2198 )
= SV1873 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4638]) ).
thf(5257,plain,
! [SV1327: $i,SV608: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV608 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV608 ) @ SV1327 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4639]) ).
thf(5258,plain,
! [SV1875: $i,SV1329: $i,SV610: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV610 ) @ SV1329 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1875 ) @ SV1329 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV610 @ SV1875 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(5259,plain,
! [SV2199: $i,SV1876: $i,SV1330: $i,SV611: $i] :
( ( ! [SY6170: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV611 @ SV1330 @ SV1876 @ SV2199 ) @ SY6170 )
= ( hAPP @ SV611 @ SY6170 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY6170 @ SV1330 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4642]) ).
thf(5260,plain,
! [SV2200: $i,SV1877: $i,SV1331: $i,SV612: $i] :
( ( ! [SY6171: $i] :
( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1331 @ SV1877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2200 )
| ~ ( c_Type_Otypings @ SV612 @ SV1877 @ SY6171 )
| ~ ( c_Type_Otyping @ SV612 @ SV1331 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY6171 @ SV2200 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4643]) ).
thf(5261,plain,
! [SV2201: $i,SV1878: $i,SV1332: $i,SV613: $i] :
( ( ( c_Type_Otyping @ SV613 @ ( c_Lambda_OdB_OAbs @ SV1332 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1878 ) @ SV2201 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV613 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1878 @ tc_Type_Otype ) @ SV1332 @ SV2201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4644]) ).
thf(5262,plain,
! [SV1333: $i,SV614: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV614 )
| ~ ( class_Power_Opower @ SV614 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4645]) ).
thf(5263,plain,
! [SV1334: $i,SV615: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV615 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV615 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV615 ) @ SV1334 @ SV615 )
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
| ( SV1334
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4646]) ).
thf(5264,plain,
! [SV2202: $i,SV1879: $i,SV1336: $i,SV618: $i] :
( ( ! [SY6172: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ SV1336 @ SV1879 @ SV2202 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY6172 @ SV2202 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY6172 @ SV2202 ) @ ( c_Suc @ SV1336 ) @ SV1879 @ SV2202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4648]) ).
thf(5265,plain,
! [SV2203: $i,SV1881: $i,SV1338: $i,SV620: $i] :
( ( ! [SY6173: $i,SY6174: $i,SY6175: $i] :
( ( c_List_Ofoldr @ SV620 @ ( c_List_Omap @ SV1338 @ SV1881 @ SV2203 @ SY6173 ) @ SY6174 @ SY6173 @ SY6175 )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ SV620 @ SV1338 @ SY6173 @ ( tc_fun @ SY6175 @ SY6175 ) @ SV2203 ) @ SV1881 @ SY6174 @ SV2203 @ SY6175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4650]) ).
thf(5266,plain,
! [SV2204: $i,SV1882: $i,SV1339: $i,SV621: $i] :
( ( ! [SY6176: $i,SY6177: $i] :
( ~ ( c_Type_Otyping @ SV621 @ SV1339 @ SV1882 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SV2204 @ SV1882 @ tc_Type_Otype ) @ SY6176 @ SY6177 )
| ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY6176 ) @ SV1339 ) @ SV2204 ) @ SY6177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4651]) ).
thf(5267,plain,
! [SV2205: $i,SV1883: $i,SV1340: $i,SV622: $i] :
( ( ! [SY6178: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV622 @ SV1340 @ SV1883 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV2205 ) @ SV1340 ) @ SY6178 )
| ~ ( c_Type_Otyping @ SV622 @ SV2205 @ SY6178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4652]) ).
thf(5268,plain,
! [SV2206: $i,SV1884: $i,SV1341: $i,SV624: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV624 @ SV1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1884 ) @ SV2206 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV624 ) @ SV1884 ) @ SV2206 ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1884 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV2206 ) @ SV1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4654]) ).
thf(5269,plain,
! [SV2207: $i,SV1885: $i,SV1342: $i,SV625: $i] :
( ( ! [SY6179: $i,SY6180: $i] :
( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1885 ) @ SV2207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY6179 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SV1885 @ SY6180 @ tc_Type_Otype ) @ SV2207 @ SY6179 )
| ~ ( c_Type_Otyping @ SV625 @ SV1342 @ SY6180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4655]) ).
thf(5270,plain,
! [SV2208: $i,SV1886: $i,SV1343: $i,SV626: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV626 @ SV1343 @ SV1886 @ SV2208 ) @ SV1343 )
= SV1886 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4656]) ).
thf(5271,plain,
! [SV2209: $i,SV1887: $i,SV1344: $i,SV627: $i] :
( ( ! [SY6181: $i,SY6182: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV627 @ SV1344 @ SV1887 @ SV2209 ) @ SY6181 ) @ SY6182 )
= ( hAPP @ ( hAPP @ SV627 @ SY6182 ) @ SY6181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4657]) ).
thf(5272,plain,
! [SV2210: $i,SV1888: $i,SV1345: $i,SV628: $i] :
( ( ! [SY6183: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV628 @ SV1345 @ SV1888 @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1345 ) @ SV2210 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY6183 )
| ~ ( c_Type_Otypings @ SV628 @ SV2210 @ SY6183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4658]) ).
thf(5273,plain,
! [SV630: $i,SV1347: $i] :
( ( ( class_Orderings_Opreorder @ SV1347 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV630 @ SV1347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4660]) ).
thf(5274,plain,
! [SV631: $i,SV1348: $i] :
( ( ( class_Orderings_Oorder @ SV1348 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV631 @ SV1348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(5275,plain,
! [SV632: $i,SV1349: $i] :
( ( ( class_Orderings_Obot @ SV1349 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV632 @ SV1349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4662]) ).
thf(5276,plain,
! [SV2211: $i,SV1890: $i,SV1350: $i,SV633: $i] :
( ( ! [SY6184: $i,SY6185: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV633 @ SV1350 @ SV1890 @ SV2211 ) @ SY6184 ) @ SY6185 )
= ( hAPP @ ( hAPP @ SV633 @ SY6185 ) @ SY6184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4663]) ).
thf(5277,plain,
! [SV2212: $i,SV1891: $i,SV1351: $i,SV634: $i] :
( ( ! [SY6186: $i,SY6187: $i] :
( ( c_COMBB @ SV634 @ SV1351 @ SV1891 @ SV2212 @ SY6186 @ SY6187 )
= ( hAPP @ SV634 @ ( hAPP @ SV1351 @ SV1891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4664]) ).
thf(5278,plain,
! [SV1892: $i,SV1353: $i,SV636: $i] :
( ( ( SV636 = SV1353 )
= $true )
| ( ( ~ ( c_fequal @ SV636 @ SV1353 @ SV1892 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4665]) ).
thf(5279,plain,
! [SV2213: $i,SV1893: $i,SV1354: $i,SV637: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV637 )
| ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV1893 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV2213 ) )
| ( SV1893 = SV2213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4666]) ).
thf(5280,plain,
! [SV1894: $i,SV1355: $i,SV638: $i] :
( ( ( SV638
!= ( c_List_Oappend @ SV638 @ SV1355 @ SV1894 ) )
= $true )
| ( ( SV1355
= ( c_List_Olist_ONil @ SV1894 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4667]) ).
thf(5281,plain,
! [SV1895: $i,SV1356: $i,SV639: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV639 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1356 @ SV1895 @ SV639 )
!= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
| ( SV1356
= ( c_HOL_Ozero__class_Ozero @ SV639 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4668]) ).
thf(5282,plain,
! [SV1357: $i,SV640: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV640 @ SV1357 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( c_lessequals @ SV640 @ SV1357 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4669]) ).
thf(5283,plain,
! [SV1358: $i,SV641: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV641 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV641 ) @ SV1358 ) @ SV1358 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1358
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4670]) ).
thf(5284,plain,
! [SV1359: $i,SV642: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV642 @ ( tc_List_Olist @ SV1359 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV642
= ( c_List_Olist_ONil @ SV1359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4671]) ).
thf(5285,plain,
! [SV2214: $i,SV1896: $i,SV1360: $i,SV643: $i] :
( ( ! [SY6188: $i] :
( ( ( c_List_Omap @ SV643 @ SV1360 @ SV1896 @ SV2214 )
!= ( c_List_Omap @ SV643 @ SY6188 @ SV1896 @ SV2214 ) )
| ( ( c_Nat_Osize__class_Osize @ SV1360 @ ( tc_List_Olist @ SV1896 ) )
= ( c_Nat_Osize__class_Osize @ SY6188 @ ( tc_List_Olist @ SV1896 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4672]) ).
thf(5286,plain,
! [SV1897: $i,SV1361: $i,SV644: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
!= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
| ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4673]) ).
thf(5287,plain,
! [SV1362: $i,SV645: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV645 @ SV1362 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1362 @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1362 = SV645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4674]) ).
thf(5288,plain,
! [SV2215: $i,SV1898: $i,SV1363: $i,SV646: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV646 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV1898 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV2215 ) )
| ( SV1898 = SV2215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4675]) ).
thf(5289,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV647 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV647 )
| ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4676]) ).
thf(5290,plain,
! [SV2216: $i,SV1900: $i,SV1365: $i,SV648: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV648 ) @ SV1365 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1900 ) @ SV2216 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV648 = SV1900 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4677]) ).
thf(5291,plain,
! [SV1366: $i,SV649: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV649 ) @ SV1366 )
= SV649 )
= $false )
| ( ( SV1366
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4678]) ).
thf(5292,plain,
! [SV1901: $i,SV1367: $i,SV650: $i] :
( ( ( ( c_List_Oappend @ SV650 @ SV1367 @ SV1901 )
!= SV650 )
= $true )
| ( ( SV1367
= ( c_List_Olist_ONil @ SV1901 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4679]) ).
thf(5293,plain,
! [SV1368: $i,SV651: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV651 ) @ SV1368 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV651
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV651
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(5294,plain,
! [SV2217: $i,SV1902: $i,SV1369: $i,SV652: $i] :
( ( ( ( c_List_Olist_ONil @ SV652 )
!= ( c_List_Omap @ SV1369 @ SV1902 @ SV2217 @ SV652 ) )
| ( SV1902
= ( c_List_Olist_ONil @ SV2217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4681]) ).
thf(5295,plain,
! [SV2218: $i,SV1903: $i,SV1370: $i,SV653: $i] :
( ( ! [SY6189: $i] :
( ( ( c_List_Oappend @ SV653 @ SV1370 @ SV1903 )
!= ( c_List_Oappend @ SV2218 @ SY6189 @ SV1903 ) )
| ( SV1370
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ SV2218 @ SV1903 ) @ SY6189 @ SV1903 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ ( c_Nat_Osize__class_Osize @ SV2218 @ ( tc_List_Olist @ SV1903 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4682]) ).
thf(5296,plain,
! [SV1371: $i,SV654: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV654 ) @ SV1371 ) )
= $false )
| ( ( ( SV1371
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV654
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4683]) ).
thf(5297,plain,
! [SV2219: $i,SV1904: $i,SV1372: $i,SV655: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
!= SV2219 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 )
!= SV655 )
| ( SV1904
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
| ( ( c_List_Oappend @ SV1904 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SV2219 @ SV1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4684]) ).
thf(5298,plain,
! [SV1373: $i,SV656: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV656 ) @ SV1373 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV656
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1373
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4685]) ).
thf(5299,plain,
! [SV1905: $i,SV1374: $i,SV657: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV657 @ SV1374 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1905 @ SV1374 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV657 = SV1905 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4686]) ).
thf(5300,plain,
! [SV2220: $i,SV1906: $i,SV1375: $i,SV659: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV659 )
| ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
!= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
| ( SV1375 = SV2220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4687]) ).
thf(5301,plain,
! [SV2221: $i,SV1907: $i,SV1376: $i,SV660: $i] :
( ( ! [SY6190: $i,SY6191: $i,SY6192: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SY6190 ) ) )
| ~ ( c_Type_Otyping @ SY6191 @ SV2221 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6191 @ SY6190 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SY6192 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4688]) ).
thf(5302,plain,
! [SV1377: $i,SV661: $i] :
( ( ( SV661
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV661 ) @ SV1377 ) )
= $false )
| ( ( SV1377
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4689]) ).
thf(5303,plain,
! [SV1908: $i,SV1378: $i,SV662: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV662 ) @ SV1378 )
= ( c_Lambda_OdB_OVar @ SV1908 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4690]) ).
thf(5304,plain,
! [SV1909: $i,SV1379: $i,SV663: $i] :
( ( ( c_Lambda_OdB_OVar @ SV663 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1379 ) @ SV1909 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4691]) ).
thf(5305,plain,
! [SV1910: $i,SV1380: $i,SV664: $i] :
( ( ( ( c_List_Olist_ONil @ SV664 )
!= ( c_List_Oreplicate @ SV1380 @ SV1910 @ SV664 ) )
= $true )
| ( ( SV1380
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4692]) ).
thf(5306,plain,
! [SV2222: $i,SV1911: $i,SV1381: $i,SV665: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV665 )
| ( ( c_Power_Opower__class_Opower @ SV1381 @ SV1911 @ SV665 )
!= ( c_Power_Opower__class_Opower @ SV1381 @ SV2222 @ SV665 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 )
| ( SV1911 = SV2222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4693]) ).
thf(5307,plain,
! [SV1912: $i,SV1382: $i,SV666: $i] :
( ( ( ( hAPP @ SV666 @ ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SV1382 @ SV1912 ) )
!= ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SV1382 @ SV1912 ) )
= $true )
| ( ( ( c_List_Omap @ SV666 @ SV1382 @ SV1912 @ SV1912 )
= SV1382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4694]) ).
thf(5308,plain,
! [SV1913: $i,SV1383: $i,SV667: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV667 ) @ SV1383 )
= ( c_Lambda_OdB_OAbs @ SV1913 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4695]) ).
thf(5309,plain,
! [SV1914: $i,SV1384: $i,SV668: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV668 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV668 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1384 @ SV1914 @ SV668 )
!= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
| ( SV1384 = SV1914 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4696]) ).
thf(5310,plain,
! [SV1915: $i,SV1385: $i,SV669: $i] :
( ( ( c_Type_Otype_OAtom @ SV669 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1385 ) @ SV1915 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(5311,plain,
! [SV2223: $i,SV1916: $i,SV1386: $i,SV670: $i] :
( ( ! [SY6193: $i] :
( ( ( c_List_Oappend @ SV670 @ SV1386 @ SV1916 )
!= ( c_List_Oappend @ SV2223 @ SY6193 @ SV1916 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ SV670 @ SV1916 )
= SV2223 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV670 @ ( tc_List_Olist @ SV1916 ) ) @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4698]) ).
thf(5312,plain,
! [SV671: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV671 )
= ( c_HOL_Ozero__class_Ozero @ SV671 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV671 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4699]) ).
thf(5313,plain,
! [SV1917: $i,SV1387: $i,SV672: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV672 ) @ SV1387 )
= ( c_Type_Otype_OAtom @ SV1917 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4700]) ).
thf(5314,plain,
! [SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ! [SY6194: $i,SY6195: $i,SY6196: $i,SY6197: $i,SY6198: $i,SY6199: $i,SY6200: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SY6194 @ SY6195 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SY6196 @ SY6197 @ SY6198 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SY6194 @ SY6199 @ SY6197 @ SY6200 ) @ SY6195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4701]) ).
thf(5315,plain,
! [SV1919: $i,SV1389: $i,SV674: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV674 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1389 @ SV674 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1919 @ SV674 ) )
| ( SV1389 = SV1919 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(5316,plain,
! [SV1390: $i,SV675: $i] :
( ( ( ( c_List_Olist_ONil @ SV675 )
= ( c_List_Orev @ SV1390 @ SV675 ) )
= $false )
| ( ( SV1390
= ( c_List_Olist_ONil @ SV675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4703]) ).
thf(5317,plain,
! [SV2225: $i,SV1920: $i,SV1391: $i,SV676: $i] :
( ( ( ( c_List_Oappend @ SV676 @ SV1391 @ SV1920 )
!= ( c_List_Oappend @ SV676 @ SV2225 @ SV1920 ) )
| ( SV1391 = SV2225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4704]) ).
thf(5318,plain,
! [SV1921: $i,SV1392: $i,SV677: $i] :
( ( ( ( c_List_Otake @ SV677 @ SV1392 @ SV1921 )
!= ( c_List_Olist_ONil @ SV1921 ) )
= $true )
| ( ( ( SV1392
= ( c_List_Olist_ONil @ SV1921 ) )
| ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4705]) ).
thf(5319,plain,
! [SV2226: $i,SV1922: $i,SV1393: $i,SV678: $i] :
( ( ! [SY6201: $i,SY6202: $i,SY6203: $i,SY6204: $i,SY6205: $i] :
( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SV2226 @ SY6201 )
!= ( c_Fun_Ocomp @ SY6202 @ SY6203 @ SY6204 @ SV2226 @ SY6201 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SY6205 ) )
= ( hAPP @ SY6202 @ ( hAPP @ SY6203 @ SY6205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4706]) ).
thf(5320,plain,
! [SV1394: $i,SV679: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV679 ) @ SV1394 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV1394
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1394
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4707]) ).
thf(5321,plain,
! [SV1923: $i,SV1395: $i,SV680: $i] :
( ( ( SV680
!= ( c_List_Oappend @ SV1395 @ SV680 @ SV1923 ) )
= $true )
| ( ( SV1395
= ( c_List_Olist_ONil @ SV1923 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4708]) ).
thf(5322,plain,
! [SV1396: $i,SV681: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV681 ) @ SV1396 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1396
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4709]) ).
thf(5323,plain,
! [SV1924: $i,SV1397: $i,SV682: $i] :
( ( ( c_List_Olist_OCons @ SV682 @ SV1397 @ SV1924 )
= ( c_List_Olist_ONil @ SV1924 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(5324,plain,
! [SV1398: $i,SV683: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV683 ) @ SV1398 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV1398
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV683
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(5325,plain,
! [SV2227: $i,SV1925: $i,SV1399: $i,SV684: $i] :
( ( ! [SY6206: $i] :
( ( ( hAPP @ SV684 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SV2227 @ SY6206 ) )
!= ( hAPP @ SV1399 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SV2227 @ SY6206 ) ) )
| ( ( c_List_Omap @ SV684 @ SV1925 @ SV2227 @ SY6206 )
= ( c_List_Omap @ SV1399 @ SV1925 @ SV2227 @ SY6206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4712]) ).
thf(5326,plain,
! [SV1926: $i,SV1400: $i,SV685: $i] :
( ( ( ( c_List_Oappend @ SV685 @ SV1400 @ SV1926 )
!= ( c_List_Olist_ONil @ SV1926 ) )
= $true )
| ( ( SV685
= ( c_List_Olist_ONil @ SV1926 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4713]) ).
thf(5327,plain,
! [SV2228: $i,SV1927: $i,SV1401: $i,SV686: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV686 ) @ SV1401 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1927 ) @ SV2228 ) )
| ( SV1401 = SV2228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4714]) ).
thf(5328,plain,
! [SV2229: $i,SV1928: $i,SV1402: $i,SV687: $i] :
( ( ! [SY6207: $i] :
( ( ( c_List_Oappend @ SV687 @ ( c_List_Olist_OCons @ SV1402 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 )
!= ( c_List_Oappend @ SV2229 @ ( c_List_Olist_OCons @ SY6207 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 ) )
| ( SV1402 = SY6207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4715]) ).
thf(5329,plain,
! [SV2230: $i,SV1929: $i,SV1403: $i,SV688: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV688 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV1929 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV2230 ) )
| ( SV1929 = SV2230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4716]) ).
thf(5330,plain,
! [SV2231: $i,SV1930: $i,SV1404: $i,SV689: $i] :
( ( ! [SY6208: $i] :
( ( ( c_List_Oreplicate @ SV689 @ SV1404 @ SV1930 )
!= ( c_List_Oreplicate @ SV2231 @ SY6208 @ SV1930 ) )
| ( SV689 = SV2231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4717]) ).
thf(5331,plain,
! [SV2232: $i,SV1931: $i,SV1405: $i,SV690: $i] :
( ( ! [SY6209: $i] :
( ( ( hAPP @ SV690 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SV2232 @ SY6209 ) )
!= ( hAPP @ SV1405 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SV2232 @ SY6209 ) ) )
| ( ( c_List_Omap @ SV690 @ SV1931 @ SV2232 @ SY6209 )
= ( c_List_Omap @ SV1405 @ SV1931 @ SV2232 @ SY6209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4718]) ).
thf(5332,plain,
! [SV1406: $i,SV691: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV691 )
= ( c_Lambda_OdB_OAbs @ SV1406 ) )
= $false )
| ( ( SV691 = SV1406 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4719]) ).
thf(5333,plain,
! [SV1932: $i,SV1407: $i,SV692: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV692 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1407 ) @ SV1932 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4720]) ).
thf(5334,plain,
! [SV1933: $i,SV1408: $i,SV693: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV693 ) @ SV1408 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1933 ) @ SV1408 ) )
= $true )
| ( ( SV693 = SV1933 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4721]) ).
thf(5335,plain,
! [SV2233: $i,SV1934: $i,SV1409: $i,SV694: $i] :
( ( ! [SY6210: $i] :
( ( ( c_List_Oappend @ SV694 @ SV1409 @ SV1934 )
!= ( c_List_Oappend @ SV2233 @ SY6210 @ SV1934 ) )
| ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ SV2233 @ SV1934 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ ( c_Nat_Osize__class_Osize @ SV2233 @ ( tc_List_Olist @ SV1934 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4722]) ).
thf(5336,plain,
! [SV1935: $i,SV1410: $i,SV695: $i] :
( ( ( ( c_List_Oappend @ SV695 @ SV1410 @ SV1935 )
!= ( c_List_Olist_ONil @ SV1935 ) )
= $true )
| ( ( SV1410
= ( c_List_Olist_ONil @ SV1935 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4723]) ).
thf(5337,plain,
! [SV2234: $i,SV1936: $i,SV1411: $i,SV696: $i] :
( ( ! [SY6211: $i] :
( ( ( c_List_Olist_OCons @ SV696 @ SV1411 @ SV1936 )
!= ( c_List_Olist_OCons @ SV2234 @ SY6211 @ SV1936 ) )
| ( SV696 = SV2234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4724]) ).
thf(5338,plain,
! [SV2235: $i,SV1937: $i,SV1412: $i,SV697: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 )
!= SV697 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1937 @ ( tc_List_Olist @ SV1412 ) ) @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SV1937 @ SV2235 @ SV1412 )
= ( c_List_Oappend @ SV697 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 ) @ SV2235 @ SV1412 ) @ SV1412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4725]) ).
thf(5339,plain,
! [SV1938: $i,SV1413: $i,SV698: $i] :
( ( ( ( c_List_Olist_ONil @ SV698 )
!= ( c_List_Oappend @ SV1413 @ SV1938 @ SV698 ) )
= $true )
| ( ( SV1413
= ( c_List_Olist_ONil @ SV698 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4726]) ).
thf(5340,plain,
! [SV2236: $i,SV1939: $i,SV1414: $i,SV699: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV699 ) @ SV1414 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1939 ) @ SV2236 ) )
| ( SV699 = SV1939 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4727]) ).
thf(5341,plain,
! [SV2237: $i,SV1940: $i,SV1415: $i,SV700: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV700 ) @ SV1415 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1940 ) @ SV2237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1415 = SV2237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4728]) ).
thf(5342,plain,
! [SV1416: $i,SV701: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV701 ) @ SV1416 ) )
= $false )
| ( ( ( SV701
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV701
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4729]) ).
thf(5343,plain,
! [SV1417: $i,SV702: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV702 )
= ( c_Lambda_OdB_OVar @ SV1417 ) )
= $false )
| ( ( SV702 = SV1417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4730]) ).
thf(5344,plain,
! [SV1941: $i,SV1418: $i,SV703: $i] :
( ( SV703
= ( c_List_Olist_OCons @ SV1418 @ SV703 @ SV1941 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4731]) ).
thf(5345,plain,
! [SV2238: $i,SV1942: $i,SV1419: $i,SV704: $i] :
( ( ! [SY6212: $i] :
( ( ( c_List_Oreplicate @ SV704 @ SV1419 @ SV1942 )
!= ( c_List_Oreplicate @ SV2238 @ SY6212 @ SV1942 ) )
| ( SV1419 = SY6212 )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4732]) ).
thf(5346,plain,
! [SV1943: $i,SV1420: $i,SV706: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SV1420 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV1943 @ SV1420 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1420 @ SV1943 @ tc_nat )
| ~ ( c_lessequals @ SV1420 @ SV706 @ tc_nat )
| ( SV706 = SV1943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4733]) ).
thf(5347,plain,
! [SV1944: $i,SV1421: $i,SV707: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV707 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1421 @ SV1944 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV707 )
= SV1421 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4734]) ).
thf(5348,plain,
! [SV2239: $i,SV1945: $i,SV1422: $i,SV708: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV708 ) @ SV1422 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1945 ) @ SV2239 ) )
| ( SV708 = SV1945 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4735]) ).
thf(5349,plain,
! [SV1946: $i,SV1423: $i,SV709: $i] :
( ( ( ( c_List_Orotate @ SV709 @ SV1423 @ SV1946 )
!= ( c_List_Olist_ONil @ SV1946 ) )
= $true )
| ( ( SV1423
= ( c_List_Olist_ONil @ SV1946 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(5350,plain,
! [SV1947: $i,SV1424: $i,SV711: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV711 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1424 @ SV1947 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SV1424 = SV1947 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4737]) ).
thf(5351,plain,
! [SV2240: $i,SV1948: $i,SV1425: $i,SV712: $i] :
( ( ! [SY6213: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
!= ( c_HOL_Ominus__class_Ominus @ SV2240 @ SY6213 @ SV712 ) )
| ( c_HOL_Oord__class_Oless @ SV2240 @ SY6213 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4738]) ).
thf(5352,plain,
! [SV2241: $i,SV1949: $i,SV1426: $i,SV713: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV713 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1426 ) @ SV1949 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SV2241 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SV1949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4739]) ).
thf(5353,plain,
! [SV1950: $i,SV1427: $i,SV714: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV714 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV714 )
| ( SV1427
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SV1427 ) @ SV1950 ) )
| ( SV1950
= ( c_HOL_Ozero__class_Ozero @ SV714 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4740]) ).
thf(5354,plain,
! [SV1951: $i,SV1428: $i,SV715: $i] :
( ( ( ( c_List_Orev @ SV715 @ SV1428 )
!= ( c_List_Orev @ SV1951 @ SV1428 ) )
= $true )
| ( ( SV715 = SV1951 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4741]) ).
thf(5355,plain,
! [SV1952: $i,SV1429: $i,SV716: $i] :
( ( ( ( c_List_Olist_ONil @ SV716 )
!= ( c_List_Oappend @ SV1429 @ SV1952 @ SV716 ) )
= $true )
| ( ( SV1952
= ( c_List_Olist_ONil @ SV716 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4742]) ).
thf(5356,plain,
! [SV1430: $i,SV717: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV717 ) @ SV1430 ) )
= $false )
| ( ( ( SV717
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1430
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4743]) ).
thf(5357,plain,
! [SV2242: $i,SV1953: $i,SV1431: $i,SV718: $i] :
( ( ( ( c_List_Omap @ SV718 @ SV1431 @ SV1953 @ SV2242 )
!= ( c_List_Olist_ONil @ SV2242 ) )
| ( SV1431
= ( c_List_Olist_ONil @ SV1953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4744]) ).
thf(5358,plain,
! [SV2243: $i,SV1954: $i,SV1432: $i,SV719: $i] :
( ( ( ( c_List_Orev @ SV719 @ SV1432 )
!= ( c_List_Olist_OCons @ SV1954 @ SV2243 @ SV1432 ) )
| ( SV719
= ( c_List_Oappend @ ( c_List_Orev @ SV2243 @ SV1432 ) @ ( c_List_Olist_OCons @ SV1954 @ ( c_List_Olist_ONil @ SV1432 ) @ SV1432 ) @ SV1432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4745]) ).
thf(5359,plain,
! [SV2244: $i,SV1955: $i,SV1433: $i,SV720: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV720 ) @ SV1433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1955 ) @ SV2244 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4746]) ).
thf(5360,plain,
! [SV2245: $i,SV1956: $i,SV1434: $i,SV721: $i] :
( ( ! [SY6214: $i] :
( ( ( c_List_Olist_OCons @ SV721 @ SV1434 @ SV1956 )
!= ( c_List_Olist_OCons @ SV2245 @ SY6214 @ SV1956 ) )
| ( SV1434 = SY6214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4747]) ).
thf(5361,plain,
! [SV2246: $i,SV1957: $i,SV1435: $i,SV722: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV722 ) @ SV1435 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1957 ) @ SV2246 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1957 @ SV1435 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV722 @ SV2246 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4748]) ).
thf(5362,plain,
! [SV2247: $i,SV1958: $i,SV1436: $i,SV723: $i] :
( ( ( ( c_List_Olist__update @ SV723 @ SV1436 @ SV1958 @ SV2247 )
!= ( c_List_Olist_ONil @ SV2247 ) )
| ( SV723
= ( c_List_Olist_ONil @ SV2247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4749]) ).
thf(5363,plain,
! [SV1437: $i,SV724: $i] :
( ( ( ( c_List_Orev @ SV724 @ SV1437 )
= ( c_List_Olist_ONil @ SV1437 ) )
= $false )
| ( ( SV724
= ( c_List_Olist_ONil @ SV1437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4750]) ).
thf(5364,plain,
! [SV2248: $i,SV1959: $i,SV1438: $i,SV725: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV725 ) @ SV1438 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1959 ) @ SV2248 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV725 = SV1959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4751]) ).
thf(5365,plain,
! [SV2249: $i,SV1960: $i,SV1439: $i,SV726: $i] :
( ( ! [SY6215: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
!= ( c_HOL_Ominus__class_Ominus @ SV2249 @ SY6215 @ SV726 ) )
| ( c_lessequals @ SY6215 @ SV2249 @ SV726 )
| ~ ( c_lessequals @ SV1960 @ SV1439 @ SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4752]) ).
thf(5366,plain,
! [SV1961: $i,SV1440: $i,SV727: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SV1440 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SV1961 ) )
= $true )
| ( ( SV1440 = SV1961 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4753]) ).
thf(5367,plain,
! [SV2250: $i,SV1962: $i,SV1441: $i,SV728: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV728 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1441 @ SV1441 @ SV728 )
!= ( c_HOL_Ominus__class_Ominus @ SV1962 @ SV2250 @ SV728 ) )
| ( SV1962 = SV2250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4754]) ).
thf(5368,plain,
! [SV1442: $i,SV729: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV729 )
| ~ ( class_Power_Opower @ SV729 )
| ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4755]) ).
thf(5369,plain,
! [SV1963: $i,SV1443: $i,SV730: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(5370,plain,
! [SV1964: $i,SV1444: $i,SV731: $i] :
( ( ( ( c_List_Oreplicate @ SV731 @ SV1444 @ SV1964 )
!= ( c_List_Olist_ONil @ SV1964 ) )
= $true )
| ( ( SV731
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(5371,plain,
! [SV732: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV732 )
= ( c_HOL_Oone__class_Oone @ SV732 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV732 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4758]) ).
thf(5372,plain,
! [SV1445: $i,SV733: $i] :
( ( ( ( c_Suc @ SV733 )
= ( c_Suc @ SV1445 ) )
= $false )
| ( ( SV733 = SV1445 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(5373,plain,
! [SV2251: $i,SV1965: $i,SV1446: $i,SV734: $i] :
( ( ! [SY6216: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV734 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2251 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SY6216 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ SV2251 )
= SY6216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4760]) ).
thf(5374,plain,
! [SV1966: $i,SV1447: $i,SV735: $i] :
( ( ( ( c_List_Orev @ SV735 @ SV1447 )
!= ( c_List_Olist_OCons @ SV1966 @ ( c_List_Olist_ONil @ SV1447 ) @ SV1447 ) )
= $true )
| ( ( SV735
= ( c_List_Olist_OCons @ SV1966 @ ( c_List_Olist_ONil @ SV1447 ) @ SV1447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(5375,plain,
! [SV1967: $i,SV1448: $i,SV736: $i] :
( ( ( ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SV1448 ) @ SV1448 )
!= ( c_List_Orev @ SV1967 @ SV1448 ) )
= $true )
| ( ( SV1967
= ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SV1448 ) @ SV1448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(5376,plain,
! [SV1449: $i,SV737: $i] :
( ( ( ( c_Suc @ SV737 )
= ( c_Suc @ SV1449 ) )
= $false )
| ( ( SV737 = SV1449 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4763]) ).
thf(5377,plain,
! [SV1968: $i,SV1450: $i,SV738: $i] :
( ( ( SV738
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SV1450 ) ) @ SV1968 @ SV1450 ) )
= $true )
| ( ( ( c_List_Oappend @ SV738 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SV1450 ) ) @ SV1968 @ SV1450 ) @ SV1450 )
= SV1968 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4764]) ).
thf(5378,plain,
! [SV2252: $i,SV1969: $i,SV1451: $i,SV740: $i] :
( ( ! [SY6217: $i] :
( ( ( hAPP @ SV740 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SV2252 @ SY6217 ) )
!= ( hAPP @ SV1451 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SV2252 @ SY6217 ) ) )
| ( ( c_List_Omap @ SV740 @ SV1969 @ SV2252 @ SY6217 )
= ( c_List_Omap @ SV1451 @ SV1969 @ SV2252 @ SY6217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4765]) ).
thf(5379,plain,
! [SV2253: $i,SV1970: $i,SV1452: $i,SV741: $i] :
( ( ( SV741
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) )
| ( ( c_List_Oappend @ SV741 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) @ SV2253 @ SV1452 ) @ SV1452 )
= ( c_List_Oappend @ SV1970 @ SV2253 @ SV1452 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ ( c_Nat_Osize__class_Osize @ SV1970 @ ( tc_List_Olist @ SV1452 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4766]) ).
thf(5380,plain,
! [SV2254: $i,SV1971: $i,SV1453: $i,SV742: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV742 ) ) @ SV1453 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1971 ) @ SV2254 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4767]) ).
thf(5381,plain,
! [SV2255: $i,SV1972: $i,SV1454: $i,SV744: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV744 ) @ SV1454 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1972 ) @ SV2255 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1454 = SV2255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4768]) ).
thf(5382,plain,
! [SV1973: $i,SV1455: $i,SV745: $i] :
( ( ( c_List_Olist_OCons @ SV745 @ SV1455 @ SV1973 )
= SV1455 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4769]) ).
thf(5383,plain,
! [SV1456: $i,SV746: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV746 )
= ( c_Type_Otype_OAtom @ SV1456 ) )
= $false )
| ( ( SV746 = SV1456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4770]) ).
thf(5384,plain,
! [SV1457: $i,SV747: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV747 ) @ SV1457 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV747
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4771]) ).
thf(5385,plain,
! [SV2256: $i,SV1974: $i,SV1458: $i,SV749: $i] :
( ( ! [SY6218: $i] :
( ( ( c_List_Oappend @ SV749 @ SV1458 @ SV1974 )
!= ( c_List_Oappend @ SV2256 @ SY6218 @ SV1974 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ SV749 @ SV1974 ) @ SV1458 @ SV1974 )
= SY6218 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV749 @ ( tc_List_Olist @ SV1974 ) ) @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4772]) ).
thf(5386,plain,
! [SV2257: $i,SV1975: $i,SV1459: $i,SV750: $i] :
( ( ! [SY6219: $i,SY6220: $i,SY6221: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SY6219 ) ) )
| ~ ( c_Type_Otyping @ SY6220 @ SV2257 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6220 @ SY6219 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SY6221 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4773]) ).
thf(5387,plain,
! [SV1976: $i,SV1460: $i,SV751: $i] :
( ( ( ( c_List_Oappend @ SV751 @ SV1460 @ SV1976 )
!= SV1460 )
= $true )
| ( ( SV751
= ( c_List_Olist_ONil @ SV1976 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(5388,plain,
! [SV1977: $i,SV1462: $i,SV753: $i] :
( ( ( c_List_Olist_ONil @ SV753 )
= ( c_List_Olist_OCons @ SV1462 @ SV1977 @ SV753 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4776]) ).
thf(5389,plain,
! [SV1978: $i,SV1463: $i,SV754: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SV1463 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SV1978 ) )
= $true )
| ( ( SV1463 = SV1978 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4777]) ).
thf(5390,plain,
! [SV2258: $i,SV1979: $i,SV1464: $i,SV755: $i] :
( ( ! [SY6222: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
!= ( c_HOL_Ominus__class_Ominus @ SV2258 @ SY6222 @ SV755 ) )
| ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SV2258 @ SY6222 @ SV755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4778]) ).
thf(5391,plain,
! [SV1980: $i,SV1465: $i,SV756: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV756 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV1465 @ SV1980 @ SV756 )
!= SV1980 )
| ( c_lessequals @ SV1465 @ SV1980 @ SV756 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(5392,plain,
! [SV2259: $i,SV1981: $i,SV1466: $i,SV757: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV757 )
| ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
!= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
| ( SV1466 = SV2259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4780]) ).
thf(5393,plain,
! [SV1982: $i,SV1467: $i,SV758: $i] :
( ( ( ( c_List_Odrop @ SV758 @ SV1467 @ SV1982 )
!= ( c_List_Olist_ONil @ SV1982 ) )
= $true )
| ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1467 @ ( tc_List_Olist @ SV1982 ) ) @ SV758 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4781]) ).
thf(5394,plain,
! [SV2260: $i,SV1983: $i,SV1468: $i,SV759: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1468 ) @ SV1983 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV2260 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV1468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4782]) ).
thf(5395,plain,
! [SV1984: $i,SV1469: $i,SV760: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV760 @ SV1469 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1984 ) )
= $true )
| ( ( SV760
= ( c_Lambda_OdB_OAbs @ SV1984 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(5396,plain,
! [SV1985: $i,SV1470: $i,SV761: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV761 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1470 @ SV1985 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV761 )
= SV1470 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(5397,plain,
! [SV2261: $i,SV1986: $i,SV1471: $i,SV762: $i] :
( ( ( ( c_List_Oappend @ SV762 @ SV1471 @ SV1986 )
!= ( c_List_Oappend @ SV2261 @ SV1471 @ SV1986 ) )
| ( SV762 = SV2261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4785]) ).
thf(5398,plain,
! [SV1987: $i,SV1472: $i,SV763: $i] :
( ( ( c_List_Olist_OCons @ SV763 @ SV1472 @ SV1987 )
= ( c_List_Olist_ONil @ SV1987 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4786]) ).
thf(5399,plain,
! [SV2262: $i,SV1988: $i,SV1473: $i,SV764: $i] :
( ( ! [SY6223: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
!= ( c_HOL_Ominus__class_Ominus @ SV2262 @ SY6223 @ SV764 ) )
| ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
| ~ ( c_lessequals @ SY6223 @ SV2262 @ SV764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4787]) ).
thf(5400,plain,
! [SV2263: $i,SV1989: $i,SV1474: $i,SV765: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV765 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1474 @ SV1989 @ SV765 )
!= ( c_HOL_Ominus__class_Ominus @ SV2263 @ SV2263 @ SV765 ) )
| ( SV1474 = SV1989 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4788]) ).
thf(5401,plain,
! [SV2264: $i,SV1990: $i,SV1476: $i,SV767: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV767 ) @ SV1476 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1990 ) @ SV2264 ) )
| ( SV1476 = SV2264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4790]) ).
thf(5402,plain,
! [SV1991: $i,SV1477: $i,SV768: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV768 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV1991 @ SV768 )
!= ( c_HOL_Ozero__class_Ozero @ SV768 ) )
| ( SV1477 = SV1991 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4791]) ).
thf(5403,plain,
! [SV1478: $i,SV769: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV769 ) @ SV1478 ) )
= $false )
| ( ( ( SV1478
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1478
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4792]) ).
thf(5404,plain,
! [SV2265: $i,SV1992: $i,SV1479: $i,SV770: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV770 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV1479 ) @ SV1992 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV2265 ) @ SV1992 ) )
| ( SV1479 = SV2265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4793]) ).
thf(5405,plain,
! [SV2266: $i,SV1993: $i,SV1480: $i,SV771: $i] :
( ( ! [SY6224: $i] :
( ( ( c_List_Oappend @ SV771 @ ( c_List_Olist_OCons @ SV1480 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 )
!= ( c_List_Oappend @ SV2266 @ ( c_List_Olist_OCons @ SY6224 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 ) )
| ( SV771 = SV2266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4794]) ).
thf(5406,plain,
! [SV772: $i,SV1: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ SV772 ) @ SV772 ) @ SV1 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV772 @ SV1 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4795]) ).
thf(5407,plain,
! [SV773: $i,SV2: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV773 @ SV2 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV773 ) @ SV773 ) @ SV2 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4796]) ).
thf(5408,plain,
! [SV1481: $i,SV775: $i,SV7: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV7 )
= $false )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV7 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1481 @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV775 @ SV1481 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(5409,plain,
! [SV1482: $i,SV776: $i,SV8: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV8 )
= $false )
| ( ( ( c_lessequals @ SV776 @ SV1482 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV776 @ SV8 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1482 @ SV8 ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4798]) ).
thf(5410,plain,
! [SV1484: $i,SV778: $i,SV10: $i] :
( ( ( ~ ( c_lessequals @ SV10 @ SV778 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1484 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV10 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV778 ) @ SV1484 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4799]) ).
thf(5411,plain,
! [SV1994: $i,SV1485: $i,SV779: $i,SV11: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
| ~ ( c_lessequals @ SV779 @ SV1994 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4800]) ).
thf(5412,plain,
! [SV1487: $i,SV14: $i,SV782: $i] :
( ( ( c_lessequals @ SV782 @ SV14 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV14 @ SV782 @ tc_nat ) ) @ SV1487 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV14 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV782 ) @ SV1487 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4802]) ).
thf(5413,plain,
! [SV1996: $i,SV1488: $i,SV783: $i,SV15: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV15 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SV1488 @ SV15 ) @ SV1996 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV1488 @ SV1996 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV1996 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4803]) ).
thf(5414,plain,
! [SV1489: $i,SV785: $i,SV17: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV17 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV785 @ SV1489 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV785 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4805]) ).
thf(5415,plain,
! [SV786: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV18 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV18 @ SV786 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(5416,plain,
! [SV1490: $i,SV788: $i,SV20: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV788 @ SV1490 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ SV788 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4807]) ).
thf(5417,plain,
! [SV789: $i,SV21: $i] :
( ( ( ~ ( class_Power_Opower @ SV21 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ ( c_Suc @ SV789 ) @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(5418,plain,
! [SV1997: $i,SV1491: $i,SV792: $i,SV24: $i] :
( ( ( ( c_List_Orev @ ( c_List_Olist__update @ SV24 @ SV792 @ SV1491 @ SV1997 ) @ SV1997 )
= ( c_List_Olist__update @ ( c_List_Orev @ SV24 @ SV1997 ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV1997 ) ) @ SV792 @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1491 @ SV1997 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV792 @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV1997 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4809]) ).
thf(5419,plain,
! [SV793: $i,SV1492: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ SV1492 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1492 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV25 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV793 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(5420,plain,
! [SV797: $i,SV1493: $i,SV29: $i] :
( ( ( ~ ( c_lessequals @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ SV797 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV797 @ SV1493 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV797 ) @ SV1493 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(5421,plain,
! [SV798: $i,SV1494: $i,SV30: $i] :
( ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV30 ) @ SV1494 ) @ SV798 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1494 @ SV798 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV30 @ ( c_HOL_Ominus__class_Ominus @ SV798 @ SV1494 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4812]) ).
thf(5422,plain,
! [SV1998: $i,SV1495: $i,SV799: $i,SV31: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV31 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SV1495 @ SV31 ) @ SV1998 @ SV31 )
| ~ ( c_lessequals @ SV1495 @ SV1998 @ SV31 )
| ~ ( c_lessequals @ SV799 @ SV1998 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4813]) ).
thf(5423,plain,
! [SV1999: $i,SV1496: $i,SV800: $i,SV32: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV32 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SV1496 @ SV32 ) @ SV1999 @ SV32 )
| ~ ( c_lessequals @ SV1496 @ SV1999 @ SV32 )
| ~ ( c_lessequals @ SV800 @ SV1999 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4814]) ).
thf(5424,plain,
! [SV2000: $i,SV1497: $i,SV801: $i,SV33: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV33 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SV1497 @ SV33 ) @ SV2000 @ SV33 )
| ~ ( c_lessequals @ SV1497 @ SV2000 @ SV33 )
| ~ ( c_lessequals @ SV801 @ SV2000 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4815]) ).
thf(5425,plain,
! [SV1498: $i,SV802: $i,SV34: $i] :
( ( ( class_Orderings_Olinorder @ SV34 )
= $false )
| ( ( c_lessequals @ SV802 @ ( c_Orderings_Oord__class_Omax @ SV802 @ SV1498 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4816]) ).
thf(5426,plain,
! [SV1499: $i,SV803: $i,SV35: $i] :
( ( ( class_Orderings_Olinorder @ SV35 )
= $false )
| ( ( c_lessequals @ SV803 @ ( c_Orderings_Oord__class_Omax @ SV1499 @ SV803 @ SV35 ) @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4817]) ).
thf(5427,plain,
! [SV810: $i,SV1500: $i,SV42: $i] :
( ( ( c_List_Odistinct @ ( c_List_Oappend @ SV42 @ SV1500 @ SV810 ) @ SV810 )
= $false )
| ( ( c_List_Odistinct @ SV42 @ SV810 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4819]) ).
thf(5428,plain,
! [SV811: $i,SV43: $i,SV1501: $i] :
( ( ( c_List_Odistinct @ ( c_List_Oappend @ SV1501 @ SV43 @ SV811 ) @ SV811 )
= $false )
| ( ( c_List_Odistinct @ SV43 @ SV811 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4820]) ).
thf(5429,plain,
! [SV2001: $i,SV1502: $i,SV815: $i,SV47: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV47 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4821]) ).
thf(5430,plain,
! [SV2002: $i,SV1504: $i,SV817: $i,SV49: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
| ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
| ~ ( c_lessequals @ SV817 @ SV2002 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4822]) ).
thf(5431,plain,
! [SV2003: $i,SV1505: $i,SV818: $i,SV50: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
| ~ ( c_lessequals @ SV818 @ SV1505 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4823]) ).
thf(5432,plain,
! [SV819: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ SV51 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV51 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV51 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV51 @ SV819 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(5433,plain,
! [SV1506: $i,SV824: $i,SV56: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV56 @ SV824 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV56 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV824 ) @ SV1506 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4829]) ).
thf(5434,plain,
! [SV825: $i,SV1507: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV57 @ SV1507 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV57 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV825 ) @ SV1507 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4830]) ).
thf(5435,plain,
! [SV826: $i,SV1508: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SV1508 ) @ SV826 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV58 @ SV826 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4831]) ).
thf(5436,plain,
! [SV1509: $i,SV827: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV59 @ SV827 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV59 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV827 ) @ SV1509 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4832]) ).
thf(5437,plain,
! [SV828: $i,SV1510: $i,SV60: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV60 @ SV1510 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV60 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV828 ) @ SV1510 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4833]) ).
thf(5438,plain,
! [SV2004: $i,SV1511: $i,SV829: $i,SV61: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV61 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
| ~ ( c_lessequals @ SV2004 @ SV1511 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4834]) ).
thf(5439,plain,
! [SV1513: $i,SV832: $i,SV65: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV65 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV832 ) @ SV1513 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV1513 ) @ SV832 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4836]) ).
thf(5440,plain,
! [SV1514: $i,SV833: $i,SV66: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV66 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SV833 ) @ SV1514 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV66 ) @ SV1514 ) @ SV833 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4837]) ).
thf(5441,plain,
! [SV1515: $i,SV835: $i,SV68: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV835 ) @ SV1515 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV1515 ) @ SV835 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4838]) ).
thf(5442,plain,
! [SV2005: $i,SV1516: $i,SV836: $i,SV69: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV69 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ SV1516 ) @ SV2005 @ SV69 @ SV69 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1516 @ SV2005 @ SV69 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4839]) ).
thf(5443,plain,
! [SV838: $i,SV71: $i,SV1518: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV71 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV838 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV838 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV1518 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4840]) ).
thf(5444,plain,
! [SV1519: $i,SV839: $i,SV72: $i] :
( ( ( c_Type_Otyping @ SV72 @ ( c_Lambda_OdB_OVar @ SV839 ) @ SV1519 )
= $false )
| ( ( ( hAPP @ SV72 @ SV839 )
= SV1519 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4841]) ).
thf(5445,plain,
! [SV2007: $i,SV1521: $i,SV841: $i,SV74: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV74 ) )
= $true )
| ( ( ( c_lessequals @ SV841 @ SV1521 @ SV74 )
| ( c_lessequals @ SV841 @ SV2007 @ SV74 )
| ~ ( c_lessequals @ SV841 @ ( c_Orderings_Oord__class_Omax @ SV2007 @ SV1521 @ SV74 ) @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(5446,plain,
! [SV2008: $i,SV1522: $i,SV842: $i,SV75: $i] :
( ( ( c_List_Olistsp @ SV75 @ SV842 @ SV1522 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV75 @ ( c_List_Oappend @ SV2008 @ SV842 @ SV1522 ) @ SV1522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(5447,plain,
! [SV2009: $i,SV1523: $i,SV843: $i,SV76: $i] :
( ( ( c_List_Olistsp @ SV76 @ SV843 @ SV1523 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV76 @ ( c_List_Oappend @ SV843 @ SV2009 @ SV1523 ) @ SV1523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4845]) ).
thf(5448,plain,
! [SV844: $i,SV1524: $i,SV77: $i] :
( ( ( SV77 = SV1524 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1524 @ SV77 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV77 ) ) @ SV844 ) @ SV1524 )
= ( c_Lambda_OdB_OVar @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4846]) ).
thf(5449,plain,
! [SV1525: $i,SV845: $i,SV78: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV78 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ ( c_HOL_Ominus__class_Ominus @ SV845 @ SV1525 @ SV78 ) ) @ SV1525 )
= SV845 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4847]) ).
thf(5450,plain,
! [SV1527: $i,SV847: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ SV80 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV847 ) @ SV1527 ) @ SV847 @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV80 @ SV1527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4848]) ).
thf(5451,plain,
! [SV1528: $i,SV848: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ SV81 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV848 ) @ SV1528 ) @ SV848 @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV81 @ SV1528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(5452,plain,
! [SV2010: $i,SV1530: $i,SV850: $i,SV83: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV83 ) @ SV850 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1530 ) @ SV2010 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV850 @ SV2010 @ tc_nat )
| ~ ( c_lessequals @ SV83 @ SV1530 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4850]) ).
thf(5453,plain,
! [SV2267: $i,SV2011: $i,SV1531: $i,SV851: $i,SV84: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV2011 ) @ SV2267 ) @ SV84 )
| ~ ( c_lessequals @ SV1531 @ SV2267 @ SV84 )
| ~ ( c_lessequals @ SV851 @ SV2011 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4851]) ).
thf(5454,plain,
! [SV2268: $i,SV2012: $i,SV1533: $i,SV853: $i,SV86: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV86 @ SV853 @ SV1533 ) @ SV2012 @ SV2268 @ SV1533 )
= ( c_List_Oappend @ SV86 @ ( c_List_Olist__update @ SV853 @ ( c_HOL_Ominus__class_Ominus @ SV2012 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SV1533 ) ) @ tc_nat ) @ SV2268 @ SV1533 ) @ SV1533 ) )
| ( c_HOL_Oord__class_Oless @ SV2012 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SV1533 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4852]) ).
thf(5455,plain,
! [SV87: $i,SV1534: $i,SV854: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV854 @ ( tc_List_Olist @ SV1534 ) ) @ SV87 @ tc_nat )
= $false )
| ( ( ( c_List_Otake @ SV87 @ SV854 @ SV1534 )
= SV854 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4853]) ).
thf(5456,plain,
! [SV92: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(5457,plain,
! [SV1536: $i,SV860: $i,SV95: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV860 ) @ SV1536 ) @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1536 @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV860 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4859]) ).
thf(5458,plain,
! [SV1537: $i,SV861: $i,SV96: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV96 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV861 @ ( c_Suc @ SV1537 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV861 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4860]) ).
thf(5459,plain,
! [SV2014: $i,SV1538: $i,SV862: $i,SV97: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV97 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV862 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV2014 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV862 @ SV2014 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(5460,plain,
! [SV2015: $i,SV1539: $i,SV863: $i,SV98: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV98 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1539 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV2015 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV2015 @ SV1539 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4862]) ).
thf(5461,plain,
! [SV1540: $i,SV864: $i,SV99: $i] :
( ( ( class_Orderings_Olinorder @ SV99 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV864 @ SV1540 @ SV99 )
= SV1540 )
| ~ ( c_lessequals @ SV864 @ SV1540 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4863]) ).
thf(5462,plain,
! [SV1541: $i,SV865: $i,SV100: $i] :
( ( ( class_Orderings_Olinorder @ SV100 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV865 @ SV1541 @ SV100 )
= SV865 )
| ~ ( c_lessequals @ SV1541 @ SV865 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4864]) ).
thf(5463,plain,
! [SV2016: $i,SV1542: $i,SV866: $i,SV101: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV1542 ) @ SV2016 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ SV1542 ) ) @ SV2016 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4865]) ).
thf(5464,plain,
! [SV2017: $i,SV1543: $i,SV867: $i,SV102: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV102 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV1543 ) @ SV2017 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV1543 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ SV2017 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(5465,plain,
! [SV2018: $i,SV1546: $i,SV870: $i,SV105: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV105 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ SV1546 ) ) @ SV2018 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV1546 ) @ SV2018 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4867]) ).
thf(5466,plain,
! [SV2019: $i,SV1547: $i,SV871: $i,SV106: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV106 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV1547 ) @ SV2019 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV1547 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ SV2019 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4868]) ).
thf(5467,plain,
! [SV2020: $i,SV1548: $i,SV872: $i,SV107: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV107 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ SV1548 ) ) @ SV2020 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV1548 ) @ SV2020 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4869]) ).
thf(5468,plain,
! [SV2021: $i,SV1549: $i,SV873: $i,SV108: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV108 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV1549 ) @ SV2021 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ SV1549 ) ) @ SV2021 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4870]) ).
thf(5469,plain,
! [SV2022: $i,SV1550: $i,SV874: $i,SV109: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV109 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SV1550 ) ) @ SV2022 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SV2022 ) ) @ SV1550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4871]) ).
thf(5470,plain,
! [SV2023: $i,SV1551: $i,SV875: $i,SV110: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV1551 ) @ SV2023 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ SV2023 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4872]) ).
thf(5471,plain,
! [SV2024: $i,SV1552: $i,SV876: $i,SV111: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV111 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ SV1552 ) ) @ SV2024 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV1552 ) @ SV2024 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5472,plain,
! [SV112: $i,SV877: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV877 ) @ SV112 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV877 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV112 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4874]) ).
thf(5473,plain,
! [SV881: $i,SV1556: $i,SV116: $i] :
( ( ( c_lessequals @ SV116 @ SV1556 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV116 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV881 ) @ SV1556 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4876]) ).
thf(5474,plain,
! [SV1557: $i,SV882: $i,SV117: $i] :
( ( ( c_lessequals @ SV117 @ SV882 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV117 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV882 ) @ SV1557 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4877]) ).
thf(5475,plain,
! [SV883: $i,SV118: $i,SV1558: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1558 ) @ SV118 ) @ SV883 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV118 @ SV883 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4878]) ).
thf(5476,plain,
! [SV884: $i,SV1559: $i,SV119: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV119 ) @ SV1559 ) @ SV884 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV119 @ SV884 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4879]) ).
thf(5477,plain,
! [SV885: $i,SV1560: $i,SV120: $i] :
( ( ( c_lessequals @ SV120 @ SV1560 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV120 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV885 ) @ SV1560 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4880]) ).
thf(5478,plain,
! [SV1561: $i,SV886: $i,SV121: $i] :
( ( ( c_lessequals @ SV121 @ SV886 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV121 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV886 ) @ SV1561 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4881]) ).
thf(5479,plain,
! [SV2026: $i,SV1563: $i,SV890: $i,SV125: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV125 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV890 @ SV1563 @ SV125 ) @ SV2026 @ SV125 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV2026 @ SV125 ) @ ( c_HOL_Ominus__class_Ominus @ SV1563 @ SV2026 @ SV125 ) @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4883]) ).
thf(5480,plain,
! [SV1566: $i,SV893: $i,SV128: $i] :
( ( ( class_Orderings_Olinorder @ SV128 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV893 @ SV1566 @ SV128 )
| ( c_lessequals @ SV1566 @ SV893 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4885]) ).
thf(5481,plain,
! [SV129: $i,SV894: $i] :
( ( ( ~ ( c_lessequals @ SV894 @ SV894 @ SV129 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV894 @ SV129 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4886]) ).
thf(5482,plain,
! [SV130: $i,SV895: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV895 @ SV895 @ SV130 )
= $true )
| ( ( c_lessequals @ SV895 @ SV895 @ SV130 )
= $true )
| ( ( class_Orderings_Olinorder @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4887]) ).
thf(5483,plain,
! [SV1567: $i,SV896: $i,SV131: $i] :
( ( ( class_Orderings_Olinorder @ SV131 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV896 @ SV1567 @ SV131 )
| ~ ( c_lessequals @ SV1567 @ SV896 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4888]) ).
thf(5484,plain,
! [SV1568: $i,SV897: $i,SV132: $i] :
( ( ( class_Orderings_Olinorder @ SV132 )
= $false )
| ( ( ( c_lessequals @ SV897 @ SV1568 @ SV132 )
| ( c_HOL_Oord__class_Oless @ SV1568 @ SV897 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4889]) ).
thf(5485,plain,
! [SV1569: $i,SV898: $i,SV133: $i] :
( ( ( class_Orderings_Olinorder @ SV133 )
= $false )
| ( ( ~ ( c_lessequals @ SV898 @ SV1569 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SV1569 @ SV898 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4890]) ).
thf(5486,plain,
! [SV1570: $i,SV899: $i,SV134: $i] :
( ( ( class_Orderings_Olinorder @ SV134 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV899 @ SV1570 @ SV134 )
| ( c_lessequals @ SV1570 @ SV899 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4891]) ).
thf(5487,plain,
! [SV1571: $i,SV900: $i,SV135: $i] :
( ( ( class_Orderings_Opreorder @ SV135 )
= $false )
| ( ( ~ ( c_lessequals @ SV900 @ SV1571 @ SV135 )
| ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV900 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4892]) ).
thf(5488,plain,
! [SV901: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ SV136 @ ( 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 @ SV136 ) @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV901 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(5489,plain,
! [SV2028: $i,SV1572: $i,SV904: $i,SV139: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
| ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
| ~ ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4895]) ).
thf(5490,plain,
! [SV2029: $i,SV1573: $i,SV905: $i,SV140: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV140 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SV1573 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SV2029 @ SV140 ) @ SV140 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 )
| ~ ( c_lessequals @ SV1573 @ SV2029 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4896]) ).
thf(5491,plain,
! [SV141: $i,SV906: $i,SV1574: $i] :
( ( ( c_lessequals @ SV1574 @ SV906 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV906 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV1574 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4897]) ).
thf(5492,plain,
! [SV907: $i,SV1575: $i,SV142: $i] :
( ( ( c_lessequals @ SV142 @ SV1575 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV142 @ SV907 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1575 @ SV907 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4898]) ).
thf(5493,plain,
! [SV908: $i,SV1576: $i,SV143: $i] :
( ( ( ~ ( c_lessequals @ SV143 @ SV1576 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV908 @ SV1576 @ tc_nat )
| ~ ( c_lessequals @ SV908 @ SV143 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SV908 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV908 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4899]) ).
thf(5494,plain,
! [SV909: $i,SV1577: $i,SV144: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SV1577 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV909 @ SV1577 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1577 @ SV909 @ tc_nat )
| ~ ( c_lessequals @ SV1577 @ SV144 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV144 @ SV909 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4900]) ).
thf(5495,plain,
! [SV2030: $i,SV1579: $i,SV912: $i,SV147: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV147 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SV1579 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SV2030 @ SV1579 @ SV147 ) @ SV147 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 )
| ~ ( c_lessequals @ SV912 @ SV2030 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4901]) ).
thf(5496,plain,
! [SV2269: $i,SV2031: $i,SV1581: $i,SV915: $i,SV151: $i] :
( ( ! [SY6225: $i] :
( ( c_List_Ofoldl @ SV151 @ SV915 @ ( c_List_Olist_OCons @ SV1581 @ SV2031 @ SV2269 ) @ SY6225 @ SV2269 )
= ( c_List_Ofoldl @ SV151 @ ( hAPP @ ( hAPP @ SV151 @ SV915 ) @ SV1581 ) @ SV2031 @ SY6225 @ SV2269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4903]) ).
thf(5497,plain,
! [SV2033: $i,SV1585: $i,SV921: $i,SV159: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV159 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV921 @ ( c_Orderings_Oord__class_Omax @ SV1585 @ SV2033 @ SV159 ) @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV921 @ SV1585 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(5498,plain,
! [SV2034: $i,SV1586: $i,SV922: $i,SV160: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV160 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV922 @ ( c_Orderings_Oord__class_Omax @ SV1586 @ SV2034 @ SV160 ) @ SV160 )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV2034 @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4906]) ).
thf(5499,plain,
! [SV2035: $i,SV1587: $i,SV923: $i,SV161: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV161 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Orderings_Oord__class_Omax @ SV1587 @ SV2035 @ SV161 ) @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV923 @ SV1587 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4907]) ).
thf(5500,plain,
! [SV2036: $i,SV1588: $i,SV924: $i,SV162: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV162 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Orderings_Oord__class_Omax @ SV1588 @ SV2036 @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2036 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4908]) ).
thf(5501,plain,
! [SV2037: $i,SV1589: $i,SV925: $i,SV163: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV163 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1589 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV925 @ SV2037 @ SV163 ) @ SV1589 @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4909]) ).
thf(5502,plain,
! [SV2270: $i,SV2038: $i,SV1590: $i,SV927: $i,SV165: $i] :
( ( ! [SY6226: $i,SY6227: $i,SY6228: $i,SY6229: $i] :
( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2038 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2270 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2038 ) @ SV2270 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6226 @ SV165 @ SV927 @ SY6227 @ SY6228 @ SY6229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4910]) ).
thf(5503,plain,
! [SV2271: $i,SV2039: $i,SV1592: $i,SV929: $i,SV168: $i] :
( ( ! [SY6230: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV168 @ SV929 @ SV1592 @ SV2039 @ SV2271 ) @ SY6230 )
= ( hAPP @ SV168 @ ( hAPP @ SV929 @ SY6230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4911]) ).
thf(5504,plain,
! [SV2272: $i,SV2040: $i,SV1593: $i,SV930: $i,SV169: $i] :
( ( ! [SY6231: $i] :
( ( hAPP @ SV169 @ ( hAPP @ SV930 @ SV1593 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV169 @ SV930 @ SV2040 @ SV2272 @ SY6231 ) @ SV1593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4912]) ).
thf(5505,plain,
! [SV2041: $i,SV1594: $i,SV931: $i,SV170: $i] :
( ( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ SV1594 @ SV2041 )
= ( c_List_Oappend @ ( c_List_Otake @ SV170 @ SV1594 @ SV2041 ) @ ( c_List_Otake @ SV931 @ ( c_List_Odrop @ SV170 @ SV1594 @ SV2041 ) @ SV2041 ) @ SV2041 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ ( c_Nat_Osize__class_Osize @ SV1594 @ ( tc_List_Olist @ SV2041 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4913]) ).
thf(5506,plain,
! [SV1595: $i,SV932: $i,SV171: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV171 )
= $false )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SV932 @ SV1595 @ SV171 @ SV171 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV171 ) @ SV1595 @ SV932 @ SV171 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4914]) ).
thf(5507,plain,
! [SV935: $i,SV174: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ SV935 ) @ SV935 ) @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4917]) ).
thf(5508,plain,
! [SV175: $i,SV936: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV936 @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV936 ) @ SV936 ) @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4918]) ).
thf(5509,plain,
! [SV176: $i,SV937: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV937 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV937 ) @ SV937 ) @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4919]) ).
thf(5510,plain,
! [SV938: $i,SV177: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV177 ) @ SV938 ) @ SV938 ) @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV938 @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(5511,plain,
! [SV2042: $i,SV1596: $i,SV939: $i,SV178: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV178 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV939 @ SV1596 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SV1596 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SV2042 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SV1596 @ SV2042 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5512,plain,
! [SV1597: $i,SV940: $i,SV179: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV179 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV940 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ ( c_HOL_Ozero__class_Ozero @ SV179 ) @ SV1597 @ SV179 @ SV179 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV179 ) @ SV940 @ SV1597 @ SV179 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4922]) ).
thf(5513,plain,
! [SV2043: $i,SV1598: $i,SV941: $i,SV180: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV180 ) )
= $true )
| ( ( ( c_lessequals @ SV941 @ SV1598 @ SV180 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2043 @ SV941 @ SV180 ) @ SV1598 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(5514,plain,
! [SV2044: $i,SV1599: $i,SV942: $i,SV181: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV181 ) )
= $true )
| ( ( ( c_lessequals @ SV942 @ SV1599 @ SV181 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV942 @ SV2044 @ SV181 ) @ SV1599 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4924]) ).
thf(5515,plain,
! [SV2045: $i,SV1600: $i,SV943: $i,SV182: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV182 ) )
= $true )
| ( ( ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1600 @ SV2045 @ SV182 ) @ SV182 )
| ~ ( c_lessequals @ SV943 @ SV2045 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4925]) ).
thf(5516,plain,
! [SV2046: $i,SV1601: $i,SV944: $i,SV183: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV183 ) )
= $true )
| ( ( ( c_lessequals @ SV944 @ ( c_Orderings_Oord__class_Omax @ SV1601 @ SV2046 @ SV183 ) @ SV183 )
| ~ ( c_lessequals @ SV944 @ SV1601 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4926]) ).
thf(5517,plain,
! [SV2047: $i,SV1602: $i,SV945: $i,SV184: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV184 ) )
= $true )
| ( ( ( c_lessequals @ SV945 @ ( c_Orderings_Oord__class_Omax @ SV1602 @ SV2047 @ SV184 ) @ SV184 )
| ~ ( c_lessequals @ SV945 @ SV2047 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4927]) ).
thf(5518,plain,
! [SV2048: $i,SV1603: $i,SV946: $i,SV185: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV185 ) )
= $true )
| ( ( ( c_lessequals @ SV946 @ ( c_Orderings_Oord__class_Omax @ SV1603 @ SV2048 @ SV185 ) @ SV185 )
| ~ ( c_lessequals @ SV946 @ SV1603 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4928]) ).
thf(5519,plain,
! [SV2049: $i,SV1604: $i,SV947: $i,SV186: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV186 ) )
= $true )
| ( ( ( c_lessequals @ SV947 @ SV1604 @ SV186 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2049 @ SV947 @ SV186 ) @ SV1604 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4929]) ).
thf(5520,plain,
! [SV2050: $i,SV1605: $i,SV948: $i,SV187: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV187 ) )
= $true )
| ( ( ( c_lessequals @ SV948 @ SV1605 @ SV187 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV948 @ SV2050 @ SV187 ) @ SV1605 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4930]) ).
thf(5521,plain,
! [SV949: $i,SV1606: $i,SV188: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV188 @ SV1606 @ tc_nat ) @ SV949 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV188 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV949 ) @ SV1606 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4931]) ).
thf(5522,plain,
! [SV950: $i,SV1607: $i,SV189: $i] :
( ( ( c_lessequals @ SV189 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1607 ) @ SV950 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV189 @ SV950 @ tc_nat ) @ SV1607 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4932]) ).
thf(5523,plain,
! [SV1608: $i,SV951: $i,SV190: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV190 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ ( c_Power_Opower__class_Opower @ SV951 @ SV1608 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV951 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4933]) ).
thf(5524,plain,
! [SV2051: $i,SV1609: $i,SV952: $i,SV191: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV191 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV952 @ SV1609 @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV952 @ SV2051 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV952 @ ( c_Orderings_Oord__class_Omax @ SV2051 @ SV1609 @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4934]) ).
thf(5525,plain,
! [SV1610: $i,SV192: $i,SV953: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV953 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SV953 ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4935]) ).
thf(5526,plain,
! [SV955: $i,SV1612: $i,SV194: $i] :
( ( ( SV194 = SV1612 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1612 @ SV194 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV194 ) @ SV955 @ SV1612 )
= ( c_Lambda_OdB_OVar @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4937]) ).
thf(5527,plain,
! [SV1614: $i,SV958: $i,SV199: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV958 ) @ SV1614 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SV1614 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ SV958 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4940]) ).
thf(5528,plain,
! [SV1615: $i,SV959: $i,SV200: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SV959 ) @ SV1615 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_lessequals @ SV1615 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SV959 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4941]) ).
thf(5529,plain,
! [SV960: $i,SV201: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV201 @ ( c_Suc @ SV960 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV201 @ SV960 @ tc_nat )
= $true )
| ( ( SV201 = SV960 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4942]) ).
thf(5530,plain,
! [SV202: $i,SV961: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV961 @ ( c_Suc @ SV202 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV961 @ SV202 @ tc_nat )
= $true )
| ( ( SV202 = SV961 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5531,plain,
! [SV962: $i,SV203: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV203 @ ( c_Suc @ SV962 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV203 @ SV962 @ tc_nat )
= $true )
| ( ( SV203 = SV962 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(5532,plain,
! [SV204: $i,SV963: $i,SV1616: $i] :
( ( ( c_lessequals @ SV1616 @ SV963 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ SV963 ) @ SV1616 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SV1616 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4945]) ).
thf(5533,plain,
! [SV964: $i,SV205: $i,SV1617: $i] :
( ( ( c_lessequals @ SV1617 @ SV205 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV964 ) @ SV1617 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV205 @ SV1617 @ tc_nat ) ) @ SV964 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(5534,plain,
! [SV2273: $i,SV2053: $i,SV1618: $i,SV965: $i,SV207: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV207 @ SV965 @ SV1618 ) @ SV2053 @ SV2273 @ SV1618 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV207 @ SV2053 @ SV2273 @ SV1618 ) @ SV965 @ SV1618 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2053 @ ( c_Nat_Osize__class_Osize @ SV207 @ ( tc_List_Olist @ SV1618 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4947]) ).
thf(5535,plain,
! [SV2274: $i,SV2054: $i,SV1619: $i,SV966: $i,SV208: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV208 @ SV966 @ SV1619 ) @ SV2054 @ SV2274 @ SV1619 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV208 @ SV2054 @ SV2274 @ SV1619 ) @ SV966 @ SV1619 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2054 @ ( c_Nat_Osize__class_Osize @ SV208 @ ( tc_List_Olist @ SV1619 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4948]) ).
thf(5536,plain,
! [SV209: $i,SV967: $i,SV1620: $i] :
( ( ( c_lessequals @ SV1620 @ SV967 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV209 @ ( c_HOL_Ominus__class_Ominus @ SV967 @ SV1620 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV209 ) @ SV1620 ) @ SV967 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(5537,plain,
! [SV969: $i,SV1621: $i,SV211: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV211 @ SV1621 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV211 @ SV969 @ tc_nat ) @ SV1621 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4950]) ).
thf(5538,plain,
! [SV971: $i,SV1623: $i,SV213: $i] :
( ( ( c_Lambda_Obeta @ SV213 @ SV1623 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1623 @ SV971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4952]) ).
thf(5539,plain,
! [SV1625: $i,SV974: $i,SV216: $i] :
( ( ( class_Orderings_Opreorder @ SV216 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV974 @ SV1625 @ SV216 )
| ( c_lessequals @ SV1625 @ SV974 @ SV216 )
| ~ ( c_lessequals @ SV974 @ SV1625 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4953]) ).
thf(5540,plain,
! [SV219: $i,SV975: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV975 @ SV975 @ SV219 )
= $false )
| ( ( class_Orderings_Oorder @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4954]) ).
thf(5541,plain,
! [SV220: $i,SV976: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV976 @ SV976 @ SV220 )
= $false )
| ( ( class_Orderings_Olinorder @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4955]) ).
thf(5542,plain,
! [SV221: $i,SV977: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV977 @ SV977 @ SV221 )
= $false )
| ( ( class_Orderings_Opreorder @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4956]) ).
thf(5543,plain,
! [SV1629: $i,SV983: $i,SV227: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SV983 ) @ SV1629 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV1629 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV983 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4959]) ).
thf(5544,plain,
! [SV2056: $i,SV1630: $i,SV988: $i,SV232: $i] :
( ( ( ( c_List_Otake @ SV232 @ ( c_List_Olist_OCons @ SV988 @ SV1630 @ SV2056 ) @ SV2056 )
= ( c_List_Olist_OCons @ SV988 @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV232 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1630 @ SV2056 ) @ SV2056 ) )
= $true )
| ( ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4960]) ).
thf(5545,plain,
! [SV1631: $i,SV989: $i,SV234: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV234 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV989 @ SV1631 @ SV234 ) @ SV234 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV989 ) @ ( c_List_Olistsum @ SV1631 @ SV234 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4962]) ).
thf(5546,plain,
! [SV2275: $i,SV2057: $i,SV1633: $i,SV991: $i,SV236: $i] :
( ( ! [SY6232: $i,SY6233: $i] :
( ( ( hAPP @ ( hAPP @ SV236 @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV991 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV2057 @ SV236 @ SV2275 @ SY6232 @ SY6233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4963]) ).
thf(5547,plain,
! [SV1634: $i,SV992: $i,SV237: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV237 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV992 @ SV1634 @ SV237 )
| ( c_HOL_Oord__class_Oless @ SV1634 @ SV992 @ SV237 )
| ( SV1634 = SV992 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4964]) ).
thf(5548,plain,
! [SV1635: $i,SV993: $i,SV238: $i] :
( ( ( class_Orderings_Olinorder @ SV238 )
= $false )
| ( ( ( SV993 = SV1635 )
| ( c_HOL_Oord__class_Oless @ SV1635 @ SV993 @ SV238 )
| ( c_HOL_Oord__class_Oless @ SV993 @ SV1635 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4965]) ).
thf(5549,plain,
! [SV239: $i,SV994: $i] :
( ( ( c_lessequals @ SV994 @ SV239 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV239 @ SV994 @ tc_nat ) )
= $true )
| ( ( SV239 = SV994 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4966]) ).
thf(5550,plain,
! [SV241: $i,SV1636: $i,SV996: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV996 @ SV1636 @ tc_nat )
= $true )
| ( ( ( SV1636 = SV996 )
| ( c_HOL_Oord__class_Oless @ SV1636 @ SV996 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV241 @ SV996 ) @ SV1636 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4968]) ).
thf(5551,plain,
! [SV2276: $i,SV2058: $i,SV1637: $i,SV997: $i,SV242: $i] :
( ( ( SV242 = SV997 )
| ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV997 )
| ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4969]) ).
thf(5552,plain,
! [SV2059: $i,SV1638: $i,SV998: $i,SV243: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV243 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV998 @ SV1638 @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2059 @ SV998 @ SV243 ) @ SV1638 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4970]) ).
thf(5553,plain,
! [SV1639: $i,SV999: $i,SV245: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV245 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SV999 @ SV1639 @ SV245 ) @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1639 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SV999 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4971]) ).
thf(5554,plain,
! [SV246: $i,SV1640: $i,SV1000: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1000 @ ( tc_List_Olist @ SV1640 ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_List_Orotate @ SV246 @ SV1000 @ SV1640 )
= SV1000 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4972]) ).
thf(5555,plain,
! [SV2060: $i,SV1641: $i,SV1001: $i,SV247: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV247 ) @ SV1001 ) @ SV1641 ) ) @ SV2060 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV247 ) @ SV2060 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1001 ) @ SV2060 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1641 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2060 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1641 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4973]) ).
thf(5556,plain,
! [SV1642: $i,SV1004: $i,SV250: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SV1004 ) @ SV1642 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SV1642 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SV1004 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4974]) ).
thf(5557,plain,
! [SV2061: $i,SV1643: $i,SV1005: $i,SV251: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV251 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(5558,plain,
! [SV255: $i,SV1647: $i,SV1009: $i] :
( ( ( ~ ( c_lessequals @ SV1009 @ SV1647 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1009 @ SV255 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1009 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1647 @ SV1009 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1647 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4978]) ).
thf(5559,plain,
! [SV1650: $i,SV1012: $i,SV258: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV1012 ) @ SV1650 ) @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1650 @ SV258 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1012 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4980]) ).
thf(5560,plain,
! [SV1651: $i,SV1013: $i,SV259: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV1013 ) @ SV1651 ) @ SV259 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1651 @ SV259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1013 @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4981]) ).
thf(5561,plain,
! [SV1655: $i,SV263: $i,SV1017: $i] :
( ( ( ~ ( c_lessequals @ SV1017 @ SV263 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV263 @ SV1655 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV263 @ SV1017 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1017 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4982]) ).
thf(5562,plain,
! [SV1018: $i,SV264: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV264 @ SV1018 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV264 )
= SV1018 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV264 ) @ SV1018 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4983]) ).
thf(5563,plain,
! [SV265: $i,SV1019: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV1019 ) @ SV265 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV265 @ SV1019 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4984]) ).
thf(5564,plain,
! [SV269: $i,SV1023: $i,SV1658: $i] :
( ( ( c_lessequals @ SV1658 @ SV1023 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV269 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1023 ) @ SV269 ) @ SV1658 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4987]) ).
thf(5565,plain,
! [SV2277: $i,SV2067: $i,SV1659: $i,SV1025: $i,SV271: $i] :
( ( ! [SY6234: $i,SY6235: $i,SY6236: $i,SY6237: $i] :
( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SV2067 ) ) @ SV2277 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SV2277 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SV2067 ) @ SV2277 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6234 @ SV1025 @ SV271 @ SY6235 @ SY6236 @ SY6237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4988]) ).
thf(5566,plain,
! [SV2278: $i,SV2068: $i,SV1660: $i,SV1026: $i,SV272: $i] :
( ( ! [SY6238: $i,SY6239: $i,SY6240: $i,SY6241: $i] :
( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SV2068 ) @ SV2278 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2068 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2278 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SY6238 @ SY6239 @ SY6240 @ SY6241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4989]) ).
thf(5567,plain,
! [SV2279: $i,SV2069: $i,SV1661: $i,SV1027: $i,SV273: $i] :
( ( ! [SY6242: $i,SY6243: $i,SY6244: $i] :
( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SV1661 )
= ( hAPP @ ( hAPP @ SV273 @ SV1661 ) @ SV1027 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2069 @ SV273 @ SV2279 @ SY6242 @ SY6243 @ SY6244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4990]) ).
thf(5568,plain,
! [SV2280: $i,SV2070: $i,SV1662: $i,SV1028: $i,SV274: $i] :
( ( ! [SY6245: $i,SY6246: $i,SY6247: $i,SY6248: $i] :
( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SV2070 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SV2070 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2280 @ SV274 @ SY6245 @ SY6246 @ SY6247 @ SY6248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4991]) ).
thf(5569,plain,
! [SV2281: $i,SV2071: $i,SV1663: $i,SV1029: $i,SV275: $i] :
( ( ! [SY6249: $i,SY6250: $i] :
( ( ( hAPP @ ( hAPP @ SV275 @ SV1029 ) @ SV1663 )
= SV1663 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2071 @ SV275 @ SV2281 @ SY6249 @ SV1029 @ SY6250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4992]) ).
thf(5570,plain,
! [SV2282: $i,SV2072: $i,SV1664: $i,SV1030: $i,SV276: $i] :
( ( ! [SY6251: $i,SY6252: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SV1030 ) @ SV1664 )
= SV1030 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2072 @ SV276 @ SV2282 @ SV1030 @ SY6251 @ SY6252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4993]) ).
thf(5571,plain,
! [SV2283: $i,SV2073: $i,SV1665: $i,SV1031: $i,SV277: $i] :
( ( ! [SY6253: $i,SY6254: $i,SY6255: $i] :
( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SV1665 )
= ( hAPP @ ( hAPP @ SV277 @ SV1665 ) @ SV1031 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SV2073 @ SV2283 @ SY6253 @ SY6254 @ SY6255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4994]) ).
thf(5572,plain,
! [SV2284: $i,SV2074: $i,SV1666: $i,SV1032: $i,SV278: $i] :
( ( ! [SY6256: $i,SY6257: $i,SY6258: $i,SY6259: $i] :
( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SV2074 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SV2074 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SV2284 @ SY6256 @ SY6257 @ SY6258 @ SY6259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4995]) ).
thf(5573,plain,
! [SV2285: $i,SV2075: $i,SV1667: $i,SV1033: $i,SV279: $i] :
( ( ! [SY6260: $i,SY6261: $i] :
( ( ( hAPP @ ( hAPP @ SV279 @ SV1033 ) @ SV1667 )
= SV1667 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SV2075 @ SV2285 @ SV1033 @ SY6260 @ SY6261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4996]) ).
thf(5574,plain,
! [SV2286: $i,SV2076: $i,SV1668: $i,SV1034: $i,SV280: $i] :
( ( ! [SY6262: $i,SY6263: $i,SY6264: $i,SY6265: $i] :
( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SV2076 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SV2076 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SV2286 @ SY6262 @ SY6263 @ SY6264 @ SY6265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4997]) ).
thf(5575,plain,
! [SV2287: $i,SV2077: $i,SV1669: $i,SV1035: $i,SV281: $i] :
( ( ! [SY6266: $i,SY6267: $i,SY6268: $i] :
( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SV1669 )
= ( hAPP @ ( hAPP @ SV281 @ SV1669 ) @ SV1035 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SV2077 @ SV2287 @ SY6266 @ SY6267 @ SY6268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4998]) ).
thf(5576,plain,
! [SV2288: $i,SV2078: $i,SV1670: $i,SV1036: $i,SV282: $i] :
( ( ! [SY6269: $i,SY6270: $i,SY6271: $i,SY6272: $i] :
( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SV2078 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV2078 ) ) @ SV1670 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SV2288 @ SY6269 @ SY6270 @ SY6271 @ SY6272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4999]) ).
thf(5577,plain,
! [SV2289: $i,SV2079: $i,SV1671: $i,SV1037: $i,SV283: $i] :
( ( ! [SY6273: $i,SY6274: $i,SY6275: $i,SY6276: $i] :
( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SV2079 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SV2079 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SV2289 @ SY6273 @ SY6274 @ SY6275 @ SY6276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5000]) ).
thf(5578,plain,
! [SV2290: $i,SV2080: $i,SV1672: $i,SV1038: $i,SV284: $i] :
( ( ! [SY6277: $i,SY6278: $i,SY6279: $i,SY6280: $i] :
( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SV2080 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SV2080 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SV2290 @ SY6277 @ SY6278 @ SY6279 @ SY6280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5001]) ).
thf(5579,plain,
! [SV2291: $i,SV2081: $i,SV1673: $i,SV1039: $i,SV285: $i] :
( ( ! [SY6281: $i,SY6282: $i,SY6283: $i,SY6284: $i,SY6285: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SV2291 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SV2291 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SY6281 @ SY6282 @ SY6283 @ SY6284 @ SY6285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5002]) ).
thf(5580,plain,
! [SV2292: $i,SV2082: $i,SV1674: $i,SV1040: $i,SV286: $i] :
( ( ! [SY6286: $i,SY6287: $i,SY6288: $i,SY6289: $i] :
( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SV2082 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SV2082 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2292 @ SV286 @ SY6286 @ SY6287 @ SY6288 @ SY6289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5003]) ).
thf(5581,plain,
! [SV2293: $i,SV2083: $i,SV1675: $i,SV1041: $i,SV287: $i] :
( ( ! [SY6290: $i,SY6291: $i,SY6292: $i,SY6293: $i] :
( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SV2083 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SV2083 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2293 @ SV287 @ SY6290 @ SY6291 @ SY6292 @ SY6293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5004]) ).
thf(5582,plain,
! [SV2294: $i,SV2084: $i,SV1676: $i,SV1042: $i,SV288: $i] :
( ( ! [SY6294: $i,SY6295: $i,SY6296: $i,SY6297: $i] :
( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SV2084 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SV2084 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2294 @ SV288 @ SY6294 @ SY6295 @ SY6296 @ SY6297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5005]) ).
thf(5583,plain,
! [SV2295: $i,SV2085: $i,SV1677: $i,SV1043: $i,SV289: $i] :
( ( ! [SY6298: $i,SY6299: $i,SY6300: $i,SY6301: $i] :
( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SV2085 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV2085 ) ) @ SV1677 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2295 @ SV289 @ SY6298 @ SY6299 @ SY6300 @ SY6301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5006]) ).
thf(5584,plain,
! [SV2296: $i,SV2086: $i,SV1678: $i,SV1044: $i,SV290: $i] :
( ( ! [SY6302: $i,SY6303: $i,SY6304: $i,SY6305: $i,SY6306: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SV2296 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SV2296 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6302 @ SV290 @ SY6303 @ SY6304 @ SY6305 @ SY6306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5007]) ).
thf(5585,plain,
! [SV2297: $i,SV2087: $i,SV1679: $i,SV1045: $i,SV291: $i] :
( ( ! [SY6307: $i,SY6308: $i,SY6309: $i,SY6310: $i,SY6311: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6307 @ SV291 @ SY6308 @ SY6309 @ SY6310 @ SY6311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5008]) ).
thf(5586,plain,
! [SV2298: $i,SV2088: $i,SV1680: $i,SV1046: $i,SV292: $i] :
( ( ! [SY6312: $i,SY6313: $i,SY6314: $i,SY6315: $i,SY6316: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SV2298 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SV2298 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6312 @ SV292 @ SY6313 @ SY6314 @ SY6315 @ SY6316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5009]) ).
thf(5587,plain,
! [SV2299: $i,SV2089: $i,SV1681: $i,SV1047: $i,SV293: $i] :
( ( ! [SY6317: $i,SY6318: $i] :
( ( ( hAPP @ ( hAPP @ SV293 @ SV1047 ) @ SV1681 )
= SV1047 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2089 @ SV293 @ SV2299 @ SY6317 @ SV1681 @ SY6318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5010]) ).
thf(5588,plain,
! [SV2300: $i,SV2090: $i,SV1682: $i,SV1048: $i,SV294: $i] :
( ( ! [SY6319: $i,SY6320: $i] :
( ( ( hAPP @ ( hAPP @ SV294 @ SV1048 ) @ SV1682 )
= SV1682 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2090 @ SV294 @ SV2300 @ SY6319 @ SV1048 @ SY6320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5011]) ).
thf(5589,plain,
! [SV2301: $i,SV2091: $i,SV1683: $i,SV1049: $i,SV295: $i] :
( ( ! [SY6321: $i,SY6322: $i] :
( ( ( hAPP @ ( hAPP @ SV295 @ SV1049 ) @ SV1683 )
= SV1683 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2091 @ SV295 @ SV2301 @ SV1683 @ SY6321 @ SY6322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5012]) ).
thf(5590,plain,
! [SV2302: $i,SV2092: $i,SV1684: $i,SV1050: $i,SV296: $i] :
( ( ! [SY6323: $i,SY6324: $i] :
( ( ( hAPP @ ( hAPP @ SV296 @ SV1050 ) @ SV1684 )
= SV1050 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2092 @ SV296 @ SV2302 @ SV1050 @ SY6323 @ SY6324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5013]) ).
thf(5591,plain,
! [SV2303: $i,SV2093: $i,SV1685: $i,SV1051: $i,SV297: $i] :
( ( ! [SY6325: $i,SY6326: $i,SY6327: $i,SY6328: $i] :
( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SV2093 ) ) @ SV2303 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SV2303 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SV2093 ) @ SV2303 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SY6325 @ SY6326 @ SY6327 @ SY6328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5014]) ).
thf(5592,plain,
! [SV2304: $i,SV2094: $i,SV1686: $i,SV1052: $i,SV298: $i] :
( ( ! [SY6329: $i,SY6330: $i,SY6331: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SV1686 )
= ( hAPP @ ( hAPP @ SV298 @ SV1686 ) @ SV1052 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2094 @ SV298 @ SV2304 @ SY6329 @ SY6330 @ SY6331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5015]) ).
thf(5593,plain,
! [SV2305: $i,SV2095: $i,SV1687: $i,SV1053: $i,SV299: $i] :
( ( ! [SY6332: $i,SY6333: $i] :
( ( ( hAPP @ ( hAPP @ SV299 @ SV1053 ) @ SV1687 )
= SV1053 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SV2095 @ SV2305 @ SV1687 @ SY6332 @ SY6333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5016]) ).
thf(5594,plain,
! [SV2306: $i,SV2096: $i,SV1688: $i,SV1054: $i,SV300: $i] :
( ( ! [SY6334: $i,SY6335: $i] :
( ( ( hAPP @ ( hAPP @ SV300 @ SV1054 ) @ SV1688 )
= SV1688 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SV2096 @ SV2306 @ SV1054 @ SY6334 @ SY6335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5017]) ).
thf(5595,plain,
! [SV2307: $i,SV2097: $i,SV1689: $i,SV1055: $i,SV301: $i] :
( ( ! [SY6336: $i,SY6337: $i] :
( ( ( hAPP @ ( hAPP @ SV301 @ SV1055 ) @ SV1055 )
= ( hAPP @ ( hAPP @ SV1689 @ ( hAPP @ ( hAPP @ SV301 @ SV2097 ) @ SV2097 ) ) @ SV1055 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SV1689 @ SV2307 @ SY6336 @ SV2097 @ SY6337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5018]) ).
thf(5596,plain,
! [SV2308: $i,SV2098: $i,SV1690: $i,SV1056: $i,SV302: $i] :
( ( ! [SY6338: $i,SY6339: $i,SY6340: $i] :
( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SV1690 @ SV2098 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SV1690 @ ( hAPP @ ( hAPP @ SV302 @ SV2098 ) @ SV2308 ) ) @ SV1056 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SV1690 @ SY6338 @ SY6339 @ SV2308 @ SY6340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5019]) ).
thf(5597,plain,
! [SV2309: $i,SV2099: $i,SV1691: $i,SV1057: $i,SV303: $i] :
( ( ! [SY6341: $i,SY6342: $i,SY6343: $i] :
( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SV1691 ) @ SV2099 ) ) @ SV2099 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SV1691 ) @ SV2309 ) ) @ SV2099 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SY6341 @ SY6342 @ SV2309 @ SY6343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5020]) ).
thf(5598,plain,
! [SV2310: $i,SV2100: $i,SV1692: $i,SV1058: $i,SV304: $i] :
( ( ! [SY6344: $i,SY6345: $i,SY6346: $i,SY6347: $i] :
( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SV2100 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SV2310 ) @ SV2100 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SV2310 ) ) @ SV2100 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SY6344 @ SY6345 @ SY6346 @ SY6347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5021]) ).
thf(5599,plain,
! [SV2101: $i,SV1693: $i,SV1059: $i,SV305: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV305 @ ( c_Type_Otype_Otype__case @ SV1059 @ SV1693 @ ( c_Type_Otype_OAtom @ SV2101 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV305 @ ( hAPP @ SV1059 @ SV2101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5022]) ).
thf(5600,plain,
! [SV2102: $i,SV1694: $i,SV1060: $i,SV306: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV306 @ ( c_Type_Otype_Otype__case @ SV1060 @ SV1694 @ ( c_Type_Otype_OAtom @ SV2102 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV306 @ ( hAPP @ SV1060 @ SV2102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5023]) ).
thf(5601,plain,
! [SV2311: $i,SV2103: $i,SV1696: $i,SV1062: $i,SV308: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1062 ) @ SV1696 ) ) @ ( c_Suc @ SV2103 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2311 ) @ SV1062 ) @ SV2103 ) ) @ SV1696 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ SV2311 ) @ SV1696 ) ) @ SV1062 ) @ SV2103 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1696 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2103 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5024]) ).
thf(5602,plain,
! [SV2312: $i,SV2104: $i,SV1699: $i,SV1066: $i,SV313: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV1699 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV2104 ) @ SV2312 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV2104 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1699 ) @ SV2312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5025]) ).
thf(5603,plain,
! [SV314: $i,SV1700: $i,SV1067: $i] :
( ( ( c_Lambda_Obeta @ SV1067 @ SV1700 )
= $false )
| ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV1067 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV314 ) @ SV1700 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5026]) ).
thf(5604,plain,
! [SV1068: $i,SV1701: $i,SV315: $i] :
( ( ( c_Lambda_Obeta @ SV315 @ SV1701 )
= $false )
| ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV315 ) @ SV1068 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1701 ) @ SV1068 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5027]) ).
thf(5605,plain,
! [SV317: $i,SV1070: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1070 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5028]) ).
thf(5606,plain,
! [SV1071: $i,SV318: $i,SV1703: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1703 @ SV318 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV318 ) @ SV1071 @ SV1703 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV318 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5607,plain,
! [SV1704: $i,SV1072: $i,SV319: $i] :
( ( ( class_Orderings_Olinorder @ SV319 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1072 @ SV1704 @ SV319 )
= ( c_Orderings_Oord__class_Omax @ SV1704 @ SV1072 @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5608,plain,
! [SV320: $i,SV1705: $i,SV1073: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1073 @ SV1705 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Oliftn @ SV320 @ ( c_Lambda_OdB_OVar @ SV1073 ) @ SV1705 )
= ( c_Lambda_OdB_OVar @ SV1073 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5609,plain,
! [SV321: $i,SV1706: $i,SV1074: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1074 @ ( tc_List_Olist @ SV1706 ) ) @ SV321 @ tc_nat )
= $false )
| ( ( ( c_List_Odrop @ SV321 @ SV1074 @ SV1706 )
= ( c_List_Olist_ONil @ SV1706 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5610,plain,
! [SV323: $i,SV1707: $i,SV1075: $i] :
( ( ( c_List_Odistinct @ SV1075 @ SV1707 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Odrop @ SV323 @ SV1075 @ SV1707 ) @ SV1707 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5033]) ).
thf(5611,plain,
! [SV1709: $i,SV1080: $i,SV328: $i] :
( ( ( class_Orderings_Oorder @ SV328 )
= $false )
| ( ( ( SV1080 = SV1709 )
| ~ ( c_lessequals @ SV1709 @ SV1080 @ SV328 )
| ~ ( c_lessequals @ SV1080 @ SV1709 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5038]) ).
thf(5612,plain,
! [SV1710: $i,SV1081: $i,SV329: $i] :
( ( ( class_Orderings_Olinorder @ SV329 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1081 @ SV1710 @ SV329 )
| ( c_HOL_Oord__class_Oless @ SV1710 @ SV1081 @ SV329 )
| ( SV1710 = SV1081 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5039]) ).
thf(5613,plain,
! [SV1711: $i,SV1082: $i,SV330: $i] :
( ( ( class_Orderings_Oorder @ SV330 )
= $false )
| ( ( ( SV1082 = SV1711 )
| ~ ( c_lessequals @ SV1711 @ SV1082 @ SV330 )
| ~ ( c_lessequals @ SV1082 @ SV1711 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5614,plain,
! [SV1712: $i,SV1083: $i,SV331: $i] :
( ( ( class_Orderings_Oorder @ SV331 )
= $false )
| ( ( ( SV1083 = SV1712 )
| ~ ( c_lessequals @ SV1083 @ SV1712 @ SV331 )
| ~ ( c_lessequals @ SV1712 @ SV1083 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5041]) ).
thf(5615,plain,
! [SV1714: $i,SV1085: $i,SV333: $i] :
( ( ( class_Orderings_Olinorder @ SV333 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1085 @ SV1714 @ SV333 )
| ( SV1714 = SV1085 )
| ( c_HOL_Oord__class_Oless @ SV1714 @ SV1085 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5616,plain,
! [SV1715: $i,SV1086: $i,SV334: $i] :
( ( ( class_Orderings_Olinorder @ SV334 )
= $false )
| ( ( ( SV1086 = SV1715 )
| ( c_HOL_Oord__class_Oless @ SV1086 @ SV1715 @ SV334 )
| ( c_HOL_Oord__class_Oless @ SV1715 @ SV1086 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5044]) ).
thf(5617,plain,
! [SV1716: $i,SV1087: $i,SV335: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV335 )
= $false )
| ( ( ( c_lessequals @ SV1087 @ SV1716 @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SV1716 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5045]) ).
thf(5618,plain,
! [SV1717: $i,SV1088: $i,SV336: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV336 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV1717 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ SV1088 @ SV1717 @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5046]) ).
thf(5619,plain,
! [SV2313: $i,SV2107: $i,SV1718: $i,SV1090: $i,SV340: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV2107 ) @ SV2313 ) @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1718 @ SV2313 @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SV2107 @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5048]) ).
thf(5620,plain,
! [SV2108: $i,SV1719: $i,SV1091: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV341 ) @ SV1091 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1719 ) @ SV2108 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1091 @ SV2108 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV341 @ SV1719 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5049]) ).
thf(5621,plain,
! [SV1720: $i,SV1095: $i,SV345: $i] :
( ( ( class_Orderings_Oorder @ SV345 )
= $false )
| ( ( ( c_lessequals @ SV1095 @ SV1720 @ SV345 )
| ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SV1720 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5053]) ).
thf(5622,plain,
! [SV1721: $i,SV1096: $i,SV346: $i] :
( ( ( class_Orderings_Opreorder @ SV346 )
= $false )
| ( ( ( c_lessequals @ SV1096 @ SV1721 @ SV346 )
| ~ ( c_HOL_Oord__class_Oless @ SV1096 @ SV1721 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5054]) ).
thf(5623,plain,
! [SV2314: $i,SV2109: $i,SV1722: $i,SV1097: $i,SV347: $i] :
( ( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1097 ) @ SV1722 ) @ SV2109 )
| ~ ( c_Type_Otyping @ SV347 @ SV1722 @ SV2314 )
| ~ ( c_Type_Otyping @ SV347 @ SV1097 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2314 ) @ SV2109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5055]) ).
thf(5624,plain,
! [SV2110: $i,SV1723: $i,SV1098: $i,SV349: $i] :
( ( ( ( c_List_Olist__update @ SV349 @ SV1098 @ SV1723 @ SV2110 )
= ( c_List_Oappend @ ( c_List_Otake @ SV1098 @ SV349 @ SV2110 ) @ ( c_List_Olist_OCons @ SV1723 @ ( c_List_Odrop @ ( c_Suc @ SV1098 ) @ SV349 @ SV2110 ) @ SV2110 ) @ SV2110 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1098 @ ( c_Nat_Osize__class_Osize @ SV349 @ ( tc_List_Olist @ SV2110 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5056]) ).
thf(5625,plain,
! [SV1724: $i,SV1099: $i,SV350: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV350 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ ( c_Power_Opower__class_Opower @ SV1099 @ ( c_Suc @ SV1724 ) @ SV350 ) @ SV350 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ SV1099 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5057]) ).
thf(5626,plain,
! [SV352: $i,SV1101: $i,SV1725: $i] :
( ( ( c_lessequals @ SV1725 @ SV1101 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1725 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV352 ) @ SV1725 ) @ ( c_Suc @ SV1101 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5058]) ).
thf(5627,plain,
! [SV1726: $i,SV1102: $i,SV353: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV353 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1102 @ SV1726 @ SV353 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1102 @ SV1726 @ SV353 ) @ ( c_HOL_Ozero__class_Ozero @ SV353 ) @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5059]) ).
thf(5628,plain,
! [SV1727: $i,SV1103: $i,SV354: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV354 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1103 @ SV1727 @ SV354 ) @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV354 )
| ~ ( c_HOL_Oord__class_Oless @ SV1103 @ SV1727 @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5060]) ).
thf(5629,plain,
! [SV1728: $i,SV1104: $i,SV355: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV355 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1104 @ SV355 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1728 @ SV355 ) @ SV355 )
| ~ ( c_HOL_Oord__class_Oless @ SV1104 @ SV1728 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5061]) ).
thf(5630,plain,
! [SV1729: $i,SV1105: $i,SV356: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV356 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1105 @ SV1729 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1105 @ SV356 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1729 @ SV356 ) @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5062]) ).
thf(5631,plain,
! [SV359: $i,SV1106: $i,SV1730: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1730 @ SV1106 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV359 @ SV1730 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV359 ) @ SV1106 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5063]) ).
thf(5632,plain,
! [SV2111: $i,SV1731: $i,SV1107: $i,SV360: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV360 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV1107 ) @ SV1731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV2111 ) @ SV1731 ) @ SV360 )
| ~ ( c_lessequals @ SV1107 @ SV2111 @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5064]) ).
thf(5633,plain,
! [SV2112: $i,SV1732: $i,SV1108: $i,SV361: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV361 ) )
= $true )
| ( ( ( c_lessequals @ SV1108 @ SV1732 @ SV361 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1108 ) @ SV2112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1732 ) @ SV2112 ) @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5065]) ).
thf(5634,plain,
! [SV2113: $i,SV1733: $i,SV1109: $i,SV362: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV362 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV1733 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV2113 ) @ SV362 )
| ~ ( c_lessequals @ SV1733 @ SV2113 @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5066]) ).
thf(5635,plain,
! [SV2114: $i,SV1734: $i,SV1110: $i,SV363: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV363 ) )
= $true )
| ( ( ( c_lessequals @ SV1110 @ SV1734 @ SV363 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1734 ) @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5067]) ).
thf(5636,plain,
! [SV2115: $i,SV1735: $i,SV1111: $i,SV364: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV364 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV1111 ) @ SV1735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV2115 ) @ SV1735 ) @ SV364 )
| ~ ( c_lessequals @ SV1111 @ SV2115 @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5068]) ).
thf(5637,plain,
! [SV2116: $i,SV1736: $i,SV1112: $i,SV365: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV365 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV1736 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV2116 ) @ SV365 )
| ~ ( c_lessequals @ SV1736 @ SV2116 @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5069]) ).
thf(5638,plain,
! [SV1113: $i,SV1737: $i,SV366: $i] :
( ( ( c_lessequals @ SV366 @ SV1737 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV366 ) @ SV1113 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1737 ) @ SV1113 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5070]) ).
thf(5639,plain,
! [SV1114: $i,SV367: $i,SV1738: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1738 ) @ SV367 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1738 ) @ SV1114 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV367 @ SV1114 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5071]) ).
thf(5640,plain,
! [SV368: $i,SV1739: $i,SV1115: $i] :
( ( ( c_lessequals @ SV1115 @ SV1739 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SV1115 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ SV1739 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5072]) ).
thf(5641,plain,
! [SV2117: $i,SV1740: $i,SV1116: $i,SV370: $i] :
( ( ( ( c_List_Olist__update @ SV370 @ SV1116 @ SV1740 @ SV2117 )
= SV370 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SV2117 ) ) @ SV1116 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5073]) ).
thf(5642,plain,
! [SV2315: $i,SV2118: $i,SV1741: $i,SV1120: $i,SV374: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV374 @ SV1120 @ SV1741 @ SV2118 ) @ SV2315 )
= ( hAPP @ SV374 @ ( c_HOL_Ominus__class_Ominus @ SV2315 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1120 @ SV2315 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5077]) ).
thf(5643,plain,
! [SV2316: $i,SV2119: $i,SV1742: $i,SV1121: $i,SV375: $i] :
( ( ! [SY6348: $i,SY6349: $i,SY6350: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ SV2119 ) )
= ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ ( c_Suc @ SV2119 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2316 @ SV375 @ SV1742 @ SY6348 @ SY6349 @ SY6350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5078]) ).
thf(5644,plain,
! [SV2317: $i,SV2120: $i,SV1743: $i,SV1122: $i,SV376: $i] :
( ( ! [SY6351: $i,SY6352: $i,SY6353: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ SV2120 ) ) @ SV1743 )
= ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ ( c_Suc @ SV2120 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2317 @ SV376 @ SV1122 @ SY6351 @ SY6352 @ SY6353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5079]) ).
thf(5645,plain,
! [SV2318: $i,SV2121: $i,SV1744: $i,SV1123: $i,SV377: $i] :
( ( ! [SY6354: $i,SY6355: $i,SY6356: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SV1744 ) )
= ( hAPP @ ( hAPP @ SV2121 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SV1744 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2318 @ SV2121 @ SV377 @ SY6354 @ SY6355 @ SY6356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5080]) ).
thf(5646,plain,
! [SV2319: $i,SV2122: $i,SV1745: $i,SV1124: $i,SV378: $i] :
( ( ! [SY6357: $i,SY6358: $i,SY6359: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SV1745 ) )
= ( hAPP @ ( hAPP @ SV2122 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SV1745 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2319 @ SV2122 @ SV378 @ SY6357 @ SY6358 @ SY6359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5081]) ).
thf(5647,plain,
! [SV380: $i,SV1126: $i,SV1746: $i] :
( ( ( c_lessequals @ SV1746 @ SV1126 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ ( c_HOL_Ominus__class_Ominus @ SV1126 @ SV1746 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV380 ) @ SV1126 ) @ SV1746 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5083]) ).
thf(5648,plain,
! [SV1747: $i,SV381: $i,SV1127: $i] :
( ( ( c_lessequals @ SV1127 @ SV381 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV381 @ SV1127 @ tc_nat ) ) @ SV1747 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV381 ) @ SV1747 ) @ SV1127 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5084]) ).
thf(5649,plain,
! [SV2124: $i,SV1749: $i,SV1129: $i,SV383: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV383 ) )
= $true )
| ( ( ( c_lessequals @ SV1129 @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SV2124 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SV1749 @ ( c_Suc @ SV2124 ) @ SV383 ) @ SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5086]) ).
thf(5650,plain,
! [SV1133: $i,SV387: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV387 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1133 @ SV387 ) @ SV387 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1133 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV387 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5089]) ).
thf(5651,plain,
! [SV388: $i,SV1134: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1134 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV388 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1134 @ SV388 ) @ SV388 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5090]) ).
thf(5652,plain,
! [SV1138: $i,SV392: $i,SV1753: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate @ SV1753 @ SV392 @ SV1138 ) @ SV1138 )
= $false )
| ( ( c_List_Odistinct @ SV392 @ SV1138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5093]) ).
thf(5653,plain,
! [SV393: $i,SV1754: $i,SV1139: $i] :
( ( ( c_List_Odistinct @ SV1139 @ SV1754 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Orotate @ SV393 @ SV1139 @ SV1754 ) @ SV1754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5094]) ).
thf(5654,plain,
! [SV2127: $i,SV1755: $i,SV1141: $i,SV395: $i] :
( ( ( c_List_Olistsp @ SV395 @ ( c_List_Oappend @ SV1141 @ SV1755 @ SV2127 ) @ SV2127 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV395 @ SV1755 @ SV2127 )
| ~ ( c_List_Olistsp @ SV395 @ SV1141 @ SV2127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5096]) ).
thf(5655,plain,
! [SV2320: $i,SV2128: $i,SV1756: $i,SV1142: $i,SV396: $i] :
( ( ! [SY6360: $i,SY6361: $i] :
( ( c_Fun_Ocomp @ SV396 @ ( c_Fun_Ocomp @ SV1142 @ SV1756 @ SV2128 @ SV2320 @ SY6360 ) @ SV2320 @ SY6361 @ SY6360 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV396 @ SV1142 @ SV2320 @ SY6361 @ SV2128 ) @ SV1756 @ SV2128 @ SY6361 @ SY6360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5097]) ).
thf(5656,plain,
! [SV1143: $i,SV397: $i,SV1757: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1757 @ SV397 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV397 ) ) @ SV1143 ) @ SV1757 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV397 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5098]) ).
thf(5657,plain,
! [SV1144: $i,SV398: $i,SV1758: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1758 @ SV398 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV398 ) ) @ SV1144 ) @ SV1758 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV398 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5099]) ).
thf(5658,plain,
! [SV1148: $i,SV1760: $i,SV403: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV1760 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1148 @ SV1760 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1760 @ SV1148 @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV403 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV403 @ SV1148 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5102]) ).
thf(5659,plain,
! [SV1149: $i,SV1761: $i,SV404: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV404 @ SV1761 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1149 @ SV1761 @ tc_nat )
| ~ ( c_lessequals @ SV1149 @ SV404 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SV1149 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1761 @ SV1149 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5103]) ).
thf(5660,plain,
! [SV2129: $i,SV1762: $i,SV1150: $i,SV405: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV405 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1762 ) @ SV2129 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2129 @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1762 @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5104]) ).
thf(5661,plain,
! [SV1151: $i,SV1763: $i,SV406: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV406 @ SV1763 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV406 ) ) @ SV1151 ) @ SV1763 )
= ( c_Lambda_OdB_OVar @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5105]) ).
thf(5662,plain,
! [SV1764: $i,SV1152: $i,SV407: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV407 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV407 ) @ ( c_Lambda_OdB_OVar @ SV1152 ) ) @ SV1764 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5106]) ).
thf(5663,plain,
! [SV1153: $i,SV408: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV408 ) @ SV1153 ) @ SV1153 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $true )
| ( ( ~ ( c_lessequals @ SV1153 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5107]) ).
thf(5664,plain,
! [SV409: $i,SV1154: $i] :
( ( ( c_lessequals @ SV1154 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV409 ) @ SV1154 ) @ SV1154 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV409 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5108]) ).
thf(5665,plain,
! [SV2130: $i,SV1765: $i,SV1155: $i,SV410: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SV1765 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SV2130 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2130 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5109]) ).
thf(5666,plain,
! [SV2131: $i,SV1766: $i,SV1156: $i,SV411: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV411 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1766 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1766 @ SV411 ) @ SV411 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SV2131 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5110]) ).
thf(5667,plain,
! [SV2132: $i,SV1767: $i,SV1157: $i,SV412: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV412 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SV1767 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SV2132 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1767 @ SV2132 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5111]) ).
thf(5668,plain,
! [SV2133: $i,SV1768: $i,SV1158: $i,SV413: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV413 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1768 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1768 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV2133 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5112]) ).
thf(5669,plain,
! [SV2135: $i,SV1770: $i,SV1161: $i,SV416: $i] :
( ( ( ( c_List_Odrop @ SV416 @ ( c_List_Olist_OCons @ SV1161 @ SV1770 @ SV2135 ) @ SV2135 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1770 @ SV2135 ) )
= $true )
| ( ( SV416
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5114]) ).
thf(5670,plain,
! [SV1168: $i,SV423: $i] :
( ( ( c_lessequals @ SV423 @ ( c_Suc @ SV1168 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV423 @ SV1168 @ tc_nat )
= $true )
| ( ( SV423
= ( c_Suc @ SV1168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5119]) ).
thf(5671,plain,
! [SV425: $i,SV1169: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1169 @ ( c_Suc @ SV425 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV425 @ SV1169 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5120]) ).
thf(5672,plain,
! [SV2138: $i,SV1773: $i,SV1171: $i,SV427: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV427 ) @ SV1171 ) @ SV1773 ) ) @ SV2138 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV427 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2138 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1171 ) @ SV2138 ) ) @ SV1773 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1773 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2138 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5121]) ).
thf(5673,plain,
! [SV428: $i,SV1774: $i,SV1172: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1172 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1774 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SV1172 ) ) @ ( c_Suc @ SV1774 ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV428 ) @ SV1774 ) ) @ SV1172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5122]) ).
thf(5674,plain,
! [SV2139: $i,SV1776: $i,SV1175: $i,SV431: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV431 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ ( c_Orderings_Oord__class_Omax @ SV1175 @ SV1776 @ SV431 ) ) @ SV2139 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1175 ) @ SV2139 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1776 ) @ SV2139 ) @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5123]) ).
thf(5675,plain,
! [SV2140: $i,SV1777: $i,SV1177: $i,SV433: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV433 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1177 @ SV1777 @ SV433 ) @ SV2140 @ SV433 )
= ( c_Orderings_Oord__class_Omax @ SV1177 @ ( c_Orderings_Oord__class_Omax @ SV1777 @ SV2140 @ SV433 ) @ SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5125]) ).
thf(5676,plain,
! [SV2141: $i,SV1778: $i,SV1178: $i,SV434: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV434 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1178 @ ( c_Orderings_Oord__class_Omax @ SV1778 @ SV2141 @ SV434 ) @ SV434 )
= ( c_Orderings_Oord__class_Omax @ SV1778 @ ( c_Orderings_Oord__class_Omax @ SV1178 @ SV2141 @ SV434 ) @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(5677,plain,
! [SV437: $i,SV1779: $i,SV1179: $i] :
( ( ( c_List_Odistinct @ SV1179 @ SV1779 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Otake @ SV437 @ SV1179 @ SV1779 ) @ SV1779 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5127]) ).
thf(5678,plain,
! [SV1780: $i,SV1183: $i,SV441: $i] :
( ( ( class_Orderings_Olinorder @ SV441 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1183 @ ( c_Orderings_Oord__class_Omax @ SV1183 @ SV1780 @ SV441 ) @ SV441 )
= ( c_Orderings_Oord__class_Omax @ SV1183 @ SV1780 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5131]) ).
thf(5679,plain,
! [SV1783: $i,SV1188: $i,SV447: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV447 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1188 ) @ SV1783 ) @ SV1783 @ SV447 )
= SV1188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5133]) ).
thf(5680,plain,
! [SV2321: $i,SV2143: $i,SV1785: $i,SV1190: $i,SV449: $i] :
( ( ! [SY6362: $i] :
( ( c_List_Ofoldl @ SV449 @ SV1190 @ ( c_List_Oappend @ SV1785 @ SV2143 @ SV2321 ) @ SY6362 @ SV2321 )
= ( c_List_Ofoldl @ SV449 @ ( c_List_Ofoldl @ SV449 @ SV1190 @ SV1785 @ SY6362 @ SV2321 ) @ SV2143 @ SY6362 @ SV2321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5134]) ).
thf(5681,plain,
! [SV2144: $i,SV1786: $i,SV1191: $i,SV450: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV450 ) )
= $true )
| ( ( ( c_lessequals @ SV1191 @ SV1786 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1786 @ SV450 ) @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SV2144 @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5135]) ).
thf(5682,plain,
! [SV2145: $i,SV1787: $i,SV1192: $i,SV451: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV451 ) )
= $true )
| ( ( ( c_lessequals @ SV1192 @ SV1787 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1787 @ SV451 ) @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SV2145 @ SV451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5136]) ).
thf(5683,plain,
! [SV2146: $i,SV1788: $i,SV1193: $i,SV452: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV452 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SV1788 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SV2146 @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ SV1788 @ SV2146 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5137]) ).
thf(5684,plain,
! [SV1196: $i,SV456: $i,SV1791: $i] :
( ( ( c_List_Odistinct @ ( c_List_Olist_OCons @ SV1791 @ SV456 @ SV1196 ) @ SV1196 )
= $false )
| ( ( c_List_Odistinct @ SV456 @ SV1196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5140]) ).
thf(5685,plain,
! [SV2322: $i,SV2149: $i,SV1792: $i,SV1197: $i,SV457: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV2149 ) @ SV2322 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1792 @ SV2322 @ SV457 )
| ~ ( c_lessequals @ SV1197 @ SV2149 @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5141]) ).
thf(5686,plain,
! [SV2323: $i,SV2150: $i,SV1793: $i,SV1198: $i,SV458: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV2150 ) @ SV2323 ) @ SV458 )
| ~ ( c_lessequals @ SV1793 @ SV2323 @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SV2150 @ SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5142]) ).
thf(5687,plain,
! [SV1204: $i,SV464: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ SV1204 @ SV464 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV464 ) @ SV1204 ) @ SV1204 ) @ SV464 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV464 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5148]) ).
thf(5688,plain,
! [SV1205: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV465 ) @ SV1205 ) @ SV1205 ) @ SV465 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1205 @ SV465 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV465 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5149]) ).
thf(5689,plain,
! [SV1206: $i,SV466: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV466 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1206 @ SV1206 @ SV466 )
= ( c_HOL_Ozero__class_Ozero @ SV466 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5150]) ).
thf(5690,plain,
! [SV1213: $i,SV474: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV474 ) )
= $true )
| ( ( SV1213
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV474 ) @ SV1213 ) @ ( c_HOL_Ozero__class_Ozero @ SV474 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5157]) ).
thf(5691,plain,
! [SV480: $i] :
( ( ( class_Power_Opower @ SV480 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV480 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV480 )
= ( c_HOL_Oone__class_Oone @ SV480 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV480 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5163]) ).
thf(5692,plain,
! [SV2324: $i,SV2151: $i,SV1794: $i,SV1220: $i,SV486: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SV1220 @ SV1794 @ SV2151 ) @ SV2151 ) @ ( c_Nat_Osize__class_Osize @ SV486 @ ( tc_List_Olist @ SV2151 ) ) @ SV2324 @ SV2151 )
= ( c_List_Oappend @ SV486 @ ( c_List_Olist_OCons @ SV2324 @ SV1794 @ SV2151 ) @ SV2151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5164]) ).
thf(5693,plain,
! [SV1795: $i,SV1223: $i,SV489: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV489 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1795 @ tc_nat ) @ SV489 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1223 @ SV489 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1795 @ SV489 ) @ SV489 ) )
| ~ ( c_lessequals @ SV1795 @ SV1223 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5694,plain,
! [SV1225: $i,SV1797: $i,SV491: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV491 @ ( c_HOL_Ominus__class_Ominus @ SV1797 @ SV1225 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV491 ) @ SV1225 ) @ SV1797 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5166]) ).
thf(5695,plain,
! [SV1226: $i,SV1798: $i,SV492: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV1798 ) @ SV1226 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV492 @ ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1798 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5167]) ).
thf(5696,plain,
! [SV2152: $i,SV1799: $i,SV1227: $i,SV493: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV493 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV1227 ) @ SV1799 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV2152 ) @ SV1799 ) @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SV2152 @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5168]) ).
thf(5697,plain,
! [SV2153: $i,SV1800: $i,SV1228: $i,SV494: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV494 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV1228 ) @ SV1800 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV2153 ) @ SV1800 ) @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SV2153 @ SV494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5169]) ).
thf(5698,plain,
! [SV2154: $i,SV1801: $i,SV1229: $i,SV495: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV495 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1801 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1229 ) @ SV2154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1801 ) @ SV2154 ) @ SV495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5170]) ).
thf(5699,plain,
! [SV2155: $i,SV1802: $i,SV1230: $i,SV496: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV496 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV1802 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV2155 ) @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1802 @ SV2155 @ SV496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5171]) ).
thf(5700,plain,
! [SV2156: $i,SV1803: $i,SV1231: $i,SV497: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV497 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV1803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV2156 ) @ SV497 )
| ~ ( c_HOL_Oord__class_Oless @ SV1803 @ SV2156 @ SV497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5172]) ).
thf(5701,plain,
! [SV2157: $i,SV1804: $i,SV1232: $i,SV498: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV498 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1232 @ SV1804 @ SV498 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1232 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1804 ) @ SV498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(5702,plain,
! [SV1233: $i,SV1805: $i,SV499: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV499 @ SV1805 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV499 ) @ SV1233 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1805 ) @ SV1233 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5174]) ).
thf(5703,plain,
! [SV1234: $i,SV500: $i,SV1806: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1806 ) @ SV500 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1806 ) @ SV1234 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV500 @ SV1234 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5175]) ).
thf(5704,plain,
! [SV501: $i,SV1807: $i,SV1235: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1235 @ SV1807 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SV1235 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV501 ) @ SV1807 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5176]) ).
thf(5705,plain,
! [SV2158: $i,SV1808: $i,SV1236: $i,SV502: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV502 ) )
= $true )
| ( ( ( c_lessequals @ SV1236 @ SV1808 @ SV502 )
| ~ ( c_lessequals @ SV1236 @ SV2158 @ SV502 )
| ~ ( c_lessequals @ SV2158 @ SV1808 @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5177]) ).
thf(5706,plain,
! [SV2159: $i,SV1809: $i,SV1237: $i,SV503: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV503 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1237 @ SV1809 @ SV503 )
| ~ ( c_lessequals @ SV1237 @ SV2159 @ SV503 )
| ~ ( c_HOL_Oord__class_Oless @ SV2159 @ SV1809 @ SV503 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5178]) ).
thf(5707,plain,
! [SV2160: $i,SV1810: $i,SV1238: $i,SV504: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV504 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1238 @ SV1810 @ SV504 )
| ~ ( c_HOL_Oord__class_Oless @ SV1238 @ SV2160 @ SV504 )
| ~ ( c_lessequals @ SV2160 @ SV1810 @ SV504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5179]) ).
thf(5708,plain,
! [SV1811: $i,SV1239: $i,SV505: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SV1239 ) @ SV1811 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SV1811 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SV1239 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5180]) ).
thf(5709,plain,
! [SV2161: $i,SV1812: $i,SV1240: $i,SV506: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV506 ) )
= $true )
| ( ( ( c_lessequals @ SV1240 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SV2161 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SV1240 @ SV2161 @ SV506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5181]) ).
thf(5710,plain,
! [SV508: $i,SV1241: $i,SV1813: $i] :
( ( ( ~ ( c_lessequals @ SV1813 @ SV1241 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV508 @ SV1813 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV508 @ SV1241 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5182]) ).
thf(5711,plain,
! [SV2162: $i,SV1814: $i,SV1244: $i,SV512: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV512 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1244 @ SV1814 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV2162 @ SV1814 @ SV512 )
| ~ ( c_lessequals @ SV1244 @ SV2162 @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5185]) ).
thf(5712,plain,
! [SV2163: $i,SV1815: $i,SV1245: $i,SV513: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV513 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1245 @ SV1815 @ SV513 )
| ~ ( c_lessequals @ SV2163 @ SV1815 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ SV1245 @ SV2163 @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5186]) ).
thf(5713,plain,
! [SV2325: $i,SV2164: $i,SV1816: $i,SV1246: $i,SV514: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
| ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2164 ) @ SV514 )
| ~ ( c_lessequals @ SV2325 @ SV2164 @ SV514 )
| ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2325 ) @ SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5187]) ).
thf(5714,plain,
! [SV2165: $i,SV1817: $i,SV1247: $i,SV515: $i] :
( ( ( c_Type_Otyping @ SV515 @ SV1247 @ SV1817 )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV2165 @ SV1247 )
| ~ ( c_Type_Otyping @ SV515 @ SV2165 @ SV1817 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5188]) ).
thf(5715,plain,
! [SV516: $i,SV1818: $i,SV1248: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SV1818 @ tc_nat ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ominus__class_Ominus @ SV1248 @ SV1818 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5716,plain,
! [SV2326: $i,SV2166: $i,SV1819: $i,SV1249: $i,SV517: $i] :
( ( ! [SY6363: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV1249 @ SV1819 @ SV2166 ) @ SV2326 @ SY6363 @ SV2166 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV2326 @ SY6363 @ SV2166 ) @ SV1249 @ SV1819 @ SV2166 ) )
| ( SV1249 = SV2326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5190]) ).
thf(5717,plain,
! [SV1250: $i,SV518: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV518 @ ( c_Suc @ SV1250 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1250 @ SV518 @ tc_nat ) )
= $true )
| ( ( SV518 = SV1250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5191]) ).
thf(5718,plain,
! [SV2327: $i,SV2168: $i,SV1821: $i,SV1257: $i,SV527: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV527 @ SV1257 @ SV1821 ) @ ( c_Suc @ SV2168 ) @ SV2327 @ SV1821 )
= ( c_List_Olist_OCons @ SV527 @ ( c_List_Olist__update @ SV1257 @ SV2168 @ SV2327 @ SV1821 ) @ SV1821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5197]) ).
thf(5719,plain,
! [SV1822: $i,SV1258: $i,SV528: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV528 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1258 ) @ SV1822 ) @ SV528 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV528 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1258 @ SV528 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1822 @ SV528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5198]) ).
thf(5720,plain,
! [SV1259: $i,SV529: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV529 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1259 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1259 @ tc_nat ) @ SV529 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5199]) ).
thf(5721,plain,
! [SV1823: $i,SV1260: $i,SV530: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV530 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1260 @ SV1823 @ SV530 ) @ SV530 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV530 ) @ ( c_List_Olistsum @ SV1260 @ SV530 ) ) @ ( c_List_Olistsum @ SV1823 @ SV530 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5200]) ).
thf(5722,plain,
! [SV1824: $i,SV1263: $i,SV533: $i] :
( ( ( class_Orderings_Oorder @ SV533 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1263 @ SV1824 @ SV533 )
| ( SV1824 = SV1263 )
| ~ ( c_lessequals @ SV1263 @ SV1824 @ SV533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5723,plain,
! [SV1825: $i,SV1264: $i,SV534: $i] :
( ( ( class_Orderings_Oorder @ SV534 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1825 @ SV534 )
| ~ ( c_lessequals @ SV1264 @ SV1825 @ SV534 )
| ( SV1825 = SV1264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5724,plain,
! [SV1265: $i,SV535: $i] :
( ( ( c_lessequals @ SV535 @ SV1265 @ tc_nat )
= $false )
| ( ( SV535 = SV1265 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV535 @ SV1265 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5204]) ).
thf(5725,plain,
! [SV1266: $i,SV536: $i] :
( ( ( c_lessequals @ SV536 @ SV1266 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV536 @ SV1266 @ tc_nat )
= $true )
| ( ( SV536 = SV1266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5205]) ).
thf(5726,plain,
! [SV1267: $i,SV537: $i] :
( ( ( c_lessequals @ SV537 @ SV1267 @ tc_nat )
= $false )
| ( ( SV537 = SV1267 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV537 @ SV1267 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5206]) ).
thf(5727,plain,
! [SV1826: $i,SV1268: $i,SV538: $i] :
( ( ( class_Orderings_Oorder @ SV538 )
= $false )
| ( ( ( SV1268 = SV1826 )
| ( c_HOL_Oord__class_Oless @ SV1268 @ SV1826 @ SV538 )
| ~ ( c_lessequals @ SV1268 @ SV1826 @ SV538 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5207]) ).
thf(5728,plain,
! [SV1827: $i,SV1269: $i,SV539: $i] :
( ( ( class_Orderings_Oorder @ SV539 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1269 @ SV1827 @ SV539 )
| ( SV1269 = SV1827 )
| ~ ( c_lessequals @ SV1269 @ SV1827 @ SV539 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5208]) ).
thf(5729,plain,
! [SV1828: $i,SV1270: $i,SV540: $i] :
( ( ( class_Orderings_Oorder @ SV540 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1270 @ SV1828 @ SV540 )
| ( SV1270 = SV1828 )
| ~ ( c_lessequals @ SV1270 @ SV1828 @ SV540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5209]) ).
thf(5730,plain,
! [SV1829: $i,SV1271: $i,SV541: $i] :
( ( ( class_Orderings_Oorder @ SV541 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1271 @ SV1829 @ SV541 )
| ~ ( c_lessequals @ SV1271 @ SV1829 @ SV541 )
| ( SV1271 = SV1829 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5210]) ).
thf(5731,plain,
! [SV1830: $i,SV1272: $i,SV542: $i] :
( ( ( class_Orderings_Olinorder @ SV542 )
= $false )
| ( ( ( SV1272 = SV1830 )
| ~ ( c_lessequals @ SV1272 @ SV1830 @ SV542 )
| ( c_HOL_Oord__class_Oless @ SV1272 @ SV1830 @ SV542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5211]) ).
thf(5732,plain,
! [SV1831: $i,SV1273: $i,SV543: $i] :
( ( ( class_Orderings_Olinorder @ SV543 )
= $false )
| ( ( ( SV1273 = SV1831 )
| ( c_HOL_Oord__class_Oless @ SV1273 @ SV1831 @ SV543 )
| ~ ( c_lessequals @ SV1273 @ SV1831 @ SV543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5212]) ).
thf(5733,plain,
! [SV2328: $i,SV2169: $i,SV1832: $i,SV1275: $i,SV546: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV546 @ SV1275 @ SV1832 @ SV2169 ) @ SV1275 @ SV2328 @ SV2169 )
= ( c_List_Olist__update @ SV546 @ SV1275 @ SV2328 @ SV2169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5213]) ).
thf(5734,plain,
! [SV1837: $i,SV1282: $i,SV553: $i] :
( ( ( class_Orderings_Oorder @ SV553 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1282 @ SV1837 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV1837 @ SV1282 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5220]) ).
thf(5735,plain,
! [SV1838: $i,SV1283: $i,SV554: $i] :
( ( ( class_Orderings_Olinorder @ SV554 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1838 @ SV554 )
| ~ ( c_HOL_Oord__class_Oless @ SV1838 @ SV1283 @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5221]) ).
thf(5736,plain,
! [SV1839: $i,SV1285: $i,SV556: $i] :
( ( ( class_Orderings_Olinorder @ SV556 )
= $false )
| ( ( ( c_lessequals @ SV1285 @ SV1839 @ SV556 )
| ( c_lessequals @ SV1839 @ SV1285 @ SV556 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5222]) ).
thf(5737,plain,
! [SV1840: $i,SV1286: $i,SV557: $i] :
( ( ( class_Orderings_Opreorder @ SV557 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1286 @ SV1840 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ SV1840 @ SV1286 @ SV557 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5223]) ).
thf(5738,plain,
! [SV1841: $i,SV1287: $i,SV558: $i] :
( ( ( class_Orderings_Opreorder @ SV558 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1287 @ SV1841 @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ SV1841 @ SV1287 @ SV558 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5224]) ).
thf(5739,plain,
! [SV1288: $i,SV559: $i] :
( ( ( hBOOL @ ( hAPP @ SV559 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV559 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV559 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5225]) ).
thf(5740,plain,
! [SV1289: $i,SV562: $i] :
( ( ( hBOOL @ ( hAPP @ SV562 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV562 @ ( v_sko__List__Xupt__Xinduct__1 @ SV562 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV562 @ SV1289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5226]) ).
thf(5741,plain,
! [SV1291: $i,SV565: $i] :
( ( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV565 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV565 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV565 @ SV1291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5227]) ).
thf(5742,plain,
! [SV2329: $i,SV2174: $i,SV1843: $i,SV1293: $i,SV574: $i] :
( ( ! [SY6364: $i,SY6365: $i] :
( ( ( hAPP @ ( hAPP @ SV574 @ SV1293 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1843 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2174 @ SV2329 @ SV574 @ SY6364 @ SV1843 @ SY6365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5228]) ).
thf(5743,plain,
! [SV1844: $i,SV1294: $i,SV575: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV575 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Omap @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ SV575 ) @ SV575 @ SV1294 ) @ SV1844 @ SV1294 @ SV575 ) @ SV575 )
= ( c_HOL_Ozero__class_Ozero @ SV575 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5229]) ).
thf(5744,plain,
! [SV2330: $i,SV2175: $i,SV1846: $i,SV1296: $i,SV577: $i] :
( ( ( c_List_Odrop @ SV577 @ ( c_List_Omap @ SV1296 @ SV1846 @ SV2175 @ SV2330 ) @ SV2330 )
= ( c_List_Omap @ SV1296 @ ( c_List_Odrop @ SV577 @ SV1846 @ SV2175 ) @ SV2175 @ SV2330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5230]) ).
thf(5745,plain,
! [SV2176: $i,SV1847: $i,SV1297: $i,SV578: $i] :
( ( ( c_List_Odistinct @ SV578 @ SV1297 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Omap @ SV1847 @ SV578 @ SV1297 @ SV2176 ) @ SV2176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5231]) ).
thf(5746,plain,
! [SV2331: $i,SV2177: $i,SV1848: $i,SV1298: $i,SV579: $i] :
( ( ( c_List_Omap @ SV579 @ ( c_List_Oappend @ SV1298 @ SV1848 @ SV2177 ) @ SV2177 @ SV2331 )
= ( c_List_Oappend @ ( c_List_Omap @ SV579 @ SV1298 @ SV2177 @ SV2331 ) @ ( c_List_Omap @ SV579 @ SV1848 @ SV2177 @ SV2331 ) @ SV2331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5232]) ).
thf(5747,plain,
! [SV2332: $i,SV2178: $i,SV1849: $i,SV1299: $i,SV580: $i] :
( ( ( c_List_Omap @ SV580 @ ( c_List_Oreplicate @ SV1299 @ SV1849 @ SV2178 ) @ SV2178 @ SV2332 )
= ( c_List_Oreplicate @ SV1299 @ ( hAPP @ SV580 @ SV1849 ) @ SV2332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5233]) ).
thf(5748,plain,
! [SV2333: $i,SV2180: $i,SV1851: $i,SV1301: $i,SV582: $i] :
( ( ( c_List_Orotate @ SV582 @ ( c_List_Omap @ SV1301 @ SV1851 @ SV2180 @ SV2333 ) @ SV2333 )
= ( c_List_Omap @ SV1301 @ ( c_List_Orotate @ SV582 @ SV1851 @ SV2180 ) @ SV2180 @ SV2333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5235]) ).
thf(5749,plain,
! [SV2334: $i,SV2182: $i,SV1853: $i,SV1303: $i,SV584: $i] :
( ( ( c_List_Otake @ SV584 @ ( c_List_Omap @ SV1303 @ SV1853 @ SV2182 @ SV2334 ) @ SV2334 )
= ( c_List_Omap @ SV1303 @ ( c_List_Otake @ SV584 @ SV1853 @ SV2182 ) @ SV2182 @ SV2334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5237]) ).
thf(5750,plain,
! [SV2335: $i,SV2183: $i,SV1855: $i,SV1305: $i,SV586: $i] :
( ( ! [SY6366: $i] :
( ( c_List_Omap @ SV586 @ ( c_List_Omap @ SV1305 @ SV1855 @ SV2183 @ SV2335 ) @ SV2335 @ SY6366 )
= ( c_List_Omap @ ( c_Fun_Ocomp @ SV586 @ SV1305 @ SV2335 @ SY6366 @ SV2183 ) @ SV1855 @ SV2183 @ SY6366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5238]) ).
thf(5751,plain,
! [SV2336: $i,SV2184: $i,SV1856: $i,SV1306: $i,SV587: $i] :
( ( ( c_List_Omap @ SV587 @ ( c_List_Olist_OCons @ SV1306 @ SV1856 @ SV2184 ) @ SV2184 @ SV2336 )
= ( c_List_Olist_OCons @ ( hAPP @ SV587 @ SV1306 ) @ ( c_List_Omap @ SV587 @ SV1856 @ SV2184 @ SV2336 ) @ SV2336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5239]) ).
thf(5752,plain,
! [SV2337: $i,SV2185: $i,SV1857: $i,SV1307: $i,SV588: $i] :
( ( ( c_List_Olist_OCons @ ( hAPP @ SV588 @ SV1307 ) @ ( c_List_Omap @ SV588 @ SV1857 @ SV2185 @ SV2337 ) @ SV2337 )
= ( c_List_Omap @ SV588 @ ( c_List_Olist_OCons @ SV1307 @ SV1857 @ SV2185 ) @ SV2185 @ SV2337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5240]) ).
thf(5753,plain,
! [SV2338: $i,SV2186: $i,SV1858: $i,SV1308: $i,SV589: $i] :
( ( ( c_List_Omap @ SV589 @ ( c_List_Olist_OCons @ SV1308 @ SV1858 @ SV2186 ) @ SV2186 @ SV2338 )
= ( c_List_Olist_OCons @ ( hAPP @ SV589 @ SV1308 ) @ ( c_List_Omap @ SV589 @ SV1858 @ SV2186 @ SV2338 ) @ SV2338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5241]) ).
thf(5754,plain,
! [SV2339: $i,SV2187: $i,SV1859: $i,SV1309: $i,SV590: $i] :
( ( ! [SY6367: $i] :
( ( c_List_Omap @ SV590 @ ( c_List_Olist__update @ SV1309 @ SV1859 @ SV2187 @ SV2339 ) @ SV2339 @ SY6367 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV590 @ SV1309 @ SV2339 @ SY6367 ) @ SV1859 @ ( hAPP @ SV590 @ SV2187 ) @ SY6367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5242]) ).
thf(5755,plain,
! [SV1861: $i,SV1313: $i,SV594: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV594 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1313 @ SV1861 @ SV594 @ SV594 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1313 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV594 ) @ SV1861 @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV594 @ SV594 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5245]) ).
thf(5756,plain,
! [SV2189: $i,SV1863: $i,SV1316: $i,SV597: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV597 ) @ SV1316 ) @ SV1863 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2189 ) @ SV1316 ) @ SV1863 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV597 @ SV2189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5247]) ).
thf(5757,plain,
! [SV2340: $i,SV2190: $i,SV1865: $i,SV1318: $i,SV599: $i] :
( ( ( c_List_Ofoldr @ SV599 @ SV1318 @ SV1865 @ SV2190 @ SV2340 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV599 @ SV2190 @ SV2340 @ SV2340 ) @ SV1865 @ ( c_List_Orev @ SV1318 @ SV2190 ) @ SV2340 @ SV2190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5248]) ).
thf(5758,plain,
! [SV2341: $i,SV2191: $i,SV1866: $i,SV1319: $i,SV600: $i] :
( ( ( c_List_Ofoldl @ SV600 @ SV1319 @ SV1866 @ SV2191 @ SV2341 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV600 @ SV2191 @ SV2341 @ SV2191 ) @ ( c_List_Orev @ SV1866 @ SV2341 ) @ SV1319 @ SV2341 @ SV2191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5249]) ).
thf(5759,plain,
! [SV2342: $i,SV2192: $i,SV1867: $i,SV1320: $i,SV601: $i] :
( ( ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1867 ) @ SV2192 ) @ SV2342 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV1320 @ SV1867 ) @ SV2192 ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ SV1867 @ SV2342 ) ) @ ( c_Type_Otype_Otype__rec @ SV601 @ SV1320 @ SV2192 @ SV2342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5250]) ).
thf(5760,plain,
! [SV2343: $i,SV2193: $i,SV1868: $i,SV1321: $i,SV602: $i] :
( ( ( c_Type_Otype_Otype__case @ SV602 @ SV1321 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1868 ) @ SV2193 ) @ SV2343 )
= ( hAPP @ ( hAPP @ SV1321 @ SV1868 ) @ SV2193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5251]) ).
thf(5761,plain,
! [SV2344: $i,SV2194: $i,SV1869: $i,SV1322: $i,SV603: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV603 @ ( c_Type_Otype_Otype__case @ SV1322 @ SV1869 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2194 ) @ SV2344 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV603 @ ( hAPP @ ( hAPP @ SV1869 @ SV2194 ) @ SV2344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5252]) ).
thf(5762,plain,
! [SV2345: $i,SV2195: $i,SV1870: $i,SV1323: $i,SV604: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV604 @ ( c_Type_Otype_Otype__case @ SV1323 @ SV1870 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2195 ) @ SV2345 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV604 @ ( hAPP @ ( hAPP @ SV1870 @ SV2195 ) @ SV2345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5253]) ).
thf(5763,plain,
! [SV2346: $i,SV2196: $i,SV1871: $i,SV1324: $i,SV605: $i] :
( ( ! [SY6368: $i] :
( ( c_List_Ofoldr @ SV605 @ ( c_List_Olist_OCons @ SV1324 @ SV1871 @ SV2196 ) @ SV2346 @ SV2196 @ SY6368 )
= ( hAPP @ ( hAPP @ SV605 @ SV1324 ) @ ( c_List_Ofoldr @ SV605 @ SV1871 @ SV2346 @ SV2196 @ SY6368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5254]) ).
thf(5764,plain,
! [SV2347: $i,SV2197: $i,SV1872: $i,SV1325: $i,SV606: $i] :
( ( ! [SY6369: $i] :
( ( c_List_Ofoldr @ SV606 @ ( c_List_Oappend @ SV1325 @ SV1872 @ SV2197 ) @ SV2347 @ SV2197 @ SY6369 )
= ( c_List_Ofoldr @ SV606 @ SV1325 @ ( c_List_Ofoldr @ SV606 @ SV1872 @ SV2347 @ SV2197 @ SY6369 ) @ SV2197 @ SY6369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5255]) ).
thf(5765,plain,
! [SV1329: $i,SV1875: $i,SV610: $i] :
( ( ( c_Lambda_Obeta @ SV610 @ SV1875 )
= $false )
| ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV610 ) @ SV1329 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1875 ) @ SV1329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5258]) ).
thf(5766,plain,
! [SV2348: $i,SV2199: $i,SV1876: $i,SV1330: $i,SV611: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV611 @ SV1330 @ SV1876 @ SV2199 ) @ SV2348 )
= ( hAPP @ SV611 @ SV2348 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2348 @ SV1330 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5259]) ).
thf(5767,plain,
! [SV2349: $i,SV2200: $i,SV1877: $i,SV1331: $i,SV612: $i] :
( ( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1331 @ SV1877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2200 )
| ~ ( c_Type_Otypings @ SV612 @ SV1877 @ SV2349 )
| ~ ( c_Type_Otyping @ SV612 @ SV1331 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2349 @ SV2200 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5260]) ).
thf(5768,plain,
! [SV2201: $i,SV1878: $i,SV1332: $i,SV613: $i] :
( ( ( c_Type_Otyping @ SV613 @ ( c_Lambda_OdB_OAbs @ SV1332 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1878 ) @ SV2201 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV613 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1878 @ tc_Type_Otype ) @ SV1332 @ SV2201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5261]) ).
thf(5769,plain,
! [SV1333: $i,SV614: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV614 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV614 )
| ~ ( class_Power_Opower @ SV614 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5262]) ).
thf(5770,plain,
! [SV1334: $i,SV615: $i] :
( ( ( ~ ( class_Power_Opower @ SV615 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV615 ) @ SV1334 @ SV615 )
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
| ( SV1334
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV615 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5263]) ).
thf(5771,plain,
! [SV2350: $i,SV2202: $i,SV1879: $i,SV1336: $i,SV618: $i] :
( ( ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ SV1336 @ SV1879 @ SV2202 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2350 @ SV2202 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV618 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2350 @ SV2202 ) @ ( c_Suc @ SV1336 ) @ SV1879 @ SV2202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5264]) ).
thf(5772,plain,
! [SV2351: $i,SV2203: $i,SV1881: $i,SV1338: $i,SV620: $i] :
( ( ! [SY6370: $i,SY6371: $i] :
( ( c_List_Ofoldr @ SV620 @ ( c_List_Omap @ SV1338 @ SV1881 @ SV2203 @ SV2351 ) @ SY6370 @ SV2351 @ SY6371 )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ SV620 @ SV1338 @ SV2351 @ ( tc_fun @ SY6371 @ SY6371 ) @ SV2203 ) @ SV1881 @ SY6370 @ SV2203 @ SY6371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5265]) ).
thf(5773,plain,
! [SV2352: $i,SV2204: $i,SV1882: $i,SV1339: $i,SV621: $i] :
( ( ! [SY6372: $i] :
( ~ ( c_Type_Otyping @ SV621 @ SV1339 @ SV1882 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SV2204 @ SV1882 @ tc_Type_Otype ) @ SV2352 @ SY6372 )
| ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2352 ) @ SV1339 ) @ SV2204 ) @ SY6372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5266]) ).
thf(5774,plain,
! [SV2353: $i,SV2205: $i,SV1883: $i,SV1340: $i,SV622: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV622 @ SV1340 @ SV1883 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV2205 ) @ SV1340 ) @ SV2353 )
| ~ ( c_Type_Otyping @ SV622 @ SV2205 @ SV2353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5267]) ).
thf(5775,plain,
! [SV2354: $i,SV2207: $i,SV1885: $i,SV1342: $i,SV625: $i] :
( ( ! [SY6373: $i] :
( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1885 ) @ SV2207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2354 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SV1885 @ SY6373 @ tc_Type_Otype ) @ SV2207 @ SV2354 )
| ~ ( c_Type_Otyping @ SV625 @ SV1342 @ SY6373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5269]) ).
thf(5776,plain,
! [SV2355: $i,SV2209: $i,SV1887: $i,SV1344: $i,SV627: $i] :
( ( ! [SY6374: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV627 @ SV1344 @ SV1887 @ SV2209 ) @ SV2355 ) @ SY6374 )
= ( hAPP @ ( hAPP @ SV627 @ SY6374 ) @ SV2355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5271]) ).
thf(5777,plain,
! [SV2356: $i,SV2210: $i,SV1888: $i,SV1345: $i,SV628: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV628 @ SV1345 @ SV1888 @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1345 ) @ SV2210 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2356 )
| ~ ( c_Type_Otypings @ SV628 @ SV2210 @ SV2356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5272]) ).
thf(5778,plain,
! [SV2357: $i,SV2211: $i,SV1890: $i,SV1350: $i,SV633: $i] :
( ( ! [SY6375: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV633 @ SV1350 @ SV1890 @ SV2211 ) @ SV2357 ) @ SY6375 )
= ( hAPP @ ( hAPP @ SV633 @ SY6375 ) @ SV2357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5276]) ).
thf(5779,plain,
! [SV2358: $i,SV2212: $i,SV1891: $i,SV1351: $i,SV634: $i] :
( ( ! [SY6376: $i] :
( ( c_COMBB @ SV634 @ SV1351 @ SV1891 @ SV2212 @ SV2358 @ SY6376 )
= ( hAPP @ SV634 @ ( hAPP @ SV1351 @ SV1891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5277]) ).
thf(5780,plain,
! [SV1892: $i,SV1353: $i,SV636: $i] :
( ( ( c_fequal @ SV636 @ SV1353 @ SV1892 )
= $false )
| ( ( SV636 = SV1353 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5278]) ).
thf(5781,plain,
! [SV2213: $i,SV1893: $i,SV1354: $i,SV637: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV637 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV1893 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV2213 ) )
| ( SV1893 = SV2213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5279]) ).
thf(5782,plain,
! [SV1894: $i,SV1355: $i,SV638: $i] :
( ( ( SV638
= ( c_List_Oappend @ SV638 @ SV1355 @ SV1894 ) )
= $false )
| ( ( SV1355
= ( c_List_Olist_ONil @ SV1894 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5280]) ).
thf(5783,plain,
! [SV1895: $i,SV1356: $i,SV639: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV639 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1356 @ SV1895 @ SV639 )
!= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
| ( SV1356
= ( c_HOL_Ozero__class_Ozero @ SV639 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5281]) ).
thf(5784,plain,
! [SV1358: $i,SV641: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV641 ) @ SV1358 ) @ SV1358 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
= $true )
| ( ( SV1358
= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV641 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5283]) ).
thf(5785,plain,
! [SV2359: $i,SV2214: $i,SV1896: $i,SV1360: $i,SV643: $i] :
( ( ( ( c_List_Omap @ SV643 @ SV1360 @ SV1896 @ SV2214 )
!= ( c_List_Omap @ SV643 @ SV2359 @ SV1896 @ SV2214 ) )
| ( ( c_Nat_Osize__class_Osize @ SV1360 @ ( tc_List_Olist @ SV1896 ) )
= ( c_Nat_Osize__class_Osize @ SV2359 @ ( tc_List_Olist @ SV1896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5285]) ).
thf(5786,plain,
! [SV1897: $i,SV1361: $i,SV644: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
!= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
| ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5286]) ).
thf(5787,plain,
! [SV645: $i,SV1362: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1362 @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1362 = SV645 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV645 @ SV1362 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5287]) ).
thf(5788,plain,
! [SV2215: $i,SV1898: $i,SV1363: $i,SV646: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV646 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV1898 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV2215 ) )
| ( SV1898 = SV2215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5288]) ).
thf(5789,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV647 )
| ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5289]) ).
thf(5790,plain,
! [SV2216: $i,SV1900: $i,SV1365: $i,SV648: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV648 ) @ SV1365 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1900 ) @ SV2216 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV648 = SV1900 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5290]) ).
thf(5791,plain,
! [SV1901: $i,SV1367: $i,SV650: $i] :
( ( ( ( c_List_Oappend @ SV650 @ SV1367 @ SV1901 )
= SV650 )
= $false )
| ( ( SV1367
= ( c_List_Olist_ONil @ SV1901 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(5792,plain,
! [SV1368: $i,SV651: $i] :
( ( ( SV651
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV651
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV651 ) @ SV1368 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5293]) ).
thf(5793,plain,
! [SV2217: $i,SV1902: $i,SV1369: $i,SV652: $i] :
( ( ( ( c_List_Olist_ONil @ SV652 )
!= ( c_List_Omap @ SV1369 @ SV1902 @ SV2217 @ SV652 ) )
= $true )
| ( ( SV1902
= ( c_List_Olist_ONil @ SV2217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5294]) ).
thf(5794,plain,
! [SV2360: $i,SV2218: $i,SV1903: $i,SV1370: $i,SV653: $i] :
( ( ( ( c_List_Oappend @ SV653 @ SV1370 @ SV1903 )
!= ( c_List_Oappend @ SV2218 @ SV2360 @ SV1903 ) )
| ( SV1370
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ SV2218 @ SV1903 ) @ SV2360 @ SV1903 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ ( c_Nat_Osize__class_Osize @ SV2218 @ ( tc_List_Olist @ SV1903 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5295]) ).
thf(5795,plain,
! [SV654: $i,SV1371: $i] :
( ( ( SV1371
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV654
= ( 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 ) @ SV654 ) @ SV1371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5296]) ).
thf(5796,plain,
! [SV2219: $i,SV1904: $i,SV1372: $i,SV655: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
!= SV2219 )
= $true )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 )
!= SV655 )
| ( SV1904
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
| ( ( c_List_Oappend @ SV1904 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SV2219 @ SV1372 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5297]) ).
thf(5797,plain,
! [SV1373: $i,SV656: $i] :
( ( ( SV656
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1373
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV656 ) @ SV1373 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5298]) ).
thf(5798,plain,
! [SV1905: $i,SV1374: $i,SV657: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV657 @ SV1374 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1905 @ SV1374 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV657 = SV1905 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5299]) ).
thf(5799,plain,
! [SV2220: $i,SV1906: $i,SV1375: $i,SV659: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV659 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
!= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
| ( SV1375 = SV2220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5300]) ).
thf(5800,plain,
! [SV2361: $i,SV2221: $i,SV1907: $i,SV1376: $i,SV660: $i] :
( ( ! [SY6377: $i,SY6378: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
| ~ ( c_Type_Otyping @ SY6377 @ SV2221 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6377 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SY6378 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5301]) ).
thf(5801,plain,
! [SV1910: $i,SV1380: $i,SV664: $i] :
( ( ( ( c_List_Olist_ONil @ SV664 )
= ( c_List_Oreplicate @ SV1380 @ SV1910 @ SV664 ) )
= $false )
| ( ( SV1380
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5802,plain,
! [SV2222: $i,SV1911: $i,SV1381: $i,SV665: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV665 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1381 @ SV1911 @ SV665 )
!= ( c_Power_Opower__class_Opower @ SV1381 @ SV2222 @ SV665 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 )
| ( SV1911 = SV2222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5306]) ).
thf(5803,plain,
! [SV1912: $i,SV1382: $i,SV666: $i] :
( ( ( ( hAPP @ SV666 @ ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SV1382 @ SV1912 ) )
= ( c_List_Osko__List__Xmap__idI__1__1 @ SV666 @ SV1382 @ SV1912 ) )
= $false )
| ( ( ( c_List_Omap @ SV666 @ SV1382 @ SV1912 @ SV1912 )
= SV1382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5307]) ).
thf(5804,plain,
! [SV1914: $i,SV1384: $i,SV668: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV668 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV668 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1384 @ SV1914 @ SV668 )
!= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
| ( SV1384 = SV1914 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5309]) ).
thf(5805,plain,
! [SV2362: $i,SV2223: $i,SV1916: $i,SV1386: $i,SV670: $i] :
( ( ( ( c_List_Oappend @ SV670 @ SV1386 @ SV1916 )
!= ( c_List_Oappend @ SV2223 @ SV2362 @ SV1916 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ SV670 @ SV1916 )
= SV2223 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV670 @ ( tc_List_Olist @ SV1916 ) ) @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5311]) ).
thf(5806,plain,
! [SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ! [SY6379: $i,SY6380: $i,SY6381: $i,SY6382: $i,SY6383: $i,SY6384: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SY6379 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SY6380 @ SY6381 @ SY6382 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SY6383 @ SY6381 @ SY6384 ) @ SY6379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5314]) ).
thf(5807,plain,
! [SV1919: $i,SV1389: $i,SV674: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV674 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1389 @ SV674 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1919 @ SV674 ) )
| ( SV1389 = SV1919 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5315]) ).
thf(5808,plain,
! [SV2225: $i,SV1920: $i,SV1391: $i,SV676: $i] :
( ( ( ( c_List_Oappend @ SV676 @ SV1391 @ SV1920 )
!= ( c_List_Oappend @ SV676 @ SV2225 @ SV1920 ) )
= $true )
| ( ( SV1391 = SV2225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5317]) ).
thf(5809,plain,
! [SV1921: $i,SV1392: $i,SV677: $i] :
( ( ( ( c_List_Otake @ SV677 @ SV1392 @ SV1921 )
= ( c_List_Olist_ONil @ SV1921 ) )
= $false )
| ( ( ( SV1392
= ( c_List_Olist_ONil @ SV1921 ) )
| ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5318]) ).
thf(5810,plain,
! [SV2364: $i,SV2226: $i,SV1922: $i,SV1393: $i,SV678: $i] :
( ( ! [SY6385: $i,SY6386: $i,SY6387: $i,SY6388: $i] :
( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SV2226 @ SV2364 )
!= ( c_Fun_Ocomp @ SY6385 @ SY6386 @ SY6387 @ SV2226 @ SV2364 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SY6388 ) )
= ( hAPP @ SY6385 @ ( hAPP @ SY6386 @ SY6388 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5319]) ).
thf(5811,plain,
! [SV679: $i,SV1394: $i] :
( ( ( SV1394
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1394
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV679 ) @ SV1394 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5320]) ).
thf(5812,plain,
! [SV1923: $i,SV1395: $i,SV680: $i] :
( ( ( SV680
= ( c_List_Oappend @ SV1395 @ SV680 @ SV1923 ) )
= $false )
| ( ( SV1395
= ( c_List_Olist_ONil @ SV1923 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5321]) ).
thf(5813,plain,
! [SV683: $i,SV1398: $i] :
( ( ( SV1398
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV683
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV683 ) @ SV1398 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5324]) ).
thf(5814,plain,
! [SV2365: $i,SV2227: $i,SV1925: $i,SV1399: $i,SV684: $i] :
( ( ( ( hAPP @ SV684 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) )
!= ( hAPP @ SV1399 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) ) )
| ( ( c_List_Omap @ SV684 @ SV1925 @ SV2227 @ SV2365 )
= ( c_List_Omap @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5325]) ).
thf(5815,plain,
! [SV1926: $i,SV1400: $i,SV685: $i] :
( ( ( ( c_List_Oappend @ SV685 @ SV1400 @ SV1926 )
= ( c_List_Olist_ONil @ SV1926 ) )
= $false )
| ( ( SV685
= ( c_List_Olist_ONil @ SV1926 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5326]) ).
thf(5816,plain,
! [SV2228: $i,SV1927: $i,SV1401: $i,SV686: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV686 ) @ SV1401 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1927 ) @ SV2228 ) )
= $true )
| ( ( SV1401 = SV2228 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5327]) ).
thf(5817,plain,
! [SV2366: $i,SV2229: $i,SV1928: $i,SV1402: $i,SV687: $i] :
( ( ( ( c_List_Oappend @ SV687 @ ( c_List_Olist_OCons @ SV1402 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 )
!= ( c_List_Oappend @ SV2229 @ ( c_List_Olist_OCons @ SV2366 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 ) )
| ( SV1402 = SV2366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5328]) ).
thf(5818,plain,
! [SV2230: $i,SV1929: $i,SV1403: $i,SV688: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV688 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV1929 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV2230 ) )
| ( SV1929 = SV2230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5329]) ).
thf(5819,plain,
! [SV2367: $i,SV2231: $i,SV1930: $i,SV1404: $i,SV689: $i] :
( ( ( ( c_List_Oreplicate @ SV689 @ SV1404 @ SV1930 )
!= ( c_List_Oreplicate @ SV2231 @ SV2367 @ SV1930 ) )
| ( SV689 = SV2231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5330]) ).
thf(5820,plain,
! [SV2368: $i,SV2232: $i,SV1931: $i,SV1405: $i,SV690: $i] :
( ( ( ( hAPP @ SV690 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) )
!= ( hAPP @ SV1405 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) ) )
| ( ( c_List_Omap @ SV690 @ SV1931 @ SV2232 @ SV2368 )
= ( c_List_Omap @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5331]) ).
thf(5821,plain,
! [SV1933: $i,SV1408: $i,SV693: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV693 ) @ SV1408 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1933 ) @ SV1408 ) )
= $false )
| ( ( SV693 = SV1933 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5334]) ).
thf(5822,plain,
! [SV2369: $i,SV2233: $i,SV1934: $i,SV1409: $i,SV694: $i] :
( ( ( ( c_List_Oappend @ SV694 @ SV1409 @ SV1934 )
!= ( c_List_Oappend @ SV2233 @ SV2369 @ SV1934 ) )
| ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ SV2233 @ SV1934 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ ( c_Nat_Osize__class_Osize @ SV2233 @ ( tc_List_Olist @ SV1934 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5335]) ).
thf(5823,plain,
! [SV1935: $i,SV1410: $i,SV695: $i] :
( ( ( ( c_List_Oappend @ SV695 @ SV1410 @ SV1935 )
= ( c_List_Olist_ONil @ SV1935 ) )
= $false )
| ( ( SV1410
= ( c_List_Olist_ONil @ SV1935 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5336]) ).
thf(5824,plain,
! [SV2370: $i,SV2234: $i,SV1936: $i,SV1411: $i,SV696: $i] :
( ( ( ( c_List_Olist_OCons @ SV696 @ SV1411 @ SV1936 )
!= ( c_List_Olist_OCons @ SV2234 @ SV2370 @ SV1936 ) )
| ( SV696 = SV2234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5337]) ).
thf(5825,plain,
! [SV2235: $i,SV1937: $i,SV1412: $i,SV697: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 )
!= SV697 )
= $true )
| ( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1937 @ ( tc_List_Olist @ SV1412 ) ) @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SV1937 @ SV2235 @ SV1412 )
= ( c_List_Oappend @ SV697 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 ) @ SV2235 @ SV1412 ) @ SV1412 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5338]) ).
thf(5826,plain,
! [SV1938: $i,SV1413: $i,SV698: $i] :
( ( ( ( c_List_Olist_ONil @ SV698 )
= ( c_List_Oappend @ SV1413 @ SV1938 @ SV698 ) )
= $false )
| ( ( SV1413
= ( c_List_Olist_ONil @ SV698 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5339]) ).
thf(5827,plain,
! [SV2236: $i,SV1939: $i,SV1414: $i,SV699: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV699 ) @ SV1414 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1939 ) @ SV2236 ) )
= $true )
| ( ( SV699 = SV1939 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5340]) ).
thf(5828,plain,
! [SV2237: $i,SV1940: $i,SV1415: $i,SV700: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV700 ) @ SV1415 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1940 ) @ SV2237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1415 = SV2237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5341]) ).
thf(5829,plain,
! [SV1416: $i,SV701: $i] :
( ( ( SV701
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV701
= ( 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 ) @ SV701 ) @ SV1416 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5342]) ).
thf(5830,plain,
! [SV2371: $i,SV2238: $i,SV1942: $i,SV1419: $i,SV704: $i] :
( ( ( ( c_List_Oreplicate @ SV704 @ SV1419 @ SV1942 )
!= ( c_List_Oreplicate @ SV2238 @ SV2371 @ SV1942 ) )
| ( SV1419 = SV2371 )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5345]) ).
thf(5831,plain,
! [SV1943: $i,SV1420: $i,SV706: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SV1420 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1943 @ SV1420 @ tc_nat ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1420 @ SV1943 @ tc_nat )
| ~ ( c_lessequals @ SV1420 @ SV706 @ tc_nat )
| ( SV706 = SV1943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5346]) ).
thf(5832,plain,
! [SV1944: $i,SV1421: $i,SV707: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV707 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1421 @ SV1944 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV707 )
= SV1421 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5347]) ).
thf(5833,plain,
! [SV2239: $i,SV1945: $i,SV1422: $i,SV708: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV708 ) @ SV1422 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1945 ) @ SV2239 ) )
= $true )
| ( ( SV708 = SV1945 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5348]) ).
thf(5834,plain,
! [SV1946: $i,SV1423: $i,SV709: $i] :
( ( ( ( c_List_Orotate @ SV709 @ SV1423 @ SV1946 )
= ( c_List_Olist_ONil @ SV1946 ) )
= $false )
| ( ( SV1423
= ( c_List_Olist_ONil @ SV1946 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5349]) ).
thf(5835,plain,
! [SV1947: $i,SV1424: $i,SV711: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV711 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1424 @ SV1947 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SV1424 = SV1947 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5836,plain,
! [SV2372: $i,SV2240: $i,SV1948: $i,SV1425: $i,SV712: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
!= ( c_HOL_Ominus__class_Ominus @ SV2240 @ SV2372 @ SV712 ) )
| ( c_HOL_Oord__class_Oless @ SV2240 @ SV2372 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5351]) ).
thf(5837,plain,
! [SV2241: $i,SV1949: $i,SV1426: $i,SV713: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV713 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1426 ) @ SV1949 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV713 @ SV2241 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SV1949 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5352]) ).
thf(5838,plain,
! [SV1950: $i,SV1427: $i,SV714: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV714 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV714 )
| ( SV1427
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SV1427 ) @ SV1950 ) )
| ( SV1950
= ( c_HOL_Ozero__class_Ozero @ SV714 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5353]) ).
thf(5839,plain,
! [SV1951: $i,SV1428: $i,SV715: $i] :
( ( ( ( c_List_Orev @ SV715 @ SV1428 )
= ( c_List_Orev @ SV1951 @ SV1428 ) )
= $false )
| ( ( SV715 = SV1951 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5840,plain,
! [SV1952: $i,SV1429: $i,SV716: $i] :
( ( ( ( c_List_Olist_ONil @ SV716 )
= ( c_List_Oappend @ SV1429 @ SV1952 @ SV716 ) )
= $false )
| ( ( SV1952
= ( c_List_Olist_ONil @ SV716 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5355]) ).
thf(5841,plain,
! [SV1430: $i,SV717: $i] :
( ( ( SV717
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1430
= ( 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 ) @ SV717 ) @ SV1430 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5356]) ).
thf(5842,plain,
! [SV2242: $i,SV1953: $i,SV1431: $i,SV718: $i] :
( ( ( ( c_List_Omap @ SV718 @ SV1431 @ SV1953 @ SV2242 )
!= ( c_List_Olist_ONil @ SV2242 ) )
= $true )
| ( ( SV1431
= ( c_List_Olist_ONil @ SV1953 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5357]) ).
thf(5843,plain,
! [SV2243: $i,SV1954: $i,SV1432: $i,SV719: $i] :
( ( ( ( c_List_Orev @ SV719 @ SV1432 )
!= ( c_List_Olist_OCons @ SV1954 @ SV2243 @ SV1432 ) )
= $true )
| ( ( SV719
= ( c_List_Oappend @ ( c_List_Orev @ SV2243 @ SV1432 ) @ ( c_List_Olist_OCons @ SV1954 @ ( c_List_Olist_ONil @ SV1432 ) @ SV1432 ) @ SV1432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5358]) ).
thf(5844,plain,
! [SV2244: $i,SV1955: $i,SV1433: $i,SV720: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV720 ) @ SV1433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1955 ) @ SV2244 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5359]) ).
thf(5845,plain,
! [SV2373: $i,SV2245: $i,SV1956: $i,SV1434: $i,SV721: $i] :
( ( ( ( c_List_Olist_OCons @ SV721 @ SV1434 @ SV1956 )
!= ( c_List_Olist_OCons @ SV2245 @ SV2373 @ SV1956 ) )
| ( SV1434 = SV2373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5360]) ).
thf(5846,plain,
! [SV2246: $i,SV1957: $i,SV1435: $i,SV722: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV722 ) @ SV1435 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1957 ) @ SV2246 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1957 @ SV1435 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV722 @ SV2246 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5361]) ).
thf(5847,plain,
! [SV2247: $i,SV1958: $i,SV1436: $i,SV723: $i] :
( ( ( ( c_List_Olist__update @ SV723 @ SV1436 @ SV1958 @ SV2247 )
!= ( c_List_Olist_ONil @ SV2247 ) )
= $true )
| ( ( SV723
= ( c_List_Olist_ONil @ SV2247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5362]) ).
thf(5848,plain,
! [SV2248: $i,SV1959: $i,SV1438: $i,SV725: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV725 ) @ SV1438 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1959 ) @ SV2248 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV725 = SV1959 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5364]) ).
thf(5849,plain,
! [SV2374: $i,SV2249: $i,SV1960: $i,SV1439: $i,SV726: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
!= ( c_HOL_Ominus__class_Ominus @ SV2249 @ SV2374 @ SV726 ) )
| ( c_lessequals @ SV2374 @ SV2249 @ SV726 )
| ~ ( c_lessequals @ SV1960 @ SV1439 @ SV726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5365]) ).
thf(5850,plain,
! [SV1961: $i,SV1440: $i,SV727: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SV1440 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV727 ) @ SV1961 ) )
= $false )
| ( ( SV1440 = SV1961 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5366]) ).
thf(5851,plain,
! [SV2250: $i,SV1962: $i,SV1441: $i,SV728: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV728 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1441 @ SV1441 @ SV728 )
!= ( c_HOL_Ominus__class_Ominus @ SV1962 @ SV2250 @ SV728 ) )
| ( SV1962 = SV2250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5367]) ).
thf(5852,plain,
! [SV1442: $i,SV729: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV729 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV729 )
| ~ ( class_Power_Opower @ SV729 )
| ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5368]) ).
thf(5853,plain,
! [SV1963: $i,SV1443: $i,SV730: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5369]) ).
thf(5854,plain,
! [SV1964: $i,SV1444: $i,SV731: $i] :
( ( ( ( c_List_Oreplicate @ SV731 @ SV1444 @ SV1964 )
= ( c_List_Olist_ONil @ SV1964 ) )
= $false )
| ( ( SV731
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5370]) ).
thf(5855,plain,
! [SV2375: $i,SV2251: $i,SV1965: $i,SV1446: $i,SV734: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV734 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2251 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2375 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ SV2251 )
= SV2375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5373]) ).
thf(5856,plain,
! [SV1966: $i,SV1447: $i,SV735: $i] :
( ( ( ( c_List_Orev @ SV735 @ SV1447 )
= ( c_List_Olist_OCons @ SV1966 @ ( c_List_Olist_ONil @ SV1447 ) @ SV1447 ) )
= $false )
| ( ( SV735
= ( c_List_Olist_OCons @ SV1966 @ ( c_List_Olist_ONil @ SV1447 ) @ SV1447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5374]) ).
thf(5857,plain,
! [SV1967: $i,SV1448: $i,SV736: $i] :
( ( ( ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SV1448 ) @ SV1448 )
= ( c_List_Orev @ SV1967 @ SV1448 ) )
= $false )
| ( ( SV1967
= ( c_List_Olist_OCons @ SV736 @ ( c_List_Olist_ONil @ SV1448 ) @ SV1448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5375]) ).
thf(5858,plain,
! [SV1968: $i,SV1450: $i,SV738: $i] :
( ( ( SV738
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SV1450 ) ) @ SV1968 @ SV1450 ) )
= $false )
| ( ( ( c_List_Oappend @ SV738 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV738 @ ( tc_List_Olist @ SV1450 ) ) @ SV1968 @ SV1450 ) @ SV1450 )
= SV1968 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5377]) ).
thf(5859,plain,
! [SV2376: $i,SV2252: $i,SV1969: $i,SV1451: $i,SV740: $i] :
( ( ( ( hAPP @ SV740 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) )
!= ( hAPP @ SV1451 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) ) )
| ( ( c_List_Omap @ SV740 @ SV1969 @ SV2252 @ SV2376 )
= ( c_List_Omap @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5378]) ).
thf(5860,plain,
! [SV2253: $i,SV1970: $i,SV1452: $i,SV741: $i] :
( ( ( SV741
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) )
= $true )
| ( ( ( ( c_List_Oappend @ SV741 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) @ SV2253 @ SV1452 ) @ SV1452 )
= ( c_List_Oappend @ SV1970 @ SV2253 @ SV1452 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ ( c_Nat_Osize__class_Osize @ SV1970 @ ( tc_List_Olist @ SV1452 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5379]) ).
thf(5861,plain,
! [SV2254: $i,SV1971: $i,SV1453: $i,SV742: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV742 ) ) @ SV1453 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1971 ) @ SV2254 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5380]) ).
thf(5862,plain,
! [SV2255: $i,SV1972: $i,SV1454: $i,SV744: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV744 ) @ SV1454 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1972 ) @ SV2255 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1454 = SV2255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5381]) ).
thf(5863,plain,
! [SV2377: $i,SV2256: $i,SV1974: $i,SV1458: $i,SV749: $i] :
( ( ( ( c_List_Oappend @ SV749 @ SV1458 @ SV1974 )
!= ( c_List_Oappend @ SV2256 @ SV2377 @ SV1974 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ SV749 @ SV1974 ) @ SV1458 @ SV1974 )
= SV2377 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV749 @ ( tc_List_Olist @ SV1974 ) ) @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5385]) ).
thf(5864,plain,
! [SV2378: $i,SV2257: $i,SV1975: $i,SV1459: $i,SV750: $i] :
( ( ! [SY6389: $i,SY6390: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
| ~ ( c_Type_Otyping @ SY6389 @ SV2257 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6389 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SY6390 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5386]) ).
thf(5865,plain,
! [SV1976: $i,SV1460: $i,SV751: $i] :
( ( ( ( c_List_Oappend @ SV751 @ SV1460 @ SV1976 )
= SV1460 )
= $false )
| ( ( SV751
= ( c_List_Olist_ONil @ SV1976 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5387]) ).
thf(5866,plain,
! [SV1978: $i,SV1463: $i,SV754: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SV1463 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ SV1978 ) )
= $false )
| ( ( SV1463 = SV1978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5389]) ).
thf(5867,plain,
! [SV2379: $i,SV2258: $i,SV1979: $i,SV1464: $i,SV755: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
!= ( c_HOL_Ominus__class_Ominus @ SV2258 @ SV2379 @ SV755 ) )
| ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SV2258 @ SV2379 @ SV755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5390]) ).
thf(5868,plain,
! [SV1980: $i,SV1465: $i,SV756: $i] :
( ( ( class_Orderings_Olinorder @ SV756 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV1465 @ SV1980 @ SV756 )
!= SV1980 )
| ( c_lessequals @ SV1465 @ SV1980 @ SV756 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5391]) ).
thf(5869,plain,
! [SV2259: $i,SV1981: $i,SV1466: $i,SV757: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV757 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
!= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
| ( SV1466 = SV2259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5392]) ).
thf(5870,plain,
! [SV1982: $i,SV1467: $i,SV758: $i] :
( ( ( ( c_List_Odrop @ SV758 @ SV1467 @ SV1982 )
= ( c_List_Olist_ONil @ SV1982 ) )
= $false )
| ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1467 @ ( tc_List_Olist @ SV1982 ) ) @ SV758 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5393]) ).
thf(5871,plain,
! [SV2260: $i,SV1983: $i,SV1468: $i,SV759: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1468 ) @ SV1983 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV759 @ SV2260 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV1468 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5394]) ).
thf(5872,plain,
! [SV1984: $i,SV1469: $i,SV760: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV760 @ SV1469 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV1984 ) )
= $false )
| ( ( SV760
= ( c_Lambda_OdB_OAbs @ SV1984 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(5873,plain,
! [SV1985: $i,SV1470: $i,SV761: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV761 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1470 @ SV1985 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV761 )
= SV1470 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5396]) ).
thf(5874,plain,
! [SV2261: $i,SV1986: $i,SV1471: $i,SV762: $i] :
( ( ( ( c_List_Oappend @ SV762 @ SV1471 @ SV1986 )
!= ( c_List_Oappend @ SV2261 @ SV1471 @ SV1986 ) )
= $true )
| ( ( SV762 = SV2261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5397]) ).
thf(5875,plain,
! [SV2380: $i,SV2262: $i,SV1988: $i,SV1473: $i,SV764: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
!= ( c_HOL_Ominus__class_Ominus @ SV2262 @ SV2380 @ SV764 ) )
| ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
| ~ ( c_lessequals @ SV2380 @ SV2262 @ SV764 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5399]) ).
thf(5876,plain,
! [SV2263: $i,SV1989: $i,SV1474: $i,SV765: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV765 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1474 @ SV1989 @ SV765 )
!= ( c_HOL_Ominus__class_Ominus @ SV2263 @ SV2263 @ SV765 ) )
| ( SV1474 = SV1989 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5400]) ).
thf(5877,plain,
! [SV2264: $i,SV1990: $i,SV1476: $i,SV767: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV767 ) @ SV1476 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1990 ) @ SV2264 ) )
= $true )
| ( ( SV1476 = SV2264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5401]) ).
thf(5878,plain,
! [SV1991: $i,SV1477: $i,SV768: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV768 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV1991 @ SV768 )
!= ( c_HOL_Ozero__class_Ozero @ SV768 ) )
| ( SV1477 = SV1991 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5402]) ).
thf(5879,plain,
! [SV769: $i,SV1478: $i] :
( ( ( SV1478
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1478
= ( 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 ) @ SV769 ) @ SV1478 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5403]) ).
thf(5880,plain,
! [SV2265: $i,SV1992: $i,SV1479: $i,SV770: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV770 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV1479 ) @ SV1992 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV2265 ) @ SV1992 ) )
| ( SV1479 = SV2265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5404]) ).
thf(5881,plain,
! [SV2381: $i,SV2266: $i,SV1993: $i,SV1480: $i,SV771: $i] :
( ( ( ( c_List_Oappend @ SV771 @ ( c_List_Olist_OCons @ SV1480 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 )
!= ( c_List_Oappend @ SV2266 @ ( c_List_Olist_OCons @ SV2381 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 ) )
| ( SV771 = SV2266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5405]) ).
thf(5882,plain,
! [SV772: $i,SV1: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV772 @ SV1 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV1 ) @ SV772 ) @ SV772 ) @ SV1 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5883,plain,
! [SV773: $i,SV2: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV773 ) @ SV773 ) @ SV2 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV773 @ SV2 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5884,plain,
! [SV1481: $i,SV7: $i,SV775: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV7 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1481 @ SV7 ) @ SV7 )
= $true )
| ( ( ~ ( c_lessequals @ SV775 @ SV1481 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5408]) ).
thf(5885,plain,
! [SV8: $i,SV1482: $i,SV776: $i] :
( ( ( c_lessequals @ SV776 @ SV1482 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV776 @ SV8 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1482 @ SV8 ) @ SV8 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5409]) ).
thf(5886,plain,
! [SV1484: $i,SV778: $i,SV10: $i] :
( ( ( c_lessequals @ SV10 @ SV778 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1484 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV10 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV778 ) @ SV1484 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5410]) ).
thf(5887,plain,
! [SV1994: $i,SV1485: $i,SV779: $i,SV11: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
| ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
| ~ ( c_lessequals @ SV779 @ SV1994 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5411]) ).
thf(5888,plain,
! [SV1996: $i,SV1488: $i,SV783: $i,SV15: $i] :
( ( ( class_Orderings_Olinorder @ SV15 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SV1488 @ SV15 ) @ SV1996 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV1488 @ SV1996 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV1996 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5413]) ).
thf(5889,plain,
! [SV1489: $i,SV785: $i,SV17: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV785 @ SV1489 @ SV17 ) @ SV17 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV785 @ SV17 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5414]) ).
thf(5890,plain,
! [SV786: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV18 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV18 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV18 @ SV786 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(5891,plain,
! [SV1490: $i,SV788: $i,SV20: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV788 @ SV1490 @ SV20 ) @ SV20 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ SV788 @ SV20 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5416]) ).
thf(5892,plain,
! [SV789: $i,SV21: $i] :
( ( ( class_Power_Opower @ SV21 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ ( c_Suc @ SV789 ) @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5417]) ).
thf(5893,plain,
! [SV1491: $i,SV1997: $i,SV24: $i,SV792: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV792 @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV1997 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Orev @ ( c_List_Olist__update @ SV24 @ SV792 @ SV1491 @ SV1997 ) @ SV1997 )
= ( c_List_Olist__update @ ( c_List_Orev @ SV24 @ SV1997 ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV24 @ ( tc_List_Olist @ SV1997 ) ) @ SV792 @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV1491 @ SV1997 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5418]) ).
thf(5894,plain,
! [SV793: $i,SV25: $i,SV1492: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1492 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV25 ) @ tc_nat ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV1492 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV793 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5419]) ).
thf(5895,plain,
! [SV797: $i,SV1493: $i,SV29: $i] :
( ( ( c_lessequals @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ SV797 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV797 @ SV1493 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV797 ) @ SV1493 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5420]) ).
thf(5896,plain,
! [SV798: $i,SV1494: $i,SV30: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV30 ) @ SV1494 ) @ SV798 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1494 @ SV798 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV30 @ ( c_HOL_Ominus__class_Ominus @ SV798 @ SV1494 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5421]) ).
thf(5897,plain,
! [SV1998: $i,SV1495: $i,SV799: $i,SV31: $i] :
( ( ( class_Orderings_Olinorder @ SV31 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SV1495 @ SV31 ) @ SV1998 @ SV31 )
| ~ ( c_lessequals @ SV1495 @ SV1998 @ SV31 )
| ~ ( c_lessequals @ SV799 @ SV1998 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5422]) ).
thf(5898,plain,
! [SV1999: $i,SV1496: $i,SV800: $i,SV32: $i] :
( ( ( class_Orderings_Olinorder @ SV32 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SV1496 @ SV32 ) @ SV1999 @ SV32 )
| ~ ( c_lessequals @ SV1496 @ SV1999 @ SV32 )
| ~ ( c_lessequals @ SV800 @ SV1999 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5423]) ).
thf(5899,plain,
! [SV2000: $i,SV1497: $i,SV801: $i,SV33: $i] :
( ( ( class_Orderings_Olinorder @ SV33 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SV1497 @ SV33 ) @ SV2000 @ SV33 )
| ~ ( c_lessequals @ SV1497 @ SV2000 @ SV33 )
| ~ ( c_lessequals @ SV801 @ SV2000 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5424]) ).
thf(5900,plain,
! [SV2001: $i,SV1502: $i,SV815: $i,SV47: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV47 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5429]) ).
thf(5901,plain,
! [SV2002: $i,SV1504: $i,SV817: $i,SV49: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
| ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
| ~ ( c_lessequals @ SV817 @ SV2002 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5430]) ).
thf(5902,plain,
! [SV2003: $i,SV1505: $i,SV818: $i,SV50: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
| ~ ( c_lessequals @ SV818 @ SV1505 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5431]) ).
thf(5903,plain,
! [SV819: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ SV51 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV51 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV51 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV51 @ SV819 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5432]) ).
thf(5904,plain,
! [SV2004: $i,SV1511: $i,SV829: $i,SV61: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV61 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
| ~ ( c_lessequals @ SV2004 @ SV1511 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5905,plain,
! [SV2005: $i,SV1516: $i,SV836: $i,SV69: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV69 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ SV1516 ) @ SV2005 @ SV69 @ SV69 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV836 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1516 @ SV2005 @ SV69 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5906,plain,
! [SV838: $i,SV71: $i,SV1518: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1518 @ SV71 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV838 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV838 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV1518 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5907,plain,
! [SV2007: $i,SV1521: $i,SV841: $i,SV74: $i] :
( ( ( class_Orderings_Olinorder @ SV74 )
= $false )
| ( ( ( c_lessequals @ SV841 @ SV1521 @ SV74 )
| ( c_lessequals @ SV841 @ SV2007 @ SV74 )
| ~ ( c_lessequals @ SV841 @ ( c_Orderings_Oord__class_Omax @ SV2007 @ SV1521 @ SV74 ) @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5908,plain,
! [SV1522: $i,SV842: $i,SV2008: $i,SV75: $i] :
( ( ( c_List_Olistsp @ SV75 @ ( c_List_Oappend @ SV2008 @ SV842 @ SV1522 ) @ SV1522 )
= $false )
| ( ( c_List_Olistsp @ SV75 @ SV842 @ SV1522 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5446]) ).
thf(5909,plain,
! [SV1523: $i,SV2009: $i,SV843: $i,SV76: $i] :
( ( ( c_List_Olistsp @ SV76 @ ( c_List_Oappend @ SV843 @ SV2009 @ SV1523 ) @ SV1523 )
= $false )
| ( ( c_List_Olistsp @ SV76 @ SV843 @ SV1523 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(5910,plain,
! [SV1530: $i,SV83: $i,SV2010: $i,SV850: $i] :
( ( ( ~ ( c_lessequals @ SV850 @ SV2010 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV83 @ SV1530 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV83 ) @ SV850 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1530 ) @ SV2010 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5452]) ).
thf(5911,plain,
! [SV2267: $i,SV2011: $i,SV1531: $i,SV851: $i,SV84: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV2011 ) @ SV2267 ) @ SV84 )
| ~ ( c_lessequals @ SV1531 @ SV2267 @ SV84 )
| ~ ( c_lessequals @ SV851 @ SV2011 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5453]) ).
thf(5912,plain,
! [SV2268: $i,SV2012: $i,SV1533: $i,SV853: $i,SV86: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV86 @ SV853 @ SV1533 ) @ SV2012 @ SV2268 @ SV1533 )
= ( c_List_Oappend @ SV86 @ ( c_List_Olist__update @ SV853 @ ( c_HOL_Ominus__class_Ominus @ SV2012 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SV1533 ) ) @ tc_nat ) @ SV2268 @ SV1533 ) @ SV1533 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2012 @ ( c_Nat_Osize__class_Osize @ SV86 @ ( tc_List_Olist @ SV1533 ) ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5454]) ).
thf(5913,plain,
! [SV92: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5456]) ).
thf(5914,plain,
! [SV1536: $i,SV860: $i,SV95: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV860 ) @ SV1536 ) @ SV95 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1536 @ SV95 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV860 @ SV95 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5457]) ).
thf(5915,plain,
! [SV96: $i,SV1537: $i,SV861: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV861 @ ( c_Suc @ SV1537 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV861 @ SV96 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5458]) ).
thf(5916,plain,
! [SV2014: $i,SV1538: $i,SV862: $i,SV97: $i] :
( ( ( class_Orderings_Opreorder @ SV97 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV862 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV2014 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV862 @ SV2014 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5459]) ).
thf(5917,plain,
! [SV2015: $i,SV1539: $i,SV863: $i,SV98: $i] :
( ( ( class_Orderings_Oorder @ SV98 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1539 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV2015 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV2015 @ SV1539 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5918,plain,
! [SV99: $i,SV1540: $i,SV864: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV864 @ SV1540 @ SV99 )
= SV1540 )
= $true )
| ( ( ~ ( c_lessequals @ SV864 @ SV1540 @ SV99 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5461]) ).
thf(5919,plain,
! [SV100: $i,SV1541: $i,SV865: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV865 @ SV1541 @ SV100 )
= SV865 )
= $true )
| ( ( ~ ( c_lessequals @ SV1541 @ SV865 @ SV100 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5462]) ).
thf(5920,plain,
! [SV2016: $i,SV1542: $i,SV866: $i,SV101: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV1542 ) @ SV2016 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV101 ) @ SV866 ) @ SV1542 ) ) @ SV2016 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5463]) ).
thf(5921,plain,
! [SV2017: $i,SV1543: $i,SV867: $i,SV102: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV102 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV1543 ) @ SV2017 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV1543 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV102 ) @ SV867 ) @ SV2017 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5464]) ).
thf(5922,plain,
! [SV2018: $i,SV1546: $i,SV870: $i,SV105: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV105 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ SV1546 ) ) @ SV2018 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV870 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV1546 ) @ SV2018 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5465]) ).
thf(5923,plain,
! [SV2019: $i,SV1547: $i,SV871: $i,SV106: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV106 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV1547 ) @ SV2019 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV1547 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ SV871 ) @ SV2019 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5466]) ).
thf(5924,plain,
! [SV2020: $i,SV1548: $i,SV872: $i,SV107: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV107 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ SV1548 ) ) @ SV2020 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV872 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV1548 ) @ SV2020 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5467]) ).
thf(5925,plain,
! [SV2021: $i,SV1549: $i,SV873: $i,SV108: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV108 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV1549 ) @ SV2021 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ SV873 ) @ SV1549 ) ) @ SV2021 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5468]) ).
thf(5926,plain,
! [SV2022: $i,SV1550: $i,SV874: $i,SV109: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV109 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SV1550 ) ) @ SV2022 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV874 ) @ SV2022 ) ) @ SV1550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5469]) ).
thf(5927,plain,
! [SV2023: $i,SV1551: $i,SV875: $i,SV110: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV110 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV1551 ) @ SV2023 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ SV875 ) @ SV2023 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5470]) ).
thf(5928,plain,
! [SV2024: $i,SV1552: $i,SV876: $i,SV111: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV111 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ SV1552 ) ) @ SV2024 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV876 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV1552 ) @ SV2024 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5471]) ).
thf(5929,plain,
! [SV2026: $i,SV1563: $i,SV890: $i,SV125: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV125 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV890 @ SV1563 @ SV125 ) @ SV2026 @ SV125 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV2026 @ SV125 ) @ ( c_HOL_Ominus__class_Ominus @ SV1563 @ SV2026 @ SV125 ) @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5479]) ).
thf(5930,plain,
! [SV128: $i,SV1566: $i,SV893: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV893 @ SV1566 @ SV128 )
= $true )
| ( ( c_lessequals @ SV1566 @ SV893 @ SV128 )
= $true )
| ( ( class_Orderings_Olinorder @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5480]) ).
thf(5931,plain,
! [SV129: $i,SV894: $i] :
( ( ( c_lessequals @ SV894 @ SV894 @ SV129 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV894 @ SV894 @ SV129 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5481]) ).
thf(5932,plain,
! [SV131: $i,SV1567: $i,SV896: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV896 @ SV1567 @ SV131 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1567 @ SV896 @ SV131 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5483]) ).
thf(5933,plain,
! [SV132: $i,SV1568: $i,SV897: $i] :
( ( ( c_lessequals @ SV897 @ SV1568 @ SV132 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1568 @ SV897 @ SV132 )
= $true )
| ( ( class_Orderings_Olinorder @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5484]) ).
thf(5934,plain,
! [SV133: $i,SV1569: $i,SV898: $i] :
( ( ( ~ ( c_lessequals @ SV898 @ SV1569 @ SV133 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1569 @ SV898 @ SV133 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5485]) ).
thf(5935,plain,
! [SV134: $i,SV1570: $i,SV899: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV899 @ SV1570 @ SV134 )
= $true )
| ( ( c_lessequals @ SV1570 @ SV899 @ SV134 )
= $true )
| ( ( class_Orderings_Olinorder @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5486]) ).
thf(5936,plain,
! [SV135: $i,SV1571: $i,SV900: $i] :
( ( ( ~ ( c_lessequals @ SV900 @ SV1571 @ SV135 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV900 @ SV135 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5487]) ).
thf(5937,plain,
! [SV2028: $i,SV1572: $i,SV904: $i,SV139: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
| ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
| ~ ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5489]) ).
thf(5938,plain,
! [SV2029: $i,SV1573: $i,SV905: $i,SV140: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV140 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SV1573 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SV2029 @ SV140 ) @ SV140 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 )
| ~ ( c_lessequals @ SV1573 @ SV2029 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5490]) ).
thf(5939,plain,
! [SV908: $i,SV1576: $i,SV143: $i] :
( ( ( c_lessequals @ SV143 @ SV1576 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV908 @ SV1576 @ tc_nat )
| ~ ( c_lessequals @ SV908 @ SV143 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SV908 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV908 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5493]) ).
thf(5940,plain,
! [SV909: $i,SV1577: $i,SV144: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SV1577 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV909 @ SV1577 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1577 @ SV909 @ tc_nat )
| ~ ( c_lessequals @ SV1577 @ SV144 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV144 @ SV909 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5494]) ).
thf(5941,plain,
! [SV2030: $i,SV1579: $i,SV912: $i,SV147: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SV1579 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SV2030 @ SV1579 @ SV147 ) @ SV147 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 )
| ~ ( c_lessequals @ SV912 @ SV2030 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(5942,plain,
! [SV2382: $i,SV2269: $i,SV2031: $i,SV1581: $i,SV915: $i,SV151: $i] :
( ( ( c_List_Ofoldl @ SV151 @ SV915 @ ( c_List_Olist_OCons @ SV1581 @ SV2031 @ SV2269 ) @ SV2382 @ SV2269 )
= ( c_List_Ofoldl @ SV151 @ ( hAPP @ ( hAPP @ SV151 @ SV915 ) @ SV1581 ) @ SV2031 @ SV2382 @ SV2269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5496]) ).
thf(5943,plain,
! [SV2033: $i,SV1585: $i,SV921: $i,SV159: $i] :
( ( ( class_Orderings_Olinorder @ SV159 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV921 @ ( c_Orderings_Oord__class_Omax @ SV1585 @ SV2033 @ SV159 ) @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV921 @ SV1585 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5497]) ).
thf(5944,plain,
! [SV2034: $i,SV1586: $i,SV922: $i,SV160: $i] :
( ( ( class_Orderings_Olinorder @ SV160 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV922 @ ( c_Orderings_Oord__class_Omax @ SV1586 @ SV2034 @ SV160 ) @ SV160 )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV2034 @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5498]) ).
thf(5945,plain,
! [SV2035: $i,SV1587: $i,SV923: $i,SV161: $i] :
( ( ( class_Orderings_Olinorder @ SV161 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Orderings_Oord__class_Omax @ SV1587 @ SV2035 @ SV161 ) @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV923 @ SV1587 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5499]) ).
thf(5946,plain,
! [SV2036: $i,SV1588: $i,SV924: $i,SV162: $i] :
( ( ( class_Orderings_Olinorder @ SV162 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Orderings_Oord__class_Omax @ SV1588 @ SV2036 @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2036 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5500]) ).
thf(5947,plain,
! [SV2037: $i,SV1589: $i,SV925: $i,SV163: $i] :
( ( ( class_Orderings_Olinorder @ SV163 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1589 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV925 @ SV2037 @ SV163 ) @ SV1589 @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5501]) ).
thf(5948,plain,
! [SV2383: $i,SV2270: $i,SV2038: $i,SV1590: $i,SV927: $i,SV165: $i] :
( ( ! [SY6391: $i,SY6392: $i,SY6393: $i] :
( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2038 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2270 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2038 ) @ SV2270 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2383 @ SV165 @ SV927 @ SY6391 @ SY6392 @ SY6393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5502]) ).
thf(5949,plain,
! [SV2384: $i,SV2271: $i,SV2039: $i,SV1592: $i,SV929: $i,SV168: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV168 @ SV929 @ SV1592 @ SV2039 @ SV2271 ) @ SV2384 )
= ( hAPP @ SV168 @ ( hAPP @ SV929 @ SV2384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5503]) ).
thf(5950,plain,
! [SV2385: $i,SV2272: $i,SV2040: $i,SV1593: $i,SV930: $i,SV169: $i] :
( ( ( hAPP @ SV169 @ ( hAPP @ SV930 @ SV1593 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV169 @ SV930 @ SV2040 @ SV2272 @ SV2385 ) @ SV1593 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5504]) ).
thf(5951,plain,
! [SV2041: $i,SV1594: $i,SV931: $i,SV170: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ ( c_Nat_Osize__class_Osize @ SV1594 @ ( tc_List_Olist @ SV2041 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Otake @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ SV931 ) @ SV1594 @ SV2041 )
= ( c_List_Oappend @ ( c_List_Otake @ SV170 @ SV1594 @ SV2041 ) @ ( c_List_Otake @ SV931 @ ( c_List_Odrop @ SV170 @ SV1594 @ SV2041 ) @ SV2041 ) @ SV2041 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5505]) ).
thf(5952,plain,
! [SV174: $i,SV935: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ SV935 ) @ SV935 ) @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5507]) ).
thf(5953,plain,
! [SV936: $i,SV175: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV175 ) @ SV936 ) @ SV936 ) @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV936 @ ( c_HOL_Ozero__class_Ozero @ SV175 ) @ SV175 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5508]) ).
thf(5954,plain,
! [SV937: $i,SV176: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV937 ) @ SV937 ) @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV937 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5509]) ).
thf(5955,plain,
! [SV177: $i,SV938: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV938 @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV177 ) @ SV938 ) @ SV938 ) @ ( c_HOL_Ozero__class_Ozero @ SV177 ) @ SV177 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5510]) ).
thf(5956,plain,
! [SV2042: $i,SV1596: $i,SV939: $i,SV178: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV178 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV939 @ SV1596 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SV1596 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SV2042 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SV1596 @ SV2042 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5511]) ).
thf(5957,plain,
! [SV2043: $i,SV1598: $i,SV941: $i,SV180: $i] :
( ( ( class_Orderings_Olinorder @ SV180 )
= $false )
| ( ( ( c_lessequals @ SV941 @ SV1598 @ SV180 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2043 @ SV941 @ SV180 ) @ SV1598 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5513]) ).
thf(5958,plain,
! [SV2044: $i,SV1599: $i,SV942: $i,SV181: $i] :
( ( ( class_Orderings_Olinorder @ SV181 )
= $false )
| ( ( ( c_lessequals @ SV942 @ SV1599 @ SV181 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV942 @ SV2044 @ SV181 ) @ SV1599 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5514]) ).
thf(5959,plain,
! [SV2045: $i,SV1600: $i,SV943: $i,SV182: $i] :
( ( ( class_Orderings_Olinorder @ SV182 )
= $false )
| ( ( ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1600 @ SV2045 @ SV182 ) @ SV182 )
| ~ ( c_lessequals @ SV943 @ SV2045 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5515]) ).
thf(5960,plain,
! [SV2046: $i,SV1601: $i,SV944: $i,SV183: $i] :
( ( ( class_Orderings_Olinorder @ SV183 )
= $false )
| ( ( ( c_lessequals @ SV944 @ ( c_Orderings_Oord__class_Omax @ SV1601 @ SV2046 @ SV183 ) @ SV183 )
| ~ ( c_lessequals @ SV944 @ SV1601 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5516]) ).
thf(5961,plain,
! [SV2047: $i,SV1602: $i,SV945: $i,SV184: $i] :
( ( ( class_Orderings_Olinorder @ SV184 )
= $false )
| ( ( ( c_lessequals @ SV945 @ ( c_Orderings_Oord__class_Omax @ SV1602 @ SV2047 @ SV184 ) @ SV184 )
| ~ ( c_lessequals @ SV945 @ SV2047 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5517]) ).
thf(5962,plain,
! [SV2048: $i,SV1603: $i,SV946: $i,SV185: $i] :
( ( ( class_Orderings_Olinorder @ SV185 )
= $false )
| ( ( ( c_lessequals @ SV946 @ ( c_Orderings_Oord__class_Omax @ SV1603 @ SV2048 @ SV185 ) @ SV185 )
| ~ ( c_lessequals @ SV946 @ SV1603 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5518]) ).
thf(5963,plain,
! [SV2049: $i,SV1604: $i,SV947: $i,SV186: $i] :
( ( ( class_Orderings_Olinorder @ SV186 )
= $false )
| ( ( ( c_lessequals @ SV947 @ SV1604 @ SV186 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2049 @ SV947 @ SV186 ) @ SV1604 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5519]) ).
thf(5964,plain,
! [SV2050: $i,SV1605: $i,SV948: $i,SV187: $i] :
( ( ( class_Orderings_Olinorder @ SV187 )
= $false )
| ( ( ( c_lessequals @ SV948 @ SV1605 @ SV187 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV948 @ SV2050 @ SV187 ) @ SV1605 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5520]) ).
thf(5965,plain,
! [SV1608: $i,SV951: $i,SV190: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ ( c_Power_Opower__class_Opower @ SV951 @ SV1608 @ SV190 ) @ SV190 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV951 @ SV190 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5523]) ).
thf(5966,plain,
! [SV2051: $i,SV1609: $i,SV952: $i,SV191: $i] :
( ( ( class_Orderings_Olinorder @ SV191 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV952 @ SV1609 @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV952 @ SV2051 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV952 @ ( c_Orderings_Oord__class_Omax @ SV2051 @ SV1609 @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5524]) ).
thf(5967,plain,
! [SV1610: $i,SV192: $i,SV953: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV953 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SV953 ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(5968,plain,
! [SV1614: $i,SV958: $i,SV199: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV958 ) @ SV1614 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1614 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ SV958 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5527]) ).
thf(5969,plain,
! [SV1615: $i,SV959: $i,SV200: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SV959 ) @ SV1615 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
= $true )
| ( ( ~ ( c_lessequals @ SV1615 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SV959 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5528]) ).
thf(5970,plain,
! [SV2273: $i,SV2053: $i,SV1618: $i,SV965: $i,SV207: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV207 @ SV965 @ SV1618 ) @ SV2053 @ SV2273 @ SV1618 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV207 @ SV2053 @ SV2273 @ SV1618 ) @ SV965 @ SV1618 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2053 @ ( c_Nat_Osize__class_Osize @ SV207 @ ( tc_List_Olist @ SV1618 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5534]) ).
thf(5971,plain,
! [SV2274: $i,SV2054: $i,SV1619: $i,SV966: $i,SV208: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV208 @ SV966 @ SV1619 ) @ SV2054 @ SV2274 @ SV1619 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV208 @ SV2054 @ SV2274 @ SV1619 ) @ SV966 @ SV1619 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2054 @ ( c_Nat_Osize__class_Osize @ SV208 @ ( tc_List_Olist @ SV1619 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5535]) ).
thf(5972,plain,
! [SV216: $i,SV1625: $i,SV974: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV974 @ SV1625 @ SV216 )
= $true )
| ( ( ( c_lessequals @ SV1625 @ SV974 @ SV216 )
| ~ ( c_lessequals @ SV974 @ SV1625 @ SV216 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5539]) ).
thf(5973,plain,
! [SV1629: $i,SV983: $i,SV227: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SV983 ) @ SV1629 ) @ SV227 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV1629 @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV983 @ SV227 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5543]) ).
thf(5974,plain,
! [SV2386: $i,SV2275: $i,SV2057: $i,SV1633: $i,SV991: $i,SV236: $i] :
( ( ! [SY6394: $i] :
( ( ( hAPP @ ( hAPP @ SV236 @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV991 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV2057 @ SV236 @ SV2275 @ SV2386 @ SY6394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5546]) ).
thf(5975,plain,
! [SV237: $i,SV1634: $i,SV992: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV992 @ SV1634 @ SV237 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1634 @ SV992 @ SV237 )
| ( SV1634 = SV992 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5547]) ).
thf(5976,plain,
! [SV238: $i,SV1635: $i,SV993: $i] :
( ( ( SV993 = SV1635 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1635 @ SV993 @ SV238 )
| ( c_HOL_Oord__class_Oless @ SV993 @ SV1635 @ SV238 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5548]) ).
thf(5977,plain,
! [SV994: $i,SV239: $i] :
( ( ( c_lessequals @ SV239 @ SV994 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV994 @ SV239 @ tc_nat )
= $false )
| ( ( SV239 = SV994 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5549]) ).
thf(5978,plain,
! [SV241: $i,SV996: $i,SV1636: $i] :
( ( ( SV1636 = SV996 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1636 @ SV996 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV996 @ SV1636 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV241 @ SV996 ) @ SV1636 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5550]) ).
thf(5979,plain,
! [SV2276: $i,SV2058: $i,SV1637: $i,SV997: $i,SV242: $i] :
( ( ( SV242 = SV997 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV997 )
| ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(5980,plain,
! [SV2059: $i,SV1638: $i,SV998: $i,SV243: $i] :
( ( ( class_Orderings_Olinorder @ SV243 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV998 @ SV1638 @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2059 @ SV998 @ SV243 ) @ SV1638 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5552]) ).
thf(5981,plain,
! [SV1639: $i,SV999: $i,SV245: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SV999 @ SV1639 @ SV245 ) @ SV245 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1639 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SV999 @ SV245 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5553]) ).
thf(5982,plain,
! [SV1001: $i,SV247: $i,SV1641: $i,SV2060: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2060 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1641 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV247 ) @ SV1001 ) @ SV1641 ) ) @ SV2060 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV247 ) @ SV2060 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1001 ) @ SV2060 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1641 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5555]) ).
thf(5983,plain,
! [SV1642: $i,SV1004: $i,SV250: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SV1004 ) @ SV1642 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1642 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ SV1004 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5556]) ).
thf(5984,plain,
! [SV2061: $i,SV1643: $i,SV1005: $i,SV251: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV251 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5557]) ).
thf(5985,plain,
! [SV255: $i,SV1647: $i,SV1009: $i] :
( ( ( c_lessequals @ SV1009 @ SV1647 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1009 @ SV255 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1009 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1647 @ SV1009 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1647 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5558]) ).
thf(5986,plain,
! [SV1650: $i,SV1012: $i,SV258: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV1012 ) @ SV1650 ) @ SV258 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1650 @ SV258 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1012 @ SV258 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5559]) ).
thf(5987,plain,
! [SV1651: $i,SV1013: $i,SV259: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV1013 ) @ SV1651 ) @ SV259 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1651 @ SV259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1013 @ SV259 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5560]) ).
thf(5988,plain,
! [SV1655: $i,SV263: $i,SV1017: $i] :
( ( ( c_lessequals @ SV1017 @ SV263 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV263 @ SV1655 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV263 @ SV1017 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1017 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5561]) ).
thf(5989,plain,
! [SV2387: $i,SV2277: $i,SV2067: $i,SV1659: $i,SV1025: $i,SV271: $i] :
( ( ! [SY6395: $i,SY6396: $i,SY6397: $i] :
( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SV2067 ) ) @ SV2277 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SV2277 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SV2067 ) @ SV2277 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2387 @ SV1025 @ SV271 @ SY6395 @ SY6396 @ SY6397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5565]) ).
thf(5990,plain,
! [SV2388: $i,SV2278: $i,SV2068: $i,SV1660: $i,SV1026: $i,SV272: $i] :
( ( ! [SY6398: $i,SY6399: $i,SY6400: $i] :
( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SV2068 ) @ SV2278 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2068 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2278 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SV2388 @ SY6398 @ SY6399 @ SY6400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5566]) ).
thf(5991,plain,
! [SV2389: $i,SV2279: $i,SV2069: $i,SV1661: $i,SV1027: $i,SV273: $i] :
( ( ! [SY6401: $i,SY6402: $i] :
( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SV1661 )
= ( hAPP @ ( hAPP @ SV273 @ SV1661 ) @ SV1027 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2069 @ SV273 @ SV2279 @ SV2389 @ SY6401 @ SY6402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5567]) ).
thf(5992,plain,
! [SV2390: $i,SV2280: $i,SV2070: $i,SV1662: $i,SV1028: $i,SV274: $i] :
( ( ! [SY6403: $i,SY6404: $i,SY6405: $i] :
( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SV2070 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SV2070 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2280 @ SV274 @ SV2390 @ SY6403 @ SY6404 @ SY6405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5568]) ).
thf(5993,plain,
! [SV2391: $i,SV2281: $i,SV2071: $i,SV1663: $i,SV1029: $i,SV275: $i] :
( ( ! [SY6406: $i] :
( ( ( hAPP @ ( hAPP @ SV275 @ SV1029 ) @ SV1663 )
= SV1663 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2071 @ SV275 @ SV2281 @ SV2391 @ SV1029 @ SY6406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5569]) ).
thf(5994,plain,
! [SV2392: $i,SV2282: $i,SV2072: $i,SV1664: $i,SV1030: $i,SV276: $i] :
( ( ! [SY6407: $i] :
( ( ( hAPP @ ( hAPP @ SV276 @ SV1030 ) @ SV1664 )
= SV1030 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2072 @ SV276 @ SV2282 @ SV1030 @ SV2392 @ SY6407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5570]) ).
thf(5995,plain,
! [SV2393: $i,SV2283: $i,SV2073: $i,SV1665: $i,SV1031: $i,SV277: $i] :
( ( ! [SY6408: $i,SY6409: $i] :
( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SV1665 )
= ( hAPP @ ( hAPP @ SV277 @ SV1665 ) @ SV1031 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SV2073 @ SV2283 @ SV2393 @ SY6408 @ SY6409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5571]) ).
thf(5996,plain,
! [SV2394: $i,SV2284: $i,SV2074: $i,SV1666: $i,SV1032: $i,SV278: $i] :
( ( ! [SY6410: $i,SY6411: $i,SY6412: $i] :
( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SV2074 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SV2074 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SV2284 @ SV2394 @ SY6410 @ SY6411 @ SY6412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5572]) ).
thf(5997,plain,
! [SV2395: $i,SV2285: $i,SV2075: $i,SV1667: $i,SV1033: $i,SV279: $i] :
( ( ! [SY6413: $i] :
( ( ( hAPP @ ( hAPP @ SV279 @ SV1033 ) @ SV1667 )
= SV1667 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SV2075 @ SV2285 @ SV1033 @ SV2395 @ SY6413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5573]) ).
thf(5998,plain,
! [SV2396: $i,SV2286: $i,SV2076: $i,SV1668: $i,SV1034: $i,SV280: $i] :
( ( ! [SY6414: $i,SY6415: $i,SY6416: $i] :
( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SV2076 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SV2076 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SV2286 @ SV2396 @ SY6414 @ SY6415 @ SY6416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5574]) ).
thf(5999,plain,
! [SV2397: $i,SV2287: $i,SV2077: $i,SV1669: $i,SV1035: $i,SV281: $i] :
( ( ! [SY6417: $i,SY6418: $i] :
( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SV1669 )
= ( hAPP @ ( hAPP @ SV281 @ SV1669 ) @ SV1035 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SV2077 @ SV2287 @ SV2397 @ SY6417 @ SY6418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5575]) ).
thf(6000,plain,
! [SV2398: $i,SV2288: $i,SV2078: $i,SV1670: $i,SV1036: $i,SV282: $i] :
( ( ! [SY6419: $i,SY6420: $i,SY6421: $i] :
( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SV2078 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV2078 ) ) @ SV1670 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SV2288 @ SV2398 @ SY6419 @ SY6420 @ SY6421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5576]) ).
thf(6001,plain,
! [SV2399: $i,SV2289: $i,SV2079: $i,SV1671: $i,SV1037: $i,SV283: $i] :
( ( ! [SY6422: $i,SY6423: $i,SY6424: $i] :
( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SV2079 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SV2079 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SV2289 @ SV2399 @ SY6422 @ SY6423 @ SY6424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5577]) ).
thf(6002,plain,
! [SV2400: $i,SV2290: $i,SV2080: $i,SV1672: $i,SV1038: $i,SV284: $i] :
( ( ! [SY6425: $i,SY6426: $i,SY6427: $i] :
( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SV2080 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SV2080 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SV2290 @ SV2400 @ SY6425 @ SY6426 @ SY6427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5578]) ).
thf(6003,plain,
! [SV2401: $i,SV2291: $i,SV2081: $i,SV1673: $i,SV1039: $i,SV285: $i] :
( ( ! [SY6428: $i,SY6429: $i,SY6430: $i,SY6431: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SV2291 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SV2291 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SV2401 @ SY6428 @ SY6429 @ SY6430 @ SY6431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5579]) ).
thf(6004,plain,
! [SV2402: $i,SV2292: $i,SV2082: $i,SV1674: $i,SV1040: $i,SV286: $i] :
( ( ! [SY6432: $i,SY6433: $i,SY6434: $i] :
( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SV2082 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SV2082 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2292 @ SV286 @ SV2402 @ SY6432 @ SY6433 @ SY6434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5580]) ).
thf(6005,plain,
! [SV2403: $i,SV2293: $i,SV2083: $i,SV1675: $i,SV1041: $i,SV287: $i] :
( ( ! [SY6435: $i,SY6436: $i,SY6437: $i] :
( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SV2083 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SV2083 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2293 @ SV287 @ SV2403 @ SY6435 @ SY6436 @ SY6437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5581]) ).
thf(6006,plain,
! [SV2404: $i,SV2294: $i,SV2084: $i,SV1676: $i,SV1042: $i,SV288: $i] :
( ( ! [SY6438: $i,SY6439: $i,SY6440: $i] :
( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SV2084 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SV2084 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2294 @ SV288 @ SV2404 @ SY6438 @ SY6439 @ SY6440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5582]) ).
thf(6007,plain,
! [SV2405: $i,SV2295: $i,SV2085: $i,SV1677: $i,SV1043: $i,SV289: $i] :
( ( ! [SY6441: $i,SY6442: $i,SY6443: $i] :
( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SV2085 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV2085 ) ) @ SV1677 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2295 @ SV289 @ SV2405 @ SY6441 @ SY6442 @ SY6443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5583]) ).
thf(6008,plain,
! [SV2406: $i,SV2296: $i,SV2086: $i,SV1678: $i,SV1044: $i,SV290: $i] :
( ( ! [SY6444: $i,SY6445: $i,SY6446: $i,SY6447: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SV2296 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SV2296 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2406 @ SV290 @ SY6444 @ SY6445 @ SY6446 @ SY6447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5584]) ).
thf(6009,plain,
! [SV2407: $i,SV2297: $i,SV2087: $i,SV1679: $i,SV1045: $i,SV291: $i] :
( ( ! [SY6448: $i,SY6449: $i,SY6450: $i,SY6451: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2407 @ SV291 @ SY6448 @ SY6449 @ SY6450 @ SY6451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5585]) ).
thf(6010,plain,
! [SV2408: $i,SV2298: $i,SV2088: $i,SV1680: $i,SV1046: $i,SV292: $i] :
( ( ! [SY6452: $i,SY6453: $i,SY6454: $i,SY6455: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SV2298 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SV2298 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2408 @ SV292 @ SY6452 @ SY6453 @ SY6454 @ SY6455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5586]) ).
thf(6011,plain,
! [SV2409: $i,SV2299: $i,SV2089: $i,SV1681: $i,SV1047: $i,SV293: $i] :
( ( ! [SY6456: $i] :
( ( ( hAPP @ ( hAPP @ SV293 @ SV1047 ) @ SV1681 )
= SV1047 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2089 @ SV293 @ SV2299 @ SV2409 @ SV1681 @ SY6456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5587]) ).
thf(6012,plain,
! [SV2410: $i,SV2300: $i,SV2090: $i,SV1682: $i,SV1048: $i,SV294: $i] :
( ( ! [SY6457: $i] :
( ( ( hAPP @ ( hAPP @ SV294 @ SV1048 ) @ SV1682 )
= SV1682 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2090 @ SV294 @ SV2300 @ SV2410 @ SV1048 @ SY6457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(6013,plain,
! [SV2411: $i,SV2301: $i,SV2091: $i,SV1683: $i,SV1049: $i,SV295: $i] :
( ( ! [SY6458: $i] :
( ( ( hAPP @ ( hAPP @ SV295 @ SV1049 ) @ SV1683 )
= SV1683 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2091 @ SV295 @ SV2301 @ SV1683 @ SV2411 @ SY6458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5589]) ).
thf(6014,plain,
! [SV2412: $i,SV2302: $i,SV2092: $i,SV1684: $i,SV1050: $i,SV296: $i] :
( ( ! [SY6459: $i] :
( ( ( hAPP @ ( hAPP @ SV296 @ SV1050 ) @ SV1684 )
= SV1050 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2092 @ SV296 @ SV2302 @ SV1050 @ SV2412 @ SY6459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5590]) ).
thf(6015,plain,
! [SV2413: $i,SV2303: $i,SV2093: $i,SV1685: $i,SV1051: $i,SV297: $i] :
( ( ! [SY6460: $i,SY6461: $i,SY6462: $i] :
( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SV2093 ) ) @ SV2303 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SV2303 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SV2093 ) @ SV2303 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SV2413 @ SY6460 @ SY6461 @ SY6462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5591]) ).
thf(6016,plain,
! [SV2414: $i,SV2304: $i,SV2094: $i,SV1686: $i,SV1052: $i,SV298: $i] :
( ( ! [SY6463: $i,SY6464: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SV1686 )
= ( hAPP @ ( hAPP @ SV298 @ SV1686 ) @ SV1052 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2094 @ SV298 @ SV2304 @ SV2414 @ SY6463 @ SY6464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5592]) ).
thf(6017,plain,
! [SV2415: $i,SV2305: $i,SV2095: $i,SV1687: $i,SV1053: $i,SV299: $i] :
( ( ! [SY6465: $i] :
( ( ( hAPP @ ( hAPP @ SV299 @ SV1053 ) @ SV1687 )
= SV1053 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SV2095 @ SV2305 @ SV1687 @ SV2415 @ SY6465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5593]) ).
thf(6018,plain,
! [SV2416: $i,SV2306: $i,SV2096: $i,SV1688: $i,SV1054: $i,SV300: $i] :
( ( ! [SY6466: $i] :
( ( ( hAPP @ ( hAPP @ SV300 @ SV1054 ) @ SV1688 )
= SV1688 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SV2096 @ SV2306 @ SV1054 @ SV2416 @ SY6466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5594]) ).
thf(6019,plain,
! [SV2417: $i,SV2307: $i,SV2097: $i,SV1689: $i,SV1055: $i,SV301: $i] :
( ( ! [SY6467: $i] :
( ( ( hAPP @ ( hAPP @ SV301 @ SV1055 ) @ SV1055 )
= ( hAPP @ ( hAPP @ SV1689 @ ( hAPP @ ( hAPP @ SV301 @ SV2097 ) @ SV2097 ) ) @ SV1055 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SV1689 @ SV2307 @ SV2417 @ SV2097 @ SY6467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5595]) ).
thf(6020,plain,
! [SV2418: $i,SV2308: $i,SV2098: $i,SV1690: $i,SV1056: $i,SV302: $i] :
( ( ! [SY6468: $i,SY6469: $i] :
( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SV1690 @ SV2098 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SV1690 @ ( hAPP @ ( hAPP @ SV302 @ SV2098 ) @ SV2308 ) ) @ SV1056 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SV1690 @ SV2418 @ SY6468 @ SV2308 @ SY6469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5596]) ).
thf(6021,plain,
! [SV2419: $i,SV2309: $i,SV2099: $i,SV1691: $i,SV1057: $i,SV303: $i] :
( ( ! [SY6470: $i,SY6471: $i] :
( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SV1691 ) @ SV2099 ) ) @ SV2099 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SV1691 ) @ SV2309 ) ) @ SV2099 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SV2419 @ SY6470 @ SV2309 @ SY6471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5597]) ).
thf(6022,plain,
! [SV2420: $i,SV2310: $i,SV2100: $i,SV1692: $i,SV1058: $i,SV304: $i] :
( ( ! [SY6472: $i,SY6473: $i,SY6474: $i] :
( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SV2100 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SV2310 ) @ SV2100 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SV2310 ) ) @ SV2100 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SV2420 @ SY6472 @ SY6473 @ SY6474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5598]) ).
thf(6023,plain,
! [SV2101: $i,SV1693: $i,SV1059: $i,SV305: $i] :
( ( ( hBOOL @ ( hAPP @ SV305 @ ( c_Type_Otype_Otype__case @ SV1059 @ SV1693 @ ( c_Type_Otype_OAtom @ SV2101 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV305 @ ( hAPP @ SV1059 @ SV2101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5599]) ).
thf(6024,plain,
! [SV2102: $i,SV1694: $i,SV1060: $i,SV306: $i] :
( ( ( hBOOL @ ( hAPP @ SV306 @ ( c_Type_Otype_Otype__case @ SV1060 @ SV1694 @ ( c_Type_Otype_OAtom @ SV2102 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV306 @ ( hAPP @ SV1060 @ SV2102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5600]) ).
thf(6025,plain,
! [SV2311: $i,SV2103: $i,SV1696: $i,SV1062: $i,SV308: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1062 ) @ SV1696 ) ) @ ( c_Suc @ SV2103 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2311 ) @ SV1062 ) @ SV2103 ) ) @ SV1696 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ SV2311 ) @ SV1696 ) ) @ SV1062 ) @ SV2103 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1696 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2103 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5601]) ).
thf(6026,plain,
! [SV2312: $i,SV2104: $i,SV1699: $i,SV1066: $i,SV313: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV1699 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV2104 ) @ SV2312 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV2104 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1699 ) @ SV2312 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5602]) ).
thf(6027,plain,
! [SV328: $i,SV1709: $i,SV1080: $i] :
( ( ( SV1080 = SV1709 )
= $true )
| ( ( ~ ( c_lessequals @ SV1709 @ SV1080 @ SV328 )
| ~ ( c_lessequals @ SV1080 @ SV1709 @ SV328 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5611]) ).
thf(6028,plain,
! [SV329: $i,SV1710: $i,SV1081: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1081 @ SV1710 @ SV329 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1710 @ SV1081 @ SV329 )
| ( SV1710 = SV1081 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5612]) ).
thf(6029,plain,
! [SV330: $i,SV1711: $i,SV1082: $i] :
( ( ( SV1082 = SV1711 )
= $true )
| ( ( ~ ( c_lessequals @ SV1711 @ SV1082 @ SV330 )
| ~ ( c_lessequals @ SV1082 @ SV1711 @ SV330 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5613]) ).
thf(6030,plain,
! [SV331: $i,SV1712: $i,SV1083: $i] :
( ( ( SV1083 = SV1712 )
= $true )
| ( ( ~ ( c_lessequals @ SV1083 @ SV1712 @ SV331 )
| ~ ( c_lessequals @ SV1712 @ SV1083 @ SV331 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5614]) ).
thf(6031,plain,
! [SV333: $i,SV1714: $i,SV1085: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1085 @ SV1714 @ SV333 )
= $true )
| ( ( ( SV1714 = SV1085 )
| ( c_HOL_Oord__class_Oless @ SV1714 @ SV1085 @ SV333 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5615]) ).
thf(6032,plain,
! [SV334: $i,SV1715: $i,SV1086: $i] :
( ( ( SV1086 = SV1715 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1086 @ SV1715 @ SV334 )
| ( c_HOL_Oord__class_Oless @ SV1715 @ SV1086 @ SV334 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5616]) ).
thf(6033,plain,
! [SV335: $i,SV1716: $i,SV1087: $i] :
( ( ( c_lessequals @ SV1087 @ SV1716 @ SV335 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SV1716 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV335 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5617]) ).
thf(6034,plain,
! [SV336: $i,SV1717: $i,SV1088: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV1717 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
= $true )
| ( ( ~ ( c_lessequals @ SV1088 @ SV1717 @ SV336 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV336 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5618]) ).
thf(6035,plain,
! [SV2313: $i,SV2107: $i,SV1718: $i,SV1090: $i,SV340: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV2107 ) @ SV2313 ) @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1718 @ SV2313 @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SV2107 @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5619]) ).
thf(6036,plain,
! [SV1719: $i,SV341: $i,SV2108: $i,SV1091: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1091 @ SV2108 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV341 @ SV1719 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV341 ) @ SV1091 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1719 ) @ SV2108 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5620]) ).
thf(6037,plain,
! [SV345: $i,SV1720: $i,SV1095: $i] :
( ( ( c_lessequals @ SV1095 @ SV1720 @ SV345 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SV1720 @ SV345 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5621]) ).
thf(6038,plain,
! [SV346: $i,SV1721: $i,SV1096: $i] :
( ( ( c_lessequals @ SV1096 @ SV1721 @ SV346 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1096 @ SV1721 @ SV346 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5622]) ).
thf(6039,plain,
! [SV2314: $i,SV2109: $i,SV1722: $i,SV1097: $i,SV347: $i] :
( ( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1097 ) @ SV1722 ) @ SV2109 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV347 @ SV1722 @ SV2314 )
| ~ ( c_Type_Otyping @ SV347 @ SV1097 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2314 ) @ SV2109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5623]) ).
thf(6040,plain,
! [SV1723: $i,SV2110: $i,SV349: $i,SV1098: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1098 @ ( c_Nat_Osize__class_Osize @ SV349 @ ( tc_List_Olist @ SV2110 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ SV349 @ SV1098 @ SV1723 @ SV2110 )
= ( c_List_Oappend @ ( c_List_Otake @ SV1098 @ SV349 @ SV2110 ) @ ( c_List_Olist_OCons @ SV1723 @ ( c_List_Odrop @ ( c_Suc @ SV1098 ) @ SV349 @ SV2110 ) @ SV2110 ) @ SV2110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5624]) ).
thf(6041,plain,
! [SV1724: $i,SV1099: $i,SV350: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ ( c_Power_Opower__class_Opower @ SV1099 @ ( c_Suc @ SV1724 ) @ SV350 ) @ SV350 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ SV1099 @ SV350 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5625]) ).
thf(6042,plain,
! [SV353: $i,SV1726: $i,SV1102: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1102 @ SV1726 @ SV353 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1102 @ SV1726 @ SV353 ) @ ( c_HOL_Ozero__class_Ozero @ SV353 ) @ SV353 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5627]) ).
thf(6043,plain,
! [SV354: $i,SV1727: $i,SV1103: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1103 @ SV1727 @ SV354 ) @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV354 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1103 @ SV1727 @ SV354 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5628]) ).
thf(6044,plain,
! [SV1728: $i,SV355: $i,SV1104: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1104 @ SV355 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1728 @ SV355 ) @ SV355 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1104 @ SV1728 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5629]) ).
thf(6045,plain,
! [SV356: $i,SV1729: $i,SV1105: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1105 @ SV1729 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1105 @ SV356 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1729 @ SV356 ) @ SV356 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV356 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5630]) ).
thf(6046,plain,
! [SV359: $i,SV1106: $i,SV1730: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1730 @ SV1106 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV359 @ SV1730 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV359 ) @ SV1106 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5631]) ).
thf(6047,plain,
! [SV2111: $i,SV1731: $i,SV1107: $i,SV360: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV360 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV1107 ) @ SV1731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV2111 ) @ SV1731 ) @ SV360 )
| ~ ( c_lessequals @ SV1107 @ SV2111 @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5632]) ).
thf(6048,plain,
! [SV2112: $i,SV1732: $i,SV1108: $i,SV361: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV361 )
= $false )
| ( ( ( c_lessequals @ SV1108 @ SV1732 @ SV361 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1108 ) @ SV2112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1732 ) @ SV2112 ) @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5633]) ).
thf(6049,plain,
! [SV2113: $i,SV1733: $i,SV1109: $i,SV362: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV362 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV1733 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV2113 ) @ SV362 )
| ~ ( c_lessequals @ SV1733 @ SV2113 @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5634]) ).
thf(6050,plain,
! [SV2114: $i,SV1734: $i,SV1110: $i,SV363: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV363 )
= $false )
| ( ( ( c_lessequals @ SV1110 @ SV1734 @ SV363 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1734 ) @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5635]) ).
thf(6051,plain,
! [SV2115: $i,SV1735: $i,SV1111: $i,SV364: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV364 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV1111 ) @ SV1735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV2115 ) @ SV1735 ) @ SV364 )
| ~ ( c_lessequals @ SV1111 @ SV2115 @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5636]) ).
thf(6052,plain,
! [SV2116: $i,SV1736: $i,SV1112: $i,SV365: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV365 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV1736 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV2116 ) @ SV365 )
| ~ ( c_lessequals @ SV1736 @ SV2116 @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5637]) ).
thf(6053,plain,
! [SV1740: $i,SV1116: $i,SV2117: $i,SV370: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV370 @ ( tc_List_Olist @ SV2117 ) ) @ SV1116 @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ SV370 @ SV1116 @ SV1740 @ SV2117 )
= SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5641]) ).
thf(6054,plain,
! [SV2315: $i,SV2118: $i,SV1741: $i,SV1120: $i,SV374: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV374 @ SV1120 @ SV1741 @ SV2118 ) @ SV2315 )
= ( hAPP @ SV374 @ ( c_HOL_Ominus__class_Ominus @ SV2315 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1120 @ SV2315 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5642]) ).
thf(6055,plain,
! [SV2421: $i,SV2316: $i,SV2119: $i,SV1742: $i,SV1121: $i,SV375: $i] :
( ( ! [SY6475: $i,SY6476: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ SV2119 ) )
= ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ ( c_Suc @ SV2119 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2316 @ SV375 @ SV1742 @ SV2421 @ SY6475 @ SY6476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5643]) ).
thf(6056,plain,
! [SV2422: $i,SV2317: $i,SV2120: $i,SV1743: $i,SV1122: $i,SV376: $i] :
( ( ! [SY6477: $i,SY6478: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ SV2120 ) ) @ SV1743 )
= ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ ( c_Suc @ SV2120 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2317 @ SV376 @ SV1122 @ SV2422 @ SY6477 @ SY6478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5644]) ).
thf(6057,plain,
! [SV2423: $i,SV2318: $i,SV2121: $i,SV1744: $i,SV1123: $i,SV377: $i] :
( ( ! [SY6479: $i,SY6480: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SV1744 ) )
= ( hAPP @ ( hAPP @ SV2121 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SV1744 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2318 @ SV2121 @ SV377 @ SV2423 @ SY6479 @ SY6480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5645]) ).
thf(6058,plain,
! [SV2424: $i,SV2319: $i,SV2122: $i,SV1745: $i,SV1124: $i,SV378: $i] :
( ( ! [SY6481: $i,SY6482: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SV1745 ) )
= ( hAPP @ ( hAPP @ SV2122 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SV1745 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2319 @ SV2122 @ SV378 @ SV2424 @ SY6481 @ SY6482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5646]) ).
thf(6059,plain,
! [SV2124: $i,SV1749: $i,SV1129: $i,SV383: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV383 )
= $false )
| ( ( ( c_lessequals @ SV1129 @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SV2124 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SV1749 @ ( c_Suc @ SV2124 ) @ SV383 ) @ SV383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5649]) ).
thf(6060,plain,
! [SV387: $i,SV1133: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1133 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV387 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1133 @ SV387 ) @ SV387 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV387 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5650]) ).
thf(6061,plain,
! [SV1134: $i,SV388: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV388 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1134 @ SV388 ) @ SV388 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1134 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5651]) ).
thf(6062,plain,
! [SV1141: $i,SV2127: $i,SV1755: $i,SV395: $i] :
( ( ( ~ ( c_List_Olistsp @ SV395 @ SV1755 @ SV2127 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV395 @ SV1141 @ SV2127 ) )
= $true )
| ( ( c_List_Olistsp @ SV395 @ ( c_List_Oappend @ SV1141 @ SV1755 @ SV2127 ) @ SV2127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5654]) ).
thf(6063,plain,
! [SV2425: $i,SV2320: $i,SV2128: $i,SV1756: $i,SV1142: $i,SV396: $i] :
( ( ! [SY6483: $i] :
( ( c_Fun_Ocomp @ SV396 @ ( c_Fun_Ocomp @ SV1142 @ SV1756 @ SV2128 @ SV2320 @ SV2425 ) @ SV2320 @ SY6483 @ SV2425 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV396 @ SV1142 @ SV2320 @ SY6483 @ SV2128 ) @ SV1756 @ SV2128 @ SY6483 @ SV2425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5655]) ).
thf(6064,plain,
! [SV1148: $i,SV1760: $i,SV403: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV1760 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1148 @ SV1760 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1760 @ SV1148 @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV403 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV403 @ SV1148 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5658]) ).
thf(6065,plain,
! [SV1149: $i,SV1761: $i,SV404: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV404 @ SV1761 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1149 @ SV1761 @ tc_nat )
| ~ ( c_lessequals @ SV1149 @ SV404 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SV1149 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1761 @ SV1149 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5659]) ).
thf(6066,plain,
! [SV2129: $i,SV1762: $i,SV1150: $i,SV405: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV405 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1762 ) @ SV2129 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2129 @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1762 @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5660]) ).
thf(6067,plain,
! [SV408: $i,SV1153: $i] :
( ( ( c_lessequals @ SV1153 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV408 ) @ SV1153 ) @ SV1153 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(6068,plain,
! [SV1154: $i,SV409: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV409 ) @ SV1154 ) @ SV1154 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
= $false )
| ( ( c_lessequals @ SV1154 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(6069,plain,
! [SV2130: $i,SV1765: $i,SV1155: $i,SV410: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV410 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SV1765 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SV2130 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2130 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5665]) ).
thf(6070,plain,
! [SV2131: $i,SV1766: $i,SV1156: $i,SV411: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV411 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1766 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1766 @ SV411 ) @ SV411 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SV2131 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5666]) ).
thf(6071,plain,
! [SV2132: $i,SV1767: $i,SV1157: $i,SV412: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV412 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SV1767 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SV2132 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1767 @ SV2132 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5667]) ).
thf(6072,plain,
! [SV2133: $i,SV1768: $i,SV1158: $i,SV413: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV413 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1768 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1768 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV2133 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5668]) ).
thf(6073,plain,
! [SV1171: $i,SV427: $i,SV2138: $i,SV1773: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1773 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2138 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV427 ) @ SV1171 ) @ SV1773 ) ) @ SV2138 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV427 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2138 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1171 ) @ SV2138 ) ) @ SV1773 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5672]) ).
thf(6074,plain,
! [SV2139: $i,SV1776: $i,SV1175: $i,SV431: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV431 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ ( c_Orderings_Oord__class_Omax @ SV1175 @ SV1776 @ SV431 ) ) @ SV2139 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1175 ) @ SV2139 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV431 ) @ SV1776 ) @ SV2139 ) @ SV431 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5674]) ).
thf(6075,plain,
! [SV2140: $i,SV1777: $i,SV1177: $i,SV433: $i] :
( ( ( class_Orderings_Olinorder @ SV433 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1177 @ SV1777 @ SV433 ) @ SV2140 @ SV433 )
= ( c_Orderings_Oord__class_Omax @ SV1177 @ ( c_Orderings_Oord__class_Omax @ SV1777 @ SV2140 @ SV433 ) @ SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5675]) ).
thf(6076,plain,
! [SV2141: $i,SV1778: $i,SV1178: $i,SV434: $i] :
( ( ( class_Orderings_Olinorder @ SV434 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1178 @ ( c_Orderings_Oord__class_Omax @ SV1778 @ SV2141 @ SV434 ) @ SV434 )
= ( c_Orderings_Oord__class_Omax @ SV1778 @ ( c_Orderings_Oord__class_Omax @ SV1178 @ SV2141 @ SV434 ) @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5676]) ).
thf(6077,plain,
! [SV2426: $i,SV2321: $i,SV2143: $i,SV1785: $i,SV1190: $i,SV449: $i] :
( ( ( c_List_Ofoldl @ SV449 @ SV1190 @ ( c_List_Oappend @ SV1785 @ SV2143 @ SV2321 ) @ SV2426 @ SV2321 )
= ( c_List_Ofoldl @ SV449 @ ( c_List_Ofoldl @ SV449 @ SV1190 @ SV1785 @ SV2426 @ SV2321 ) @ SV2143 @ SV2426 @ SV2321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5680]) ).
thf(6078,plain,
! [SV2144: $i,SV1786: $i,SV1191: $i,SV450: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV450 )
= $false )
| ( ( ( c_lessequals @ SV1191 @ SV1786 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1786 @ SV450 ) @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SV2144 @ SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5681]) ).
thf(6079,plain,
! [SV2145: $i,SV1787: $i,SV1192: $i,SV451: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV451 )
= $false )
| ( ( ( c_lessequals @ SV1192 @ SV1787 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1787 @ SV451 ) @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SV2145 @ SV451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5682]) ).
thf(6080,plain,
! [SV2146: $i,SV1788: $i,SV1193: $i,SV452: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV452 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SV1788 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SV2146 @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ SV1788 @ SV2146 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5683]) ).
thf(6081,plain,
! [SV2322: $i,SV2149: $i,SV1792: $i,SV1197: $i,SV457: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV2149 ) @ SV2322 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1792 @ SV2322 @ SV457 )
| ~ ( c_lessequals @ SV1197 @ SV2149 @ SV457 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5685]) ).
thf(6082,plain,
! [SV2323: $i,SV2150: $i,SV1793: $i,SV1198: $i,SV458: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV2150 ) @ SV2323 ) @ SV458 )
| ~ ( c_lessequals @ SV1793 @ SV2323 @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SV2150 @ SV458 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5686]) ).
thf(6083,plain,
! [SV1204: $i,SV464: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV464 ) @ SV1204 ) @ SV1204 ) @ SV464 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV464 ) @ SV1204 @ SV464 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV464 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5687]) ).
thf(6084,plain,
! [SV1205: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1205 @ SV465 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV465 ) @ SV1205 ) @ SV1205 ) @ SV465 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5688]) ).
thf(6085,plain,
! [SV1206: $i,SV466: $i] :
( ( ( class_Int_Onumber__ring @ SV466 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1206 @ SV1206 @ SV466 )
= ( c_HOL_Ozero__class_Ozero @ SV466 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5689]) ).
thf(6086,plain,
! [SV1213: $i,SV474: $i] :
( ( ( class_Int_Onumber__ring @ SV474 )
= $false )
| ( ( SV1213
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV474 ) @ SV1213 ) @ ( c_HOL_Ozero__class_Ozero @ SV474 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5690]) ).
thf(6087,plain,
! [SV489: $i,SV1795: $i,SV1223: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1795 @ tc_nat ) @ SV489 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1223 @ SV489 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1795 @ SV489 ) @ SV489 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1795 @ SV1223 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5693]) ).
thf(6088,plain,
! [SV2152: $i,SV1799: $i,SV1227: $i,SV493: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV493 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV1227 ) @ SV1799 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV2152 ) @ SV1799 ) @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SV2152 @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(6089,plain,
! [SV2153: $i,SV1800: $i,SV1228: $i,SV494: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV494 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV1228 ) @ SV1800 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV2153 ) @ SV1800 ) @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SV2153 @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(6090,plain,
! [SV2154: $i,SV1801: $i,SV1229: $i,SV495: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV495 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1801 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1229 ) @ SV2154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1801 ) @ SV2154 ) @ SV495 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5698]) ).
thf(6091,plain,
! [SV2155: $i,SV1802: $i,SV1230: $i,SV496: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV496 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV1802 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV2155 ) @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1802 @ SV2155 @ SV496 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5699]) ).
thf(6092,plain,
! [SV2156: $i,SV1803: $i,SV1231: $i,SV497: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV497 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV1803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV2156 ) @ SV497 )
| ~ ( c_HOL_Oord__class_Oless @ SV1803 @ SV2156 @ SV497 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5700]) ).
thf(6093,plain,
! [SV2157: $i,SV1804: $i,SV1232: $i,SV498: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV498 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1232 @ SV1804 @ SV498 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1232 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1804 ) @ SV498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5701]) ).
thf(6094,plain,
! [SV2158: $i,SV1808: $i,SV1236: $i,SV502: $i] :
( ( ( class_Orderings_Oorder @ SV502 )
= $false )
| ( ( ( c_lessequals @ SV1236 @ SV1808 @ SV502 )
| ~ ( c_lessequals @ SV1236 @ SV2158 @ SV502 )
| ~ ( c_lessequals @ SV2158 @ SV1808 @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(6095,plain,
! [SV2159: $i,SV1809: $i,SV1237: $i,SV503: $i] :
( ( ( class_Orderings_Oorder @ SV503 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1237 @ SV1809 @ SV503 )
| ~ ( c_lessequals @ SV1237 @ SV2159 @ SV503 )
| ~ ( c_HOL_Oord__class_Oless @ SV2159 @ SV1809 @ SV503 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5706]) ).
thf(6096,plain,
! [SV2160: $i,SV1810: $i,SV1238: $i,SV504: $i] :
( ( ( class_Orderings_Oorder @ SV504 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1238 @ SV1810 @ SV504 )
| ~ ( c_HOL_Oord__class_Oless @ SV1238 @ SV2160 @ SV504 )
| ~ ( c_lessequals @ SV2160 @ SV1810 @ SV504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5707]) ).
thf(6097,plain,
! [SV1811: $i,SV1239: $i,SV505: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SV1239 ) @ SV1811 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
= $true )
| ( ( ~ ( c_lessequals @ SV1811 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
| ~ ( c_lessequals @ SV1239 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5708]) ).
thf(6098,plain,
! [SV2161: $i,SV1812: $i,SV1240: $i,SV506: $i] :
( ( ( class_Orderings_Opreorder @ SV506 )
= $false )
| ( ( ( c_lessequals @ SV1240 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SV2161 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SV1240 @ SV2161 @ SV506 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5709]) ).
thf(6099,plain,
! [SV508: $i,SV1241: $i,SV1813: $i] :
( ( ( c_lessequals @ SV1813 @ SV1241 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV508 @ SV1813 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV508 @ SV1241 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(6100,plain,
! [SV2162: $i,SV1814: $i,SV1244: $i,SV512: $i] :
( ( ( class_Orderings_Opreorder @ SV512 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1244 @ SV1814 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV2162 @ SV1814 @ SV512 )
| ~ ( c_lessequals @ SV1244 @ SV2162 @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5711]) ).
thf(6101,plain,
! [SV2163: $i,SV1815: $i,SV1245: $i,SV513: $i] :
( ( ( class_Orderings_Opreorder @ SV513 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1245 @ SV1815 @ SV513 )
| ~ ( c_lessequals @ SV2163 @ SV1815 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ SV1245 @ SV2163 @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5712]) ).
thf(6102,plain,
! [SV2325: $i,SV2164: $i,SV1816: $i,SV1246: $i,SV514: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV514 ) )
= $true )
| ( ( ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2164 ) @ SV514 )
| ~ ( c_lessequals @ SV2325 @ SV2164 @ SV514 )
| ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2325 ) @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5713]) ).
thf(6103,plain,
! [SV1817: $i,SV515: $i,SV1247: $i,SV2165: $i] :
( ( ( ~ ( c_Lambda_Obeta @ SV2165 @ SV1247 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV515 @ SV2165 @ SV1817 ) )
= $true )
| ( ( c_Type_Otyping @ SV515 @ SV1247 @ SV1817 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5714]) ).
thf(6104,plain,
! [SV516: $i,SV1818: $i,SV1248: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1248 @ SV1818 @ tc_nat )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ominus__class_Ominus @ SV1248 @ SV1818 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5715]) ).
thf(6105,plain,
! [SV2427: $i,SV2326: $i,SV2166: $i,SV1819: $i,SV1249: $i,SV517: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV1249 @ SV1819 @ SV2166 ) @ SV2326 @ SV2427 @ SV2166 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV2326 @ SV2427 @ SV2166 ) @ SV1249 @ SV1819 @ SV2166 ) )
| ( SV1249 = SV2326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5716]) ).
thf(6106,plain,
! [SV518: $i,SV1250: $i] :
( ( ( c_lessequals @ SV1250 @ SV518 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV518 @ ( c_Suc @ SV1250 ) @ tc_nat )
= $false )
| ( ( SV518 = SV1250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5717]) ).
thf(6107,plain,
! [SV529: $i,SV1259: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1259 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV529 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1259 @ tc_nat ) @ SV529 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5720]) ).
thf(6108,plain,
! [SV533: $i,SV1824: $i,SV1263: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1263 @ SV1824 @ SV533 )
= $true )
| ( ( ( SV1824 = SV1263 )
| ~ ( c_lessequals @ SV1263 @ SV1824 @ SV533 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV533 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5722]) ).
thf(6109,plain,
! [SV534: $i,SV1825: $i,SV1264: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1825 @ SV534 )
= $true )
| ( ( ~ ( c_lessequals @ SV1264 @ SV1825 @ SV534 )
| ( SV1825 = SV1264 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV534 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5723]) ).
thf(6110,plain,
! [SV538: $i,SV1826: $i,SV1268: $i] :
( ( ( SV1268 = SV1826 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1268 @ SV1826 @ SV538 )
| ~ ( c_lessequals @ SV1268 @ SV1826 @ SV538 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV538 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5727]) ).
thf(6111,plain,
! [SV539: $i,SV1827: $i,SV1269: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1269 @ SV1827 @ SV539 )
= $true )
| ( ( ( SV1269 = SV1827 )
| ~ ( c_lessequals @ SV1269 @ SV1827 @ SV539 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5728]) ).
thf(6112,plain,
! [SV540: $i,SV1828: $i,SV1270: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1270 @ SV1828 @ SV540 )
= $true )
| ( ( ( SV1270 = SV1828 )
| ~ ( c_lessequals @ SV1270 @ SV1828 @ SV540 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5729]) ).
thf(6113,plain,
! [SV541: $i,SV1829: $i,SV1271: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1271 @ SV1829 @ SV541 )
= $true )
| ( ( ~ ( c_lessequals @ SV1271 @ SV1829 @ SV541 )
| ( SV1271 = SV1829 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5730]) ).
thf(6114,plain,
! [SV542: $i,SV1830: $i,SV1272: $i] :
( ( ( SV1272 = SV1830 )
= $true )
| ( ( ~ ( c_lessequals @ SV1272 @ SV1830 @ SV542 )
| ( c_HOL_Oord__class_Oless @ SV1272 @ SV1830 @ SV542 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5731]) ).
thf(6115,plain,
! [SV543: $i,SV1831: $i,SV1273: $i] :
( ( ( SV1273 = SV1831 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1273 @ SV1831 @ SV543 )
| ~ ( c_lessequals @ SV1273 @ SV1831 @ SV543 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV543 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5732]) ).
thf(6116,plain,
! [SV553: $i,SV1837: $i,SV1282: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1282 @ SV1837 @ SV553 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1837 @ SV1282 @ SV553 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5734]) ).
thf(6117,plain,
! [SV554: $i,SV1838: $i,SV1283: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1838 @ SV554 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1838 @ SV1283 @ SV554 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV554 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5735]) ).
thf(6118,plain,
! [SV556: $i,SV1839: $i,SV1285: $i] :
( ( ( c_lessequals @ SV1285 @ SV1839 @ SV556 )
= $true )
| ( ( c_lessequals @ SV1839 @ SV1285 @ SV556 )
= $true )
| ( ( class_Orderings_Olinorder @ SV556 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5736]) ).
thf(6119,plain,
! [SV557: $i,SV1840: $i,SV1286: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1286 @ SV1840 @ SV557 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1840 @ SV1286 @ SV557 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV557 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5737]) ).
thf(6120,plain,
! [SV558: $i,SV1841: $i,SV1287: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1287 @ SV1841 @ SV558 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1841 @ SV1287 @ SV558 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV558 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5738]) ).
thf(6121,plain,
! [SV1291: $i,SV565: $i] :
( ( ( hBOOL @ ( hAPP @ SV565 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV565 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV565 @ SV1291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5741]) ).
thf(6122,plain,
! [SV2428: $i,SV2329: $i,SV2174: $i,SV1843: $i,SV1293: $i,SV574: $i] :
( ( ! [SY6484: $i] :
( ( ( hAPP @ ( hAPP @ SV574 @ SV1293 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1843 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2174 @ SV2329 @ SV574 @ SV2428 @ SV1843 @ SY6484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5742]) ).
thf(6123,plain,
! [SV2176: $i,SV1297: $i,SV578: $i,SV1847: $i] :
( ( ( c_List_Odistinct @ ( c_List_Omap @ SV1847 @ SV578 @ SV1297 @ SV2176 ) @ SV2176 )
= $false )
| ( ( c_List_Odistinct @ SV578 @ SV1297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5745]) ).
thf(6124,plain,
! [SV2429: $i,SV2335: $i,SV2183: $i,SV1855: $i,SV1305: $i,SV586: $i] :
( ( ( c_List_Omap @ SV586 @ ( c_List_Omap @ SV1305 @ SV1855 @ SV2183 @ SV2335 ) @ SV2335 @ SV2429 )
= ( c_List_Omap @ ( c_Fun_Ocomp @ SV586 @ SV1305 @ SV2335 @ SV2429 @ SV2183 ) @ SV1855 @ SV2183 @ SV2429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5750]) ).
thf(6125,plain,
! [SV2430: $i,SV2339: $i,SV2187: $i,SV1859: $i,SV1309: $i,SV590: $i] :
( ( ( c_List_Omap @ SV590 @ ( c_List_Olist__update @ SV1309 @ SV1859 @ SV2187 @ SV2339 ) @ SV2339 @ SV2430 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV590 @ SV1309 @ SV2339 @ SV2430 ) @ SV1859 @ ( hAPP @ SV590 @ SV2187 ) @ SV2430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5754]) ).
thf(6126,plain,
! [SV1863: $i,SV1316: $i,SV2189: $i,SV597: $i] :
( ( ( c_Lambda_Obeta @ SV597 @ SV2189 )
= $false )
| ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV597 ) @ SV1316 ) @ SV1863 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2189 ) @ SV1316 ) @ SV1863 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5756]) ).
thf(6127,plain,
! [SV2344: $i,SV2194: $i,SV1869: $i,SV1322: $i,SV603: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV603 @ ( c_Type_Otype_Otype__case @ SV1322 @ SV1869 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2194 ) @ SV2344 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV603 @ ( hAPP @ ( hAPP @ SV1869 @ SV2194 ) @ SV2344 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5761]) ).
thf(6128,plain,
! [SV2345: $i,SV2195: $i,SV1870: $i,SV1323: $i,SV604: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV604 @ ( c_Type_Otype_Otype__case @ SV1323 @ SV1870 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2195 ) @ SV2345 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV604 @ ( hAPP @ ( hAPP @ SV1870 @ SV2195 ) @ SV2345 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5762]) ).
thf(6129,plain,
! [SV2431: $i,SV2346: $i,SV2196: $i,SV1871: $i,SV1324: $i,SV605: $i] :
( ( ( c_List_Ofoldr @ SV605 @ ( c_List_Olist_OCons @ SV1324 @ SV1871 @ SV2196 ) @ SV2346 @ SV2196 @ SV2431 )
= ( hAPP @ ( hAPP @ SV605 @ SV1324 ) @ ( c_List_Ofoldr @ SV605 @ SV1871 @ SV2346 @ SV2196 @ SV2431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5763]) ).
thf(6130,plain,
! [SV2432: $i,SV2347: $i,SV2197: $i,SV1872: $i,SV1325: $i,SV606: $i] :
( ( ( c_List_Ofoldr @ SV606 @ ( c_List_Oappend @ SV1325 @ SV1872 @ SV2197 ) @ SV2347 @ SV2197 @ SV2432 )
= ( c_List_Ofoldr @ SV606 @ SV1325 @ ( c_List_Ofoldr @ SV606 @ SV1872 @ SV2347 @ SV2197 @ SV2432 ) @ SV2197 @ SV2432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5764]) ).
thf(6131,plain,
! [SV2348: $i,SV2199: $i,SV1876: $i,SV1330: $i,SV611: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV611 @ SV1330 @ SV1876 @ SV2199 ) @ SV2348 )
= ( hAPP @ SV611 @ SV2348 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2348 @ SV1330 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5766]) ).
thf(6132,plain,
! [SV2349: $i,SV2200: $i,SV1877: $i,SV1331: $i,SV612: $i] :
( ( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1331 @ SV1877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2200 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV612 @ SV1877 @ SV2349 )
| ~ ( c_Type_Otyping @ SV612 @ SV1331 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2349 @ SV2200 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5767]) ).
thf(6133,plain,
! [SV2201: $i,SV1332: $i,SV1878: $i,SV613: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV613 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1878 @ tc_Type_Otype ) @ SV1332 @ SV2201 )
= $false )
| ( ( c_Type_Otyping @ SV613 @ ( c_Lambda_OdB_OAbs @ SV1332 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1878 ) @ SV2201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5768]) ).
thf(6134,plain,
! [SV1333: $i,SV614: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV614 )
| ~ ( class_Power_Opower @ SV614 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5769]) ).
thf(6135,plain,
! [SV1334: $i,SV615: $i] :
( ( ( class_Power_Opower @ SV615 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV615 ) @ SV1334 @ SV615 )
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
| ( SV1334
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV615 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(6136,plain,
! [SV2433: $i,SV2351: $i,SV2203: $i,SV1881: $i,SV1338: $i,SV620: $i] :
( ( ! [SY6485: $i] :
( ( c_List_Ofoldr @ SV620 @ ( c_List_Omap @ SV1338 @ SV1881 @ SV2203 @ SV2351 ) @ SV2433 @ SV2351 @ SY6485 )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ SV620 @ SV1338 @ SV2351 @ ( tc_fun @ SY6485 @ SY6485 ) @ SV2203 ) @ SV1881 @ SV2433 @ SV2203 @ SY6485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5772]) ).
thf(6137,plain,
! [SV2434: $i,SV2352: $i,SV2204: $i,SV1882: $i,SV1339: $i,SV621: $i] :
( ( ~ ( c_Type_Otyping @ SV621 @ SV1339 @ SV1882 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SV2204 @ SV1882 @ tc_Type_Otype ) @ SV2352 @ SV2434 )
| ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2352 ) @ SV1339 ) @ SV2204 ) @ SV2434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5773]) ).
thf(6138,plain,
! [SV2353: $i,SV2205: $i,SV1883: $i,SV1340: $i,SV622: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV622 @ SV1340 @ SV1883 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV2205 ) @ SV1340 ) @ SV2353 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV622 @ SV2205 @ SV2353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5774]) ).
thf(6139,plain,
! [SV2435: $i,SV2354: $i,SV2207: $i,SV1885: $i,SV1342: $i,SV625: $i] :
( ( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1885 ) @ SV2207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2354 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SV1885 @ SV2435 @ tc_Type_Otype ) @ SV2207 @ SV2354 )
| ~ ( c_Type_Otyping @ SV625 @ SV1342 @ SV2435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5775]) ).
thf(6140,plain,
! [SV2436: $i,SV2355: $i,SV2209: $i,SV1887: $i,SV1344: $i,SV627: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV627 @ SV1344 @ SV1887 @ SV2209 ) @ SV2355 ) @ SV2436 )
= ( hAPP @ ( hAPP @ SV627 @ SV2436 ) @ SV2355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5776]) ).
thf(6141,plain,
! [SV2356: $i,SV2210: $i,SV1888: $i,SV1345: $i,SV628: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV628 @ SV1345 @ SV1888 @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1345 ) @ SV2210 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2356 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV628 @ SV2210 @ SV2356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5777]) ).
thf(6142,plain,
! [SV2437: $i,SV2357: $i,SV2211: $i,SV1890: $i,SV1350: $i,SV633: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV633 @ SV1350 @ SV1890 @ SV2211 ) @ SV2357 ) @ SV2437 )
= ( hAPP @ ( hAPP @ SV633 @ SV2437 ) @ SV2357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5778]) ).
thf(6143,plain,
! [SV2438: $i,SV2358: $i,SV2212: $i,SV1891: $i,SV1351: $i,SV634: $i] :
( ( ( c_COMBB @ SV634 @ SV1351 @ SV1891 @ SV2212 @ SV2358 @ SV2438 )
= ( hAPP @ SV634 @ ( hAPP @ SV1351 @ SV1891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5779]) ).
thf(6144,plain,
! [SV2213: $i,SV1893: $i,SV1354: $i,SV637: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV1893 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV2213 ) )
| ( SV1893 = SV2213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5781]) ).
thf(6145,plain,
! [SV639: $i,SV1895: $i,SV1356: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1356 @ SV1895 @ SV639 )
!= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
= $true )
| ( ( SV1356
= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5783]) ).
thf(6146,plain,
! [SV1358: $i,SV641: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV641 ) @ SV1358 ) @ SV1358 )
= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
= $false )
| ( ( SV1358
= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV641 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5784]) ).
thf(6147,plain,
! [SV2359: $i,SV2214: $i,SV1896: $i,SV1360: $i,SV643: $i] :
( ( ( ( c_List_Omap @ SV643 @ SV1360 @ SV1896 @ SV2214 )
!= ( c_List_Omap @ SV643 @ SV2359 @ SV1896 @ SV2214 ) )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ SV1360 @ ( tc_List_Olist @ SV1896 ) )
= ( c_Nat_Osize__class_Osize @ SV2359 @ ( tc_List_Olist @ SV1896 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5785]) ).
thf(6148,plain,
! [SV1897: $i,SV1361: $i,SV644: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
!= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
| ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5786]) ).
thf(6149,plain,
! [SV645: $i,SV1362: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1362 @ SV645 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1362 = SV645 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV645 @ SV1362 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5787]) ).
thf(6150,plain,
! [SV2215: $i,SV1898: $i,SV1363: $i,SV646: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV646 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV1898 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV2215 ) )
| ( SV1898 = SV2215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(6151,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV647 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV647 )
| ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5789]) ).
thf(6152,plain,
! [SV2216: $i,SV1900: $i,SV1365: $i,SV648: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV648 ) @ SV1365 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1900 ) @ SV2216 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV648 = SV1900 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5790]) ).
thf(6153,plain,
! [SV2217: $i,SV1902: $i,SV1369: $i,SV652: $i] :
( ( ( ( c_List_Olist_ONil @ SV652 )
= ( c_List_Omap @ SV1369 @ SV1902 @ SV2217 @ SV652 ) )
= $false )
| ( ( SV1902
= ( c_List_Olist_ONil @ SV2217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5793]) ).
thf(6154,plain,
! [SV2360: $i,SV2218: $i,SV1903: $i,SV1370: $i,SV653: $i] :
( ( ( ( c_List_Oappend @ SV653 @ SV1370 @ SV1903 )
!= ( c_List_Oappend @ SV2218 @ SV2360 @ SV1903 ) )
= $true )
| ( ( ( SV1370
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ SV2218 @ SV1903 ) @ SV2360 @ SV1903 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ ( c_Nat_Osize__class_Osize @ SV2218 @ ( tc_List_Olist @ SV1903 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5794]) ).
thf(6155,plain,
! [SV2219: $i,SV1904: $i,SV1372: $i,SV655: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= SV2219 )
= $false )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 )
!= SV655 )
| ( SV1904
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
| ( ( c_List_Oappend @ SV1904 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SV2219 @ SV1372 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5796]) ).
thf(6156,plain,
! [SV2220: $i,SV1906: $i,SV1375: $i,SV659: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV659 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
!= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
| ( SV1375 = SV2220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5799]) ).
thf(6157,plain,
! [SV2439: $i,SV2361: $i,SV2221: $i,SV1907: $i,SV1376: $i,SV660: $i] :
( ( ! [SY6486: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
| ~ ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SY6486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5800]) ).
thf(6158,plain,
! [SV2222: $i,SV1911: $i,SV1381: $i,SV665: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV665 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1381 @ SV1911 @ SV665 )
!= ( c_Power_Opower__class_Opower @ SV1381 @ SV2222 @ SV665 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 )
| ( SV1911 = SV2222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5802]) ).
thf(6159,plain,
! [SV1914: $i,SV1384: $i,SV668: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV668 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1384 @ SV1914 @ SV668 )
!= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
| ( SV1384 = SV1914 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV668 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5804]) ).
thf(6160,plain,
! [SV2362: $i,SV2223: $i,SV1916: $i,SV1386: $i,SV670: $i] :
( ( ( ( c_List_Oappend @ SV670 @ SV1386 @ SV1916 )
!= ( c_List_Oappend @ SV2223 @ SV2362 @ SV1916 ) )
= $true )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ SV670 @ SV1916 )
= SV2223 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV670 @ ( tc_List_Olist @ SV1916 ) ) @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5805]) ).
thf(6161,plain,
! [SV2440: $i,SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ! [SY6487: $i,SY6488: $i,SY6489: $i,SY6490: $i,SY6491: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SV2440 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SY6487 @ SY6488 @ SY6489 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SY6490 @ SY6488 @ SY6491 ) @ SV2440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5806]) ).
thf(6162,plain,
! [SV1919: $i,SV674: $i,SV1389: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1389 @ SV674 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1919 @ SV674 ) )
= $true )
| ( ( SV1389 = SV1919 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV674 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5807]) ).
thf(6163,plain,
! [SV2225: $i,SV1920: $i,SV1391: $i,SV676: $i] :
( ( ( ( c_List_Oappend @ SV676 @ SV1391 @ SV1920 )
= ( c_List_Oappend @ SV676 @ SV2225 @ SV1920 ) )
= $false )
| ( ( SV1391 = SV2225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5808]) ).
thf(6164,plain,
! [SV677: $i,SV1921: $i,SV1392: $i] :
( ( ( SV1392
= ( c_List_Olist_ONil @ SV1921 ) )
= $true )
| ( ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Otake @ SV677 @ SV1392 @ SV1921 )
= ( c_List_Olist_ONil @ SV1921 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5809]) ).
thf(6165,plain,
! [SV2441: $i,SV2364: $i,SV2226: $i,SV1922: $i,SV1393: $i,SV678: $i] :
( ( ! [SY6492: $i,SY6493: $i,SY6494: $i] :
( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SV2226 @ SV2364 )
!= ( c_Fun_Ocomp @ SV2441 @ SY6492 @ SY6493 @ SV2226 @ SV2364 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SY6494 ) )
= ( hAPP @ SV2441 @ ( hAPP @ SY6492 @ SY6494 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5810]) ).
thf(6166,plain,
! [SV2365: $i,SV2227: $i,SV1925: $i,SV1399: $i,SV684: $i] :
( ( ( ( hAPP @ SV684 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) )
!= ( hAPP @ SV1399 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) ) )
= $true )
| ( ( ( c_List_Omap @ SV684 @ SV1925 @ SV2227 @ SV2365 )
= ( c_List_Omap @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5814]) ).
thf(6167,plain,
! [SV2228: $i,SV1927: $i,SV1401: $i,SV686: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV686 ) @ SV1401 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1927 ) @ SV2228 ) )
= $false )
| ( ( SV1401 = SV2228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5816]) ).
thf(6168,plain,
! [SV2366: $i,SV2229: $i,SV1928: $i,SV1402: $i,SV687: $i] :
( ( ( ( c_List_Oappend @ SV687 @ ( c_List_Olist_OCons @ SV1402 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 )
!= ( c_List_Oappend @ SV2229 @ ( c_List_Olist_OCons @ SV2366 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 ) )
= $true )
| ( ( SV1402 = SV2366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5817]) ).
thf(6169,plain,
! [SV2230: $i,SV1929: $i,SV1403: $i,SV688: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV688 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV1929 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV2230 ) )
| ( SV1929 = SV2230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5818]) ).
thf(6170,plain,
! [SV2367: $i,SV2231: $i,SV1930: $i,SV1404: $i,SV689: $i] :
( ( ( ( c_List_Oreplicate @ SV689 @ SV1404 @ SV1930 )
!= ( c_List_Oreplicate @ SV2231 @ SV2367 @ SV1930 ) )
= $true )
| ( ( SV689 = SV2231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5819]) ).
thf(6171,plain,
! [SV2368: $i,SV2232: $i,SV1931: $i,SV1405: $i,SV690: $i] :
( ( ( ( hAPP @ SV690 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) )
!= ( hAPP @ SV1405 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) ) )
= $true )
| ( ( ( c_List_Omap @ SV690 @ SV1931 @ SV2232 @ SV2368 )
= ( c_List_Omap @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5820]) ).
thf(6172,plain,
! [SV2369: $i,SV2233: $i,SV1934: $i,SV1409: $i,SV694: $i] :
( ( ( ( c_List_Oappend @ SV694 @ SV1409 @ SV1934 )
!= ( c_List_Oappend @ SV2233 @ SV2369 @ SV1934 ) )
= $true )
| ( ( ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ SV2233 @ SV1934 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ ( c_Nat_Osize__class_Osize @ SV2233 @ ( tc_List_Olist @ SV1934 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5822]) ).
thf(6173,plain,
! [SV2370: $i,SV2234: $i,SV1936: $i,SV1411: $i,SV696: $i] :
( ( ( ( c_List_Olist_OCons @ SV696 @ SV1411 @ SV1936 )
!= ( c_List_Olist_OCons @ SV2234 @ SV2370 @ SV1936 ) )
= $true )
| ( ( SV696 = SV2234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5824]) ).
thf(6174,plain,
! [SV2235: $i,SV1937: $i,SV1412: $i,SV697: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 )
= SV697 )
= $false )
| ( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1937 @ ( tc_List_Olist @ SV1412 ) ) @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SV1937 @ SV2235 @ SV1412 )
= ( c_List_Oappend @ SV697 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 ) @ SV2235 @ SV1412 ) @ SV1412 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5825]) ).
thf(6175,plain,
! [SV2236: $i,SV1939: $i,SV1414: $i,SV699: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV699 ) @ SV1414 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1939 ) @ SV2236 ) )
= $false )
| ( ( SV699 = SV1939 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5827]) ).
thf(6176,plain,
! [SV2237: $i,SV1940: $i,SV1415: $i,SV700: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV700 ) @ SV1415 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1940 ) @ SV2237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1415 = SV2237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5828]) ).
thf(6177,plain,
! [SV2371: $i,SV2238: $i,SV1942: $i,SV1419: $i,SV704: $i] :
( ( ( ( c_List_Oreplicate @ SV704 @ SV1419 @ SV1942 )
!= ( c_List_Oreplicate @ SV2238 @ SV2371 @ SV1942 ) )
= $true )
| ( ( ( SV1419 = SV2371 )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5830]) ).
thf(6178,plain,
! [SV706: $i,SV1943: $i,SV1420: $i] :
( ( ( ~ ( c_lessequals @ SV1420 @ SV1943 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1420 @ SV706 @ tc_nat )
| ( SV706 = SV1943 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SV1420 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1943 @ SV1420 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5831]) ).
thf(6179,plain,
! [SV2239: $i,SV1945: $i,SV1422: $i,SV708: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV708 ) @ SV1422 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1945 ) @ SV2239 ) )
= $false )
| ( ( SV708 = SV1945 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5833]) ).
thf(6180,plain,
! [SV711: $i,SV1947: $i,SV1424: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1424 @ SV1947 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
= $true )
| ( ( SV1424 = SV1947 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV711 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5835]) ).
thf(6181,plain,
! [SV2372: $i,SV2240: $i,SV1948: $i,SV1425: $i,SV712: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV712 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
!= ( c_HOL_Ominus__class_Ominus @ SV2240 @ SV2372 @ SV712 ) )
| ( c_HOL_Oord__class_Oless @ SV2240 @ SV2372 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5836]) ).
thf(6182,plain,
! [SV2241: $i,SV1949: $i,SV1426: $i,SV713: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV713 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1426 ) @ SV1949 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV713 @ SV2241 ) )
| ( hBOOL @ ( hAPP @ SV713 @ SV1949 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5837]) ).
thf(6183,plain,
! [SV1950: $i,SV1427: $i,SV714: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV714 ) )
= $true )
| ( ( ( SV1427
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SV1427 ) @ SV1950 ) )
| ( SV1950
= ( c_HOL_Ozero__class_Ozero @ SV714 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV714 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5838]) ).
thf(6184,plain,
! [SV2242: $i,SV1953: $i,SV1431: $i,SV718: $i] :
( ( ( ( c_List_Omap @ SV718 @ SV1431 @ SV1953 @ SV2242 )
= ( c_List_Olist_ONil @ SV2242 ) )
= $false )
| ( ( SV1431
= ( c_List_Olist_ONil @ SV1953 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5842]) ).
thf(6185,plain,
! [SV2243: $i,SV1954: $i,SV1432: $i,SV719: $i] :
( ( ( ( c_List_Orev @ SV719 @ SV1432 )
= ( c_List_Olist_OCons @ SV1954 @ SV2243 @ SV1432 ) )
= $false )
| ( ( SV719
= ( c_List_Oappend @ ( c_List_Orev @ SV2243 @ SV1432 ) @ ( c_List_Olist_OCons @ SV1954 @ ( c_List_Olist_ONil @ SV1432 ) @ SV1432 ) @ SV1432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5843]) ).
thf(6186,plain,
! [SV2373: $i,SV2245: $i,SV1956: $i,SV1434: $i,SV721: $i] :
( ( ( ( c_List_Olist_OCons @ SV721 @ SV1434 @ SV1956 )
!= ( c_List_Olist_OCons @ SV2245 @ SV2373 @ SV1956 ) )
= $true )
| ( ( SV1434 = SV2373 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5845]) ).
thf(6187,plain,
! [SV2246: $i,SV1957: $i,SV1435: $i,SV722: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV722 ) @ SV1435 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1957 ) @ SV2246 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1957 @ SV1435 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV722 @ SV2246 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(6188,plain,
! [SV2247: $i,SV1958: $i,SV1436: $i,SV723: $i] :
( ( ( ( c_List_Olist__update @ SV723 @ SV1436 @ SV1958 @ SV2247 )
= ( c_List_Olist_ONil @ SV2247 ) )
= $false )
| ( ( SV723
= ( c_List_Olist_ONil @ SV2247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5847]) ).
thf(6189,plain,
! [SV2248: $i,SV1959: $i,SV1438: $i,SV725: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV725 ) @ SV1438 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1959 ) @ SV2248 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV725 = SV1959 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5848]) ).
thf(6190,plain,
! [SV2374: $i,SV2249: $i,SV1960: $i,SV1439: $i,SV726: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV726 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
!= ( c_HOL_Ominus__class_Ominus @ SV2249 @ SV2374 @ SV726 ) )
| ( c_lessequals @ SV2374 @ SV2249 @ SV726 )
| ~ ( c_lessequals @ SV1960 @ SV1439 @ SV726 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5849]) ).
thf(6191,plain,
! [SV2250: $i,SV1962: $i,SV1441: $i,SV728: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV728 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1441 @ SV1441 @ SV728 )
!= ( c_HOL_Ominus__class_Ominus @ SV1962 @ SV2250 @ SV728 ) )
| ( SV1962 = SV2250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5851]) ).
thf(6192,plain,
! [SV1442: $i,SV729: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV729 )
| ~ ( class_Power_Opower @ SV729 )
| ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5852]) ).
thf(6193,plain,
! [SV1963: $i,SV1443: $i,SV730: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5853]) ).
thf(6194,plain,
! [SV2375: $i,SV2251: $i,SV1965: $i,SV1446: $i,SV734: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV734 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2251 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2375 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ SV2251 )
= SV2375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5855]) ).
thf(6195,plain,
! [SV2376: $i,SV2252: $i,SV1969: $i,SV1451: $i,SV740: $i] :
( ( ( ( hAPP @ SV740 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) )
!= ( hAPP @ SV1451 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) ) )
= $true )
| ( ( ( c_List_Omap @ SV740 @ SV1969 @ SV2252 @ SV2376 )
= ( c_List_Omap @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5859]) ).
thf(6196,plain,
! [SV2253: $i,SV1970: $i,SV1452: $i,SV741: $i] :
( ( ( SV741
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) )
= $false )
| ( ( ( ( c_List_Oappend @ SV741 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) @ SV2253 @ SV1452 ) @ SV1452 )
= ( c_List_Oappend @ SV1970 @ SV2253 @ SV1452 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ ( c_Nat_Osize__class_Osize @ SV1970 @ ( tc_List_Olist @ SV1452 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5860]) ).
thf(6197,plain,
! [SV2255: $i,SV1972: $i,SV1454: $i,SV744: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV744 ) @ SV1454 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1972 ) @ SV2255 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1454 = SV2255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5862]) ).
thf(6198,plain,
! [SV2377: $i,SV2256: $i,SV1974: $i,SV1458: $i,SV749: $i] :
( ( ( ( c_List_Oappend @ SV749 @ SV1458 @ SV1974 )
!= ( c_List_Oappend @ SV2256 @ SV2377 @ SV1974 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ SV749 @ SV1974 ) @ SV1458 @ SV1974 )
= SV2377 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV749 @ ( tc_List_Olist @ SV1974 ) ) @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5863]) ).
thf(6199,plain,
! [SV2442: $i,SV2378: $i,SV2257: $i,SV1975: $i,SV1459: $i,SV750: $i] :
( ( ! [SY6495: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
| ~ ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SY6495 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5864]) ).
thf(6200,plain,
! [SV2379: $i,SV2258: $i,SV1979: $i,SV1464: $i,SV755: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV755 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
!= ( c_HOL_Ominus__class_Ominus @ SV2258 @ SV2379 @ SV755 ) )
| ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SV2258 @ SV2379 @ SV755 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5867]) ).
thf(6201,plain,
! [SV756: $i,SV1980: $i,SV1465: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV1465 @ SV1980 @ SV756 )
!= SV1980 )
= $true )
| ( ( c_lessequals @ SV1465 @ SV1980 @ SV756 )
= $true )
| ( ( class_Orderings_Olinorder @ SV756 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5868]) ).
thf(6202,plain,
! [SV2259: $i,SV1981: $i,SV1466: $i,SV757: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
!= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
| ( SV1466 = SV2259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(6203,plain,
! [SV2260: $i,SV1983: $i,SV1468: $i,SV759: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1468 ) @ SV1983 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV759 @ SV2260 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV1468 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5871]) ).
thf(6204,plain,
! [SV2261: $i,SV1986: $i,SV1471: $i,SV762: $i] :
( ( ( ( c_List_Oappend @ SV762 @ SV1471 @ SV1986 )
= ( c_List_Oappend @ SV2261 @ SV1471 @ SV1986 ) )
= $false )
| ( ( SV762 = SV2261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5874]) ).
thf(6205,plain,
! [SV2380: $i,SV2262: $i,SV1988: $i,SV1473: $i,SV764: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV764 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
!= ( c_HOL_Ominus__class_Ominus @ SV2262 @ SV2380 @ SV764 ) )
| ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
| ~ ( c_lessequals @ SV2380 @ SV2262 @ SV764 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5875]) ).
thf(6206,plain,
! [SV2263: $i,SV1989: $i,SV1474: $i,SV765: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV765 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1474 @ SV1989 @ SV765 )
!= ( c_HOL_Ominus__class_Ominus @ SV2263 @ SV2263 @ SV765 ) )
| ( SV1474 = SV1989 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5876]) ).
thf(6207,plain,
! [SV2264: $i,SV1990: $i,SV1476: $i,SV767: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV767 ) @ SV1476 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1990 ) @ SV2264 ) )
= $false )
| ( ( SV1476 = SV2264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5877]) ).
thf(6208,plain,
! [SV768: $i,SV1991: $i,SV1477: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV1991 @ SV768 )
!= ( c_HOL_Ozero__class_Ozero @ SV768 ) )
= $true )
| ( ( SV1477 = SV1991 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV768 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5878]) ).
thf(6209,plain,
! [SV2265: $i,SV1992: $i,SV1479: $i,SV770: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV770 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV1479 ) @ SV1992 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV2265 ) @ SV1992 ) )
| ( SV1479 = SV2265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5880]) ).
thf(6210,plain,
! [SV2381: $i,SV2266: $i,SV1993: $i,SV1480: $i,SV771: $i] :
( ( ( ( c_List_Oappend @ SV771 @ ( c_List_Olist_OCons @ SV1480 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 )
!= ( c_List_Oappend @ SV2266 @ ( c_List_Olist_OCons @ SV2381 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 ) )
= $true )
| ( ( SV771 = SV2266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5881]) ).
thf(6211,plain,
! [SV7: $i,SV1481: $i,SV775: $i] :
( ( ( c_lessequals @ SV775 @ SV1481 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV775 @ SV7 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1481 @ SV7 ) @ SV7 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5884]) ).
thf(6212,plain,
! [SV1482: $i,SV8: $i,SV776: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV776 @ SV8 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1482 @ SV8 ) @ SV8 )
= $false )
| ( ( c_lessequals @ SV776 @ SV1482 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5885]) ).
thf(6213,plain,
! [SV778: $i,SV10: $i,SV1484: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1484 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV10 @ SV778 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV10 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV778 ) @ SV1484 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5886]) ).
thf(6214,plain,
! [SV1994: $i,SV1485: $i,SV779: $i,SV11: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV11 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
| ~ ( c_lessequals @ SV779 @ SV1994 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5887]) ).
thf(6215,plain,
! [SV1996: $i,SV15: $i,SV1488: $i,SV783: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SV1488 @ SV15 ) @ SV1996 @ SV15 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1488 @ SV1996 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV1996 @ SV15 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5888]) ).
thf(6216,plain,
! [SV1489: $i,SV785: $i,SV17: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV785 @ SV17 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV785 @ SV1489 @ SV17 ) @ SV17 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5889]) ).
thf(6217,plain,
! [SV1490: $i,SV788: $i,SV20: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ SV788 @ SV20 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV788 @ SV1490 @ SV20 ) @ SV20 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5891]) ).
thf(6218,plain,
! [SV793: $i,SV25: $i,SV1492: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1492 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV25 ) @ tc_nat )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV1492 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV793 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5894]) ).
thf(6219,plain,
! [SV29: $i,SV1493: $i,SV797: $i] :
( ( ( c_lessequals @ SV797 @ SV1493 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ SV797 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV29 ) @ SV797 ) @ SV1493 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5895]) ).
thf(6220,plain,
! [SV30: $i,SV798: $i,SV1494: $i] :
( ( ( c_lessequals @ SV1494 @ SV798 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV30 ) @ SV1494 ) @ SV798 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV30 @ ( c_HOL_Ominus__class_Ominus @ SV798 @ SV1494 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5896]) ).
thf(6221,plain,
! [SV1998: $i,SV31: $i,SV1495: $i,SV799: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SV1495 @ SV31 ) @ SV1998 @ SV31 )
= $true )
| ( ( ~ ( c_lessequals @ SV1495 @ SV1998 @ SV31 )
| ~ ( c_lessequals @ SV799 @ SV1998 @ SV31 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5897]) ).
thf(6222,plain,
! [SV1999: $i,SV32: $i,SV1496: $i,SV800: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SV1496 @ SV32 ) @ SV1999 @ SV32 )
= $true )
| ( ( ~ ( c_lessequals @ SV1496 @ SV1999 @ SV32 )
| ~ ( c_lessequals @ SV800 @ SV1999 @ SV32 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5898]) ).
thf(6223,plain,
! [SV2000: $i,SV33: $i,SV1497: $i,SV801: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SV1497 @ SV33 ) @ SV2000 @ SV33 )
= $true )
| ( ( ~ ( c_lessequals @ SV1497 @ SV2000 @ SV33 )
| ~ ( c_lessequals @ SV801 @ SV2000 @ SV33 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5899]) ).
thf(6224,plain,
! [SV2001: $i,SV47: $i,SV1502: $i,SV815: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5900]) ).
thf(6225,plain,
! [SV2002: $i,SV1504: $i,SV817: $i,SV49: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV49 ) )
= $true )
| ( ( ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
| ~ ( c_lessequals @ SV817 @ SV2002 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5901]) ).
thf(6226,plain,
! [SV2003: $i,SV1505: $i,SV818: $i,SV50: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 ) )
= $true )
| ( ( ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
| ~ ( c_lessequals @ SV818 @ SV1505 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5902]) ).
thf(6227,plain,
! [SV2004: $i,SV61: $i,SV1511: $i,SV829: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
= $true )
| ( ( ~ ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
| ~ ( c_lessequals @ SV2004 @ SV1511 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5904]) ).
thf(6228,plain,
! [SV71: $i,SV838: $i,SV1518: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1518 @ SV838 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1518 @ SV71 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV838 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV71 @ SV1518 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5906]) ).
thf(6229,plain,
! [SV2007: $i,SV74: $i,SV1521: $i,SV841: $i] :
( ( ( c_lessequals @ SV841 @ SV1521 @ SV74 )
= $true )
| ( ( ( c_lessequals @ SV841 @ SV2007 @ SV74 )
| ~ ( c_lessequals @ SV841 @ ( c_Orderings_Oord__class_Omax @ SV2007 @ SV1521 @ SV74 ) @ SV74 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5907]) ).
thf(6230,plain,
! [SV1530: $i,SV83: $i,SV2010: $i,SV850: $i] :
( ( ( c_lessequals @ SV850 @ SV2010 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV83 @ SV1530 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV83 ) @ SV850 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1530 ) @ SV2010 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(6231,plain,
! [SV2267: $i,SV2011: $i,SV1531: $i,SV851: $i,SV84: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV2011 ) @ SV2267 ) @ SV84 )
| ~ ( c_lessequals @ SV1531 @ SV2267 @ SV84 )
| ~ ( c_lessequals @ SV851 @ SV2011 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(6232,plain,
! [SV92: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5913]) ).
thf(6233,plain,
! [SV860: $i,SV1536: $i,SV95: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1536 @ SV95 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV860 @ SV95 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV860 ) @ SV1536 ) @ SV95 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5914]) ).
thf(6234,plain,
! [SV1537: $i,SV96: $i,SV861: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV861 @ SV96 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV861 @ ( c_Suc @ SV1537 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5915]) ).
thf(6235,plain,
! [SV2014: $i,SV97: $i,SV1538: $i,SV862: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV862 @ SV1538 @ SV97 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2014 @ SV1538 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV862 @ SV2014 @ SV97 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5916]) ).
thf(6236,plain,
! [SV2015: $i,SV98: $i,SV1539: $i,SV863: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1539 @ SV98 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV2015 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV2015 @ SV1539 @ SV98 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5917]) ).
thf(6237,plain,
! [SV99: $i,SV1540: $i,SV864: $i] :
( ( ( c_lessequals @ SV864 @ SV1540 @ SV99 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV864 @ SV1540 @ SV99 )
= SV1540 )
= $true )
| ( ( class_Orderings_Olinorder @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5918]) ).
thf(6238,plain,
! [SV100: $i,SV865: $i,SV1541: $i] :
( ( ( c_lessequals @ SV1541 @ SV865 @ SV100 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV865 @ SV1541 @ SV100 )
= SV865 )
= $true )
| ( ( class_Orderings_Olinorder @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5919]) ).
thf(6239,plain,
! [SV129: $i,SV894: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV894 @ SV894 @ SV129 )
= $false )
| ( ( c_lessequals @ SV894 @ SV894 @ SV129 )
= $false )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5931]) ).
thf(6240,plain,
! [SV131: $i,SV1567: $i,SV896: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV896 @ SV1567 @ SV131 )
= $false )
| ( ( ~ ( c_lessequals @ SV1567 @ SV896 @ SV131 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5932]) ).
thf(6241,plain,
! [SV133: $i,SV1569: $i,SV898: $i] :
( ( ( c_lessequals @ SV898 @ SV1569 @ SV133 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1569 @ SV898 @ SV133 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5934]) ).
thf(6242,plain,
! [SV135: $i,SV1571: $i,SV900: $i] :
( ( ( c_lessequals @ SV900 @ SV1571 @ SV135 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV900 @ SV135 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5936]) ).
thf(6243,plain,
! [SV2028: $i,SV1572: $i,SV904: $i,SV139: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV139 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
| ~ ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5937]) ).
thf(6244,plain,
! [SV2029: $i,SV140: $i,SV1573: $i,SV905: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SV1573 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SV2029 @ SV140 ) @ SV140 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 )
| ~ ( c_lessequals @ SV1573 @ SV2029 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5938]) ).
thf(6245,plain,
! [SV143: $i,SV1576: $i,SV908: $i] :
( ( ( ~ ( c_lessequals @ SV908 @ SV1576 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV908 @ SV143 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV143 @ SV1576 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SV908 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV908 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5939]) ).
thf(6246,plain,
! [SV144: $i,SV909: $i,SV1577: $i] :
( ( ( ~ ( c_lessequals @ SV1577 @ SV909 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1577 @ SV144 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SV1577 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV909 @ SV1577 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV144 @ SV909 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5940]) ).
thf(6247,plain,
! [SV2030: $i,SV147: $i,SV1579: $i,SV912: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SV1579 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SV2030 @ SV1579 @ SV147 ) @ SV147 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 )
| ~ ( c_lessequals @ SV912 @ SV2030 @ SV147 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5941]) ).
thf(6248,plain,
! [SV159: $i,SV2033: $i,SV1585: $i,SV921: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV921 @ ( c_Orderings_Oord__class_Omax @ SV1585 @ SV2033 @ SV159 ) @ SV159 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV921 @ SV1585 @ SV159 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5943]) ).
thf(6249,plain,
! [SV160: $i,SV2034: $i,SV1586: $i,SV922: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV922 @ ( c_Orderings_Oord__class_Omax @ SV1586 @ SV2034 @ SV160 ) @ SV160 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV2034 @ SV160 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5944]) ).
thf(6250,plain,
! [SV161: $i,SV2035: $i,SV1587: $i,SV923: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Orderings_Oord__class_Omax @ SV1587 @ SV2035 @ SV161 ) @ SV161 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV923 @ SV1587 @ SV161 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5945]) ).
thf(6251,plain,
! [SV162: $i,SV2036: $i,SV1588: $i,SV924: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Orderings_Oord__class_Omax @ SV1588 @ SV2036 @ SV162 ) @ SV162 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2036 @ SV162 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5946]) ).
thf(6252,plain,
! [SV2037: $i,SV163: $i,SV1589: $i,SV925: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1589 @ SV163 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV925 @ SV2037 @ SV163 ) @ SV1589 @ SV163 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5947]) ).
thf(6253,plain,
! [SV2443: $i,SV2383: $i,SV2270: $i,SV2038: $i,SV1590: $i,SV927: $i,SV165: $i] :
( ( ! [SY6496: $i,SY6497: $i] :
( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2038 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2270 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2038 ) @ SV2270 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2383 @ SV165 @ SV927 @ SV2443 @ SY6496 @ SY6497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5948]) ).
thf(6254,plain,
! [SV2042: $i,SV178: $i,SV1596: $i,SV939: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV939 @ SV1596 @ SV178 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SV1596 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SV2042 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SV1596 @ SV2042 @ SV178 ) @ SV178 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5956]) ).
thf(6255,plain,
! [SV2043: $i,SV180: $i,SV1598: $i,SV941: $i] :
( ( ( c_lessequals @ SV941 @ SV1598 @ SV180 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2043 @ SV941 @ SV180 ) @ SV1598 @ SV180 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5957]) ).
thf(6256,plain,
! [SV2044: $i,SV181: $i,SV1599: $i,SV942: $i] :
( ( ( c_lessequals @ SV942 @ SV1599 @ SV181 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV942 @ SV2044 @ SV181 ) @ SV1599 @ SV181 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5958]) ).
thf(6257,plain,
! [SV182: $i,SV2045: $i,SV1600: $i,SV943: $i] :
( ( ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1600 @ SV2045 @ SV182 ) @ SV182 )
= $true )
| ( ( ~ ( c_lessequals @ SV943 @ SV2045 @ SV182 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5959]) ).
thf(6258,plain,
! [SV183: $i,SV2046: $i,SV1601: $i,SV944: $i] :
( ( ( c_lessequals @ SV944 @ ( c_Orderings_Oord__class_Omax @ SV1601 @ SV2046 @ SV183 ) @ SV183 )
= $true )
| ( ( ~ ( c_lessequals @ SV944 @ SV1601 @ SV183 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5960]) ).
thf(6259,plain,
! [SV184: $i,SV2047: $i,SV1602: $i,SV945: $i] :
( ( ( c_lessequals @ SV945 @ ( c_Orderings_Oord__class_Omax @ SV1602 @ SV2047 @ SV184 ) @ SV184 )
= $true )
| ( ( ~ ( c_lessequals @ SV945 @ SV2047 @ SV184 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5961]) ).
thf(6260,plain,
! [SV185: $i,SV2048: $i,SV1603: $i,SV946: $i] :
( ( ( c_lessequals @ SV946 @ ( c_Orderings_Oord__class_Omax @ SV1603 @ SV2048 @ SV185 ) @ SV185 )
= $true )
| ( ( ~ ( c_lessequals @ SV946 @ SV1603 @ SV185 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5962]) ).
thf(6261,plain,
! [SV2049: $i,SV186: $i,SV1604: $i,SV947: $i] :
( ( ( c_lessequals @ SV947 @ SV1604 @ SV186 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2049 @ SV947 @ SV186 ) @ SV1604 @ SV186 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5963]) ).
thf(6262,plain,
! [SV2050: $i,SV187: $i,SV1605: $i,SV948: $i] :
( ( ( c_lessequals @ SV948 @ SV1605 @ SV187 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV948 @ SV2050 @ SV187 ) @ SV1605 @ SV187 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5964]) ).
thf(6263,plain,
! [SV1608: $i,SV951: $i,SV190: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV951 @ SV190 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ ( c_Power_Opower__class_Opower @ SV951 @ SV1608 @ SV190 ) @ SV190 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5965]) ).
thf(6264,plain,
! [SV2051: $i,SV191: $i,SV1609: $i,SV952: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV952 @ SV1609 @ SV191 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV952 @ SV2051 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV952 @ ( c_Orderings_Oord__class_Omax @ SV2051 @ SV1609 @ SV191 ) @ SV191 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5966]) ).
thf(6265,plain,
! [SV1610: $i,SV953: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV953 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV192 ) ) @ SV953 ) @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5967]) ).
thf(6266,plain,
! [SV958: $i,SV199: $i,SV1614: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1614 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV958 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV958 ) @ SV1614 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5968]) ).
thf(6267,plain,
! [SV959: $i,SV200: $i,SV1615: $i] :
( ( ( ~ ( c_lessequals @ SV1615 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV959 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SV959 ) @ SV1615 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5969]) ).
thf(6268,plain,
! [SV2273: $i,SV965: $i,SV1618: $i,SV207: $i,SV2053: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2053 @ ( c_Nat_Osize__class_Osize @ SV207 @ ( tc_List_Olist @ SV1618 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV207 @ SV965 @ SV1618 ) @ SV2053 @ SV2273 @ SV1618 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV207 @ SV2053 @ SV2273 @ SV1618 ) @ SV965 @ SV1618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5970]) ).
thf(6269,plain,
! [SV2274: $i,SV966: $i,SV1619: $i,SV208: $i,SV2054: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2054 @ ( c_Nat_Osize__class_Osize @ SV208 @ ( tc_List_Olist @ SV1619 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV208 @ SV966 @ SV1619 ) @ SV2054 @ SV2274 @ SV1619 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV208 @ SV2054 @ SV2274 @ SV1619 ) @ SV966 @ SV1619 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5971]) ).
thf(6270,plain,
! [SV216: $i,SV974: $i,SV1625: $i] :
( ( ( c_lessequals @ SV1625 @ SV974 @ SV216 )
= $true )
| ( ( ~ ( c_lessequals @ SV974 @ SV1625 @ SV216 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV974 @ SV1625 @ SV216 )
= $true )
| ( ( class_Orderings_Opreorder @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5972]) ).
thf(6271,plain,
! [SV983: $i,SV1629: $i,SV227: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV1629 @ SV227 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV983 @ SV227 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SV983 ) @ SV1629 ) @ SV227 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5973]) ).
thf(6272,plain,
! [SV2444: $i,SV2386: $i,SV2275: $i,SV2057: $i,SV1633: $i,SV991: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ SV236 @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV991 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV2057 @ SV236 @ SV2275 @ SV2386 @ SV2444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5974]) ).
thf(6273,plain,
! [SV237: $i,SV992: $i,SV1634: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1634 @ SV992 @ SV237 )
= $true )
| ( ( SV1634 = SV992 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV992 @ SV1634 @ SV237 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5975]) ).
thf(6274,plain,
! [SV238: $i,SV993: $i,SV1635: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1635 @ SV993 @ SV238 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV993 @ SV1635 @ SV238 )
= $true )
| ( ( SV993 = SV1635 )
= $true )
| ( ( class_Orderings_Olinorder @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5976]) ).
thf(6275,plain,
! [SV242: $i,SV997: $i,SV2276: $i,SV2058: $i,SV1637: $i] :
( ( ( ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV997 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 ) )
= $true )
| ( ( SV242 = SV997 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5979]) ).
thf(6276,plain,
! [SV2059: $i,SV243: $i,SV1638: $i,SV998: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV998 @ SV1638 @ SV243 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2059 @ SV998 @ SV243 ) @ SV1638 @ SV243 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5980]) ).
thf(6277,plain,
! [SV999: $i,SV245: $i,SV1639: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1639 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SV999 @ SV245 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SV999 @ SV1639 @ SV245 ) @ SV245 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5981]) ).
thf(6278,plain,
! [SV1004: $i,SV250: $i,SV1642: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1642 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1004 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SV1004 ) @ SV1642 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5983]) ).
thf(6279,plain,
! [SV2061: $i,SV251: $i,SV1643: $i,SV1005: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5984]) ).
thf(6280,plain,
! [SV1647: $i,SV255: $i,SV1009: $i] :
( ( ( c_lessequals @ SV1009 @ SV255 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1009 @ SV1647 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1009 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1647 @ SV1009 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1647 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5985]) ).
thf(6281,plain,
! [SV1012: $i,SV1650: $i,SV258: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1650 @ SV258 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1012 @ SV258 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV1012 ) @ SV1650 ) @ SV258 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5986]) ).
thf(6282,plain,
! [SV1013: $i,SV1651: $i,SV259: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1651 @ SV259 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1013 @ SV259 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV1013 ) @ SV1651 ) @ SV259 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5987]) ).
thf(6283,plain,
! [SV1017: $i,SV1655: $i,SV263: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV263 @ SV1655 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1017 @ SV263 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV263 @ SV1017 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1017 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5988]) ).
thf(6284,plain,
! [SV2445: $i,SV2387: $i,SV2277: $i,SV2067: $i,SV1659: $i,SV1025: $i,SV271: $i] :
( ( ! [SY6498: $i,SY6499: $i] :
( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SV2067 ) ) @ SV2277 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SV2277 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SV2067 ) @ SV2277 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2387 @ SV1025 @ SV271 @ SV2445 @ SY6498 @ SY6499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5989]) ).
thf(6285,plain,
! [SV2446: $i,SV2388: $i,SV2278: $i,SV2068: $i,SV1660: $i,SV1026: $i,SV272: $i] :
( ( ! [SY6500: $i,SY6501: $i] :
( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SV2068 ) @ SV2278 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2068 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2278 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SV2388 @ SV2446 @ SY6500 @ SY6501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5990]) ).
thf(6286,plain,
! [SV2447: $i,SV2389: $i,SV2279: $i,SV2069: $i,SV1661: $i,SV1027: $i,SV273: $i] :
( ( ! [SY6502: $i] :
( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SV1661 )
= ( hAPP @ ( hAPP @ SV273 @ SV1661 ) @ SV1027 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2069 @ SV273 @ SV2279 @ SV2389 @ SV2447 @ SY6502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5991]) ).
thf(6287,plain,
! [SV2448: $i,SV2390: $i,SV2280: $i,SV2070: $i,SV1662: $i,SV1028: $i,SV274: $i] :
( ( ! [SY6503: $i,SY6504: $i] :
( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SV2070 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SV2070 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2280 @ SV274 @ SV2390 @ SV2448 @ SY6503 @ SY6504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5992]) ).
thf(6288,plain,
! [SV2449: $i,SV2391: $i,SV2281: $i,SV2071: $i,SV1663: $i,SV1029: $i,SV275: $i] :
( ( ( ( hAPP @ ( hAPP @ SV275 @ SV1029 ) @ SV1663 )
= SV1663 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2071 @ SV275 @ SV2281 @ SV2391 @ SV1029 @ SV2449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5993]) ).
thf(6289,plain,
! [SV2450: $i,SV2392: $i,SV2282: $i,SV2072: $i,SV1664: $i,SV1030: $i,SV276: $i] :
( ( ( ( hAPP @ ( hAPP @ SV276 @ SV1030 ) @ SV1664 )
= SV1030 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2072 @ SV276 @ SV2282 @ SV1030 @ SV2392 @ SV2450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5994]) ).
thf(6290,plain,
! [SV2451: $i,SV2393: $i,SV2283: $i,SV2073: $i,SV1665: $i,SV1031: $i,SV277: $i] :
( ( ! [SY6505: $i] :
( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SV1665 )
= ( hAPP @ ( hAPP @ SV277 @ SV1665 ) @ SV1031 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SV2073 @ SV2283 @ SV2393 @ SV2451 @ SY6505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5995]) ).
thf(6291,plain,
! [SV2452: $i,SV2394: $i,SV2284: $i,SV2074: $i,SV1666: $i,SV1032: $i,SV278: $i] :
( ( ! [SY6506: $i,SY6507: $i] :
( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SV2074 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SV2074 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SV2284 @ SV2394 @ SV2452 @ SY6506 @ SY6507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5996]) ).
thf(6292,plain,
! [SV2453: $i,SV2395: $i,SV2285: $i,SV2075: $i,SV1667: $i,SV1033: $i,SV279: $i] :
( ( ( ( hAPP @ ( hAPP @ SV279 @ SV1033 ) @ SV1667 )
= SV1667 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SV2075 @ SV2285 @ SV1033 @ SV2395 @ SV2453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5997]) ).
thf(6293,plain,
! [SV2454: $i,SV2396: $i,SV2286: $i,SV2076: $i,SV1668: $i,SV1034: $i,SV280: $i] :
( ( ! [SY6508: $i,SY6509: $i] :
( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SV2076 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SV2076 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SV2286 @ SV2396 @ SV2454 @ SY6508 @ SY6509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5998]) ).
thf(6294,plain,
! [SV2455: $i,SV2397: $i,SV2287: $i,SV2077: $i,SV1669: $i,SV1035: $i,SV281: $i] :
( ( ! [SY6510: $i] :
( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SV1669 )
= ( hAPP @ ( hAPP @ SV281 @ SV1669 ) @ SV1035 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SV2077 @ SV2287 @ SV2397 @ SV2455 @ SY6510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5999]) ).
thf(6295,plain,
! [SV2456: $i,SV2398: $i,SV2288: $i,SV2078: $i,SV1670: $i,SV1036: $i,SV282: $i] :
( ( ! [SY6511: $i,SY6512: $i] :
( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SV2078 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV2078 ) ) @ SV1670 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SV2288 @ SV2398 @ SV2456 @ SY6511 @ SY6512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6000]) ).
thf(6296,plain,
! [SV2457: $i,SV2399: $i,SV2289: $i,SV2079: $i,SV1671: $i,SV1037: $i,SV283: $i] :
( ( ! [SY6513: $i,SY6514: $i] :
( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SV2079 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SV2079 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SV2289 @ SV2399 @ SV2457 @ SY6513 @ SY6514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6001]) ).
thf(6297,plain,
! [SV2458: $i,SV2400: $i,SV2290: $i,SV2080: $i,SV1672: $i,SV1038: $i,SV284: $i] :
( ( ! [SY6515: $i,SY6516: $i] :
( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SV2080 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SV2080 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SV2290 @ SV2400 @ SV2458 @ SY6515 @ SY6516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6002]) ).
thf(6298,plain,
! [SV2459: $i,SV2401: $i,SV2291: $i,SV2081: $i,SV1673: $i,SV1039: $i,SV285: $i] :
( ( ! [SY6517: $i,SY6518: $i,SY6519: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SV2291 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SV2291 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SV2401 @ SV2459 @ SY6517 @ SY6518 @ SY6519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6003]) ).
thf(6299,plain,
! [SV2460: $i,SV2402: $i,SV2292: $i,SV2082: $i,SV1674: $i,SV1040: $i,SV286: $i] :
( ( ! [SY6520: $i,SY6521: $i] :
( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SV2082 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SV2082 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2292 @ SV286 @ SV2402 @ SV2460 @ SY6520 @ SY6521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6004]) ).
thf(6300,plain,
! [SV2461: $i,SV2403: $i,SV2293: $i,SV2083: $i,SV1675: $i,SV1041: $i,SV287: $i] :
( ( ! [SY6522: $i,SY6523: $i] :
( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SV2083 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SV2083 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2293 @ SV287 @ SV2403 @ SV2461 @ SY6522 @ SY6523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6005]) ).
thf(6301,plain,
! [SV2462: $i,SV2404: $i,SV2294: $i,SV2084: $i,SV1676: $i,SV1042: $i,SV288: $i] :
( ( ! [SY6524: $i,SY6525: $i] :
( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SV2084 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SV2084 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2294 @ SV288 @ SV2404 @ SV2462 @ SY6524 @ SY6525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6006]) ).
thf(6302,plain,
! [SV2463: $i,SV2405: $i,SV2295: $i,SV2085: $i,SV1677: $i,SV1043: $i,SV289: $i] :
( ( ! [SY6526: $i,SY6527: $i] :
( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SV2085 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV2085 ) ) @ SV1677 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2295 @ SV289 @ SV2405 @ SV2463 @ SY6526 @ SY6527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6007]) ).
thf(6303,plain,
! [SV2464: $i,SV2406: $i,SV2296: $i,SV2086: $i,SV1678: $i,SV1044: $i,SV290: $i] :
( ( ! [SY6528: $i,SY6529: $i,SY6530: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SV2296 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SV2296 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2406 @ SV290 @ SV2464 @ SY6528 @ SY6529 @ SY6530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6008]) ).
thf(6304,plain,
! [SV2465: $i,SV2407: $i,SV2297: $i,SV2087: $i,SV1679: $i,SV1045: $i,SV291: $i] :
( ( ! [SY6531: $i,SY6532: $i,SY6533: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2407 @ SV291 @ SV2465 @ SY6531 @ SY6532 @ SY6533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6009]) ).
thf(6305,plain,
! [SV2466: $i,SV2408: $i,SV2298: $i,SV2088: $i,SV1680: $i,SV1046: $i,SV292: $i] :
( ( ! [SY6534: $i,SY6535: $i,SY6536: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SV2298 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SV2298 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2408 @ SV292 @ SV2466 @ SY6534 @ SY6535 @ SY6536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6010]) ).
thf(6306,plain,
! [SV2467: $i,SV2409: $i,SV2299: $i,SV2089: $i,SV1681: $i,SV1047: $i,SV293: $i] :
( ( ( ( hAPP @ ( hAPP @ SV293 @ SV1047 ) @ SV1681 )
= SV1047 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2089 @ SV293 @ SV2299 @ SV2409 @ SV1681 @ SV2467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6011]) ).
thf(6307,plain,
! [SV2468: $i,SV2410: $i,SV2300: $i,SV2090: $i,SV1682: $i,SV1048: $i,SV294: $i] :
( ( ( ( hAPP @ ( hAPP @ SV294 @ SV1048 ) @ SV1682 )
= SV1682 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2090 @ SV294 @ SV2300 @ SV2410 @ SV1048 @ SV2468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6012]) ).
thf(6308,plain,
! [SV2469: $i,SV2411: $i,SV2301: $i,SV2091: $i,SV1683: $i,SV1049: $i,SV295: $i] :
( ( ( ( hAPP @ ( hAPP @ SV295 @ SV1049 ) @ SV1683 )
= SV1683 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2091 @ SV295 @ SV2301 @ SV1683 @ SV2411 @ SV2469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6013]) ).
thf(6309,plain,
! [SV2470: $i,SV2412: $i,SV2302: $i,SV2092: $i,SV1684: $i,SV1050: $i,SV296: $i] :
( ( ( ( hAPP @ ( hAPP @ SV296 @ SV1050 ) @ SV1684 )
= SV1050 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2092 @ SV296 @ SV2302 @ SV1050 @ SV2412 @ SV2470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6014]) ).
thf(6310,plain,
! [SV2471: $i,SV2413: $i,SV2303: $i,SV2093: $i,SV1685: $i,SV1051: $i,SV297: $i] :
( ( ! [SY6537: $i,SY6538: $i] :
( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SV2093 ) ) @ SV2303 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SV2303 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SV2093 ) @ SV2303 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SV2413 @ SV2471 @ SY6537 @ SY6538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6015]) ).
thf(6311,plain,
! [SV2472: $i,SV2414: $i,SV2304: $i,SV2094: $i,SV1686: $i,SV1052: $i,SV298: $i] :
( ( ! [SY6539: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SV1686 )
= ( hAPP @ ( hAPP @ SV298 @ SV1686 ) @ SV1052 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2094 @ SV298 @ SV2304 @ SV2414 @ SV2472 @ SY6539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6016]) ).
thf(6312,plain,
! [SV2473: $i,SV2415: $i,SV2305: $i,SV2095: $i,SV1687: $i,SV1053: $i,SV299: $i] :
( ( ( ( hAPP @ ( hAPP @ SV299 @ SV1053 ) @ SV1687 )
= SV1053 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SV2095 @ SV2305 @ SV1687 @ SV2415 @ SV2473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6017]) ).
thf(6313,plain,
! [SV2474: $i,SV2416: $i,SV2306: $i,SV2096: $i,SV1688: $i,SV1054: $i,SV300: $i] :
( ( ( ( hAPP @ ( hAPP @ SV300 @ SV1054 ) @ SV1688 )
= SV1688 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SV2096 @ SV2306 @ SV1054 @ SV2416 @ SV2474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6018]) ).
thf(6314,plain,
! [SV2475: $i,SV2417: $i,SV2307: $i,SV2097: $i,SV1689: $i,SV1055: $i,SV301: $i] :
( ( ( ( hAPP @ ( hAPP @ SV301 @ SV1055 ) @ SV1055 )
= ( hAPP @ ( hAPP @ SV1689 @ ( hAPP @ ( hAPP @ SV301 @ SV2097 ) @ SV2097 ) ) @ SV1055 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SV1689 @ SV2307 @ SV2417 @ SV2097 @ SV2475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6019]) ).
thf(6315,plain,
! [SV2476: $i,SV2418: $i,SV2308: $i,SV2098: $i,SV1690: $i,SV1056: $i,SV302: $i] :
( ( ! [SY6540: $i] :
( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SV1690 @ SV2098 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SV1690 @ ( hAPP @ ( hAPP @ SV302 @ SV2098 ) @ SV2308 ) ) @ SV1056 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SV1690 @ SV2418 @ SV2476 @ SV2308 @ SY6540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6020]) ).
thf(6316,plain,
! [SV2477: $i,SV2419: $i,SV2309: $i,SV2099: $i,SV1691: $i,SV1057: $i,SV303: $i] :
( ( ! [SY6541: $i] :
( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SV1691 ) @ SV2099 ) ) @ SV2099 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SV1691 ) @ SV2309 ) ) @ SV2099 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SV2419 @ SV2477 @ SV2309 @ SY6541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6021]) ).
thf(6317,plain,
! [SV2478: $i,SV2420: $i,SV2310: $i,SV2100: $i,SV1692: $i,SV1058: $i,SV304: $i] :
( ( ! [SY6542: $i,SY6543: $i] :
( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SV2100 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SV2310 ) @ SV2100 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SV2310 ) ) @ SV2100 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SV2420 @ SV2478 @ SY6542 @ SY6543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6022]) ).
thf(6318,plain,
! [SV2311: $i,SV1062: $i,SV308: $i,SV2103: $i,SV1696: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1696 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2103 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1062 ) @ SV1696 ) ) @ ( c_Suc @ SV2103 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2311 ) @ SV1062 ) @ SV2103 ) ) @ SV1696 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV308 ) @ SV2311 ) @ SV1696 ) ) @ SV1062 ) @ SV2103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6025]) ).
thf(6319,plain,
! [SV2312: $i,SV2104: $i,SV1699: $i,SV1066: $i,SV313: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV313 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV1699 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV2104 ) @ SV2312 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1066 ) @ SV2104 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV313 ) @ SV1699 ) @ SV2312 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6026]) ).
thf(6320,plain,
! [SV328: $i,SV1080: $i,SV1709: $i] :
( ( ( ~ ( c_lessequals @ SV1709 @ SV1080 @ SV328 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1080 @ SV1709 @ SV328 ) )
= $true )
| ( ( SV1080 = SV1709 )
= $true )
| ( ( class_Orderings_Oorder @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6027]) ).
thf(6321,plain,
! [SV329: $i,SV1081: $i,SV1710: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1710 @ SV1081 @ SV329 )
= $true )
| ( ( SV1710 = SV1081 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1081 @ SV1710 @ SV329 )
= $true )
| ( ( class_Orderings_Olinorder @ SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6028]) ).
thf(6322,plain,
! [SV330: $i,SV1082: $i,SV1711: $i] :
( ( ( ~ ( c_lessequals @ SV1711 @ SV1082 @ SV330 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1082 @ SV1711 @ SV330 ) )
= $true )
| ( ( SV1082 = SV1711 )
= $true )
| ( ( class_Orderings_Oorder @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6029]) ).
thf(6323,plain,
! [SV331: $i,SV1712: $i,SV1083: $i] :
( ( ( ~ ( c_lessequals @ SV1083 @ SV1712 @ SV331 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1712 @ SV1083 @ SV331 ) )
= $true )
| ( ( SV1083 = SV1712 )
= $true )
| ( ( class_Orderings_Oorder @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6030]) ).
thf(6324,plain,
! [SV333: $i,SV1085: $i,SV1714: $i] :
( ( ( SV1714 = SV1085 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1714 @ SV1085 @ SV333 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1085 @ SV1714 @ SV333 )
= $true )
| ( ( class_Orderings_Olinorder @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6031]) ).
thf(6325,plain,
! [SV334: $i,SV1715: $i,SV1086: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1086 @ SV1715 @ SV334 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1715 @ SV1086 @ SV334 )
= $true )
| ( ( SV1086 = SV1715 )
= $true )
| ( ( class_Orderings_Olinorder @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6032]) ).
thf(6326,plain,
! [SV335: $i,SV1716: $i,SV1087: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SV1716 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
= $false )
| ( ( c_lessequals @ SV1087 @ SV1716 @ SV335 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV335 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6033]) ).
thf(6327,plain,
! [SV336: $i,SV1717: $i,SV1088: $i] :
( ( ( c_lessequals @ SV1088 @ SV1717 @ SV336 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1088 @ SV1717 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV336 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6034]) ).
thf(6328,plain,
! [SV2313: $i,SV2107: $i,SV1718: $i,SV1090: $i,SV340: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV2107 ) @ SV2313 ) @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1718 @ SV2313 @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SV2107 @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6035]) ).
thf(6329,plain,
! [SV1719: $i,SV341: $i,SV2108: $i,SV1091: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1091 @ SV2108 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV341 @ SV1719 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV341 ) @ SV1091 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1719 ) @ SV2108 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6036]) ).
thf(6330,plain,
! [SV345: $i,SV1720: $i,SV1095: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1095 @ SV1720 @ SV345 )
= $false )
| ( ( c_lessequals @ SV1095 @ SV1720 @ SV345 )
= $true )
| ( ( class_Orderings_Oorder @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6037]) ).
thf(6331,plain,
! [SV346: $i,SV1721: $i,SV1096: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1096 @ SV1721 @ SV346 )
= $false )
| ( ( c_lessequals @ SV1096 @ SV1721 @ SV346 )
= $true )
| ( ( class_Orderings_Opreorder @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6038]) ).
thf(6332,plain,
! [SV2109: $i,SV1097: $i,SV2314: $i,SV1722: $i,SV347: $i] :
( ( ( ~ ( c_Type_Otyping @ SV347 @ SV1722 @ SV2314 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV347 @ SV1097 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2314 ) @ SV2109 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1097 ) @ SV1722 ) @ SV2109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6039]) ).
thf(6333,plain,
! [SV1724: $i,SV1099: $i,SV350: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ SV1099 @ SV350 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV350 ) @ ( c_Power_Opower__class_Opower @ SV1099 @ ( c_Suc @ SV1724 ) @ SV350 ) @ SV350 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6041]) ).
thf(6334,plain,
! [SV353: $i,SV1726: $i,SV1102: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1102 @ SV1726 @ SV353 ) @ ( c_HOL_Ozero__class_Ozero @ SV353 ) @ SV353 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1102 @ SV1726 @ SV353 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6042]) ).
thf(6335,plain,
! [SV354: $i,SV1727: $i,SV1103: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1103 @ SV1727 @ SV354 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1103 @ SV1727 @ SV354 ) @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV354 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6043]) ).
thf(6336,plain,
! [SV355: $i,SV1728: $i,SV1104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1104 @ SV1728 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1104 @ SV355 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1728 @ SV355 ) @ SV355 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6044]) ).
thf(6337,plain,
! [SV1729: $i,SV356: $i,SV1105: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1105 @ SV356 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1729 @ SV356 ) @ SV356 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1105 @ SV1729 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6045]) ).
thf(6338,plain,
! [SV1106: $i,SV1730: $i,SV359: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV359 @ SV1730 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1730 @ SV1106 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV359 ) @ SV1106 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6046]) ).
thf(6339,plain,
! [SV2111: $i,SV1731: $i,SV1107: $i,SV360: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV1107 ) @ SV1731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV2111 ) @ SV1731 ) @ SV360 )
= $true )
| ( ( ~ ( c_lessequals @ SV1107 @ SV2111 @ SV360 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV360 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6047]) ).
thf(6340,plain,
! [SV2112: $i,SV361: $i,SV1732: $i,SV1108: $i] :
( ( ( c_lessequals @ SV1108 @ SV1732 @ SV361 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1108 ) @ SV2112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1732 ) @ SV2112 ) @ SV361 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6048]) ).
thf(6341,plain,
! [SV2113: $i,SV1733: $i,SV1109: $i,SV362: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV1733 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV2113 ) @ SV362 )
= $true )
| ( ( ~ ( c_lessequals @ SV1733 @ SV2113 @ SV362 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6049]) ).
thf(6342,plain,
! [SV2114: $i,SV363: $i,SV1734: $i,SV1110: $i] :
( ( ( c_lessequals @ SV1110 @ SV1734 @ SV363 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1734 ) @ SV363 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6050]) ).
thf(6343,plain,
! [SV2115: $i,SV1735: $i,SV1111: $i,SV364: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV1111 ) @ SV1735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV2115 ) @ SV1735 ) @ SV364 )
= $true )
| ( ( ~ ( c_lessequals @ SV1111 @ SV2115 @ SV364 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6051]) ).
thf(6344,plain,
! [SV2116: $i,SV1736: $i,SV1112: $i,SV365: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV1736 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV2116 ) @ SV365 )
= $true )
| ( ( ~ ( c_lessequals @ SV1736 @ SV2116 @ SV365 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6052]) ).
thf(6345,plain,
! [SV2118: $i,SV1741: $i,SV374: $i,SV2315: $i,SV1120: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1120 @ SV2315 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( c_Type_Oshift @ SV374 @ SV1120 @ SV1741 @ SV2118 ) @ SV2315 )
= ( hAPP @ SV374 @ ( c_HOL_Ominus__class_Ominus @ SV2315 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6054]) ).
thf(6346,plain,
! [SV2479: $i,SV2421: $i,SV2316: $i,SV2119: $i,SV1742: $i,SV1121: $i,SV375: $i] :
( ( ! [SY6544: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ SV2119 ) )
= ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ ( c_Suc @ SV2119 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2316 @ SV375 @ SV1742 @ SV2421 @ SV2479 @ SY6544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6055]) ).
thf(6347,plain,
! [SV2480: $i,SV2422: $i,SV2317: $i,SV2120: $i,SV1743: $i,SV1122: $i,SV376: $i] :
( ( ! [SY6545: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ SV2120 ) ) @ SV1743 )
= ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ ( c_Suc @ SV2120 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2317 @ SV376 @ SV1122 @ SV2422 @ SV2480 @ SY6545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6056]) ).
thf(6348,plain,
! [SV2481: $i,SV2423: $i,SV2318: $i,SV2121: $i,SV1744: $i,SV1123: $i,SV377: $i] :
( ( ! [SY6546: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SV1744 ) )
= ( hAPP @ ( hAPP @ SV2121 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SV1744 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2318 @ SV2121 @ SV377 @ SV2423 @ SV2481 @ SY6546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6057]) ).
thf(6349,plain,
! [SV2482: $i,SV2424: $i,SV2319: $i,SV2122: $i,SV1745: $i,SV1124: $i,SV378: $i] :
( ( ! [SY6547: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SV1745 ) )
= ( hAPP @ ( hAPP @ SV2122 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SV1745 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2319 @ SV2122 @ SV378 @ SV2424 @ SV2482 @ SY6547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6058]) ).
thf(6350,plain,
! [SV2124: $i,SV383: $i,SV1749: $i,SV1129: $i] :
( ( ( c_lessequals @ SV1129 @ SV1749 @ SV383 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1749 @ SV383 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SV2124 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SV1749 @ ( c_Suc @ SV2124 ) @ SV383 ) @ SV383 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6059]) ).
thf(6351,plain,
! [SV1141: $i,SV2127: $i,SV1755: $i,SV395: $i] :
( ( ( c_List_Olistsp @ SV395 @ SV1755 @ SV2127 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV395 @ SV1141 @ SV2127 ) )
= $true )
| ( ( c_List_Olistsp @ SV395 @ ( c_List_Oappend @ SV1141 @ SV1755 @ SV2127 ) @ SV2127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6062]) ).
thf(6352,plain,
! [SV2483: $i,SV2425: $i,SV2320: $i,SV2128: $i,SV1756: $i,SV1142: $i,SV396: $i] :
( ( ( c_Fun_Ocomp @ SV396 @ ( c_Fun_Ocomp @ SV1142 @ SV1756 @ SV2128 @ SV2320 @ SV2425 ) @ SV2320 @ SV2483 @ SV2425 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV396 @ SV1142 @ SV2320 @ SV2483 @ SV2128 ) @ SV1756 @ SV2128 @ SV2483 @ SV2425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6063]) ).
thf(6353,plain,
! [SV403: $i,SV1148: $i,SV1760: $i] :
( ( ( ~ ( c_lessequals @ SV1760 @ SV1148 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1760 @ SV403 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV1760 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1148 @ SV1760 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV403 @ SV1148 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6064]) ).
thf(6354,plain,
! [SV404: $i,SV1761: $i,SV1149: $i] :
( ( ( ~ ( c_lessequals @ SV1149 @ SV1761 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1149 @ SV404 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV404 @ SV1761 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SV1149 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1761 @ SV1149 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6065]) ).
thf(6355,plain,
! [SV2129: $i,SV1762: $i,SV405: $i,SV1150: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1762 ) @ SV2129 ) @ SV405 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2129 @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1762 @ SV405 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV405 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6066]) ).
thf(6356,plain,
! [SV2130: $i,SV410: $i,SV1765: $i,SV1155: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SV1765 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SV2130 @ SV410 ) @ SV410 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2130 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV410 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6069]) ).
thf(6357,plain,
! [SV411: $i,SV2131: $i,SV1766: $i,SV1156: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1766 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1766 @ SV411 ) @ SV411 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SV2131 @ SV411 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6070]) ).
thf(6358,plain,
! [SV2132: $i,SV412: $i,SV1767: $i,SV1157: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SV1767 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SV2132 @ SV412 ) @ SV412 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1767 @ SV2132 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6071]) ).
thf(6359,plain,
! [SV413: $i,SV2133: $i,SV1768: $i,SV1158: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1768 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1768 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV2133 @ SV413 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6072]) ).
thf(6360,plain,
! [SV450: $i,SV2144: $i,SV1786: $i,SV1191: $i] :
( ( ( c_lessequals @ SV1191 @ SV1786 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1786 @ SV450 ) @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SV2144 @ SV450 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV450 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6078]) ).
thf(6361,plain,
! [SV451: $i,SV2145: $i,SV1787: $i,SV1192: $i] :
( ( ( c_lessequals @ SV1192 @ SV1787 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1787 @ SV451 ) @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SV2145 @ SV451 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6079]) ).
thf(6362,plain,
! [SV2146: $i,SV452: $i,SV1788: $i,SV1193: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SV1788 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SV2146 @ SV452 ) @ SV452 )
= $true )
| ( ( ~ ( c_lessequals @ SV1788 @ SV2146 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV452 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6080]) ).
thf(6363,plain,
! [SV2322: $i,SV2149: $i,SV1792: $i,SV1197: $i,SV457: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV2149 ) @ SV2322 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1792 @ SV2322 @ SV457 )
| ~ ( c_lessequals @ SV1197 @ SV2149 @ SV457 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6081]) ).
thf(6364,plain,
! [SV2323: $i,SV2150: $i,SV1793: $i,SV1198: $i,SV458: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV2150 ) @ SV2323 ) @ SV458 )
| ~ ( c_lessequals @ SV1793 @ SV2323 @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SV2150 @ SV458 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6082]) ).
thf(6365,plain,
! [SV489: $i,SV1223: $i,SV1795: $i] :
( ( ( c_lessequals @ SV1795 @ SV1223 @ tc_nat )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1795 @ tc_nat ) @ SV489 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1223 @ SV489 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1795 @ SV489 ) @ SV489 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6087]) ).
thf(6366,plain,
! [SV2152: $i,SV1799: $i,SV1227: $i,SV493: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV1227 ) @ SV1799 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV2152 ) @ SV1799 ) @ SV493 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SV2152 @ SV493 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6088]) ).
thf(6367,plain,
! [SV2153: $i,SV1800: $i,SV1228: $i,SV494: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV1228 ) @ SV1800 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV2153 ) @ SV1800 ) @ SV494 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SV2153 @ SV494 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6089]) ).
thf(6368,plain,
! [SV2154: $i,SV495: $i,SV1801: $i,SV1229: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1801 @ SV495 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1229 ) @ SV2154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1801 ) @ SV2154 ) @ SV495 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6090]) ).
thf(6369,plain,
! [SV2155: $i,SV1802: $i,SV1230: $i,SV496: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV1802 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV2155 ) @ SV496 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1802 @ SV2155 @ SV496 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6091]) ).
thf(6370,plain,
! [SV2156: $i,SV1803: $i,SV1231: $i,SV497: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV1803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV2156 ) @ SV497 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1803 @ SV2156 @ SV497 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6092]) ).
thf(6371,plain,
! [SV2157: $i,SV498: $i,SV1804: $i,SV1232: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1232 @ SV1804 @ SV498 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1232 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1804 ) @ SV498 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6093]) ).
thf(6372,plain,
! [SV2158: $i,SV502: $i,SV1808: $i,SV1236: $i] :
( ( ( c_lessequals @ SV1236 @ SV1808 @ SV502 )
= $true )
| ( ( ~ ( c_lessequals @ SV1236 @ SV2158 @ SV502 )
| ~ ( c_lessequals @ SV2158 @ SV1808 @ SV502 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6094]) ).
thf(6373,plain,
! [SV2159: $i,SV503: $i,SV1809: $i,SV1237: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1237 @ SV1809 @ SV503 )
= $true )
| ( ( ~ ( c_lessequals @ SV1237 @ SV2159 @ SV503 )
| ~ ( c_HOL_Oord__class_Oless @ SV2159 @ SV1809 @ SV503 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV503 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6095]) ).
thf(6374,plain,
! [SV2160: $i,SV504: $i,SV1810: $i,SV1238: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1238 @ SV1810 @ SV504 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1238 @ SV2160 @ SV504 )
| ~ ( c_lessequals @ SV2160 @ SV1810 @ SV504 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV504 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6096]) ).
thf(6375,plain,
! [SV1239: $i,SV505: $i,SV1811: $i] :
( ( ( ~ ( c_lessequals @ SV1811 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1239 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SV1239 ) @ SV1811 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6097]) ).
thf(6376,plain,
! [SV2161: $i,SV506: $i,SV1812: $i,SV1240: $i] :
( ( ( c_lessequals @ SV1240 @ SV1812 @ SV506 )
= $true )
| ( ( ~ ( c_lessequals @ SV2161 @ SV1812 @ SV506 )
| ~ ( c_lessequals @ SV1240 @ SV2161 @ SV506 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6098]) ).
thf(6377,plain,
! [SV1241: $i,SV1813: $i,SV508: $i] :
( ( ( c_lessequals @ SV508 @ SV1813 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1813 @ SV1241 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV508 @ SV1241 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6099]) ).
thf(6378,plain,
! [SV2162: $i,SV512: $i,SV1814: $i,SV1244: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1244 @ SV1814 @ SV512 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2162 @ SV1814 @ SV512 )
| ~ ( c_lessequals @ SV1244 @ SV2162 @ SV512 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV512 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6100]) ).
thf(6379,plain,
! [SV2163: $i,SV513: $i,SV1815: $i,SV1245: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1245 @ SV1815 @ SV513 )
= $true )
| ( ( ~ ( c_lessequals @ SV2163 @ SV1815 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ SV1245 @ SV2163 @ SV513 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6101]) ).
thf(6380,plain,
! [SV2325: $i,SV2164: $i,SV1816: $i,SV1246: $i,SV514: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
= $false )
| ( ( ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2164 ) @ SV514 )
| ~ ( c_lessequals @ SV2325 @ SV2164 @ SV514 )
| ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2325 ) @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6102]) ).
thf(6381,plain,
! [SV1817: $i,SV515: $i,SV1247: $i,SV2165: $i] :
( ( ( c_Lambda_Obeta @ SV2165 @ SV1247 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV515 @ SV2165 @ SV1817 ) )
= $true )
| ( ( c_Type_Otyping @ SV515 @ SV1247 @ SV1817 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6103]) ).
thf(6382,plain,
! [SV1818: $i,SV1248: $i,SV516: $i] :
( ( ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ominus__class_Ominus @ SV1248 @ SV1818 @ tc_nat ) ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1248 @ SV1818 @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6104]) ).
thf(6383,plain,
! [SV2427: $i,SV2326: $i,SV2166: $i,SV1819: $i,SV1249: $i,SV517: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV1249 @ SV1819 @ SV2166 ) @ SV2326 @ SV2427 @ SV2166 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV517 @ SV2326 @ SV2427 @ SV2166 ) @ SV1249 @ SV1819 @ SV2166 ) )
= $true )
| ( ( SV1249 = SV2326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6105]) ).
thf(6384,plain,
! [SV533: $i,SV1263: $i,SV1824: $i] :
( ( ( SV1824 = SV1263 )
= $true )
| ( ( ~ ( c_lessequals @ SV1263 @ SV1824 @ SV533 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1263 @ SV1824 @ SV533 )
= $true )
| ( ( class_Orderings_Oorder @ SV533 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6108]) ).
thf(6385,plain,
! [SV534: $i,SV1825: $i,SV1264: $i] :
( ( ( ~ ( c_lessequals @ SV1264 @ SV1825 @ SV534 ) )
= $true )
| ( ( SV1825 = SV1264 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1825 @ SV534 )
= $true )
| ( ( class_Orderings_Oorder @ SV534 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6109]) ).
thf(6386,plain,
! [SV538: $i,SV1826: $i,SV1268: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1268 @ SV1826 @ SV538 )
= $true )
| ( ( ~ ( c_lessequals @ SV1268 @ SV1826 @ SV538 ) )
= $true )
| ( ( SV1268 = SV1826 )
= $true )
| ( ( class_Orderings_Oorder @ SV538 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6110]) ).
thf(6387,plain,
! [SV539: $i,SV1827: $i,SV1269: $i] :
( ( ( SV1269 = SV1827 )
= $true )
| ( ( ~ ( c_lessequals @ SV1269 @ SV1827 @ SV539 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1269 @ SV1827 @ SV539 )
= $true )
| ( ( class_Orderings_Oorder @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6111]) ).
thf(6388,plain,
! [SV540: $i,SV1828: $i,SV1270: $i] :
( ( ( SV1270 = SV1828 )
= $true )
| ( ( ~ ( c_lessequals @ SV1270 @ SV1828 @ SV540 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1270 @ SV1828 @ SV540 )
= $true )
| ( ( class_Orderings_Oorder @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6112]) ).
thf(6389,plain,
! [SV541: $i,SV1829: $i,SV1271: $i] :
( ( ( ~ ( c_lessequals @ SV1271 @ SV1829 @ SV541 ) )
= $true )
| ( ( SV1271 = SV1829 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1271 @ SV1829 @ SV541 )
= $true )
| ( ( class_Orderings_Oorder @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6113]) ).
thf(6390,plain,
! [SV542: $i,SV1830: $i,SV1272: $i] :
( ( ( ~ ( c_lessequals @ SV1272 @ SV1830 @ SV542 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1272 @ SV1830 @ SV542 )
= $true )
| ( ( SV1272 = SV1830 )
= $true )
| ( ( class_Orderings_Olinorder @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6114]) ).
thf(6391,plain,
! [SV543: $i,SV1831: $i,SV1273: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1273 @ SV1831 @ SV543 )
= $true )
| ( ( ~ ( c_lessequals @ SV1273 @ SV1831 @ SV543 ) )
= $true )
| ( ( SV1273 = SV1831 )
= $true )
| ( ( class_Orderings_Olinorder @ SV543 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6115]) ).
thf(6392,plain,
! [SV553: $i,SV1837: $i,SV1282: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1282 @ SV1837 @ SV553 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1837 @ SV1282 @ SV553 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6116]) ).
thf(6393,plain,
! [SV554: $i,SV1838: $i,SV1283: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1838 @ SV554 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1838 @ SV1283 @ SV554 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV554 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6117]) ).
thf(6394,plain,
! [SV557: $i,SV1840: $i,SV1286: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1286 @ SV1840 @ SV557 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1840 @ SV1286 @ SV557 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV557 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6119]) ).
thf(6395,plain,
! [SV558: $i,SV1841: $i,SV1287: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1287 @ SV1841 @ SV558 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1841 @ SV1287 @ SV558 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV558 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6120]) ).
thf(6396,plain,
! [SV2484: $i,SV2428: $i,SV2329: $i,SV2174: $i,SV1843: $i,SV1293: $i,SV574: $i] :
( ( ( ( hAPP @ ( hAPP @ SV574 @ SV1293 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1843 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2174 @ SV2329 @ SV574 @ SV2428 @ SV1843 @ SV2484 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6122]) ).
thf(6397,plain,
! [SV2344: $i,SV2194: $i,SV1869: $i,SV1322: $i,SV603: $i] :
( ( ( hBOOL @ ( hAPP @ SV603 @ ( c_Type_Otype_Otype__case @ SV1322 @ SV1869 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2194 ) @ SV2344 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV603 @ ( hAPP @ ( hAPP @ SV1869 @ SV2194 ) @ SV2344 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6127]) ).
thf(6398,plain,
! [SV2345: $i,SV2195: $i,SV1870: $i,SV1323: $i,SV604: $i] :
( ( ( hBOOL @ ( hAPP @ SV604 @ ( c_Type_Otype_Otype__case @ SV1323 @ SV1870 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2195 ) @ SV2345 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV604 @ ( hAPP @ ( hAPP @ SV1870 @ SV2195 ) @ SV2345 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6128]) ).
thf(6399,plain,
! [SV2199: $i,SV1876: $i,SV611: $i,SV1330: $i,SV2348: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2348 @ SV1330 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( c_Type_Oshift @ SV611 @ SV1330 @ SV1876 @ SV2199 ) @ SV2348 )
= ( hAPP @ SV611 @ SV2348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6131]) ).
thf(6400,plain,
! [SV2200: $i,SV1331: $i,SV2349: $i,SV1877: $i,SV612: $i] :
( ( ( ~ ( c_Type_Otypings @ SV612 @ SV1877 @ SV2349 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV612 @ SV1331 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2349 @ SV2200 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1331 @ SV1877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6132]) ).
thf(6401,plain,
! [SV1333: $i,SV614: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV614 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV614 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6134]) ).
thf(6402,plain,
! [SV1334: $i,SV615: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV615 ) @ SV1334 @ SV615 )
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
= $true )
| ( ( SV1334
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV615 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV615 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6135]) ).
thf(6403,plain,
! [SV2485: $i,SV2433: $i,SV2351: $i,SV2203: $i,SV1881: $i,SV1338: $i,SV620: $i] :
( ( ( c_List_Ofoldr @ SV620 @ ( c_List_Omap @ SV1338 @ SV1881 @ SV2203 @ SV2351 ) @ SV2433 @ SV2351 @ SV2485 )
= ( c_List_Ofoldr @ ( c_Fun_Ocomp @ SV620 @ SV1338 @ SV2351 @ ( tc_fun @ SV2485 @ SV2485 ) @ SV2203 ) @ SV1881 @ SV2433 @ SV2203 @ SV2485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6136]) ).
thf(6404,plain,
! [SV2434: $i,SV2352: $i,SV2204: $i,SV1882: $i,SV1339: $i,SV621: $i] :
( ( ( ~ ( c_Type_Otyping @ SV621 @ SV1339 @ SV1882 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SV2204 @ SV1882 @ tc_Type_Otype ) @ SV2352 @ SV2434 )
| ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2352 ) @ SV1339 ) @ SV2204 ) @ SV2434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6137]) ).
thf(6405,plain,
! [SV1883: $i,SV1340: $i,SV2353: $i,SV2205: $i,SV622: $i] :
( ( ( c_Type_Otyping @ SV622 @ SV2205 @ SV2353 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV622 @ SV1340 @ SV1883 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV2205 ) @ SV1340 ) @ SV2353 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6138]) ).
thf(6406,plain,
! [SV2435: $i,SV2354: $i,SV2207: $i,SV1885: $i,SV1342: $i,SV625: $i] :
( ( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1885 ) @ SV2207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2354 )
= $true )
| ( ( ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SV1885 @ SV2435 @ tc_Type_Otype ) @ SV2207 @ SV2354 )
| ~ ( c_Type_Otyping @ SV625 @ SV1342 @ SV2435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6139]) ).
thf(6407,plain,
! [SV1888: $i,SV1345: $i,SV2356: $i,SV2210: $i,SV628: $i] :
( ( ( c_Type_Otypings @ SV628 @ SV2210 @ SV2356 )
= $false )
| ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV628 @ SV1345 @ SV1888 @ tc_Type_Otype ) @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ c_Lambda_Olift @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1345 ) @ SV2210 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2356 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6141]) ).
thf(6408,plain,
! [SV2213: $i,SV1893: $i,SV1354: $i,SV637: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV637 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV1893 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV2213 ) )
| ( SV1893 = SV2213 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6144]) ).
thf(6409,plain,
! [SV639: $i,SV1895: $i,SV1356: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1356 @ SV1895 @ SV639 )
= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
= $false )
| ( ( SV1356
= ( c_HOL_Ozero__class_Ozero @ SV639 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6145]) ).
thf(6410,plain,
! [SV2359: $i,SV2214: $i,SV1896: $i,SV1360: $i,SV643: $i] :
( ( ( ( c_List_Omap @ SV643 @ SV1360 @ SV1896 @ SV2214 )
= ( c_List_Omap @ SV643 @ SV2359 @ SV1896 @ SV2214 ) )
= $false )
| ( ( ( c_Nat_Osize__class_Osize @ SV1360 @ ( tc_List_Olist @ SV1896 ) )
= ( c_Nat_Osize__class_Osize @ SV2359 @ ( tc_List_Olist @ SV1896 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6147]) ).
thf(6411,plain,
! [SV1897: $i,SV1361: $i,SV644: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
| ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6148]) ).
thf(6412,plain,
! [SV2215: $i,SV1898: $i,SV1363: $i,SV646: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV1898 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV2215 ) )
= $true )
| ( ( SV1898 = SV2215 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV646 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6150]) ).
thf(6413,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV647 )
| ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6151]) ).
thf(6414,plain,
! [SV2360: $i,SV2218: $i,SV1903: $i,SV1370: $i,SV653: $i] :
( ( ( ( c_List_Oappend @ SV653 @ SV1370 @ SV1903 )
= ( c_List_Oappend @ SV2218 @ SV2360 @ SV1903 ) )
= $false )
| ( ( ( SV1370
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ SV2218 @ SV1903 ) @ SV2360 @ SV1903 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ ( c_Nat_Osize__class_Osize @ SV2218 @ ( tc_List_Olist @ SV1903 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6154]) ).
thf(6415,plain,
! [SV2219: $i,SV1904: $i,SV1372: $i,SV655: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 )
!= SV655 )
= $true )
| ( ( ( SV1904
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
| ( ( c_List_Oappend @ SV1904 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SV2219 @ SV1372 ) ) )
= $true )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= SV2219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6155]) ).
thf(6416,plain,
! [SV2220: $i,SV659: $i,SV1906: $i,SV1375: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
!= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
= $true )
| ( ( ( SV1375 = SV2220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV659 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6156]) ).
thf(6417,plain,
! [SV2486: $i,SV2439: $i,SV2361: $i,SV2221: $i,SV1907: $i,SV1376: $i,SV660: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
| ~ ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6157]) ).
thf(6418,plain,
! [SV2222: $i,SV665: $i,SV1911: $i,SV1381: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1381 @ SV1911 @ SV665 )
!= ( c_Power_Opower__class_Opower @ SV1381 @ SV2222 @ SV665 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 )
| ( SV1911 = SV2222 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6158]) ).
thf(6419,plain,
! [SV1914: $i,SV1384: $i,SV668: $i] :
( ( ( class_Int_Onumber__ring @ SV668 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1384 @ SV1914 @ SV668 )
!= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
| ( SV1384 = SV1914 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV668 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6159]) ).
thf(6420,plain,
! [SV2362: $i,SV2223: $i,SV1916: $i,SV1386: $i,SV670: $i] :
( ( ( ( c_List_Oappend @ SV670 @ SV1386 @ SV1916 )
= ( c_List_Oappend @ SV2223 @ SV2362 @ SV1916 ) )
= $false )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ SV670 @ SV1916 )
= SV2223 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV670 @ ( tc_List_Olist @ SV1916 ) ) @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6160]) ).
thf(6421,plain,
! [SV2487: $i,SV2440: $i,SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ! [SY6548: $i,SY6549: $i,SY6550: $i,SY6551: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SV2440 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SV2487 @ SY6548 @ SY6549 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SY6550 @ SY6548 @ SY6551 ) @ SV2440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6161]) ).
thf(6422,plain,
! [SV1919: $i,SV674: $i,SV1389: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1389 @ SV674 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1919 @ SV674 ) )
= $false )
| ( ( SV1389 = SV1919 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV674 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6162]) ).
thf(6423,plain,
! [SV2488: $i,SV2441: $i,SV2364: $i,SV2226: $i,SV1922: $i,SV1393: $i,SV678: $i] :
( ( ! [SY6552: $i,SY6553: $i] :
( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SV2226 @ SV2364 )
!= ( c_Fun_Ocomp @ SV2441 @ SV2488 @ SY6552 @ SV2226 @ SV2364 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SY6553 ) )
= ( hAPP @ SV2441 @ ( hAPP @ SV2488 @ SY6553 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6165]) ).
thf(6424,plain,
! [SV2365: $i,SV2227: $i,SV1925: $i,SV1399: $i,SV684: $i] :
( ( ( ( hAPP @ SV684 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) )
= ( hAPP @ SV1399 @ ( c_List_Osko__List__Xmap__eq__conv__1__1 @ SV684 @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) ) )
= $false )
| ( ( ( c_List_Omap @ SV684 @ SV1925 @ SV2227 @ SV2365 )
= ( c_List_Omap @ SV1399 @ SV1925 @ SV2227 @ SV2365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6166]) ).
thf(6425,plain,
! [SV2366: $i,SV2229: $i,SV1928: $i,SV1402: $i,SV687: $i] :
( ( ( ( c_List_Oappend @ SV687 @ ( c_List_Olist_OCons @ SV1402 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 )
= ( c_List_Oappend @ SV2229 @ ( c_List_Olist_OCons @ SV2366 @ ( c_List_Olist_ONil @ SV1928 ) @ SV1928 ) @ SV1928 ) )
= $false )
| ( ( SV1402 = SV2366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6168]) ).
thf(6426,plain,
! [SV2230: $i,SV1929: $i,SV1403: $i,SV688: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV1929 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV2230 ) )
= $true )
| ( ( SV1929 = SV2230 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV688 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6169]) ).
thf(6427,plain,
! [SV2367: $i,SV2231: $i,SV1930: $i,SV1404: $i,SV689: $i] :
( ( ( ( c_List_Oreplicate @ SV689 @ SV1404 @ SV1930 )
= ( c_List_Oreplicate @ SV2231 @ SV2367 @ SV1930 ) )
= $false )
| ( ( SV689 = SV2231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6170]) ).
thf(6428,plain,
! [SV2368: $i,SV2232: $i,SV1931: $i,SV1405: $i,SV690: $i] :
( ( ( ( hAPP @ SV690 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) )
= ( hAPP @ SV1405 @ ( c_List_Osko__List__Xmap__ext__1__1 @ SV690 @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) ) )
= $false )
| ( ( ( c_List_Omap @ SV690 @ SV1931 @ SV2232 @ SV2368 )
= ( c_List_Omap @ SV1405 @ SV1931 @ SV2232 @ SV2368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6171]) ).
thf(6429,plain,
! [SV2369: $i,SV2233: $i,SV1934: $i,SV1409: $i,SV694: $i] :
( ( ( ( c_List_Oappend @ SV694 @ SV1409 @ SV1934 )
= ( c_List_Oappend @ SV2233 @ SV2369 @ SV1934 ) )
= $false )
| ( ( ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ SV2233 @ SV1934 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ ( c_Nat_Osize__class_Osize @ SV2233 @ ( tc_List_Olist @ SV1934 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6172]) ).
thf(6430,plain,
! [SV2370: $i,SV2234: $i,SV1936: $i,SV1411: $i,SV696: $i] :
( ( ( ( c_List_Olist_OCons @ SV696 @ SV1411 @ SV1936 )
= ( c_List_Olist_OCons @ SV2234 @ SV2370 @ SV1936 ) )
= $false )
| ( ( SV696 = SV2234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6173]) ).
thf(6431,plain,
! [SV2235: $i,SV697: $i,SV1412: $i,SV1937: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1937 @ ( tc_List_Olist @ SV1412 ) ) @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_Oappend @ SV1937 @ SV2235 @ SV1412 )
= ( c_List_Oappend @ SV697 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 ) @ SV2235 @ SV1412 ) @ SV1412 ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV697 @ ( tc_List_Olist @ SV1412 ) ) @ SV1937 @ SV1412 )
= SV697 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6174]) ).
thf(6432,plain,
! [SV2371: $i,SV2238: $i,SV1942: $i,SV1419: $i,SV704: $i] :
( ( ( ( c_List_Oreplicate @ SV704 @ SV1419 @ SV1942 )
= ( c_List_Oreplicate @ SV2238 @ SV2371 @ SV1942 ) )
= $false )
| ( ( ( SV1419 = SV2371 )
| ( SV704
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6177]) ).
thf(6433,plain,
! [SV706: $i,SV1943: $i,SV1420: $i] :
( ( ( c_lessequals @ SV1420 @ SV1943 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1420 @ SV706 @ tc_nat )
| ( SV706 = SV1943 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SV1420 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1943 @ SV1420 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6178]) ).
thf(6434,plain,
! [SV711: $i,SV1947: $i,SV1424: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1424 @ SV1947 @ SV711 )
= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
= $false )
| ( ( SV1424 = SV1947 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV711 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6180]) ).
thf(6435,plain,
! [SV2372: $i,SV2240: $i,SV1948: $i,SV1425: $i,SV712: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
!= ( c_HOL_Ominus__class_Ominus @ SV2240 @ SV2372 @ SV712 ) )
| ( c_HOL_Oord__class_Oless @ SV2240 @ SV2372 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6181]) ).
thf(6436,plain,
! [SV1426: $i,SV1949: $i,SV2241: $i,SV713: $i] :
( ( ( hBOOL @ ( hAPP @ SV713 @ SV2241 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV713 @ SV1949 ) )
= $true )
| ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV713 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1426 ) @ SV1949 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6182]) ).
thf(6437,plain,
! [SV1950: $i,SV1427: $i,SV714: $i] :
( ( ( class_Int_Onumber__ring @ SV714 )
= $false )
| ( ( ( SV1427
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SV1427 ) @ SV1950 ) )
| ( SV1950
= ( c_HOL_Ozero__class_Ozero @ SV714 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV714 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6183]) ).
thf(6438,plain,
! [SV2373: $i,SV2245: $i,SV1956: $i,SV1434: $i,SV721: $i] :
( ( ( ( c_List_Olist_OCons @ SV721 @ SV1434 @ SV1956 )
= ( c_List_Olist_OCons @ SV2245 @ SV2373 @ SV1956 ) )
= $false )
| ( ( SV1434 = SV2373 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6186]) ).
thf(6439,plain,
! [SV2246: $i,SV722: $i,SV1435: $i,SV1957: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1957 @ SV1435 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV722 @ SV2246 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV722 ) @ SV1435 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1957 ) @ SV2246 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6187]) ).
thf(6440,plain,
! [SV2374: $i,SV2249: $i,SV1960: $i,SV1439: $i,SV726: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
!= ( c_HOL_Ominus__class_Ominus @ SV2249 @ SV2374 @ SV726 ) )
| ( c_lessequals @ SV2374 @ SV2249 @ SV726 )
| ~ ( c_lessequals @ SV1960 @ SV1439 @ SV726 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6190]) ).
thf(6441,plain,
! [SV2250: $i,SV1962: $i,SV728: $i,SV1441: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1441 @ SV1441 @ SV728 )
!= ( c_HOL_Ominus__class_Ominus @ SV1962 @ SV2250 @ SV728 ) )
= $true )
| ( ( SV1962 = SV2250 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV728 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6191]) ).
thf(6442,plain,
! [SV1442: $i,SV729: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV729 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV729 )
| ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6192]) ).
thf(6443,plain,
! [SV1963: $i,SV1443: $i,SV730: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6193]) ).
thf(6444,plain,
! [SV2375: $i,SV2251: $i,SV1965: $i,SV1446: $i,SV734: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV734 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2251 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2375 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ SV2251 )
= SV2375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6194]) ).
thf(6445,plain,
! [SV2376: $i,SV2252: $i,SV1969: $i,SV1451: $i,SV740: $i] :
( ( ( ( hAPP @ SV740 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) )
= ( hAPP @ SV1451 @ ( c_List_Osko__List__Xmap__cong__1__1 @ SV740 @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) ) )
= $false )
| ( ( ( c_List_Omap @ SV740 @ SV1969 @ SV2252 @ SV2376 )
= ( c_List_Omap @ SV1451 @ SV1969 @ SV2252 @ SV2376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6195]) ).
thf(6446,plain,
! [SV2253: $i,SV1970: $i,SV1452: $i,SV741: $i] :
( ( ( ( c_List_Oappend @ SV741 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) @ SV2253 @ SV1452 ) @ SV1452 )
= ( c_List_Oappend @ SV1970 @ SV2253 @ SV1452 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ ( c_Nat_Osize__class_Osize @ SV1970 @ ( tc_List_Olist @ SV1452 ) ) @ tc_nat ) )
= $true )
| ( ( SV741
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6196]) ).
thf(6447,plain,
! [SV2377: $i,SV2256: $i,SV1974: $i,SV1458: $i,SV749: $i] :
( ( ( ( c_List_Oappend @ SV749 @ SV1458 @ SV1974 )
= ( c_List_Oappend @ SV2256 @ SV2377 @ SV1974 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ SV749 @ SV1974 ) @ SV1458 @ SV1974 )
= SV2377 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV749 @ ( tc_List_Olist @ SV1974 ) ) @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6198]) ).
thf(6448,plain,
! [SV2489: $i,SV2442: $i,SV2378: $i,SV2257: $i,SV1975: $i,SV1459: $i,SV750: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
| ~ ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6199]) ).
thf(6449,plain,
! [SV2379: $i,SV2258: $i,SV1979: $i,SV1464: $i,SV755: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
!= ( c_HOL_Ominus__class_Ominus @ SV2258 @ SV2379 @ SV755 ) )
| ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SV2258 @ SV2379 @ SV755 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6200]) ).
thf(6450,plain,
! [SV756: $i,SV1980: $i,SV1465: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV1465 @ SV1980 @ SV756 )
= SV1980 )
= $false )
| ( ( c_lessequals @ SV1465 @ SV1980 @ SV756 )
= $true )
| ( ( class_Orderings_Olinorder @ SV756 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6201]) ).
thf(6451,plain,
! [SV2259: $i,SV757: $i,SV1981: $i,SV1466: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
!= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
= $true )
| ( ( ( SV1466 = SV2259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6202]) ).
thf(6452,plain,
! [SV1983: $i,SV1468: $i,SV2260: $i,SV759: $i] :
( ( ( hBOOL @ ( hAPP @ SV759 @ SV2260 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV759 @ SV1468 ) )
= $true )
| ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1468 ) @ SV1983 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6203]) ).
thf(6453,plain,
! [SV2380: $i,SV2262: $i,SV1988: $i,SV1473: $i,SV764: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
!= ( c_HOL_Ominus__class_Ominus @ SV2262 @ SV2380 @ SV764 ) )
| ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
| ~ ( c_lessequals @ SV2380 @ SV2262 @ SV764 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6205]) ).
thf(6454,plain,
! [SV2263: $i,SV765: $i,SV1989: $i,SV1474: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1474 @ SV1989 @ SV765 )
!= ( c_HOL_Ominus__class_Ominus @ SV2263 @ SV2263 @ SV765 ) )
= $true )
| ( ( SV1474 = SV1989 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV765 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6206]) ).
thf(6455,plain,
! [SV768: $i,SV1991: $i,SV1477: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV1991 @ SV768 )
= ( c_HOL_Ozero__class_Ozero @ SV768 ) )
= $false )
| ( ( SV1477 = SV1991 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV768 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6208]) ).
thf(6456,plain,
! [SV2265: $i,SV1992: $i,SV1479: $i,SV770: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV1479 ) @ SV1992 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV2265 ) @ SV1992 ) )
= $true )
| ( ( SV1479 = SV2265 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV770 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6209]) ).
thf(6457,plain,
! [SV2381: $i,SV2266: $i,SV1993: $i,SV1480: $i,SV771: $i] :
( ( ( ( c_List_Oappend @ SV771 @ ( c_List_Olist_OCons @ SV1480 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 )
= ( c_List_Oappend @ SV2266 @ ( c_List_Olist_OCons @ SV2381 @ ( c_List_Olist_ONil @ SV1993 ) @ SV1993 ) @ SV1993 ) )
= $false )
| ( ( SV771 = SV2266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6210]) ).
thf(6458,plain,
! [SV1994: $i,SV1485: $i,SV779: $i,SV11: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
| ~ ( c_lessequals @ SV779 @ SV1994 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6214]) ).
thf(6459,plain,
! [SV783: $i,SV15: $i,SV1996: $i,SV1488: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1488 @ SV1996 @ SV15 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV1996 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SV1488 @ SV15 ) @ SV1996 @ SV15 )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6215]) ).
thf(6460,plain,
! [SV793: $i,SV1492: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1492 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV25 ) @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV1492 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV793 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6218]) ).
thf(6461,plain,
! [SV799: $i,SV31: $i,SV1998: $i,SV1495: $i] :
( ( ( ~ ( c_lessequals @ SV1495 @ SV1998 @ SV31 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV799 @ SV1998 @ SV31 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SV1495 @ SV31 ) @ SV1998 @ SV31 )
= $true )
| ( ( class_Orderings_Olinorder @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6221]) ).
thf(6462,plain,
! [SV800: $i,SV32: $i,SV1999: $i,SV1496: $i] :
( ( ( ~ ( c_lessequals @ SV1496 @ SV1999 @ SV32 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV800 @ SV1999 @ SV32 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SV1496 @ SV32 ) @ SV1999 @ SV32 )
= $true )
| ( ( class_Orderings_Olinorder @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6222]) ).
thf(6463,plain,
! [SV801: $i,SV33: $i,SV2000: $i,SV1497: $i] :
( ( ( ~ ( c_lessequals @ SV1497 @ SV2000 @ SV33 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV801 @ SV2000 @ SV33 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SV1497 @ SV33 ) @ SV2000 @ SV33 )
= $true )
| ( ( class_Orderings_Olinorder @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6223]) ).
thf(6464,plain,
! [SV1502: $i,SV2001: $i,SV47: $i,SV815: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6224]) ).
thf(6465,plain,
! [SV2002: $i,SV1504: $i,SV817: $i,SV49: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
= $false )
| ( ( ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
| ~ ( c_lessequals @ SV817 @ SV2002 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6225]) ).
thf(6466,plain,
! [SV2003: $i,SV1505: $i,SV818: $i,SV50: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
| ~ ( c_lessequals @ SV818 @ SV1505 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6226]) ).
thf(6467,plain,
! [SV1511: $i,SV2004: $i,SV61: $i,SV829: $i] :
( ( ( ~ ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
| ~ ( c_lessequals @ SV2004 @ SV1511 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6227]) ).
thf(6468,plain,
! [SV1521: $i,SV74: $i,SV2007: $i,SV841: $i] :
( ( ( c_lessequals @ SV841 @ SV2007 @ SV74 )
= $true )
| ( ( ~ ( c_lessequals @ SV841 @ ( c_Orderings_Oord__class_Omax @ SV2007 @ SV1521 @ SV74 ) @ SV74 ) )
= $true )
| ( ( c_lessequals @ SV841 @ SV1521 @ SV74 )
= $true )
| ( ( class_Orderings_Olinorder @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6229]) ).
thf(6469,plain,
! [SV2010: $i,SV850: $i,SV1530: $i,SV83: $i] :
( ( ( c_lessequals @ SV83 @ SV1530 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV850 @ SV2010 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV83 ) @ SV850 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1530 ) @ SV2010 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6230]) ).
thf(6470,plain,
! [SV2267: $i,SV2011: $i,SV1531: $i,SV851: $i,SV84: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV2011 ) @ SV2267 ) @ SV84 )
= $true )
| ( ( ~ ( c_lessequals @ SV1531 @ SV2267 @ SV84 )
| ~ ( c_lessequals @ SV851 @ SV2011 @ SV84 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6231]) ).
thf(6471,plain,
! [SV860: $i,SV1536: $i,SV95: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1536 @ SV95 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV860 @ SV95 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV860 ) @ SV1536 ) @ SV95 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6233]) ).
thf(6472,plain,
! [SV1537: $i,SV96: $i,SV861: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV861 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV861 @ SV96 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV861 @ ( c_Suc @ SV1537 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6234]) ).
thf(6473,plain,
! [SV862: $i,SV97: $i,SV1538: $i,SV2014: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2014 @ SV1538 @ SV97 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV862 @ SV2014 @ SV97 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV862 @ SV1538 @ SV97 )
= $true )
| ( ( class_Orderings_Opreorder @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6235]) ).
thf(6474,plain,
! [SV1539: $i,SV98: $i,SV2015: $i,SV863: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV2015 @ SV98 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2015 @ SV1539 @ SV98 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1539 @ SV98 )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6236]) ).
thf(6475,plain,
! [SV131: $i,SV896: $i,SV1567: $i] :
( ( ( c_lessequals @ SV1567 @ SV896 @ SV131 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV896 @ SV1567 @ SV131 )
= $false )
| ( ( class_Orderings_Olinorder @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6240]) ).
thf(6476,plain,
! [SV133: $i,SV898: $i,SV1569: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1569 @ SV898 @ SV133 )
= $false )
| ( ( c_lessequals @ SV898 @ SV1569 @ SV133 )
= $false )
| ( ( class_Orderings_Olinorder @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6241]) ).
thf(6477,plain,
! [SV135: $i,SV900: $i,SV1571: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1571 @ SV900 @ SV135 )
= $false )
| ( ( c_lessequals @ SV900 @ SV1571 @ SV135 )
= $false )
| ( ( class_Orderings_Opreorder @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6242]) ).
thf(6478,plain,
! [SV2028: $i,SV1572: $i,SV904: $i,SV139: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
| ~ ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6243]) ).
thf(6479,plain,
! [SV2029: $i,SV1573: $i,SV905: $i,SV140: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1573 @ SV2029 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SV1573 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SV2029 @ SV140 ) @ SV140 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6244]) ).
thf(6480,plain,
! [SV143: $i,SV1576: $i,SV908: $i] :
( ( ( c_lessequals @ SV908 @ SV1576 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV908 @ SV143 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV143 @ SV1576 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SV908 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV908 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6245]) ).
thf(6481,plain,
! [SV144: $i,SV909: $i,SV1577: $i] :
( ( ( c_lessequals @ SV1577 @ SV909 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1577 @ SV144 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SV1577 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV909 @ SV1577 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV144 @ SV909 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6246]) ).
thf(6482,plain,
! [SV1579: $i,SV2030: $i,SV912: $i,SV147: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV912 @ SV2030 @ SV147 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SV1579 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SV2030 @ SV1579 @ SV147 ) @ SV147 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6247]) ).
thf(6483,plain,
! [SV2033: $i,SV159: $i,SV1585: $i,SV921: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV921 @ SV1585 @ SV159 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV921 @ ( c_Orderings_Oord__class_Omax @ SV1585 @ SV2033 @ SV159 ) @ SV159 )
= $true )
| ( ( class_Orderings_Olinorder @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6248]) ).
thf(6484,plain,
! [SV1586: $i,SV160: $i,SV2034: $i,SV922: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV922 @ SV2034 @ SV160 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV922 @ ( c_Orderings_Oord__class_Omax @ SV1586 @ SV2034 @ SV160 ) @ SV160 )
= $true )
| ( ( class_Orderings_Olinorder @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6249]) ).
thf(6485,plain,
! [SV2035: $i,SV161: $i,SV1587: $i,SV923: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV923 @ SV1587 @ SV161 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Orderings_Oord__class_Omax @ SV1587 @ SV2035 @ SV161 ) @ SV161 )
= $true )
| ( ( class_Orderings_Olinorder @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6250]) ).
thf(6486,plain,
! [SV1588: $i,SV162: $i,SV2036: $i,SV924: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV924 @ SV2036 @ SV162 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Orderings_Oord__class_Omax @ SV1588 @ SV2036 @ SV162 ) @ SV162 )
= $true )
| ( ( class_Orderings_Olinorder @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6251]) ).
thf(6487,plain,
! [SV1589: $i,SV163: $i,SV2037: $i,SV925: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV925 @ SV2037 @ SV163 ) @ SV1589 @ SV163 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1589 @ SV163 )
= $true )
| ( ( class_Orderings_Olinorder @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6252]) ).
thf(6488,plain,
! [SV2490: $i,SV2443: $i,SV2383: $i,SV2270: $i,SV2038: $i,SV1590: $i,SV927: $i,SV165: $i] :
( ( ! [SY6554: $i] :
( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2038 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2270 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2038 ) @ SV2270 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2383 @ SV165 @ SV927 @ SV2443 @ SV2490 @ SY6554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6253]) ).
thf(6489,plain,
! [SV2042: $i,SV939: $i,SV1596: $i,SV178: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SV1596 @ SV178 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SV2042 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SV1596 @ SV2042 @ SV178 ) @ SV178 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV939 @ SV1596 @ SV178 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6254]) ).
thf(6490,plain,
! [SV1598: $i,SV180: $i,SV941: $i,SV2043: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2043 @ SV941 @ SV180 ) @ SV1598 @ SV180 )
= $false )
| ( ( c_lessequals @ SV941 @ SV1598 @ SV180 )
= $true )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6255]) ).
thf(6491,plain,
! [SV1599: $i,SV181: $i,SV2044: $i,SV942: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV942 @ SV2044 @ SV181 ) @ SV1599 @ SV181 )
= $false )
| ( ( c_lessequals @ SV942 @ SV1599 @ SV181 )
= $true )
| ( ( class_Orderings_Olinorder @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6256]) ).
thf(6492,plain,
! [SV1600: $i,SV182: $i,SV2045: $i,SV943: $i] :
( ( ( c_lessequals @ SV943 @ SV2045 @ SV182 )
= $false )
| ( ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1600 @ SV2045 @ SV182 ) @ SV182 )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6257]) ).
thf(6493,plain,
! [SV2046: $i,SV183: $i,SV1601: $i,SV944: $i] :
( ( ( c_lessequals @ SV944 @ SV1601 @ SV183 )
= $false )
| ( ( c_lessequals @ SV944 @ ( c_Orderings_Oord__class_Omax @ SV1601 @ SV2046 @ SV183 ) @ SV183 )
= $true )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6258]) ).
thf(6494,plain,
! [SV1602: $i,SV184: $i,SV2047: $i,SV945: $i] :
( ( ( c_lessequals @ SV945 @ SV2047 @ SV184 )
= $false )
| ( ( c_lessequals @ SV945 @ ( c_Orderings_Oord__class_Omax @ SV1602 @ SV2047 @ SV184 ) @ SV184 )
= $true )
| ( ( class_Orderings_Olinorder @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6259]) ).
thf(6495,plain,
! [SV2048: $i,SV185: $i,SV1603: $i,SV946: $i] :
( ( ( c_lessequals @ SV946 @ SV1603 @ SV185 )
= $false )
| ( ( c_lessequals @ SV946 @ ( c_Orderings_Oord__class_Omax @ SV1603 @ SV2048 @ SV185 ) @ SV185 )
= $true )
| ( ( class_Orderings_Olinorder @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6260]) ).
thf(6496,plain,
! [SV1604: $i,SV186: $i,SV947: $i,SV2049: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2049 @ SV947 @ SV186 ) @ SV1604 @ SV186 )
= $false )
| ( ( c_lessequals @ SV947 @ SV1604 @ SV186 )
= $true )
| ( ( class_Orderings_Olinorder @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6261]) ).
thf(6497,plain,
! [SV1605: $i,SV187: $i,SV2050: $i,SV948: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV948 @ SV2050 @ SV187 ) @ SV1605 @ SV187 )
= $false )
| ( ( c_lessequals @ SV948 @ SV1605 @ SV187 )
= $true )
| ( ( class_Orderings_Olinorder @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6262]) ).
thf(6498,plain,
! [SV1609: $i,SV191: $i,SV2051: $i,SV952: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV952 @ SV2051 @ SV191 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV952 @ ( c_Orderings_Oord__class_Omax @ SV2051 @ SV1609 @ SV191 ) @ SV191 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV952 @ SV1609 @ SV191 )
= $true )
| ( ( class_Orderings_Olinorder @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6264]) ).
thf(6499,plain,
! [SV958: $i,SV199: $i,SV1614: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1614 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $false )
| ( ( ~ ( c_lessequals @ SV958 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV958 ) @ SV1614 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6266]) ).
thf(6500,plain,
! [SV959: $i,SV200: $i,SV1615: $i] :
( ( ( c_lessequals @ SV1615 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV959 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SV959 ) @ SV1615 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6267]) ).
thf(6501,plain,
! [SV216: $i,SV1625: $i,SV974: $i] :
( ( ( c_lessequals @ SV974 @ SV1625 @ SV216 )
= $false )
| ( ( c_lessequals @ SV1625 @ SV974 @ SV216 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV974 @ SV1625 @ SV216 )
= $true )
| ( ( class_Orderings_Opreorder @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6270]) ).
thf(6502,plain,
! [SV983: $i,SV1629: $i,SV227: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV1629 @ SV227 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV983 @ SV227 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SV983 ) @ SV1629 ) @ SV227 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6271]) ).
thf(6503,plain,
! [SV2444: $i,SV2386: $i,SV2275: $i,SV2057: $i,SV1633: $i,SV991: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ SV236 @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV991 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV2057 @ SV236 @ SV2275 @ SV2386 @ SV2444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6272]) ).
thf(6504,plain,
! [SV242: $i,SV997: $i,SV2276: $i,SV2058: $i,SV1637: $i] :
( ( ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV997 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 ) )
= $true )
| ( ( SV242 = SV997 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6275]) ).
thf(6505,plain,
! [SV1638: $i,SV243: $i,SV998: $i,SV2059: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2059 @ SV998 @ SV243 ) @ SV1638 @ SV243 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV998 @ SV1638 @ SV243 )
= $true )
| ( ( class_Orderings_Olinorder @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6276]) ).
thf(6506,plain,
! [SV999: $i,SV245: $i,SV1639: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1639 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SV999 @ SV245 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SV999 @ SV1639 @ SV245 ) @ SV245 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6277]) ).
thf(6507,plain,
! [SV1004: $i,SV250: $i,SV1642: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1642 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1004 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SV1004 ) @ SV1642 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6278]) ).
thf(6508,plain,
! [SV2061: $i,SV1005: $i,SV251: $i,SV1643: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6279]) ).
thf(6509,plain,
! [SV1012: $i,SV1650: $i,SV258: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1650 @ SV258 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1012 @ SV258 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV1012 ) @ SV1650 ) @ SV258 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6281]) ).
thf(6510,plain,
! [SV1013: $i,SV1651: $i,SV259: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1651 @ SV259 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1013 @ SV259 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV1013 ) @ SV1651 ) @ SV259 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6282]) ).
thf(6511,plain,
! [SV2491: $i,SV2445: $i,SV2387: $i,SV2277: $i,SV2067: $i,SV1659: $i,SV1025: $i,SV271: $i] :
( ( ! [SY6555: $i] :
( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SV2067 ) ) @ SV2277 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SV2277 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SV2067 ) @ SV2277 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2387 @ SV1025 @ SV271 @ SV2445 @ SV2491 @ SY6555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6284]) ).
thf(6512,plain,
! [SV2492: $i,SV2446: $i,SV2388: $i,SV2278: $i,SV2068: $i,SV1660: $i,SV1026: $i,SV272: $i] :
( ( ! [SY6556: $i] :
( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SV2068 ) @ SV2278 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2068 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2278 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SV2388 @ SV2446 @ SV2492 @ SY6556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6285]) ).
thf(6513,plain,
! [SV2493: $i,SV2447: $i,SV2389: $i,SV2279: $i,SV2069: $i,SV1661: $i,SV1027: $i,SV273: $i] :
( ( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SV1661 )
= ( hAPP @ ( hAPP @ SV273 @ SV1661 ) @ SV1027 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2069 @ SV273 @ SV2279 @ SV2389 @ SV2447 @ SV2493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6286]) ).
thf(6514,plain,
! [SV2494: $i,SV2448: $i,SV2390: $i,SV2280: $i,SV2070: $i,SV1662: $i,SV1028: $i,SV274: $i] :
( ( ! [SY6557: $i] :
( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SV2070 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SV2070 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2280 @ SV274 @ SV2390 @ SV2448 @ SV2494 @ SY6557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6287]) ).
thf(6515,plain,
! [SV2449: $i,SV2391: $i,SV2281: $i,SV2071: $i,SV1663: $i,SV1029: $i,SV275: $i] :
( ( ( ( hAPP @ ( hAPP @ SV275 @ SV1029 ) @ SV1663 )
= SV1663 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2071 @ SV275 @ SV2281 @ SV2391 @ SV1029 @ SV2449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6288]) ).
thf(6516,plain,
! [SV2450: $i,SV2392: $i,SV2282: $i,SV2072: $i,SV1664: $i,SV1030: $i,SV276: $i] :
( ( ( ( hAPP @ ( hAPP @ SV276 @ SV1030 ) @ SV1664 )
= SV1030 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2072 @ SV276 @ SV2282 @ SV1030 @ SV2392 @ SV2450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6289]) ).
thf(6517,plain,
! [SV2495: $i,SV2451: $i,SV2393: $i,SV2283: $i,SV2073: $i,SV1665: $i,SV1031: $i,SV277: $i] :
( ( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SV1665 )
= ( hAPP @ ( hAPP @ SV277 @ SV1665 ) @ SV1031 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SV2073 @ SV2283 @ SV2393 @ SV2451 @ SV2495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6290]) ).
thf(6518,plain,
! [SV2496: $i,SV2452: $i,SV2394: $i,SV2284: $i,SV2074: $i,SV1666: $i,SV1032: $i,SV278: $i] :
( ( ! [SY6558: $i] :
( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SV2074 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SV2074 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SV2284 @ SV2394 @ SV2452 @ SV2496 @ SY6558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6291]) ).
thf(6519,plain,
! [SV2453: $i,SV2395: $i,SV2285: $i,SV2075: $i,SV1667: $i,SV1033: $i,SV279: $i] :
( ( ( ( hAPP @ ( hAPP @ SV279 @ SV1033 ) @ SV1667 )
= SV1667 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SV2075 @ SV2285 @ SV1033 @ SV2395 @ SV2453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6292]) ).
thf(6520,plain,
! [SV2497: $i,SV2454: $i,SV2396: $i,SV2286: $i,SV2076: $i,SV1668: $i,SV1034: $i,SV280: $i] :
( ( ! [SY6559: $i] :
( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SV2076 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SV2076 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SV2286 @ SV2396 @ SV2454 @ SV2497 @ SY6559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6293]) ).
thf(6521,plain,
! [SV2498: $i,SV2455: $i,SV2397: $i,SV2287: $i,SV2077: $i,SV1669: $i,SV1035: $i,SV281: $i] :
( ( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SV1669 )
= ( hAPP @ ( hAPP @ SV281 @ SV1669 ) @ SV1035 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SV2077 @ SV2287 @ SV2397 @ SV2455 @ SV2498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6294]) ).
thf(6522,plain,
! [SV2499: $i,SV2456: $i,SV2398: $i,SV2288: $i,SV2078: $i,SV1670: $i,SV1036: $i,SV282: $i] :
( ( ! [SY6560: $i] :
( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SV2078 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV2078 ) ) @ SV1670 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SV2288 @ SV2398 @ SV2456 @ SV2499 @ SY6560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6295]) ).
thf(6523,plain,
! [SV2500: $i,SV2457: $i,SV2399: $i,SV2289: $i,SV2079: $i,SV1671: $i,SV1037: $i,SV283: $i] :
( ( ! [SY6561: $i] :
( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SV2079 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SV2079 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SV2289 @ SV2399 @ SV2457 @ SV2500 @ SY6561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6296]) ).
thf(6524,plain,
! [SV2501: $i,SV2458: $i,SV2400: $i,SV2290: $i,SV2080: $i,SV1672: $i,SV1038: $i,SV284: $i] :
( ( ! [SY6562: $i] :
( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SV2080 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SV2080 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SV2290 @ SV2400 @ SV2458 @ SV2501 @ SY6562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6297]) ).
thf(6525,plain,
! [SV2502: $i,SV2459: $i,SV2401: $i,SV2291: $i,SV2081: $i,SV1673: $i,SV1039: $i,SV285: $i] :
( ( ! [SY6563: $i,SY6564: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SV2291 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SV2291 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SV2401 @ SV2459 @ SV2502 @ SY6563 @ SY6564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6298]) ).
thf(6526,plain,
! [SV2503: $i,SV2460: $i,SV2402: $i,SV2292: $i,SV2082: $i,SV1674: $i,SV1040: $i,SV286: $i] :
( ( ! [SY6565: $i] :
( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SV2082 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SV2082 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2292 @ SV286 @ SV2402 @ SV2460 @ SV2503 @ SY6565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6299]) ).
thf(6527,plain,
! [SV2504: $i,SV2461: $i,SV2403: $i,SV2293: $i,SV2083: $i,SV1675: $i,SV1041: $i,SV287: $i] :
( ( ! [SY6566: $i] :
( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SV2083 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SV2083 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2293 @ SV287 @ SV2403 @ SV2461 @ SV2504 @ SY6566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6300]) ).
thf(6528,plain,
! [SV2505: $i,SV2462: $i,SV2404: $i,SV2294: $i,SV2084: $i,SV1676: $i,SV1042: $i,SV288: $i] :
( ( ! [SY6567: $i] :
( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SV2084 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SV2084 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2294 @ SV288 @ SV2404 @ SV2462 @ SV2505 @ SY6567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6301]) ).
thf(6529,plain,
! [SV2506: $i,SV2463: $i,SV2405: $i,SV2295: $i,SV2085: $i,SV1677: $i,SV1043: $i,SV289: $i] :
( ( ! [SY6568: $i] :
( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SV2085 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV2085 ) ) @ SV1677 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2295 @ SV289 @ SV2405 @ SV2463 @ SV2506 @ SY6568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6302]) ).
thf(6530,plain,
! [SV2507: $i,SV2464: $i,SV2406: $i,SV2296: $i,SV2086: $i,SV1678: $i,SV1044: $i,SV290: $i] :
( ( ! [SY6569: $i,SY6570: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SV2296 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SV2296 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2406 @ SV290 @ SV2464 @ SV2507 @ SY6569 @ SY6570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6303]) ).
thf(6531,plain,
! [SV2508: $i,SV2465: $i,SV2407: $i,SV2297: $i,SV2087: $i,SV1679: $i,SV1045: $i,SV291: $i] :
( ( ! [SY6571: $i,SY6572: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2407 @ SV291 @ SV2465 @ SV2508 @ SY6571 @ SY6572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6304]) ).
thf(6532,plain,
! [SV2509: $i,SV2466: $i,SV2408: $i,SV2298: $i,SV2088: $i,SV1680: $i,SV1046: $i,SV292: $i] :
( ( ! [SY6573: $i,SY6574: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SV2298 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SV2298 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2408 @ SV292 @ SV2466 @ SV2509 @ SY6573 @ SY6574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6305]) ).
thf(6533,plain,
! [SV2467: $i,SV2409: $i,SV2299: $i,SV2089: $i,SV1681: $i,SV1047: $i,SV293: $i] :
( ( ( ( hAPP @ ( hAPP @ SV293 @ SV1047 ) @ SV1681 )
= SV1047 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2089 @ SV293 @ SV2299 @ SV2409 @ SV1681 @ SV2467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6306]) ).
thf(6534,plain,
! [SV2468: $i,SV2410: $i,SV2300: $i,SV2090: $i,SV1682: $i,SV1048: $i,SV294: $i] :
( ( ( ( hAPP @ ( hAPP @ SV294 @ SV1048 ) @ SV1682 )
= SV1682 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2090 @ SV294 @ SV2300 @ SV2410 @ SV1048 @ SV2468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6307]) ).
thf(6535,plain,
! [SV2469: $i,SV2411: $i,SV2301: $i,SV2091: $i,SV1683: $i,SV1049: $i,SV295: $i] :
( ( ( ( hAPP @ ( hAPP @ SV295 @ SV1049 ) @ SV1683 )
= SV1683 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2091 @ SV295 @ SV2301 @ SV1683 @ SV2411 @ SV2469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6308]) ).
thf(6536,plain,
! [SV2470: $i,SV2412: $i,SV2302: $i,SV2092: $i,SV1684: $i,SV1050: $i,SV296: $i] :
( ( ( ( hAPP @ ( hAPP @ SV296 @ SV1050 ) @ SV1684 )
= SV1050 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2092 @ SV296 @ SV2302 @ SV1050 @ SV2412 @ SV2470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6309]) ).
thf(6537,plain,
! [SV2510: $i,SV2471: $i,SV2413: $i,SV2303: $i,SV2093: $i,SV1685: $i,SV1051: $i,SV297: $i] :
( ( ! [SY6575: $i] :
( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SV2093 ) ) @ SV2303 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SV2303 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SV2093 ) @ SV2303 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SV2413 @ SV2471 @ SV2510 @ SY6575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6310]) ).
thf(6538,plain,
! [SV2511: $i,SV2472: $i,SV2414: $i,SV2304: $i,SV2094: $i,SV1686: $i,SV1052: $i,SV298: $i] :
( ( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SV1686 )
= ( hAPP @ ( hAPP @ SV298 @ SV1686 ) @ SV1052 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2094 @ SV298 @ SV2304 @ SV2414 @ SV2472 @ SV2511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6311]) ).
thf(6539,plain,
! [SV2473: $i,SV2415: $i,SV2305: $i,SV2095: $i,SV1687: $i,SV1053: $i,SV299: $i] :
( ( ( ( hAPP @ ( hAPP @ SV299 @ SV1053 ) @ SV1687 )
= SV1053 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SV2095 @ SV2305 @ SV1687 @ SV2415 @ SV2473 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6312]) ).
thf(6540,plain,
! [SV2474: $i,SV2416: $i,SV2306: $i,SV2096: $i,SV1688: $i,SV1054: $i,SV300: $i] :
( ( ( ( hAPP @ ( hAPP @ SV300 @ SV1054 ) @ SV1688 )
= SV1688 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SV2096 @ SV2306 @ SV1054 @ SV2416 @ SV2474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6313]) ).
thf(6541,plain,
! [SV2475: $i,SV2417: $i,SV2307: $i,SV2097: $i,SV1689: $i,SV1055: $i,SV301: $i] :
( ( ( ( hAPP @ ( hAPP @ SV301 @ SV1055 ) @ SV1055 )
= ( hAPP @ ( hAPP @ SV1689 @ ( hAPP @ ( hAPP @ SV301 @ SV2097 ) @ SV2097 ) ) @ SV1055 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SV1689 @ SV2307 @ SV2417 @ SV2097 @ SV2475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6314]) ).
thf(6542,plain,
! [SV2512: $i,SV2476: $i,SV2418: $i,SV2308: $i,SV2098: $i,SV1690: $i,SV1056: $i,SV302: $i] :
( ( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SV1690 @ SV2098 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SV1690 @ ( hAPP @ ( hAPP @ SV302 @ SV2098 ) @ SV2308 ) ) @ SV1056 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SV1690 @ SV2418 @ SV2476 @ SV2308 @ SV2512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6315]) ).
thf(6543,plain,
! [SV2513: $i,SV2477: $i,SV2419: $i,SV2309: $i,SV2099: $i,SV1691: $i,SV1057: $i,SV303: $i] :
( ( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SV1691 ) @ SV2099 ) ) @ SV2099 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SV1691 ) @ SV2309 ) ) @ SV2099 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SV2419 @ SV2477 @ SV2309 @ SV2513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6316]) ).
thf(6544,plain,
! [SV2514: $i,SV2478: $i,SV2420: $i,SV2310: $i,SV2100: $i,SV1692: $i,SV1058: $i,SV304: $i] :
( ( ! [SY6576: $i] :
( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SV2100 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SV2310 ) @ SV2100 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SV2310 ) ) @ SV2100 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SV2420 @ SV2478 @ SV2514 @ SY6576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6317]) ).
thf(6545,plain,
! [SV328: $i,SV1080: $i,SV1709: $i] :
( ( ( c_lessequals @ SV1709 @ SV1080 @ SV328 )
= $false )
| ( ( ~ ( c_lessequals @ SV1080 @ SV1709 @ SV328 ) )
= $true )
| ( ( SV1080 = SV1709 )
= $true )
| ( ( class_Orderings_Oorder @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6320]) ).
thf(6546,plain,
! [SV330: $i,SV1082: $i,SV1711: $i] :
( ( ( c_lessequals @ SV1711 @ SV1082 @ SV330 )
= $false )
| ( ( ~ ( c_lessequals @ SV1082 @ SV1711 @ SV330 ) )
= $true )
| ( ( SV1082 = SV1711 )
= $true )
| ( ( class_Orderings_Oorder @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6322]) ).
thf(6547,plain,
! [SV331: $i,SV1712: $i,SV1083: $i] :
( ( ( c_lessequals @ SV1083 @ SV1712 @ SV331 )
= $false )
| ( ( ~ ( c_lessequals @ SV1712 @ SV1083 @ SV331 ) )
= $true )
| ( ( SV1083 = SV1712 )
= $true )
| ( ( class_Orderings_Oorder @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6323]) ).
thf(6548,plain,
! [SV2313: $i,SV2107: $i,SV1718: $i,SV1090: $i,SV340: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV2107 ) @ SV2313 ) @ SV340 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1718 @ SV2313 @ SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SV2107 @ SV340 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6328]) ).
thf(6549,plain,
! [SV2108: $i,SV1091: $i,SV1719: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV341 @ SV1719 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1091 @ SV2108 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV341 ) @ SV1091 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1719 ) @ SV2108 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6329]) ).
thf(6550,plain,
! [SV2109: $i,SV1097: $i,SV2314: $i,SV1722: $i,SV347: $i] :
( ( ( c_Type_Otyping @ SV347 @ SV1722 @ SV2314 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV347 @ SV1097 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2314 ) @ SV2109 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1097 ) @ SV1722 ) @ SV2109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6332]) ).
thf(6551,plain,
! [SV1731: $i,SV360: $i,SV2111: $i,SV1107: $i] :
( ( ( c_lessequals @ SV1107 @ SV2111 @ SV360 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV1107 ) @ SV1731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV360 ) @ SV2111 ) @ SV1731 ) @ SV360 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV360 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6339]) ).
thf(6552,plain,
! [SV1732: $i,SV2112: $i,SV1108: $i,SV361: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1108 ) @ SV2112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV361 ) @ SV1732 ) @ SV2112 ) @ SV361 )
= $false )
| ( ( c_lessequals @ SV1108 @ SV1732 @ SV361 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6340]) ).
thf(6553,plain,
! [SV1109: $i,SV362: $i,SV2113: $i,SV1733: $i] :
( ( ( c_lessequals @ SV1733 @ SV2113 @ SV362 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV1733 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV362 ) @ SV1109 ) @ SV2113 ) @ SV362 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6341]) ).
thf(6554,plain,
! [SV1734: $i,SV1110: $i,SV2114: $i,SV363: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV363 ) @ SV2114 ) @ SV1734 ) @ SV363 )
= $false )
| ( ( c_lessequals @ SV1110 @ SV1734 @ SV363 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6342]) ).
thf(6555,plain,
! [SV1735: $i,SV364: $i,SV2115: $i,SV1111: $i] :
( ( ( c_lessequals @ SV1111 @ SV2115 @ SV364 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV1111 ) @ SV1735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV364 ) @ SV2115 ) @ SV1735 ) @ SV364 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6343]) ).
thf(6556,plain,
! [SV1112: $i,SV365: $i,SV2116: $i,SV1736: $i] :
( ( ( c_lessequals @ SV1736 @ SV2116 @ SV365 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV1736 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV365 ) @ SV1112 ) @ SV2116 ) @ SV365 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6344]) ).
thf(6557,plain,
! [SV2515: $i,SV2479: $i,SV2421: $i,SV2316: $i,SV2119: $i,SV1742: $i,SV1121: $i,SV375: $i] :
( ( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ SV2119 ) )
= ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ ( c_Suc @ SV2119 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2316 @ SV375 @ SV1742 @ SV2421 @ SV2479 @ SV2515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6346]) ).
thf(6558,plain,
! [SV2516: $i,SV2480: $i,SV2422: $i,SV2317: $i,SV2120: $i,SV1743: $i,SV1122: $i,SV376: $i] :
( ( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ SV2120 ) ) @ SV1743 )
= ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ ( c_Suc @ SV2120 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2317 @ SV376 @ SV1122 @ SV2422 @ SV2480 @ SV2516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6347]) ).
thf(6559,plain,
! [SV2517: $i,SV2481: $i,SV2423: $i,SV2318: $i,SV2121: $i,SV1744: $i,SV1123: $i,SV377: $i] :
( ( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SV1744 ) )
= ( hAPP @ ( hAPP @ SV2121 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SV1744 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2318 @ SV2121 @ SV377 @ SV2423 @ SV2481 @ SV2517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6348]) ).
thf(6560,plain,
! [SV2518: $i,SV2482: $i,SV2424: $i,SV2319: $i,SV2122: $i,SV1745: $i,SV1124: $i,SV378: $i] :
( ( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SV1745 ) )
= ( hAPP @ ( hAPP @ SV2122 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SV1745 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2319 @ SV2122 @ SV378 @ SV2424 @ SV2482 @ SV2518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6349]) ).
thf(6561,plain,
! [SV2124: $i,SV1129: $i,SV1749: $i,SV383: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1749 @ SV383 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SV2124 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SV1749 @ ( c_Suc @ SV2124 ) @ SV383 ) @ SV383 ) )
= $true )
| ( ( c_lessequals @ SV1129 @ SV1749 @ SV383 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6350]) ).
thf(6562,plain,
! [SV1755: $i,SV2127: $i,SV1141: $i,SV395: $i] :
( ( ( c_List_Olistsp @ SV395 @ SV1141 @ SV2127 )
= $false )
| ( ( c_List_Olistsp @ SV395 @ SV1755 @ SV2127 )
= $false )
| ( ( c_List_Olistsp @ SV395 @ ( c_List_Oappend @ SV1141 @ SV1755 @ SV2127 ) @ SV2127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6351]) ).
thf(6563,plain,
! [SV403: $i,SV1148: $i,SV1760: $i] :
( ( ( c_lessequals @ SV1760 @ SV1148 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1760 @ SV403 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV1760 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1148 @ SV1760 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV403 @ SV1148 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6353]) ).
thf(6564,plain,
! [SV404: $i,SV1761: $i,SV1149: $i] :
( ( ( c_lessequals @ SV1149 @ SV1761 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1149 @ SV404 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV404 @ SV1761 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SV1149 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1761 @ SV1149 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6354]) ).
thf(6565,plain,
! [SV1762: $i,SV405: $i,SV2129: $i,SV1150: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2129 @ SV405 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1762 @ SV405 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1762 ) @ SV2129 ) @ SV405 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV405 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6355]) ).
thf(6566,plain,
! [SV1155: $i,SV410: $i,SV2130: $i,SV1765: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2130 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SV1765 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SV2130 @ SV410 ) @ SV410 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV410 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6356]) ).
thf(6567,plain,
! [SV1766: $i,SV411: $i,SV1156: $i,SV2131: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1766 @ SV411 ) @ SV411 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SV2131 @ SV411 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1766 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6357]) ).
thf(6568,plain,
! [SV2132: $i,SV1767: $i,SV1157: $i,SV412: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1767 @ SV2132 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SV1767 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SV2132 @ SV412 ) @ SV412 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6358]) ).
thf(6569,plain,
! [SV1768: $i,SV413: $i,SV1158: $i,SV2133: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1768 @ SV413 ) @ SV413 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV2133 @ SV413 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1768 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6359]) ).
thf(6570,plain,
! [SV1786: $i,SV450: $i,SV1191: $i,SV2144: $i] :
( ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1786 @ SV450 ) @ SV450 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SV2144 @ SV450 ) )
= $true )
| ( ( c_lessequals @ SV1191 @ SV1786 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV450 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6360]) ).
thf(6571,plain,
! [SV1787: $i,SV451: $i,SV1192: $i,SV2145: $i] :
( ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1787 @ SV451 ) @ SV451 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SV2145 @ SV451 ) )
= $true )
| ( ( c_lessequals @ SV1192 @ SV1787 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6361]) ).
thf(6572,plain,
! [SV1193: $i,SV452: $i,SV2146: $i,SV1788: $i] :
( ( ( ~ ( c_lessequals @ SV1788 @ SV2146 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SV1788 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SV2146 @ SV452 ) @ SV452 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV452 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6362]) ).
thf(6573,plain,
! [SV2322: $i,SV2149: $i,SV1792: $i,SV1197: $i,SV457: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV2149 ) @ SV2322 ) @ SV457 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1792 @ SV2322 @ SV457 )
| ~ ( c_lessequals @ SV1197 @ SV2149 @ SV457 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6363]) ).
thf(6574,plain,
! [SV2323: $i,SV2150: $i,SV1793: $i,SV1198: $i,SV458: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV2150 ) @ SV2323 ) @ SV458 )
= $true )
| ( ( ~ ( c_lessequals @ SV1793 @ SV2323 @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SV2150 @ SV458 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6364]) ).
thf(6575,plain,
! [SV1799: $i,SV493: $i,SV2152: $i,SV1227: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1227 @ SV2152 @ SV493 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV1227 ) @ SV1799 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV2152 ) @ SV1799 ) @ SV493 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6366]) ).
thf(6576,plain,
! [SV1800: $i,SV494: $i,SV2153: $i,SV1228: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1228 @ SV2153 @ SV494 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV1228 ) @ SV1800 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV494 ) @ SV2153 ) @ SV1800 ) @ SV494 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6367]) ).
thf(6577,plain,
! [SV1801: $i,SV2154: $i,SV1229: $i,SV495: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1229 ) @ SV2154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1801 ) @ SV2154 ) @ SV495 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1801 @ SV495 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6368]) ).
thf(6578,plain,
! [SV1230: $i,SV496: $i,SV2155: $i,SV1802: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1802 @ SV2155 @ SV496 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV1802 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV496 ) @ SV1230 ) @ SV2155 ) @ SV496 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6369]) ).
thf(6579,plain,
! [SV1231: $i,SV497: $i,SV2156: $i,SV1803: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1803 @ SV2156 @ SV497 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV1803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV1231 ) @ SV2156 ) @ SV497 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6370]) ).
thf(6580,plain,
! [SV1804: $i,SV1232: $i,SV2157: $i,SV498: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1232 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV498 ) @ SV2157 ) @ SV1804 ) @ SV498 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1232 @ SV1804 @ SV498 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6371]) ).
thf(6581,plain,
! [SV1808: $i,SV502: $i,SV2158: $i,SV1236: $i] :
( ( ( ~ ( c_lessequals @ SV1236 @ SV2158 @ SV502 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2158 @ SV1808 @ SV502 ) )
= $true )
| ( ( c_lessequals @ SV1236 @ SV1808 @ SV502 )
= $true )
| ( ( class_Orderings_Oorder @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6372]) ).
thf(6582,plain,
! [SV1809: $i,SV503: $i,SV2159: $i,SV1237: $i] :
( ( ( ~ ( c_lessequals @ SV1237 @ SV2159 @ SV503 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2159 @ SV1809 @ SV503 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1237 @ SV1809 @ SV503 )
= $true )
| ( ( class_Orderings_Oorder @ SV503 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6373]) ).
thf(6583,plain,
! [SV1810: $i,SV504: $i,SV2160: $i,SV1238: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1238 @ SV2160 @ SV504 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2160 @ SV1810 @ SV504 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1238 @ SV1810 @ SV504 )
= $true )
| ( ( class_Orderings_Oorder @ SV504 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6374]) ).
thf(6584,plain,
! [SV1239: $i,SV505: $i,SV1811: $i] :
( ( ( c_lessequals @ SV1811 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
= $false )
| ( ( ~ ( c_lessequals @ SV1239 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SV1239 ) @ SV1811 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6375]) ).
thf(6585,plain,
! [SV1240: $i,SV506: $i,SV1812: $i,SV2161: $i] :
( ( ( ~ ( c_lessequals @ SV2161 @ SV1812 @ SV506 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1240 @ SV2161 @ SV506 ) )
= $true )
| ( ( c_lessequals @ SV1240 @ SV1812 @ SV506 )
= $true )
| ( ( class_Orderings_Opreorder @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6376]) ).
thf(6586,plain,
! [SV1244: $i,SV512: $i,SV1814: $i,SV2162: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2162 @ SV1814 @ SV512 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1244 @ SV2162 @ SV512 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1244 @ SV1814 @ SV512 )
= $true )
| ( ( class_Orderings_Opreorder @ SV512 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6378]) ).
thf(6587,plain,
! [SV1245: $i,SV513: $i,SV1815: $i,SV2163: $i] :
( ( ( ~ ( c_lessequals @ SV2163 @ SV1815 @ SV513 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1245 @ SV2163 @ SV513 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1245 @ SV1815 @ SV513 )
= $true )
| ( ( class_Orderings_Opreorder @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6379]) ).
thf(6588,plain,
! [SV2325: $i,SV2164: $i,SV1816: $i,SV514: $i,SV1246: $i] :
( ( ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2164 ) @ SV514 )
= $true )
| ( ( ~ ( c_lessequals @ SV2325 @ SV2164 @ SV514 )
| ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2325 ) @ SV514 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6380]) ).
thf(6589,plain,
! [SV1247: $i,SV1817: $i,SV2165: $i,SV515: $i] :
( ( ( c_Type_Otyping @ SV515 @ SV2165 @ SV1817 )
= $false )
| ( ( c_Lambda_Obeta @ SV2165 @ SV1247 )
= $false )
| ( ( c_Type_Otyping @ SV515 @ SV1247 @ SV1817 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6381]) ).
thf(6590,plain,
! [SV533: $i,SV1824: $i,SV1263: $i] :
( ( ( c_lessequals @ SV1263 @ SV1824 @ SV533 )
= $false )
| ( ( SV1824 = SV1263 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1263 @ SV1824 @ SV533 )
= $true )
| ( ( class_Orderings_Oorder @ SV533 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6384]) ).
thf(6591,plain,
! [SV534: $i,SV1825: $i,SV1264: $i] :
( ( ( c_lessequals @ SV1264 @ SV1825 @ SV534 )
= $false )
| ( ( SV1825 = SV1264 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1825 @ SV534 )
= $true )
| ( ( class_Orderings_Oorder @ SV534 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6385]) ).
thf(6592,plain,
! [SV538: $i,SV1826: $i,SV1268: $i] :
( ( ( c_lessequals @ SV1268 @ SV1826 @ SV538 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1268 @ SV1826 @ SV538 )
= $true )
| ( ( SV1268 = SV1826 )
= $true )
| ( ( class_Orderings_Oorder @ SV538 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6386]) ).
thf(6593,plain,
! [SV539: $i,SV1827: $i,SV1269: $i] :
( ( ( c_lessequals @ SV1269 @ SV1827 @ SV539 )
= $false )
| ( ( SV1269 = SV1827 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1269 @ SV1827 @ SV539 )
= $true )
| ( ( class_Orderings_Oorder @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6387]) ).
thf(6594,plain,
! [SV540: $i,SV1828: $i,SV1270: $i] :
( ( ( c_lessequals @ SV1270 @ SV1828 @ SV540 )
= $false )
| ( ( SV1270 = SV1828 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1270 @ SV1828 @ SV540 )
= $true )
| ( ( class_Orderings_Oorder @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6388]) ).
thf(6595,plain,
! [SV541: $i,SV1829: $i,SV1271: $i] :
( ( ( c_lessequals @ SV1271 @ SV1829 @ SV541 )
= $false )
| ( ( SV1271 = SV1829 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1271 @ SV1829 @ SV541 )
= $true )
| ( ( class_Orderings_Oorder @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6389]) ).
thf(6596,plain,
! [SV542: $i,SV1830: $i,SV1272: $i] :
( ( ( c_lessequals @ SV1272 @ SV1830 @ SV542 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1272 @ SV1830 @ SV542 )
= $true )
| ( ( SV1272 = SV1830 )
= $true )
| ( ( class_Orderings_Olinorder @ SV542 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6390]) ).
thf(6597,plain,
! [SV543: $i,SV1831: $i,SV1273: $i] :
( ( ( c_lessequals @ SV1273 @ SV1831 @ SV543 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1273 @ SV1831 @ SV543 )
= $true )
| ( ( SV1273 = SV1831 )
= $true )
| ( ( class_Orderings_Olinorder @ SV543 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6391]) ).
thf(6598,plain,
! [SV553: $i,SV1282: $i,SV1837: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1837 @ SV1282 @ SV553 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1282 @ SV1837 @ SV553 )
= $false )
| ( ( class_Orderings_Oorder @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6392]) ).
thf(6599,plain,
! [SV554: $i,SV1283: $i,SV1838: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1838 @ SV1283 @ SV554 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1838 @ SV554 )
= $false )
| ( ( class_Orderings_Olinorder @ SV554 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6393]) ).
thf(6600,plain,
! [SV557: $i,SV1286: $i,SV1840: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1840 @ SV1286 @ SV557 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1286 @ SV1840 @ SV557 )
= $false )
| ( ( class_Orderings_Opreorder @ SV557 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6394]) ).
thf(6601,plain,
! [SV558: $i,SV1287: $i,SV1841: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1841 @ SV1287 @ SV558 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1287 @ SV1841 @ SV558 )
= $false )
| ( ( class_Orderings_Opreorder @ SV558 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6395]) ).
thf(6602,plain,
! [SV2484: $i,SV2428: $i,SV2329: $i,SV2174: $i,SV1843: $i,SV1293: $i,SV574: $i] :
( ( ( ( hAPP @ ( hAPP @ SV574 @ SV1293 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1843 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2174 @ SV2329 @ SV574 @ SV2428 @ SV1843 @ SV2484 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6396]) ).
thf(6603,plain,
! [SV2200: $i,SV1331: $i,SV2349: $i,SV1877: $i,SV612: $i] :
( ( ( c_Type_Otypings @ SV612 @ SV1877 @ SV2349 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV612 @ SV1331 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2349 @ SV2200 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1331 @ SV1877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6400]) ).
thf(6604,plain,
! [SV1333: $i,SV614: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV614 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV614 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6401]) ).
thf(6605,plain,
! [SV2434: $i,SV2352: $i,SV2204: $i,SV1882: $i,SV1339: $i,SV621: $i] :
( ( ( c_Type_Otyping @ SV621 @ SV1339 @ SV1882 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SV2204 @ SV1882 @ tc_Type_Otype ) @ SV2352 @ SV2434 )
| ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2352 ) @ SV1339 ) @ SV2204 ) @ SV2434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6404]) ).
thf(6606,plain,
! [SV1342: $i,SV2354: $i,SV2207: $i,SV2435: $i,SV1885: $i,SV625: $i] :
( ( ( ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SV1885 @ SV2435 @ tc_Type_Otype ) @ SV2207 @ SV2354 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV625 @ SV1342 @ SV2435 ) )
= $true )
| ( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1885 ) @ SV2207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2354 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6406]) ).
thf(6607,plain,
! [SV2213: $i,SV1893: $i,SV1354: $i,SV637: $i] :
( ( ( class_Int_Onumber__ring @ SV637 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV1893 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV2213 ) )
| ( SV1893 = SV2213 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6408]) ).
thf(6608,plain,
! [SV1361: $i,SV1897: $i,SV644: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
| ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6411]) ).
thf(6609,plain,
! [SV2215: $i,SV1898: $i,SV1363: $i,SV646: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV1898 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV646 ) @ SV1363 ) @ SV2215 ) )
= $false )
| ( ( SV1898 = SV2215 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV646 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6412]) ).
thf(6610,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV647 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6413]) ).
thf(6611,plain,
! [SV2360: $i,SV2218: $i,SV1903: $i,SV653: $i,SV1370: $i] :
( ( ( SV1370
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ SV2218 @ SV1903 ) @ SV2360 @ SV1903 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ ( c_Nat_Osize__class_Osize @ SV2218 @ ( tc_List_Olist @ SV1903 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Oappend @ SV653 @ SV1370 @ SV1903 )
= ( c_List_Oappend @ SV2218 @ SV2360 @ SV1903 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6414]) ).
thf(6612,plain,
! [SV2219: $i,SV1904: $i,SV1372: $i,SV655: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 )
= SV655 )
= $false )
| ( ( ( SV1904
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
| ( ( c_List_Oappend @ SV1904 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SV2219 @ SV1372 ) ) )
= $true )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= SV2219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6415]) ).
thf(6613,plain,
! [SV2220: $i,SV659: $i,SV1906: $i,SV1375: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
= $false )
| ( ( ( SV1375 = SV2220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV659 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6416]) ).
thf(6614,plain,
! [SV2486: $i,SV2439: $i,SV2361: $i,SV2221: $i,SV1907: $i,SV1376: $i,SV660: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
| ~ ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6417]) ).
thf(6615,plain,
! [SV2222: $i,SV665: $i,SV1911: $i,SV1381: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1381 @ SV1911 @ SV665 )
= ( c_Power_Opower__class_Opower @ SV1381 @ SV2222 @ SV665 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 )
| ( SV1911 = SV2222 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6418]) ).
thf(6616,plain,
! [SV668: $i,SV1914: $i,SV1384: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1384 @ SV1914 @ SV668 )
!= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
= $true )
| ( ( SV1384 = SV1914 )
= $true )
| ( ( class_Int_Onumber__ring @ SV668 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV668 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6419]) ).
thf(6617,plain,
! [SV2362: $i,SV1386: $i,SV670: $i,SV1916: $i,SV2223: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ SV670 @ SV1916 )
= SV2223 )
= $true )
| ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV670 @ ( tc_List_Olist @ SV1916 ) ) @ ( c_Nat_Osize__class_Osize @ SV2223 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_Oappend @ SV670 @ SV1386 @ SV1916 )
= ( c_List_Oappend @ SV2223 @ SV2362 @ SV1916 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6420]) ).
thf(6618,plain,
! [SV2519: $i,SV2487: $i,SV2440: $i,SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ! [SY6577: $i,SY6578: $i,SY6579: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SV2440 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SV2487 @ SV2519 @ SY6577 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SY6578 @ SV2519 @ SY6579 ) @ SV2440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6421]) ).
thf(6619,plain,
! [SV2520: $i,SV2488: $i,SV2441: $i,SV2364: $i,SV2226: $i,SV1922: $i,SV1393: $i,SV678: $i] :
( ( ! [SY6580: $i] :
( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SV2226 @ SV2364 )
!= ( c_Fun_Ocomp @ SV2441 @ SV2488 @ SV2520 @ SV2226 @ SV2364 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SY6580 ) )
= ( hAPP @ SV2441 @ ( hAPP @ SV2488 @ SY6580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6423]) ).
thf(6620,plain,
! [SV2230: $i,SV1929: $i,SV1403: $i,SV688: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV1929 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV688 ) @ SV1403 ) @ SV2230 ) )
= $false )
| ( ( SV1929 = SV2230 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV688 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6426]) ).
thf(6621,plain,
! [SV2369: $i,SV1409: $i,SV2233: $i,SV1934: $i,SV694: $i] :
( ( ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ SV2233 @ SV1934 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ ( c_Nat_Osize__class_Osize @ SV2233 @ ( tc_List_Olist @ SV1934 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Oappend @ SV694 @ SV1409 @ SV1934 )
= ( c_List_Oappend @ SV2233 @ SV2369 @ SV1934 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6429]) ).
thf(6622,plain,
! [SV2238: $i,SV1942: $i,SV704: $i,SV2371: $i,SV1419: $i] :
( ( ( SV1419 = SV2371 )
= $true )
| ( ( SV704
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Oreplicate @ SV704 @ SV1419 @ SV1942 )
= ( c_List_Oreplicate @ SV2238 @ SV2371 @ SV1942 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6432]) ).
thf(6623,plain,
! [SV1943: $i,SV706: $i,SV1420: $i] :
( ( ( ~ ( c_lessequals @ SV1420 @ SV706 @ tc_nat ) )
= $true )
| ( ( SV706 = SV1943 )
= $true )
| ( ( c_lessequals @ SV1420 @ SV1943 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SV1420 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1943 @ SV1420 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6433]) ).
thf(6624,plain,
! [SV2372: $i,SV2240: $i,SV712: $i,SV1948: $i,SV1425: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
!= ( c_HOL_Ominus__class_Ominus @ SV2240 @ SV2372 @ SV712 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2240 @ SV2372 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6435]) ).
thf(6625,plain,
! [SV1950: $i,SV714: $i,SV1427: $i] :
( ( ( SV1427
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SV1427 ) @ SV1950 ) )
= $true )
| ( ( SV1950
= ( c_HOL_Ozero__class_Ozero @ SV714 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV714 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV714 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6437]) ).
thf(6626,plain,
! [SV2246: $i,SV722: $i,SV1435: $i,SV1957: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1957 @ SV1435 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV722 @ SV2246 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV722 ) @ SV1435 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1957 ) @ SV2246 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6439]) ).
thf(6627,plain,
! [SV2374: $i,SV2249: $i,SV726: $i,SV1960: $i,SV1439: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
!= ( c_HOL_Ominus__class_Ominus @ SV2249 @ SV2374 @ SV726 ) )
= $true )
| ( ( ( c_lessequals @ SV2374 @ SV2249 @ SV726 )
| ~ ( c_lessequals @ SV1960 @ SV1439 @ SV726 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6440]) ).
thf(6628,plain,
! [SV2250: $i,SV1962: $i,SV728: $i,SV1441: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1441 @ SV1441 @ SV728 )
= ( c_HOL_Ominus__class_Ominus @ SV1962 @ SV2250 @ SV728 ) )
= $false )
| ( ( SV1962 = SV2250 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV728 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6441]) ).
thf(6629,plain,
! [SV1442: $i,SV729: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV729 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV729 )
| ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6442]) ).
thf(6630,plain,
! [SV1443: $i,SV1963: $i,SV730: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6443]) ).
thf(6631,plain,
! [SV2375: $i,SV2251: $i,SV1965: $i,SV1446: $i,SV734: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2251 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2375 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ SV2251 )
= SV2375 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6444]) ).
thf(6632,plain,
! [SV2253: $i,SV1970: $i,SV1452: $i,SV741: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ ( c_Nat_Osize__class_Osize @ SV1970 @ ( tc_List_Olist @ SV1452 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Oappend @ SV741 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) @ SV2253 @ SV1452 ) @ SV1452 )
= ( c_List_Oappend @ SV1970 @ SV2253 @ SV1452 ) )
= $true )
| ( ( SV741
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV741 @ ( tc_List_Olist @ SV1452 ) ) @ SV1970 @ SV1452 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6446]) ).
thf(6633,plain,
! [SV2377: $i,SV1458: $i,SV749: $i,SV1974: $i,SV2256: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ SV749 @ SV1974 ) @ SV1458 @ SV1974 )
= SV2377 )
= $true )
| ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV749 @ ( tc_List_Olist @ SV1974 ) ) @ ( c_Nat_Osize__class_Osize @ SV2256 @ ( tc_List_Olist @ SV1974 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_Oappend @ SV749 @ SV1458 @ SV1974 )
= ( c_List_Oappend @ SV2256 @ SV2377 @ SV1974 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6447]) ).
thf(6634,plain,
! [SV2489: $i,SV2442: $i,SV2378: $i,SV2257: $i,SV1975: $i,SV1459: $i,SV750: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
| ~ ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6448]) ).
thf(6635,plain,
! [SV2379: $i,SV2258: $i,SV755: $i,SV1979: $i,SV1464: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
!= ( c_HOL_Ominus__class_Ominus @ SV2258 @ SV2379 @ SV755 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SV2258 @ SV2379 @ SV755 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6449]) ).
thf(6636,plain,
! [SV2259: $i,SV757: $i,SV1981: $i,SV1466: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
= $false )
| ( ( ( SV1466 = SV2259 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6451]) ).
thf(6637,plain,
! [SV2380: $i,SV2262: $i,SV764: $i,SV1988: $i,SV1473: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
!= ( c_HOL_Ominus__class_Ominus @ SV2262 @ SV2380 @ SV764 ) )
= $true )
| ( ( ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
| ~ ( c_lessequals @ SV2380 @ SV2262 @ SV764 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6453]) ).
thf(6638,plain,
! [SV2263: $i,SV765: $i,SV1989: $i,SV1474: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1474 @ SV1989 @ SV765 )
= ( c_HOL_Ominus__class_Ominus @ SV2263 @ SV2263 @ SV765 ) )
= $false )
| ( ( SV1474 = SV1989 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV765 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6454]) ).
thf(6639,plain,
! [SV2265: $i,SV1992: $i,SV1479: $i,SV770: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV1479 ) @ SV1992 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV770 ) @ SV2265 ) @ SV1992 ) )
= $false )
| ( ( SV1479 = SV2265 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV770 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6456]) ).
thf(6640,plain,
! [SV1994: $i,SV1485: $i,SV11: $i,SV779: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
= $true )
| ( ( ~ ( c_lessequals @ SV779 @ SV1994 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6458]) ).
thf(6641,plain,
! [SV783: $i,SV15: $i,SV1996: $i,SV1488: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1488 @ SV1996 @ SV15 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV1996 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SV1488 @ SV15 ) @ SV1996 @ SV15 )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6459]) ).
thf(6642,plain,
! [SV799: $i,SV31: $i,SV1998: $i,SV1495: $i] :
( ( ( c_lessequals @ SV1495 @ SV1998 @ SV31 )
= $false )
| ( ( ~ ( c_lessequals @ SV799 @ SV1998 @ SV31 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SV1495 @ SV31 ) @ SV1998 @ SV31 )
= $true )
| ( ( class_Orderings_Olinorder @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6461]) ).
thf(6643,plain,
! [SV800: $i,SV32: $i,SV1999: $i,SV1496: $i] :
( ( ( c_lessequals @ SV1496 @ SV1999 @ SV32 )
= $false )
| ( ( ~ ( c_lessequals @ SV800 @ SV1999 @ SV32 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SV1496 @ SV32 ) @ SV1999 @ SV32 )
= $true )
| ( ( class_Orderings_Olinorder @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6462]) ).
thf(6644,plain,
! [SV801: $i,SV33: $i,SV2000: $i,SV1497: $i] :
( ( ( c_lessequals @ SV1497 @ SV2000 @ SV33 )
= $false )
| ( ( ~ ( c_lessequals @ SV801 @ SV2000 @ SV33 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SV1497 @ SV33 ) @ SV2000 @ SV33 )
= $true )
| ( ( class_Orderings_Olinorder @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6463]) ).
thf(6645,plain,
! [SV1502: $i,SV2001: $i,SV47: $i,SV815: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
| ~ ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6464]) ).
thf(6646,plain,
! [SV2002: $i,SV1504: $i,SV49: $i,SV817: $i] :
( ( ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
= $true )
| ( ( ~ ( c_lessequals @ SV817 @ SV2002 @ SV49 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6465]) ).
thf(6647,plain,
! [SV2003: $i,SV1505: $i,SV50: $i,SV818: $i] :
( ( ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
= $true )
| ( ( ~ ( c_lessequals @ SV818 @ SV1505 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6466]) ).
thf(6648,plain,
! [SV1511: $i,SV2004: $i,SV61: $i,SV829: $i] :
( ( ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
| ~ ( c_lessequals @ SV2004 @ SV1511 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6467]) ).
thf(6649,plain,
! [SV74: $i,SV1521: $i,SV2007: $i,SV841: $i] :
( ( ( c_lessequals @ SV841 @ ( c_Orderings_Oord__class_Omax @ SV2007 @ SV1521 @ SV74 ) @ SV74 )
= $false )
| ( ( c_lessequals @ SV841 @ SV2007 @ SV74 )
= $true )
| ( ( c_lessequals @ SV841 @ SV1521 @ SV74 )
= $true )
| ( ( class_Orderings_Olinorder @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6468]) ).
thf(6650,plain,
! [SV2011: $i,SV851: $i,SV84: $i,SV2267: $i,SV1531: $i] :
( ( ( ~ ( c_lessequals @ SV1531 @ SV2267 @ SV84 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV851 @ SV2011 @ SV84 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV2011 ) @ SV2267 ) @ SV84 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6470]) ).
thf(6651,plain,
! [SV1536: $i,SV860: $i,SV95: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV860 @ SV95 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1536 @ SV95 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV860 ) @ SV1536 ) @ SV95 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6471]) ).
thf(6652,plain,
! [SV1537: $i,SV861: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV861 @ SV96 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV861 @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV861 @ ( c_Suc @ SV1537 ) @ SV96 ) @ ( c_HOL_Oone__class_Oone @ SV96 ) @ SV96 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6472]) ).
thf(6653,plain,
! [SV862: $i,SV97: $i,SV1538: $i,SV2014: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2014 @ SV1538 @ SV97 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV862 @ SV2014 @ SV97 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV862 @ SV1538 @ SV97 )
= $true )
| ( ( class_Orderings_Opreorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6473]) ).
thf(6654,plain,
! [SV1539: $i,SV98: $i,SV2015: $i,SV863: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV2015 @ SV98 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2015 @ SV1539 @ SV98 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1539 @ SV98 )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6474]) ).
thf(6655,plain,
! [SV2028: $i,SV1572: $i,SV139: $i,SV904: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6478]) ).
thf(6656,plain,
! [SV2029: $i,SV1573: $i,SV905: $i,SV140: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 )
= $false )
| ( ( ~ ( c_lessequals @ SV1573 @ SV2029 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SV1573 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SV2029 @ SV140 ) @ SV140 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6479]) ).
thf(6657,plain,
! [SV1576: $i,SV143: $i,SV908: $i] :
( ( ( c_lessequals @ SV908 @ SV143 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV908 @ SV1576 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV143 @ SV1576 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV143 @ SV908 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV908 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6480]) ).
thf(6658,plain,
! [SV909: $i,SV144: $i,SV1577: $i] :
( ( ( c_lessequals @ SV1577 @ SV144 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1577 @ SV909 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV144 @ SV1577 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV909 @ SV1577 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV144 @ SV909 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6481]) ).
thf(6659,plain,
! [SV1579: $i,SV2030: $i,SV912: $i,SV147: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 )
= $false )
| ( ( ~ ( c_lessequals @ SV912 @ SV2030 @ SV147 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SV1579 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SV2030 @ SV1579 @ SV147 ) @ SV147 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6482]) ).
thf(6660,plain,
! [SV2521: $i,SV2490: $i,SV2443: $i,SV2383: $i,SV2270: $i,SV2038: $i,SV1590: $i,SV927: $i,SV165: $i] :
( ( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2038 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2270 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2038 ) @ SV2270 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2383 @ SV165 @ SV927 @ SV2443 @ SV2490 @ SV2521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6488]) ).
thf(6661,plain,
! [SV2042: $i,SV939: $i,SV1596: $i,SV178: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SV1596 @ SV178 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SV2042 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SV1596 @ SV2042 @ SV178 ) @ SV178 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV939 @ SV1596 @ SV178 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6489]) ).
thf(6662,plain,
! [SV191: $i,SV1609: $i,SV2051: $i,SV952: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV952 @ ( c_Orderings_Oord__class_Omax @ SV2051 @ SV1609 @ SV191 ) @ SV191 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV952 @ SV2051 @ SV191 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV952 @ SV1609 @ SV191 )
= $true )
| ( ( class_Orderings_Olinorder @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6498]) ).
thf(6663,plain,
! [SV1614: $i,SV199: $i,SV958: $i] :
( ( ( c_lessequals @ SV958 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1614 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV958 ) @ SV1614 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6499]) ).
thf(6664,plain,
! [SV1615: $i,SV200: $i,SV959: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV959 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
= $false )
| ( ( c_lessequals @ SV1615 @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV200 ) @ SV959 ) @ SV1615 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6500]) ).
thf(6665,plain,
! [SV1629: $i,SV983: $i,SV227: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV983 @ SV227 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV1629 @ SV227 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV227 ) @ SV983 ) @ SV1629 ) @ SV227 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6502]) ).
thf(6666,plain,
! [SV991: $i,SV2444: $i,SV2386: $i,SV2275: $i,SV236: $i,SV2057: $i,SV1633: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV2057 @ SV236 @ SV2275 @ SV2386 @ SV2444 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV236 @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV991 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6503]) ).
thf(6667,plain,
! [SV997: $i,SV242: $i,SV2276: $i,SV2058: $i,SV1637: $i] :
( ( ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV242 )
= $false )
| ( ( c_Type_Otyping @ SV1637 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2058 ) @ SV2276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV997 )
= $false )
| ( ( SV242 = SV997 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6504]) ).
thf(6668,plain,
! [SV1639: $i,SV999: $i,SV245: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ SV999 @ SV245 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1639 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV245 ) @ ( c_Power_Opower__class_Opower @ SV999 @ SV1639 @ SV245 ) @ SV245 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6506]) ).
thf(6669,plain,
! [SV1642: $i,SV250: $i,SV1004: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1004 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1642 @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV250 ) @ SV1004 ) @ SV1642 ) @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV250 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6507]) ).
thf(6670,plain,
! [SV2061: $i,SV1005: $i,SV251: $i,SV1643: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
| ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6508]) ).
thf(6671,plain,
! [SV1650: $i,SV1012: $i,SV258: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1012 @ SV258 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ SV1650 @ SV258 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV258 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV1012 ) @ SV1650 ) @ SV258 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6509]) ).
thf(6672,plain,
! [SV1651: $i,SV1013: $i,SV259: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1013 @ SV259 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV1651 @ SV259 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV1013 ) @ SV1651 ) @ SV259 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6510]) ).
thf(6673,plain,
! [SV2522: $i,SV2491: $i,SV2445: $i,SV2387: $i,SV2277: $i,SV2067: $i,SV1659: $i,SV1025: $i,SV271: $i] :
( ( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SV2067 ) ) @ SV2277 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SV2277 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SV2067 ) @ SV2277 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2387 @ SV1025 @ SV271 @ SV2445 @ SV2491 @ SV2522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6511]) ).
thf(6674,plain,
! [SV2523: $i,SV2492: $i,SV2446: $i,SV2388: $i,SV2278: $i,SV2068: $i,SV1660: $i,SV1026: $i,SV272: $i] :
( ( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SV2068 ) @ SV2278 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2068 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2278 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SV2388 @ SV2446 @ SV2492 @ SV2523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6512]) ).
thf(6675,plain,
! [SV2493: $i,SV2447: $i,SV2389: $i,SV2279: $i,SV2069: $i,SV1661: $i,SV1027: $i,SV273: $i] :
( ( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SV1661 )
= ( hAPP @ ( hAPP @ SV273 @ SV1661 ) @ SV1027 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2069 @ SV273 @ SV2279 @ SV2389 @ SV2447 @ SV2493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6513]) ).
thf(6676,plain,
! [SV2524: $i,SV2494: $i,SV2448: $i,SV2390: $i,SV2280: $i,SV2070: $i,SV1662: $i,SV1028: $i,SV274: $i] :
( ( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SV2070 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SV2070 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2280 @ SV274 @ SV2390 @ SV2448 @ SV2494 @ SV2524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6514]) ).
thf(6677,plain,
! [SV1663: $i,SV2449: $i,SV1029: $i,SV2391: $i,SV2281: $i,SV275: $i,SV2071: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2071 @ SV275 @ SV2281 @ SV2391 @ SV1029 @ SV2449 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV275 @ SV1029 ) @ SV1663 )
= SV1663 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6515]) ).
thf(6678,plain,
! [SV1664: $i,SV2450: $i,SV2392: $i,SV1030: $i,SV2282: $i,SV276: $i,SV2072: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2072 @ SV276 @ SV2282 @ SV1030 @ SV2392 @ SV2450 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV276 @ SV1030 ) @ SV1664 )
= SV1030 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6516]) ).
thf(6679,plain,
! [SV2495: $i,SV2451: $i,SV2393: $i,SV2283: $i,SV2073: $i,SV1665: $i,SV1031: $i,SV277: $i] :
( ( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SV1665 )
= ( hAPP @ ( hAPP @ SV277 @ SV1665 ) @ SV1031 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SV2073 @ SV2283 @ SV2393 @ SV2451 @ SV2495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6517]) ).
thf(6680,plain,
! [SV2525: $i,SV2496: $i,SV2452: $i,SV2394: $i,SV2284: $i,SV2074: $i,SV1666: $i,SV1032: $i,SV278: $i] :
( ( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SV2074 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SV2074 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SV2284 @ SV2394 @ SV2452 @ SV2496 @ SV2525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6518]) ).
thf(6681,plain,
! [SV1667: $i,SV2453: $i,SV2395: $i,SV1033: $i,SV2285: $i,SV2075: $i,SV279: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV279 @ SV2075 @ SV2285 @ SV1033 @ SV2395 @ SV2453 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV279 @ SV1033 ) @ SV1667 )
= SV1667 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6519]) ).
thf(6682,plain,
! [SV2526: $i,SV2497: $i,SV2454: $i,SV2396: $i,SV2286: $i,SV2076: $i,SV1668: $i,SV1034: $i,SV280: $i] :
( ( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SV2076 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SV2076 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SV2286 @ SV2396 @ SV2454 @ SV2497 @ SV2526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6520]) ).
thf(6683,plain,
! [SV2498: $i,SV2455: $i,SV2397: $i,SV2287: $i,SV2077: $i,SV1669: $i,SV1035: $i,SV281: $i] :
( ( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SV1669 )
= ( hAPP @ ( hAPP @ SV281 @ SV1669 ) @ SV1035 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SV2077 @ SV2287 @ SV2397 @ SV2455 @ SV2498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6521]) ).
thf(6684,plain,
! [SV2527: $i,SV2499: $i,SV2456: $i,SV2398: $i,SV2288: $i,SV2078: $i,SV1670: $i,SV1036: $i,SV282: $i] :
( ( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SV2078 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV2078 ) ) @ SV1670 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SV2288 @ SV2398 @ SV2456 @ SV2499 @ SV2527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6522]) ).
thf(6685,plain,
! [SV2528: $i,SV2500: $i,SV2457: $i,SV2399: $i,SV2289: $i,SV2079: $i,SV1671: $i,SV1037: $i,SV283: $i] :
( ( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SV2079 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SV2079 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SV2289 @ SV2399 @ SV2457 @ SV2500 @ SV2528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6523]) ).
thf(6686,plain,
! [SV2529: $i,SV2501: $i,SV2458: $i,SV2400: $i,SV2290: $i,SV2080: $i,SV1672: $i,SV1038: $i,SV284: $i] :
( ( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SV2080 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SV2080 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SV2290 @ SV2400 @ SV2458 @ SV2501 @ SV2529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6524]) ).
thf(6687,plain,
! [SV2530: $i,SV2502: $i,SV2459: $i,SV2401: $i,SV2291: $i,SV2081: $i,SV1673: $i,SV1039: $i,SV285: $i] :
( ( ! [SY6581: $i] :
( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SV2291 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SV2291 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SV2401 @ SV2459 @ SV2502 @ SV2530 @ SY6581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6525]) ).
thf(6688,plain,
! [SV2531: $i,SV2503: $i,SV2460: $i,SV2402: $i,SV2292: $i,SV2082: $i,SV1674: $i,SV1040: $i,SV286: $i] :
( ( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SV2082 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SV2082 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2292 @ SV286 @ SV2402 @ SV2460 @ SV2503 @ SV2531 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6526]) ).
thf(6689,plain,
! [SV2532: $i,SV2504: $i,SV2461: $i,SV2403: $i,SV2293: $i,SV2083: $i,SV1675: $i,SV1041: $i,SV287: $i] :
( ( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SV2083 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SV2083 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2293 @ SV287 @ SV2403 @ SV2461 @ SV2504 @ SV2532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6527]) ).
thf(6690,plain,
! [SV2533: $i,SV2505: $i,SV2462: $i,SV2404: $i,SV2294: $i,SV2084: $i,SV1676: $i,SV1042: $i,SV288: $i] :
( ( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SV2084 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SV2084 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2294 @ SV288 @ SV2404 @ SV2462 @ SV2505 @ SV2533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6528]) ).
thf(6691,plain,
! [SV2534: $i,SV2506: $i,SV2463: $i,SV2405: $i,SV2295: $i,SV2085: $i,SV1677: $i,SV1043: $i,SV289: $i] :
( ( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SV2085 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV2085 ) ) @ SV1677 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2295 @ SV289 @ SV2405 @ SV2463 @ SV2506 @ SV2534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6529]) ).
thf(6692,plain,
! [SV2535: $i,SV2507: $i,SV2464: $i,SV2406: $i,SV2296: $i,SV2086: $i,SV1678: $i,SV1044: $i,SV290: $i] :
( ( ! [SY6582: $i] :
( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SV2296 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SV2296 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2406 @ SV290 @ SV2464 @ SV2507 @ SV2535 @ SY6582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6530]) ).
thf(6693,plain,
! [SV2536: $i,SV2508: $i,SV2465: $i,SV2407: $i,SV2297: $i,SV2087: $i,SV1679: $i,SV1045: $i,SV291: $i] :
( ( ! [SY6583: $i] :
( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2407 @ SV291 @ SV2465 @ SV2508 @ SV2536 @ SY6583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6531]) ).
thf(6694,plain,
! [SV2537: $i,SV2509: $i,SV2466: $i,SV2408: $i,SV2298: $i,SV2088: $i,SV1680: $i,SV1046: $i,SV292: $i] :
( ( ! [SY6584: $i] :
( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SV2298 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SV2298 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2408 @ SV292 @ SV2466 @ SV2509 @ SV2537 @ SY6584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6532]) ).
thf(6695,plain,
! [SV1047: $i,SV2467: $i,SV1681: $i,SV2409: $i,SV2299: $i,SV293: $i,SV2089: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2089 @ SV293 @ SV2299 @ SV2409 @ SV1681 @ SV2467 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV293 @ SV1047 ) @ SV1681 )
= SV1047 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6533]) ).
thf(6696,plain,
! [SV1682: $i,SV2468: $i,SV1048: $i,SV2410: $i,SV2300: $i,SV294: $i,SV2090: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2090 @ SV294 @ SV2300 @ SV2410 @ SV1048 @ SV2468 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV294 @ SV1048 ) @ SV1682 )
= SV1682 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6534]) ).
thf(6697,plain,
! [SV1049: $i,SV2469: $i,SV2411: $i,SV1683: $i,SV2301: $i,SV295: $i,SV2091: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2091 @ SV295 @ SV2301 @ SV1683 @ SV2411 @ SV2469 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV295 @ SV1049 ) @ SV1683 )
= SV1683 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6535]) ).
thf(6698,plain,
! [SV1684: $i,SV2470: $i,SV2412: $i,SV1050: $i,SV2302: $i,SV296: $i,SV2092: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2092 @ SV296 @ SV2302 @ SV1050 @ SV2412 @ SV2470 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV296 @ SV1050 ) @ SV1684 )
= SV1050 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6536]) ).
thf(6699,plain,
! [SV2538: $i,SV2510: $i,SV2471: $i,SV2413: $i,SV2303: $i,SV2093: $i,SV1685: $i,SV1051: $i,SV297: $i] :
( ( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SV2093 ) ) @ SV2303 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SV2303 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SV2093 ) @ SV2303 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SV2413 @ SV2471 @ SV2510 @ SV2538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6537]) ).
thf(6700,plain,
! [SV2511: $i,SV2472: $i,SV2414: $i,SV2304: $i,SV2094: $i,SV1686: $i,SV1052: $i,SV298: $i] :
( ( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SV1686 )
= ( hAPP @ ( hAPP @ SV298 @ SV1686 ) @ SV1052 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2094 @ SV298 @ SV2304 @ SV2414 @ SV2472 @ SV2511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6538]) ).
thf(6701,plain,
! [SV1053: $i,SV2473: $i,SV2415: $i,SV1687: $i,SV2305: $i,SV2095: $i,SV299: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV299 @ SV2095 @ SV2305 @ SV1687 @ SV2415 @ SV2473 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV299 @ SV1053 ) @ SV1687 )
= SV1053 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6539]) ).
thf(6702,plain,
! [SV1688: $i,SV2474: $i,SV2416: $i,SV1054: $i,SV2306: $i,SV2096: $i,SV300: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV300 @ SV2096 @ SV2306 @ SV1054 @ SV2416 @ SV2474 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV300 @ SV1054 ) @ SV1688 )
= SV1688 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6540]) ).
thf(6703,plain,
! [SV1055: $i,SV2475: $i,SV2097: $i,SV2417: $i,SV2307: $i,SV1689: $i,SV301: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV301 @ SV1689 @ SV2307 @ SV2417 @ SV2097 @ SV2475 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV301 @ SV1055 ) @ SV1055 )
= ( hAPP @ ( hAPP @ SV1689 @ ( hAPP @ ( hAPP @ SV301 @ SV2097 ) @ SV2097 ) ) @ SV1055 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6541]) ).
thf(6704,plain,
! [SV2512: $i,SV2476: $i,SV2418: $i,SV2308: $i,SV2098: $i,SV1690: $i,SV1056: $i,SV302: $i] :
( ( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SV1690 @ SV2098 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SV1690 @ ( hAPP @ ( hAPP @ SV302 @ SV2098 ) @ SV2308 ) ) @ SV1056 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SV1690 @ SV2418 @ SV2476 @ SV2308 @ SV2512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6542]) ).
thf(6705,plain,
! [SV2513: $i,SV2477: $i,SV2419: $i,SV2309: $i,SV2099: $i,SV1691: $i,SV1057: $i,SV303: $i] :
( ( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SV1691 ) @ SV2099 ) ) @ SV2099 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SV1691 ) @ SV2309 ) ) @ SV2099 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SV2419 @ SV2477 @ SV2309 @ SV2513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6543]) ).
thf(6706,plain,
! [SV2539: $i,SV2514: $i,SV2478: $i,SV2420: $i,SV2310: $i,SV2100: $i,SV1692: $i,SV1058: $i,SV304: $i] :
( ( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SV2100 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SV2310 ) @ SV2100 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SV2310 ) ) @ SV2100 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SV2420 @ SV2478 @ SV2514 @ SV2539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6544]) ).
thf(6707,plain,
! [SV328: $i,SV1709: $i,SV1080: $i] :
( ( ( c_lessequals @ SV1080 @ SV1709 @ SV328 )
= $false )
| ( ( c_lessequals @ SV1709 @ SV1080 @ SV328 )
= $false )
| ( ( SV1080 = SV1709 )
= $true )
| ( ( class_Orderings_Oorder @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6545]) ).
thf(6708,plain,
! [SV330: $i,SV1711: $i,SV1082: $i] :
( ( ( c_lessequals @ SV1082 @ SV1711 @ SV330 )
= $false )
| ( ( c_lessequals @ SV1711 @ SV1082 @ SV330 )
= $false )
| ( ( SV1082 = SV1711 )
= $true )
| ( ( class_Orderings_Oorder @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6546]) ).
thf(6709,plain,
! [SV331: $i,SV1083: $i,SV1712: $i] :
( ( ( c_lessequals @ SV1712 @ SV1083 @ SV331 )
= $false )
| ( ( c_lessequals @ SV1083 @ SV1712 @ SV331 )
= $false )
| ( ( SV1083 = SV1712 )
= $true )
| ( ( class_Orderings_Oorder @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6547]) ).
thf(6710,plain,
! [SV2107: $i,SV1090: $i,SV340: $i,SV2313: $i,SV1718: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1718 @ SV2313 @ SV340 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SV2107 @ SV340 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV2107 ) @ SV2313 ) @ SV340 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6548]) ).
thf(6711,plain,
! [SV1722: $i,SV2109: $i,SV2314: $i,SV1097: $i,SV347: $i] :
( ( ( c_Type_Otyping @ SV347 @ SV1097 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2314 ) @ SV2109 ) )
= $false )
| ( ( c_Type_Otyping @ SV347 @ SV1722 @ SV2314 )
= $false )
| ( ( c_Type_Otyping @ SV347 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1097 ) @ SV1722 ) @ SV2109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6550]) ).
thf(6712,plain,
! [SV2515: $i,SV2479: $i,SV2421: $i,SV2316: $i,SV2119: $i,SV1742: $i,SV1121: $i,SV375: $i] :
( ( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ SV2119 ) )
= ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ ( c_Suc @ SV2119 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2316 @ SV375 @ SV1742 @ SV2421 @ SV2479 @ SV2515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6557]) ).
thf(6713,plain,
! [SV2516: $i,SV2480: $i,SV2422: $i,SV2317: $i,SV2120: $i,SV1743: $i,SV1122: $i,SV376: $i] :
( ( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ SV2120 ) ) @ SV1743 )
= ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ ( c_Suc @ SV2120 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2317 @ SV376 @ SV1122 @ SV2422 @ SV2480 @ SV2516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6558]) ).
thf(6714,plain,
! [SV2517: $i,SV2481: $i,SV2423: $i,SV2318: $i,SV2121: $i,SV1744: $i,SV1123: $i,SV377: $i] :
( ( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SV1744 ) )
= ( hAPP @ ( hAPP @ SV2121 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SV1744 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2318 @ SV2121 @ SV377 @ SV2423 @ SV2481 @ SV2517 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6559]) ).
thf(6715,plain,
! [SV2518: $i,SV2482: $i,SV2424: $i,SV2319: $i,SV2122: $i,SV1745: $i,SV1124: $i,SV378: $i] :
( ( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SV1745 ) )
= ( hAPP @ ( hAPP @ SV2122 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SV1745 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2319 @ SV2122 @ SV378 @ SV2424 @ SV2482 @ SV2518 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6560]) ).
thf(6716,plain,
! [SV2124: $i,SV1129: $i,SV1749: $i,SV383: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1749 @ SV383 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SV2124 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SV1749 @ ( c_Suc @ SV2124 ) @ SV383 ) @ SV383 ) )
= $true )
| ( ( c_lessequals @ SV1129 @ SV1749 @ SV383 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6561]) ).
thf(6717,plain,
! [SV1148: $i,SV403: $i,SV1760: $i] :
( ( ( c_lessequals @ SV1760 @ SV403 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1760 @ SV1148 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV1760 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1148 @ SV1760 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV403 @ SV1148 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6563]) ).
thf(6718,plain,
! [SV1761: $i,SV404: $i,SV1149: $i] :
( ( ( c_lessequals @ SV1149 @ SV404 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1149 @ SV1761 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV404 @ SV1761 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV404 @ SV1149 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1761 @ SV1149 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6564]) ).
thf(6719,plain,
! [SV1762: $i,SV405: $i,SV2129: $i,SV1150: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1150 @ SV2129 @ SV405 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1762 @ SV405 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1762 ) @ SV2129 ) @ SV405 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6565]) ).
thf(6720,plain,
! [SV1155: $i,SV410: $i,SV2130: $i,SV1765: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1765 @ SV2130 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SV1765 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SV2130 @ SV410 ) @ SV410 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6566]) ).
thf(6721,plain,
! [SV1766: $i,SV411: $i,SV1156: $i,SV2131: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1766 @ SV411 ) @ SV411 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SV2131 @ SV411 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1766 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6567]) ).
thf(6722,plain,
! [SV2132: $i,SV1767: $i,SV1157: $i,SV412: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1767 @ SV2132 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SV1767 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SV2132 @ SV412 ) @ SV412 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6568]) ).
thf(6723,plain,
! [SV1768: $i,SV413: $i,SV1158: $i,SV2133: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1768 @ SV413 ) @ SV413 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV2133 @ SV413 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1768 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6569]) ).
thf(6724,plain,
! [SV1786: $i,SV450: $i,SV1191: $i,SV2144: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1786 @ SV450 ) @ SV450 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SV2144 @ SV450 ) )
= $true )
| ( ( c_lessequals @ SV1191 @ SV1786 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV450 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6570]) ).
thf(6725,plain,
! [SV1787: $i,SV451: $i,SV1192: $i,SV2145: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1787 @ SV451 ) @ SV451 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SV2145 @ SV451 ) )
= $true )
| ( ( c_lessequals @ SV1192 @ SV1787 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6571]) ).
thf(6726,plain,
! [SV1193: $i,SV452: $i,SV2146: $i,SV1788: $i] :
( ( ( c_lessequals @ SV1788 @ SV2146 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SV1788 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SV2146 @ SV452 ) @ SV452 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV452 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6572]) ).
thf(6727,plain,
! [SV2149: $i,SV1197: $i,SV457: $i,SV2322: $i,SV1792: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1792 @ SV2322 @ SV457 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1197 @ SV2149 @ SV457 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV2149 ) @ SV2322 ) @ SV457 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6573]) ).
thf(6728,plain,
! [SV2150: $i,SV1198: $i,SV458: $i,SV2323: $i,SV1793: $i] :
( ( ( ~ ( c_lessequals @ SV1793 @ SV2323 @ SV458 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SV2150 @ SV458 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV2150 ) @ SV2323 ) @ SV458 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6574]) ).
thf(6729,plain,
! [SV1808: $i,SV502: $i,SV2158: $i,SV1236: $i] :
( ( ( c_lessequals @ SV1236 @ SV2158 @ SV502 )
= $false )
| ( ( ~ ( c_lessequals @ SV2158 @ SV1808 @ SV502 ) )
= $true )
| ( ( c_lessequals @ SV1236 @ SV1808 @ SV502 )
= $true )
| ( ( class_Orderings_Oorder @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6581]) ).
thf(6730,plain,
! [SV1809: $i,SV503: $i,SV2159: $i,SV1237: $i] :
( ( ( c_lessequals @ SV1237 @ SV2159 @ SV503 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2159 @ SV1809 @ SV503 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1237 @ SV1809 @ SV503 )
= $true )
| ( ( class_Orderings_Oorder @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6582]) ).
thf(6731,plain,
! [SV1810: $i,SV504: $i,SV2160: $i,SV1238: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1238 @ SV2160 @ SV504 )
= $false )
| ( ( ~ ( c_lessequals @ SV2160 @ SV1810 @ SV504 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1238 @ SV1810 @ SV504 )
= $true )
| ( ( class_Orderings_Oorder @ SV504 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6583]) ).
thf(6732,plain,
! [SV1811: $i,SV505: $i,SV1239: $i] :
( ( ( c_lessequals @ SV1239 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
= $false )
| ( ( c_lessequals @ SV1811 @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV505 ) @ SV1239 ) @ SV1811 ) @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV505 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV505 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6584]) ).
thf(6733,plain,
! [SV1240: $i,SV506: $i,SV1812: $i,SV2161: $i] :
( ( ( c_lessequals @ SV2161 @ SV1812 @ SV506 )
= $false )
| ( ( ~ ( c_lessequals @ SV1240 @ SV2161 @ SV506 ) )
= $true )
| ( ( c_lessequals @ SV1240 @ SV1812 @ SV506 )
= $true )
| ( ( class_Orderings_Opreorder @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6585]) ).
thf(6734,plain,
! [SV1244: $i,SV512: $i,SV1814: $i,SV2162: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2162 @ SV1814 @ SV512 )
= $false )
| ( ( ~ ( c_lessequals @ SV1244 @ SV2162 @ SV512 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1244 @ SV1814 @ SV512 )
= $true )
| ( ( class_Orderings_Opreorder @ SV512 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6586]) ).
thf(6735,plain,
! [SV1245: $i,SV513: $i,SV1815: $i,SV2163: $i] :
( ( ( c_lessequals @ SV2163 @ SV1815 @ SV513 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1245 @ SV2163 @ SV513 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1245 @ SV1815 @ SV513 )
= $true )
| ( ( class_Orderings_Opreorder @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6587]) ).
thf(6736,plain,
! [SV1816: $i,SV1246: $i,SV514: $i,SV2164: $i,SV2325: $i] :
( ( ( ~ ( c_lessequals @ SV2325 @ SV2164 @ SV514 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2325 ) @ SV514 ) )
= $true )
| ( ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2164 ) @ SV514 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6588]) ).
thf(6737,plain,
! [SV1293: $i,SV2484: $i,SV1843: $i,SV2428: $i,SV574: $i,SV2329: $i,SV2174: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2174 @ SV2329 @ SV574 @ SV2428 @ SV1843 @ SV2484 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV574 @ SV1293 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1843 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6602]) ).
thf(6738,plain,
! [SV1877: $i,SV2200: $i,SV2349: $i,SV1331: $i,SV612: $i] :
( ( ( c_Type_Otyping @ SV612 @ SV1331 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2349 @ SV2200 @ tc_Type_Otype @ tc_Type_Otype ) )
= $false )
| ( ( c_Type_Otypings @ SV612 @ SV1877 @ SV2349 )
= $false )
| ( ( c_Type_Otyping @ SV612 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1331 @ SV1877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6603]) ).
thf(6739,plain,
! [SV1333: $i,SV614: $i] :
( ( ( ~ ( class_Power_Opower @ SV614 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6604]) ).
thf(6740,plain,
! [SV1339: $i,SV2434: $i,SV2352: $i,SV1882: $i,SV2204: $i,SV621: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SV2204 @ SV1882 @ tc_Type_Otype ) @ SV2352 @ SV2434 ) )
= $true )
| ( ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2352 ) @ SV1339 ) @ SV2204 ) @ SV2434 )
= $true )
| ( ( c_Type_Otyping @ SV621 @ SV1339 @ SV1882 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6605]) ).
thf(6741,plain,
! [SV1342: $i,SV2354: $i,SV2207: $i,SV2435: $i,SV1885: $i,SV625: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SV1885 @ SV2435 @ tc_Type_Otype ) @ SV2207 @ SV2354 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV625 @ SV1342 @ SV2435 ) )
= $true )
| ( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1885 ) @ SV2207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2354 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6606]) ).
thf(6742,plain,
! [SV2213: $i,SV1893: $i,SV1354: $i,SV637: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV1893 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV2213 ) )
= $true )
| ( ( SV1893 = SV2213 )
= $true )
| ( ( class_Int_Onumber__ring @ SV637 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6607]) ).
thf(6743,plain,
! [SV1361: $i,SV1897: $i,SV644: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
| ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6608]) ).
thf(6744,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV647 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV647 )
| ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6610]) ).
thf(6745,plain,
! [SV2360: $i,SV1370: $i,SV2218: $i,SV1903: $i,SV653: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ ( c_Nat_Osize__class_Osize @ SV2218 @ ( tc_List_Olist @ SV1903 ) ) @ tc_nat )
= $false )
| ( ( SV1370
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV653 @ ( tc_List_Olist @ SV1903 ) ) @ SV2218 @ SV1903 ) @ SV2360 @ SV1903 ) )
= $true )
| ( ( ( c_List_Oappend @ SV653 @ SV1370 @ SV1903 )
= ( c_List_Oappend @ SV2218 @ SV2360 @ SV1903 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6611]) ).
thf(6746,plain,
! [SV2219: $i,SV655: $i,SV1372: $i,SV1904: $i] :
( ( ( SV1904
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
= $true )
| ( ( ( c_List_Oappend @ SV1904 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SV2219 @ SV1372 ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 )
= SV655 )
= $false )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= SV2219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6612]) ).
thf(6747,plain,
! [SV1906: $i,SV659: $i,SV2220: $i,SV1375: $i] :
( ( ( SV1375 = SV2220 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV659 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6613]) ).
thf(6748,plain,
! [SV2486: $i,SV2439: $i,SV2361: $i,SV2221: $i,SV1907: $i,SV1376: $i,SV660: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
| ~ ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6614]) ).
thf(6749,plain,
! [SV2222: $i,SV1911: $i,SV1381: $i,SV665: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 ) )
= $true )
| ( ( SV1911 = SV2222 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1381 @ SV1911 @ SV665 )
= ( c_Power_Opower__class_Opower @ SV1381 @ SV2222 @ SV665 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6615]) ).
thf(6750,plain,
! [SV668: $i,SV1914: $i,SV1384: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1384 @ SV1914 @ SV668 )
= ( c_HOL_Ozero__class_Ozero @ SV668 ) )
= $false )
| ( ( SV1384 = SV1914 )
= $true )
| ( ( class_Int_Onumber__ring @ SV668 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV668 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6616]) ).
thf(6751,plain,
! [SV2540: $i,SV2519: $i,SV2487: $i,SV2440: $i,SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ! [SY6585: $i,SY6586: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SV2440 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SV2487 @ SV2519 @ SV2540 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SY6585 @ SV2519 @ SY6586 ) @ SV2440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6618]) ).
thf(6752,plain,
! [SV2541: $i,SV2520: $i,SV2488: $i,SV2441: $i,SV2364: $i,SV2226: $i,SV1922: $i,SV1393: $i,SV678: $i] :
( ( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SV2226 @ SV2364 )
!= ( c_Fun_Ocomp @ SV2441 @ SV2488 @ SV2520 @ SV2226 @ SV2364 ) )
| ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SV2541 ) )
= ( hAPP @ SV2441 @ ( hAPP @ SV2488 @ SV2541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6619]) ).
thf(6753,plain,
! [SV2369: $i,SV1409: $i,SV2233: $i,SV1934: $i,SV694: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ ( c_Nat_Osize__class_Osize @ SV2233 @ ( tc_List_Olist @ SV1934 ) ) @ tc_nat )
= $false )
| ( ( SV694
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV694 @ ( tc_List_Olist @ SV1934 ) ) @ SV2233 @ SV1934 ) )
= $true )
| ( ( ( c_List_Oappend @ SV694 @ SV1409 @ SV1934 )
= ( c_List_Oappend @ SV2233 @ SV2369 @ SV1934 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6621]) ).
thf(6754,plain,
! [SV1943: $i,SV706: $i,SV1420: $i] :
( ( ( c_lessequals @ SV1420 @ SV706 @ tc_nat )
= $false )
| ( ( SV706 = SV1943 )
= $true )
| ( ( c_lessequals @ SV1420 @ SV1943 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV706 @ SV1420 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1943 @ SV1420 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6623]) ).
thf(6755,plain,
! [SV2372: $i,SV2240: $i,SV712: $i,SV1948: $i,SV1425: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
= ( c_HOL_Ominus__class_Ominus @ SV2240 @ SV2372 @ SV712 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV2240 @ SV2372 @ SV712 )
| ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6624]) ).
thf(6756,plain,
! [SV1950: $i,SV714: $i,SV1427: $i] :
( ( ( SV1427
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV714 ) @ SV1427 ) @ SV1950 ) )
= $false )
| ( ( SV1950
= ( c_HOL_Ozero__class_Ozero @ SV714 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV714 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV714 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6625]) ).
thf(6757,plain,
! [SV2374: $i,SV2249: $i,SV726: $i,SV1960: $i,SV1439: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
= ( c_HOL_Ominus__class_Ominus @ SV2249 @ SV2374 @ SV726 ) )
= $false )
| ( ( ( c_lessequals @ SV2374 @ SV2249 @ SV726 )
| ~ ( c_lessequals @ SV1960 @ SV1439 @ SV726 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6627]) ).
thf(6758,plain,
! [SV1442: $i,SV729: $i] :
( ( ( ~ ( class_Power_Opower @ SV729 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6629]) ).
thf(6759,plain,
! [SV1443: $i,SV1963: $i,SV730: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6630]) ).
thf(6760,plain,
! [SV2375: $i,SV2251: $i,SV1965: $i,SV1446: $i,SV734: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2251 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1965 ) @ SV2375 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV734 ) @ SV1446 ) @ SV2251 )
= SV2375 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6631]) ).
thf(6761,plain,
! [SV2489: $i,SV2442: $i,SV2378: $i,SV2257: $i,SV1975: $i,SV1459: $i,SV750: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
| ~ ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6634]) ).
thf(6762,plain,
! [SV2379: $i,SV2258: $i,SV755: $i,SV1979: $i,SV1464: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
= ( c_HOL_Ominus__class_Ominus @ SV2258 @ SV2379 @ SV755 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
| ~ ( c_HOL_Oord__class_Oless @ SV2258 @ SV2379 @ SV755 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6635]) ).
thf(6763,plain,
! [SV757: $i,SV1981: $i,SV2259: $i,SV1466: $i] :
( ( ( SV1466 = SV2259 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6636]) ).
thf(6764,plain,
! [SV2380: $i,SV2262: $i,SV764: $i,SV1988: $i,SV1473: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
= ( c_HOL_Ominus__class_Ominus @ SV2262 @ SV2380 @ SV764 ) )
= $false )
| ( ( ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
| ~ ( c_lessequals @ SV2380 @ SV2262 @ SV764 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6637]) ).
thf(6765,plain,
! [SV1485: $i,SV11: $i,SV1994: $i,SV779: $i] :
( ( ( ~ ( c_lessequals @ SV779 @ SV1994 @ SV11 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6640]) ).
thf(6766,plain,
! [SV1488: $i,SV15: $i,SV1996: $i,SV783: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV783 @ SV1996 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1488 @ SV1996 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV783 @ SV1488 @ SV15 ) @ SV1996 @ SV15 )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6641]) ).
thf(6767,plain,
! [SV1495: $i,SV31: $i,SV1998: $i,SV799: $i] :
( ( ( c_lessequals @ SV799 @ SV1998 @ SV31 )
= $false )
| ( ( c_lessequals @ SV1495 @ SV1998 @ SV31 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV799 @ SV1495 @ SV31 ) @ SV1998 @ SV31 )
= $true )
| ( ( class_Orderings_Olinorder @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6642]) ).
thf(6768,plain,
! [SV1496: $i,SV32: $i,SV1999: $i,SV800: $i] :
( ( ( c_lessequals @ SV800 @ SV1999 @ SV32 )
= $false )
| ( ( c_lessequals @ SV1496 @ SV1999 @ SV32 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV800 @ SV1496 @ SV32 ) @ SV1999 @ SV32 )
= $true )
| ( ( class_Orderings_Olinorder @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6643]) ).
thf(6769,plain,
! [SV1497: $i,SV33: $i,SV2000: $i,SV801: $i] :
( ( ( c_lessequals @ SV801 @ SV2000 @ SV33 )
= $false )
| ( ( c_lessequals @ SV1497 @ SV2000 @ SV33 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV801 @ SV1497 @ SV33 ) @ SV2000 @ SV33 )
= $true )
| ( ( class_Orderings_Olinorder @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6644]) ).
thf(6770,plain,
! [SV1502: $i,SV2001: $i,SV815: $i,SV47: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6645]) ).
thf(6771,plain,
! [SV1504: $i,SV49: $i,SV2002: $i,SV817: $i] :
( ( ( ~ ( c_lessequals @ SV817 @ SV2002 @ SV49 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) )
= $true )
| ( ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6646]) ).
thf(6772,plain,
! [SV2003: $i,SV50: $i,SV1505: $i,SV818: $i] :
( ( ( ~ ( c_lessequals @ SV818 @ SV1505 @ SV50 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 ) )
= $true )
| ( ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6647]) ).
thf(6773,plain,
! [SV1511: $i,SV2004: $i,SV829: $i,SV61: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2004 @ SV1511 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6648]) ).
thf(6774,plain,
! [SV2011: $i,SV851: $i,SV84: $i,SV2267: $i,SV1531: $i] :
( ( ( c_lessequals @ SV1531 @ SV2267 @ SV84 )
= $false )
| ( ( ~ ( c_lessequals @ SV851 @ SV2011 @ SV84 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV2011 ) @ SV2267 ) @ SV84 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6650]) ).
thf(6775,plain,
! [SV1538: $i,SV97: $i,SV2014: $i,SV862: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV862 @ SV2014 @ SV97 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2014 @ SV1538 @ SV97 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV862 @ SV1538 @ SV97 )
= $true )
| ( ( class_Orderings_Opreorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6653]) ).
thf(6776,plain,
! [SV863: $i,SV98: $i,SV1539: $i,SV2015: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2015 @ SV1539 @ SV98 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV2015 @ SV98 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1539 @ SV98 )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6654]) ).
thf(6777,plain,
! [SV1572: $i,SV139: $i,SV2028: $i,SV904: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6655]) ).
thf(6778,plain,
! [SV905: $i,SV140: $i,SV2029: $i,SV1573: $i] :
( ( ( c_lessequals @ SV1573 @ SV2029 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV140 ) @ SV905 @ SV140 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV905 @ SV1573 @ SV140 ) @ ( c_Power_Opower__class_Opower @ SV905 @ SV2029 @ SV140 ) @ SV140 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6656]) ).
thf(6779,plain,
! [SV1579: $i,SV147: $i,SV2030: $i,SV912: $i] :
( ( ( c_lessequals @ SV912 @ SV2030 @ SV147 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV912 @ SV147 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV912 @ SV1579 @ SV147 ) @ ( c_Power_Opower__class_Opower @ SV2030 @ SV1579 @ SV147 ) @ SV147 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6659]) ).
thf(6780,plain,
! [SV2521: $i,SV2490: $i,SV2443: $i,SV2383: $i,SV2270: $i,SV2038: $i,SV1590: $i,SV927: $i,SV165: $i] :
( ( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2038 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2270 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2038 ) @ SV2270 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2383 @ SV165 @ SV927 @ SV2443 @ SV2490 @ SV2521 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6660]) ).
thf(6781,plain,
! [SV1596: $i,SV178: $i,SV2042: $i,SV939: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV939 @ SV2042 @ SV178 ) @ ( c_Power_Opower__class_Opower @ SV1596 @ SV2042 @ SV178 ) @ SV178 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ SV1596 @ SV178 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV939 @ SV1596 @ SV178 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6661]) ).
thf(6782,plain,
! [SV1643: $i,SV2061: $i,SV1005: $i,SV251: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6670]) ).
thf(6783,plain,
! [SV2522: $i,SV2491: $i,SV2445: $i,SV2387: $i,SV2277: $i,SV2067: $i,SV1659: $i,SV1025: $i,SV271: $i] :
( ( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SV2067 ) ) @ SV2277 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SV2277 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SV2067 ) @ SV2277 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2387 @ SV1025 @ SV271 @ SV2445 @ SV2491 @ SV2522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6673]) ).
thf(6784,plain,
! [SV2523: $i,SV2492: $i,SV2446: $i,SV2388: $i,SV2278: $i,SV2068: $i,SV1660: $i,SV1026: $i,SV272: $i] :
( ( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SV2068 ) @ SV2278 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2068 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2278 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SV2388 @ SV2446 @ SV2492 @ SV2523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6674]) ).
thf(6785,plain,
! [SV1661: $i,SV1027: $i,SV2493: $i,SV2447: $i,SV2389: $i,SV2279: $i,SV273: $i,SV2069: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2069 @ SV273 @ SV2279 @ SV2389 @ SV2447 @ SV2493 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV273 @ SV1027 ) @ SV1661 )
= ( hAPP @ ( hAPP @ SV273 @ SV1661 ) @ SV1027 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6675]) ).
thf(6786,plain,
! [SV2524: $i,SV2494: $i,SV2448: $i,SV2390: $i,SV2280: $i,SV2070: $i,SV1662: $i,SV1028: $i,SV274: $i] :
( ( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SV2070 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SV2070 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2280 @ SV274 @ SV2390 @ SV2448 @ SV2494 @ SV2524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6676]) ).
thf(6787,plain,
! [SV1665: $i,SV1031: $i,SV2495: $i,SV2451: $i,SV2393: $i,SV2283: $i,SV2073: $i,SV277: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV277 @ SV2073 @ SV2283 @ SV2393 @ SV2451 @ SV2495 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV277 @ SV1031 ) @ SV1665 )
= ( hAPP @ ( hAPP @ SV277 @ SV1665 ) @ SV1031 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6679]) ).
thf(6788,plain,
! [SV2525: $i,SV2496: $i,SV2452: $i,SV2394: $i,SV2284: $i,SV2074: $i,SV1666: $i,SV1032: $i,SV278: $i] :
( ( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SV2074 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SV2074 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SV2284 @ SV2394 @ SV2452 @ SV2496 @ SV2525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6680]) ).
thf(6789,plain,
! [SV2526: $i,SV2497: $i,SV2454: $i,SV2396: $i,SV2286: $i,SV2076: $i,SV1668: $i,SV1034: $i,SV280: $i] :
( ( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SV2076 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SV2076 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SV2286 @ SV2396 @ SV2454 @ SV2497 @ SV2526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6682]) ).
thf(6790,plain,
! [SV1669: $i,SV1035: $i,SV2498: $i,SV2455: $i,SV2397: $i,SV2287: $i,SV2077: $i,SV281: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV281 @ SV2077 @ SV2287 @ SV2397 @ SV2455 @ SV2498 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV281 @ SV1035 ) @ SV1669 )
= ( hAPP @ ( hAPP @ SV281 @ SV1669 ) @ SV1035 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6683]) ).
thf(6791,plain,
! [SV2527: $i,SV2499: $i,SV2456: $i,SV2398: $i,SV2288: $i,SV2078: $i,SV1670: $i,SV1036: $i,SV282: $i] :
( ( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SV2078 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV2078 ) ) @ SV1670 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SV2288 @ SV2398 @ SV2456 @ SV2499 @ SV2527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6684]) ).
thf(6792,plain,
! [SV2528: $i,SV2500: $i,SV2457: $i,SV2399: $i,SV2289: $i,SV2079: $i,SV1671: $i,SV1037: $i,SV283: $i] :
( ( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SV2079 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SV2079 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SV2289 @ SV2399 @ SV2457 @ SV2500 @ SV2528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6685]) ).
thf(6793,plain,
! [SV2529: $i,SV2501: $i,SV2458: $i,SV2400: $i,SV2290: $i,SV2080: $i,SV1672: $i,SV1038: $i,SV284: $i] :
( ( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SV2080 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SV2080 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SV2290 @ SV2400 @ SV2458 @ SV2501 @ SV2529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6686]) ).
thf(6794,plain,
! [SV2542: $i,SV2530: $i,SV2502: $i,SV2459: $i,SV2401: $i,SV2291: $i,SV2081: $i,SV1673: $i,SV1039: $i,SV285: $i] :
( ( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SV2291 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SV2291 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SV2401 @ SV2459 @ SV2502 @ SV2530 @ SV2542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6687]) ).
thf(6795,plain,
! [SV2531: $i,SV2503: $i,SV2460: $i,SV2402: $i,SV2292: $i,SV2082: $i,SV1674: $i,SV1040: $i,SV286: $i] :
( ( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SV2082 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SV2082 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2292 @ SV286 @ SV2402 @ SV2460 @ SV2503 @ SV2531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6688]) ).
thf(6796,plain,
! [SV2532: $i,SV2504: $i,SV2461: $i,SV2403: $i,SV2293: $i,SV2083: $i,SV1675: $i,SV1041: $i,SV287: $i] :
( ( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SV2083 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SV2083 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2293 @ SV287 @ SV2403 @ SV2461 @ SV2504 @ SV2532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6689]) ).
thf(6797,plain,
! [SV2533: $i,SV2505: $i,SV2462: $i,SV2404: $i,SV2294: $i,SV2084: $i,SV1676: $i,SV1042: $i,SV288: $i] :
( ( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SV2084 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SV2084 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2294 @ SV288 @ SV2404 @ SV2462 @ SV2505 @ SV2533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6690]) ).
thf(6798,plain,
! [SV2534: $i,SV2506: $i,SV2463: $i,SV2405: $i,SV2295: $i,SV2085: $i,SV1677: $i,SV1043: $i,SV289: $i] :
( ( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SV2085 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV2085 ) ) @ SV1677 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2295 @ SV289 @ SV2405 @ SV2463 @ SV2506 @ SV2534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6691]) ).
thf(6799,plain,
! [SV2543: $i,SV2535: $i,SV2507: $i,SV2464: $i,SV2406: $i,SV2296: $i,SV2086: $i,SV1678: $i,SV1044: $i,SV290: $i] :
( ( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SV2296 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SV2296 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2406 @ SV290 @ SV2464 @ SV2507 @ SV2535 @ SV2543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6692]) ).
thf(6800,plain,
! [SV2544: $i,SV2536: $i,SV2508: $i,SV2465: $i,SV2407: $i,SV2297: $i,SV2087: $i,SV1679: $i,SV1045: $i,SV291: $i] :
( ( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2407 @ SV291 @ SV2465 @ SV2508 @ SV2536 @ SV2544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6693]) ).
thf(6801,plain,
! [SV2545: $i,SV2537: $i,SV2509: $i,SV2466: $i,SV2408: $i,SV2298: $i,SV2088: $i,SV1680: $i,SV1046: $i,SV292: $i] :
( ( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SV2298 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SV2298 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2408 @ SV292 @ SV2466 @ SV2509 @ SV2537 @ SV2545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6694]) ).
thf(6802,plain,
! [SV2538: $i,SV2510: $i,SV2471: $i,SV2413: $i,SV2303: $i,SV2093: $i,SV1685: $i,SV1051: $i,SV297: $i] :
( ( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SV2093 ) ) @ SV2303 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SV2303 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SV2093 ) @ SV2303 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SV2413 @ SV2471 @ SV2510 @ SV2538 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6699]) ).
thf(6803,plain,
! [SV1686: $i,SV1052: $i,SV2511: $i,SV2472: $i,SV2414: $i,SV2304: $i,SV298: $i,SV2094: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2094 @ SV298 @ SV2304 @ SV2414 @ SV2472 @ SV2511 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV298 @ SV1052 ) @ SV1686 )
= ( hAPP @ ( hAPP @ SV298 @ SV1686 ) @ SV1052 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6700]) ).
thf(6804,plain,
! [SV2098: $i,SV1056: $i,SV2512: $i,SV2308: $i,SV2476: $i,SV2418: $i,SV1690: $i,SV302: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV302 @ SV1690 @ SV2418 @ SV2476 @ SV2308 @ SV2512 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV302 @ SV1056 ) @ ( hAPP @ ( hAPP @ SV1690 @ SV2098 ) @ SV1056 ) )
= ( hAPP @ ( hAPP @ SV1690 @ ( hAPP @ ( hAPP @ SV302 @ SV2098 ) @ SV2308 ) ) @ SV1056 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6704]) ).
thf(6805,plain,
! [SV2099: $i,SV1691: $i,SV2513: $i,SV2309: $i,SV2477: $i,SV2419: $i,SV1057: $i,SV303: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV303 @ SV1057 @ SV2419 @ SV2477 @ SV2309 @ SV2513 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV303 @ ( hAPP @ ( hAPP @ SV1057 @ SV1691 ) @ SV2099 ) ) @ SV2099 )
= ( hAPP @ ( hAPP @ SV1057 @ ( hAPP @ ( hAPP @ SV303 @ SV1691 ) @ SV2309 ) ) @ SV2099 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6705]) ).
thf(6806,plain,
! [SV2539: $i,SV2514: $i,SV2478: $i,SV2420: $i,SV2310: $i,SV2100: $i,SV1692: $i,SV1058: $i,SV304: $i] :
( ( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SV2100 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SV2310 ) @ SV2100 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SV2310 ) ) @ SV2100 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SV2420 @ SV2478 @ SV2514 @ SV2539 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6706]) ).
thf(6807,plain,
! [SV2107: $i,SV1090: $i,SV340: $i,SV2313: $i,SV1718: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1718 @ SV2313 @ SV340 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1090 @ SV2107 @ SV340 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV2107 ) @ SV2313 ) @ SV340 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6710]) ).
thf(6808,plain,
! [SV2119: $i,SV1121: $i,SV2515: $i,SV2479: $i,SV2421: $i,SV1742: $i,SV375: $i,SV2316: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2316 @ SV375 @ SV1742 @ SV2421 @ SV2479 @ SV2515 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV1121 ) @ ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ SV2119 ) )
= ( hAPP @ ( hAPP @ SV1742 @ SV1121 ) @ ( c_Suc @ SV2119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6712]) ).
thf(6809,plain,
! [SV2120: $i,SV1743: $i,SV2516: $i,SV2480: $i,SV2422: $i,SV1122: $i,SV376: $i,SV2317: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2317 @ SV376 @ SV1122 @ SV2422 @ SV2480 @ SV2516 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ SV2120 ) ) @ SV1743 )
= ( hAPP @ ( hAPP @ SV1122 @ SV1743 ) @ ( c_Suc @ SV2120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6713]) ).
thf(6810,plain,
! [SV1744: $i,SV1123: $i,SV2517: $i,SV2481: $i,SV2423: $i,SV377: $i,SV2121: $i,SV2318: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2318 @ SV2121 @ SV377 @ SV2423 @ SV2481 @ SV2517 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ ( c_Suc @ SV1744 ) )
= ( hAPP @ ( hAPP @ SV2121 @ SV1123 ) @ ( hAPP @ ( hAPP @ SV377 @ SV1123 ) @ SV1744 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6714]) ).
thf(6811,plain,
! [SV1745: $i,SV1124: $i,SV2518: $i,SV2482: $i,SV2424: $i,SV378: $i,SV2122: $i,SV2319: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2319 @ SV2122 @ SV378 @ SV2424 @ SV2482 @ SV2518 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ ( c_Suc @ SV1745 ) )
= ( hAPP @ ( hAPP @ SV2122 @ SV1124 ) @ ( hAPP @ ( hAPP @ SV378 @ SV1124 ) @ SV1745 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6715]) ).
thf(6812,plain,
! [SV1749: $i,SV383: $i,SV2124: $i,SV1129: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1129 @ ( c_Suc @ SV2124 ) @ SV383 ) @ ( c_Power_Opower__class_Opower @ SV1749 @ ( c_Suc @ SV2124 ) @ SV383 ) @ SV383 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1749 @ SV383 )
= $false )
| ( ( c_lessequals @ SV1129 @ SV1749 @ SV383 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6716]) ).
thf(6813,plain,
! [SV2129: $i,SV1150: $i,SV1762: $i,SV405: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1762 @ SV405 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1150 @ SV2129 @ SV405 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1150 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1762 ) @ SV2129 ) @ SV405 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6719]) ).
thf(6814,plain,
! [SV2130: $i,SV1765: $i,SV1155: $i,SV410: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV410 ) @ SV1155 @ SV410 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1765 @ SV2130 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1155 @ SV1765 @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1155 @ SV2130 @ SV410 ) @ SV410 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6720]) ).
thf(6815,plain,
! [SV1766: $i,SV1156: $i,SV2131: $i,SV411: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV411 ) @ SV2131 @ SV411 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1156 @ SV411 ) @ ( c_Power_Opower__class_Opower @ SV2131 @ SV1766 @ SV411 ) @ SV411 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1766 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6721]) ).
thf(6816,plain,
! [SV1157: $i,SV412: $i,SV2132: $i,SV1767: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1767 @ SV2132 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV412 ) @ SV1157 @ SV412 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1157 @ SV1767 @ SV412 ) @ ( c_Power_Opower__class_Opower @ SV1157 @ SV2132 @ SV412 ) @ SV412 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6722]) ).
thf(6817,plain,
! [SV1768: $i,SV1158: $i,SV2133: $i,SV413: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV2133 @ SV413 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1158 @ SV413 ) @ ( c_Power_Opower__class_Opower @ SV2133 @ SV1768 @ SV413 ) @ SV413 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1768 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6723]) ).
thf(6818,plain,
! [SV1786: $i,SV1191: $i,SV2144: $i,SV450: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV450 ) @ SV2144 @ SV450 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1191 @ SV450 ) @ ( c_Power_Opower__class_Opower @ SV2144 @ SV1786 @ SV450 ) @ SV450 )
= $false )
| ( ( c_lessequals @ SV1191 @ SV1786 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV450 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6724]) ).
thf(6819,plain,
! [SV1787: $i,SV1192: $i,SV2145: $i,SV451: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV451 ) @ SV2145 @ SV451 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1192 @ SV451 ) @ ( c_Power_Opower__class_Opower @ SV2145 @ SV1787 @ SV451 ) @ SV451 )
= $false )
| ( ( c_lessequals @ SV1192 @ SV1787 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6725]) ).
thf(6820,plain,
! [SV2146: $i,SV1788: $i,SV1193: $i,SV452: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV452 ) @ SV1193 @ SV452 )
= $false )
| ( ( c_lessequals @ SV1788 @ SV2146 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1193 @ SV1788 @ SV452 ) @ ( c_Power_Opower__class_Opower @ SV1193 @ SV2146 @ SV452 ) @ SV452 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV452 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6726]) ).
thf(6821,plain,
! [SV2149: $i,SV1197: $i,SV457: $i,SV2322: $i,SV1792: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1792 @ SV2322 @ SV457 )
= $false )
| ( ( ~ ( c_lessequals @ SV1197 @ SV2149 @ SV457 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV2149 ) @ SV2322 ) @ SV457 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6727]) ).
thf(6822,plain,
! [SV2150: $i,SV1198: $i,SV458: $i,SV2323: $i,SV1793: $i] :
( ( ( c_lessequals @ SV1793 @ SV2323 @ SV458 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1198 @ SV2150 @ SV458 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV2150 ) @ SV2323 ) @ SV458 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6728]) ).
thf(6823,plain,
! [SV1236: $i,SV502: $i,SV1808: $i,SV2158: $i] :
( ( ( c_lessequals @ SV2158 @ SV1808 @ SV502 )
= $false )
| ( ( c_lessequals @ SV1236 @ SV2158 @ SV502 )
= $false )
| ( ( c_lessequals @ SV1236 @ SV1808 @ SV502 )
= $true )
| ( ( class_Orderings_Oorder @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6729]) ).
thf(6824,plain,
! [SV1237: $i,SV503: $i,SV1809: $i,SV2159: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2159 @ SV1809 @ SV503 )
= $false )
| ( ( c_lessequals @ SV1237 @ SV2159 @ SV503 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1237 @ SV1809 @ SV503 )
= $true )
| ( ( class_Orderings_Oorder @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6730]) ).
thf(6825,plain,
! [SV1238: $i,SV504: $i,SV1810: $i,SV2160: $i] :
( ( ( c_lessequals @ SV2160 @ SV1810 @ SV504 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1238 @ SV2160 @ SV504 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1238 @ SV1810 @ SV504 )
= $true )
| ( ( class_Orderings_Oorder @ SV504 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6731]) ).
thf(6826,plain,
! [SV1812: $i,SV506: $i,SV2161: $i,SV1240: $i] :
( ( ( c_lessequals @ SV1240 @ SV2161 @ SV506 )
= $false )
| ( ( c_lessequals @ SV2161 @ SV1812 @ SV506 )
= $false )
| ( ( c_lessequals @ SV1240 @ SV1812 @ SV506 )
= $true )
| ( ( class_Orderings_Opreorder @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6733]) ).
thf(6827,plain,
! [SV1814: $i,SV512: $i,SV2162: $i,SV1244: $i] :
( ( ( c_lessequals @ SV1244 @ SV2162 @ SV512 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2162 @ SV1814 @ SV512 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1244 @ SV1814 @ SV512 )
= $true )
| ( ( class_Orderings_Opreorder @ SV512 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6734]) ).
thf(6828,plain,
! [SV1815: $i,SV513: $i,SV2163: $i,SV1245: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1245 @ SV2163 @ SV513 )
= $false )
| ( ( c_lessequals @ SV2163 @ SV1815 @ SV513 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1245 @ SV1815 @ SV513 )
= $true )
| ( ( class_Orderings_Opreorder @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6735]) ).
thf(6829,plain,
! [SV1816: $i,SV1246: $i,SV514: $i,SV2164: $i,SV2325: $i] :
( ( ( c_lessequals @ SV2325 @ SV2164 @ SV514 )
= $false )
| ( ( ~ ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2325 ) @ SV514 ) )
= $true )
| ( ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2164 ) @ SV514 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6736]) ).
thf(6830,plain,
! [SV1333: $i,SV614: $i] :
( ( ( class_Power_Opower @ SV614 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
| ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6739]) ).
thf(6831,plain,
! [SV1339: $i,SV2434: $i,SV2352: $i,SV1882: $i,SV2204: $i,SV621: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV621 @ SV2204 @ SV1882 @ tc_Type_Otype ) @ SV2352 @ SV2434 )
= $false )
| ( ( c_Type_Otyping @ SV621 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV2352 ) @ SV1339 ) @ SV2204 ) @ SV2434 )
= $true )
| ( ( c_Type_Otyping @ SV621 @ SV1339 @ SV1882 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6740]) ).
thf(6832,plain,
! [SV2354: $i,SV2207: $i,SV1885: $i,SV2435: $i,SV1342: $i,SV625: $i] :
( ( ( c_Type_Otyping @ SV625 @ SV1342 @ SV2435 )
= $false )
| ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV625 @ SV1885 @ SV2435 @ tc_Type_Otype ) @ SV2207 @ SV2354 )
= $false )
| ( ( c_Type_Otypings @ SV625 @ ( c_List_Omap @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ c_Lambda_Osubst @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1342 ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1885 ) @ SV2207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2354 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6741]) ).
thf(6833,plain,
! [SV2213: $i,SV1893: $i,SV1354: $i,SV637: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV1893 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1354 ) @ SV2213 ) )
= $false )
| ( ( SV1893 = SV2213 )
= $true )
| ( ( class_Int_Onumber__ring @ SV637 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6742]) ).
thf(6834,plain,
! [SV1897: $i,SV1361: $i,SV644: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 ) )
= $true )
| ( ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6743]) ).
thf(6835,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ( ~ ( class_Power_Opower @ SV647 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6744]) ).
thf(6836,plain,
! [SV2219: $i,SV655: $i,SV1372: $i,SV1904: $i] :
( ( ( SV1904
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) )
= $false )
| ( ( ( c_List_Oappend @ SV1904 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= ( c_List_Oappend @ SV655 @ SV2219 @ SV1372 ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 )
= SV655 )
= $false )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1372 ) ) @ SV1904 @ SV1372 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1904 @ ( tc_List_Olist @ SV1372 ) ) @ SV655 @ SV1372 ) @ SV2219 @ SV1372 ) @ SV1372 )
= SV2219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6746]) ).
thf(6837,plain,
! [SV1906: $i,SV1375: $i,SV2220: $i,SV659: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) )
= $true )
| ( ( SV1375 = SV2220 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV659 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6747]) ).
thf(6838,plain,
! [SV660: $i,SV2486: $i,SV1376: $i,SV2439: $i,SV2361: $i,SV2221: $i,SV1907: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6748]) ).
thf(6839,plain,
! [SV2222: $i,SV1911: $i,SV1381: $i,SV665: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV665 ) @ SV1381 @ SV665 )
= $false )
| ( ( SV1911 = SV2222 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1381 @ SV1911 @ SV665 )
= ( c_Power_Opower__class_Opower @ SV1381 @ SV2222 @ SV665 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6749]) ).
thf(6840,plain,
! [SV2546: $i,SV2540: $i,SV2519: $i,SV2487: $i,SV2440: $i,SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ! [SY6587: $i] :
( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SV2440 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SV2487 @ SV2519 @ SV2540 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SV2546 @ SV2519 @ SY6587 ) @ SV2440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6751]) ).
thf(6841,plain,
! [SV2541: $i,SV2520: $i,SV2488: $i,SV2441: $i,SV2364: $i,SV2226: $i,SV1922: $i,SV1393: $i,SV678: $i] :
( ( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SV2226 @ SV2364 )
!= ( c_Fun_Ocomp @ SV2441 @ SV2488 @ SV2520 @ SV2226 @ SV2364 ) )
= $true )
| ( ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SV2541 ) )
= ( hAPP @ SV2441 @ ( hAPP @ SV2488 @ SV2541 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6752]) ).
thf(6842,plain,
! [SV1948: $i,SV1425: $i,SV712: $i,SV2372: $i,SV2240: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2240 @ SV2372 @ SV712 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
= ( c_HOL_Ominus__class_Ominus @ SV2240 @ SV2372 @ SV712 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6755]) ).
thf(6843,plain,
! [SV1439: $i,SV1960: $i,SV726: $i,SV2249: $i,SV2374: $i] :
( ( ( c_lessequals @ SV2374 @ SV2249 @ SV726 )
= $true )
| ( ( ~ ( c_lessequals @ SV1960 @ SV1439 @ SV726 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
= ( c_HOL_Ominus__class_Ominus @ SV2249 @ SV2374 @ SV726 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6757]) ).
thf(6844,plain,
! [SV1442: $i,SV729: $i] :
( ( ( class_Power_Opower @ SV729 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
!= ( c_HOL_Ozero__class_Ozero @ SV729 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6758]) ).
thf(6845,plain,
! [SV1963: $i,SV1443: $i,SV730: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 ) )
= $true )
| ( ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6759]) ).
thf(6846,plain,
! [SV1459: $i,SV2489: $i,SV750: $i,SV2442: $i,SV2378: $i,SV2257: $i,SV1975: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6761]) ).
thf(6847,plain,
! [SV2379: $i,SV2258: $i,SV755: $i,SV1979: $i,SV1464: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2258 @ SV2379 @ SV755 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
= ( c_HOL_Ominus__class_Ominus @ SV2258 @ SV2379 @ SV755 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6762]) ).
thf(6848,plain,
! [SV1466: $i,SV2259: $i,SV757: $i,SV1981: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true )
| ( ( SV1466 = SV2259 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6763]) ).
thf(6849,plain,
! [SV2262: $i,SV2380: $i,SV764: $i,SV1473: $i,SV1988: $i] :
( ( ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
= $true )
| ( ( ~ ( c_lessequals @ SV2380 @ SV2262 @ SV764 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
= ( c_HOL_Ominus__class_Ominus @ SV2262 @ SV2380 @ SV764 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6764]) ).
thf(6850,plain,
! [SV1485: $i,SV11: $i,SV1994: $i,SV779: $i] :
( ( ( c_lessequals @ SV779 @ SV1994 @ SV11 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6765]) ).
thf(6851,plain,
! [SV1502: $i,SV2001: $i,SV815: $i,SV47: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6770]) ).
thf(6852,plain,
! [SV1504: $i,SV49: $i,SV2002: $i,SV817: $i] :
( ( ( c_lessequals @ SV817 @ SV2002 @ SV49 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 ) )
= $true )
| ( ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6771]) ).
thf(6853,plain,
! [SV2003: $i,SV50: $i,SV1505: $i,SV818: $i] :
( ( ( c_lessequals @ SV818 @ SV1505 @ SV50 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 ) )
= $true )
| ( ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6772]) ).
thf(6854,plain,
! [SV1511: $i,SV2004: $i,SV829: $i,SV61: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
= $false )
| ( ( ~ ( c_lessequals @ SV2004 @ SV1511 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6773]) ).
thf(6855,plain,
! [SV2267: $i,SV1531: $i,SV84: $i,SV2011: $i,SV851: $i] :
( ( ( c_lessequals @ SV851 @ SV2011 @ SV84 )
= $false )
| ( ( c_lessequals @ SV1531 @ SV2267 @ SV84 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV851 ) @ SV1531 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV2011 ) @ SV2267 ) @ SV84 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6774]) ).
thf(6856,plain,
! [SV1572: $i,SV139: $i,SV2028: $i,SV904: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6777]) ).
thf(6857,plain,
! [SV2270: $i,SV2038: $i,SV1590: $i,SV2521: $i,SV2490: $i,SV2443: $i,SV927: $i,SV165: $i,SV2383: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2383 @ SV165 @ SV927 @ SV2443 @ SV2490 @ SV2521 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV165 @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2038 ) ) @ ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ SV2270 ) )
= ( hAPP @ ( hAPP @ SV927 @ SV1590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2038 ) @ SV2270 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6780]) ).
thf(6858,plain,
! [SV1643: $i,SV2061: $i,SV1005: $i,SV251: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6782]) ).
thf(6859,plain,
! [SV2277: $i,SV2067: $i,SV1659: $i,SV2522: $i,SV2491: $i,SV2445: $i,SV271: $i,SV1025: $i,SV2387: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2387 @ SV1025 @ SV271 @ SV2445 @ SV2491 @ SV2522 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV271 @ ( hAPP @ ( hAPP @ SV1025 @ SV1659 ) @ SV2067 ) ) @ SV2277 )
= ( hAPP @ ( hAPP @ SV1025 @ ( hAPP @ ( hAPP @ SV271 @ SV1659 ) @ SV2277 ) ) @ ( hAPP @ ( hAPP @ SV271 @ SV2067 ) @ SV2277 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6783]) ).
thf(6860,plain,
! [SV2278: $i,SV2068: $i,SV1026: $i,SV2523: $i,SV2492: $i,SV2446: $i,SV2388: $i,SV272: $i,SV1660: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1660 @ SV272 @ SV2388 @ SV2446 @ SV2492 @ SV2523 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ ( hAPP @ ( hAPP @ SV1660 @ SV2068 ) @ SV2278 ) )
= ( hAPP @ ( hAPP @ SV1660 @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2068 ) ) @ ( hAPP @ ( hAPP @ SV272 @ SV1026 ) @ SV2278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6784]) ).
thf(6861,plain,
! [SV2070: $i,SV1662: $i,SV1028: $i,SV2524: $i,SV2494: $i,SV2448: $i,SV2390: $i,SV274: $i,SV2280: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2280 @ SV274 @ SV2390 @ SV2448 @ SV2494 @ SV2524 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ ( hAPP @ ( hAPP @ SV274 @ SV1662 ) @ SV2070 ) )
= ( hAPP @ ( hAPP @ SV274 @ ( hAPP @ ( hAPP @ SV274 @ SV1028 ) @ SV1662 ) ) @ SV2070 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6786]) ).
thf(6862,plain,
! [SV2074: $i,SV1666: $i,SV1032: $i,SV2525: $i,SV2496: $i,SV2452: $i,SV2394: $i,SV2284: $i,SV278: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV278 @ SV2284 @ SV2394 @ SV2452 @ SV2496 @ SV2525 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ ( hAPP @ ( hAPP @ SV278 @ SV1666 ) @ SV2074 ) )
= ( hAPP @ ( hAPP @ SV278 @ ( hAPP @ ( hAPP @ SV278 @ SV1032 ) @ SV1666 ) ) @ SV2074 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6788]) ).
thf(6863,plain,
! [SV2076: $i,SV1668: $i,SV1034: $i,SV2526: $i,SV2497: $i,SV2454: $i,SV2396: $i,SV2286: $i,SV280: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV280 @ SV2286 @ SV2396 @ SV2454 @ SV2497 @ SV2526 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ ( hAPP @ ( hAPP @ SV280 @ SV1668 ) @ SV2076 ) )
= ( hAPP @ ( hAPP @ SV280 @ ( hAPP @ ( hAPP @ SV280 @ SV1034 ) @ SV1668 ) ) @ SV2076 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6789]) ).
thf(6864,plain,
! [SV2078: $i,SV1670: $i,SV1036: $i,SV2527: $i,SV2499: $i,SV2456: $i,SV2398: $i,SV2288: $i,SV282: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV282 @ SV2288 @ SV2398 @ SV2456 @ SV2499 @ SV2527 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV1670 ) ) @ SV2078 )
= ( hAPP @ ( hAPP @ SV282 @ ( hAPP @ ( hAPP @ SV282 @ SV1036 ) @ SV2078 ) ) @ SV1670 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6791]) ).
thf(6865,plain,
! [SV2079: $i,SV1671: $i,SV1037: $i,SV2528: $i,SV2500: $i,SV2457: $i,SV2399: $i,SV2289: $i,SV283: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV283 @ SV2289 @ SV2399 @ SV2457 @ SV2500 @ SV2528 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ SV2079 ) )
= ( hAPP @ ( hAPP @ SV283 @ SV1671 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1037 ) @ SV2079 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6792]) ).
thf(6866,plain,
! [SV2080: $i,SV1672: $i,SV1038: $i,SV2529: $i,SV2501: $i,SV2458: $i,SV2400: $i,SV2290: $i,SV284: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV284 @ SV2290 @ SV2400 @ SV2458 @ SV2501 @ SV2529 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV284 @ ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ SV1672 ) ) @ SV2080 )
= ( hAPP @ ( hAPP @ SV284 @ SV1038 ) @ ( hAPP @ ( hAPP @ SV284 @ SV1672 ) @ SV2080 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6793]) ).
thf(6867,plain,
! [SV2542: $i,SV2530: $i,SV2502: $i,SV2459: $i,SV2401: $i,SV2291: $i,SV2081: $i,SV1673: $i,SV1039: $i,SV285: $i] :
( ( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SV2291 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SV2291 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SV2401 @ SV2459 @ SV2502 @ SV2530 @ SV2542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6794]) ).
thf(6868,plain,
! [SV2082: $i,SV1674: $i,SV1040: $i,SV2531: $i,SV2503: $i,SV2460: $i,SV2402: $i,SV286: $i,SV2292: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2292 @ SV286 @ SV2402 @ SV2460 @ SV2503 @ SV2531 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ SV2082 ) )
= ( hAPP @ ( hAPP @ SV286 @ SV1674 ) @ ( hAPP @ ( hAPP @ SV286 @ SV1040 ) @ SV2082 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6795]) ).
thf(6869,plain,
! [SV2083: $i,SV1675: $i,SV1041: $i,SV2532: $i,SV2504: $i,SV2461: $i,SV2403: $i,SV287: $i,SV2293: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2293 @ SV287 @ SV2403 @ SV2461 @ SV2504 @ SV2532 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ ( hAPP @ ( hAPP @ SV287 @ SV1675 ) @ SV2083 ) )
= ( hAPP @ ( hAPP @ SV287 @ ( hAPP @ ( hAPP @ SV287 @ SV1041 ) @ SV1675 ) ) @ SV2083 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6796]) ).
thf(6870,plain,
! [SV2084: $i,SV1676: $i,SV1042: $i,SV2533: $i,SV2505: $i,SV2462: $i,SV2404: $i,SV288: $i,SV2294: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2294 @ SV288 @ SV2404 @ SV2462 @ SV2505 @ SV2533 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV288 @ ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ SV1676 ) ) @ SV2084 )
= ( hAPP @ ( hAPP @ SV288 @ SV1042 ) @ ( hAPP @ ( hAPP @ SV288 @ SV1676 ) @ SV2084 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6797]) ).
thf(6871,plain,
! [SV2085: $i,SV1677: $i,SV1043: $i,SV2534: $i,SV2506: $i,SV2463: $i,SV2405: $i,SV289: $i,SV2295: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2295 @ SV289 @ SV2405 @ SV2463 @ SV2506 @ SV2534 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV1677 ) ) @ SV2085 )
= ( hAPP @ ( hAPP @ SV289 @ ( hAPP @ ( hAPP @ SV289 @ SV1043 ) @ SV2085 ) ) @ SV1677 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6798]) ).
thf(6872,plain,
! [SV2543: $i,SV2535: $i,SV2507: $i,SV2464: $i,SV2406: $i,SV2296: $i,SV2086: $i,SV1678: $i,SV1044: $i,SV290: $i] :
( ( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SV2296 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SV2296 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2406 @ SV290 @ SV2464 @ SV2507 @ SV2535 @ SV2543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6799]) ).
thf(6873,plain,
! [SV2544: $i,SV2536: $i,SV2508: $i,SV2465: $i,SV2407: $i,SV2297: $i,SV2087: $i,SV1679: $i,SV1045: $i,SV291: $i] :
( ( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2407 @ SV291 @ SV2465 @ SV2508 @ SV2536 @ SV2544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6800]) ).
thf(6874,plain,
! [SV2545: $i,SV2537: $i,SV2509: $i,SV2466: $i,SV2408: $i,SV2298: $i,SV2088: $i,SV1680: $i,SV1046: $i,SV292: $i] :
( ( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SV2298 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SV2298 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2408 @ SV292 @ SV2466 @ SV2509 @ SV2537 @ SV2545 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6801]) ).
thf(6875,plain,
! [SV2303: $i,SV2093: $i,SV1685: $i,SV2538: $i,SV2510: $i,SV2471: $i,SV2413: $i,SV297: $i,SV1051: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1051 @ SV297 @ SV2413 @ SV2471 @ SV2510 @ SV2538 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV297 @ ( hAPP @ ( hAPP @ SV1051 @ SV1685 ) @ SV2093 ) ) @ SV2303 )
= ( hAPP @ ( hAPP @ SV1051 @ ( hAPP @ ( hAPP @ SV297 @ SV1685 ) @ SV2303 ) ) @ ( hAPP @ ( hAPP @ SV297 @ SV2093 ) @ SV2303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6802]) ).
thf(6876,plain,
! [SV2310: $i,SV2100: $i,SV1692: $i,SV2539: $i,SV2514: $i,SV2478: $i,SV2420: $i,SV1058: $i,SV304: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV304 @ SV1058 @ SV2420 @ SV2478 @ SV2514 @ SV2539 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV304 @ ( hAPP @ ( hAPP @ SV1058 @ SV1692 ) @ SV2100 ) ) @ ( hAPP @ ( hAPP @ SV1058 @ SV2310 ) @ SV2100 ) )
= ( hAPP @ ( hAPP @ SV1058 @ ( hAPP @ ( hAPP @ SV304 @ SV1692 ) @ SV2310 ) ) @ SV2100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6806]) ).
thf(6877,plain,
! [SV2313: $i,SV1718: $i,SV340: $i,SV2107: $i,SV1090: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1090 @ SV2107 @ SV340 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1718 @ SV2313 @ SV340 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV1090 ) @ SV1718 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV340 ) @ SV2107 ) @ SV2313 ) @ SV340 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6807]) ).
thf(6878,plain,
! [SV2322: $i,SV1792: $i,SV457: $i,SV2149: $i,SV1197: $i] :
( ( ( c_lessequals @ SV1197 @ SV2149 @ SV457 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1792 @ SV2322 @ SV457 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1197 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV2149 ) @ SV2322 ) @ SV457 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6821]) ).
thf(6879,plain,
! [SV2323: $i,SV1793: $i,SV458: $i,SV2150: $i,SV1198: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1198 @ SV2150 @ SV458 )
= $false )
| ( ( c_lessequals @ SV1793 @ SV2323 @ SV458 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV1198 ) @ SV1793 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV458 ) @ SV2150 ) @ SV2323 ) @ SV458 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6822]) ).
thf(6880,plain,
! [SV2164: $i,SV2325: $i,SV1816: $i,SV514: $i,SV1246: $i] :
( ( ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2325 ) @ SV514 )
= $false )
| ( ( c_lessequals @ SV2325 @ SV2164 @ SV514 )
= $false )
| ( ( c_lessequals @ SV1246 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1816 ) @ SV2164 ) @ SV514 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6829]) ).
thf(6881,plain,
! [SV1333: $i,SV614: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV614 ) @ SV1333 @ SV614 )
= ( c_HOL_Ozero__class_Ozero @ SV614 ) )
= $true )
| ( ( SV1333
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV614 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6830]) ).
thf(6882,plain,
! [SV1897: $i,SV1361: $i,SV644: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1361 @ SV644 )
= $false )
| ( ( SV1897
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV644 ) @ SV1897 @ SV644 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV644 ) @ SV1361 ) @ SV1897 )
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV644 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6834]) ).
thf(6883,plain,
! [SV1899: $i,SV1364: $i,SV647: $i] :
( ( ( class_Power_Opower @ SV647 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6835]) ).
thf(6884,plain,
! [SV1906: $i,SV1375: $i,SV2220: $i,SV659: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 ) )
= $true )
| ( ( SV1375 = SV2220 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV659 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6837]) ).
thf(6885,plain,
! [SV660: $i,SV2486: $i,SV1907: $i,SV2361: $i,SV1376: $i,SV2221: $i,SV2439: $i] :
( ( ( ~ ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6838]) ).
thf(6886,plain,
! [SV2547: $i,SV2546: $i,SV2540: $i,SV2519: $i,SV2487: $i,SV2440: $i,SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SV2440 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SV2487 @ SV2519 @ SV2540 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SV2546 @ SV2519 @ SV2547 ) @ SV2440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6840]) ).
thf(6887,plain,
! [SV2541: $i,SV2520: $i,SV2488: $i,SV2441: $i,SV2364: $i,SV2226: $i,SV1922: $i,SV1393: $i,SV678: $i] :
( ( ( ( c_Fun_Ocomp @ SV678 @ SV1393 @ SV1922 @ SV2226 @ SV2364 )
= ( c_Fun_Ocomp @ SV2441 @ SV2488 @ SV2520 @ SV2226 @ SV2364 ) )
= $false )
| ( ( ( hAPP @ SV678 @ ( hAPP @ SV1393 @ SV2541 ) )
= ( hAPP @ SV2441 @ ( hAPP @ SV2488 @ SV2541 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6841]) ).
thf(6888,plain,
! [SV2372: $i,SV2240: $i,SV712: $i,SV1948: $i,SV1425: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1425 @ SV1948 @ SV712 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2240 @ SV2372 @ SV712 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1425 @ SV1948 @ SV712 )
= ( c_HOL_Ominus__class_Ominus @ SV2240 @ SV2372 @ SV712 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV712 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6842]) ).
thf(6889,plain,
! [SV2249: $i,SV2374: $i,SV726: $i,SV1439: $i,SV1960: $i] :
( ( ( c_lessequals @ SV1960 @ SV1439 @ SV726 )
= $false )
| ( ( c_lessequals @ SV2374 @ SV2249 @ SV726 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1439 @ SV1960 @ SV726 )
= ( c_HOL_Ominus__class_Ominus @ SV2249 @ SV2374 @ SV726 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV726 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6843]) ).
thf(6890,plain,
! [SV729: $i,SV1442: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1442 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV729 )
= ( c_HOL_Ozero__class_Ozero @ SV729 ) )
= $false )
| ( ( class_Power_Opower @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV729 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV729 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6844]) ).
thf(6891,plain,
! [SV1963: $i,SV1443: $i,SV730: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1443 @ SV730 )
= $false )
| ( ( SV1443
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV730 ) @ SV1963 @ SV730 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV730 ) @ SV1443 ) @ SV1963 )
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV730 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6845]) ).
thf(6892,plain,
! [SV1459: $i,SV2489: $i,SV1975: $i,SV2378: $i,SV750: $i,SV2257: $i,SV2442: $i] :
( ( ( ~ ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6846]) ).
thf(6893,plain,
! [SV1979: $i,SV1464: $i,SV755: $i,SV2379: $i,SV2258: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2258 @ SV2379 @ SV755 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1464 @ SV1979 @ SV755 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1464 @ SV1979 @ SV755 )
= ( c_HOL_Ominus__class_Ominus @ SV2258 @ SV2379 @ SV755 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV755 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6847]) ).
thf(6894,plain,
! [SV1466: $i,SV2259: $i,SV757: $i,SV1981: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true )
| ( ( SV1466 = SV2259 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6848]) ).
thf(6895,plain,
! [SV1473: $i,SV1988: $i,SV764: $i,SV2262: $i,SV2380: $i] :
( ( ( c_lessequals @ SV2380 @ SV2262 @ SV764 )
= $false )
| ( ( c_lessequals @ SV1988 @ SV1473 @ SV764 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1473 @ SV1988 @ SV764 )
= ( c_HOL_Ominus__class_Ominus @ SV2262 @ SV2380 @ SV764 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV764 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6849]) ).
thf(6896,plain,
! [SV1994: $i,SV779: $i,SV1485: $i,SV11: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ SV1485 @ SV11 )
= $false )
| ( ( c_lessequals @ SV779 @ SV1994 @ SV11 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV779 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV11 ) @ SV1485 ) @ SV1994 ) @ SV11 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV11 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6850]) ).
thf(6897,plain,
! [SV815: $i,SV47: $i,SV1502: $i,SV2001: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2001 @ SV1502 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV47 ) @ SV815 @ SV47 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV815 @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV47 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV815 @ SV1502 @ SV47 ) @ ( c_Power_Opower__class_Opower @ SV815 @ SV2001 @ SV47 ) @ SV47 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6851]) ).
thf(6898,plain,
! [SV2002: $i,SV817: $i,SV1504: $i,SV49: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV1504 @ SV49 )
= $false )
| ( ( c_lessequals @ SV817 @ SV2002 @ SV49 )
= $false )
| ( ( c_lessequals @ SV817 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1504 ) @ SV2002 ) @ SV49 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV49 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6852]) ).
thf(6899,plain,
! [SV1505: $i,SV818: $i,SV2003: $i,SV50: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV2003 @ SV50 )
= $false )
| ( ( c_lessequals @ SV818 @ SV1505 @ SV50 )
= $false )
| ( ( c_lessequals @ SV818 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV1505 ) @ SV2003 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6853]) ).
thf(6900,plain,
! [SV829: $i,SV61: $i,SV1511: $i,SV2004: $i] :
( ( ( c_lessequals @ SV2004 @ SV1511 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV829 @ SV61 )
= $false )
| ( ( c_lessequals @ SV829 @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV829 @ SV1511 @ SV61 ) @ ( c_Power_Opower__class_Opower @ SV829 @ SV2004 @ SV61 ) @ SV61 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6854]) ).
thf(6901,plain,
! [SV2028: $i,SV904: $i,SV1572: $i,SV139: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV1572 @ SV139 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV904 @ SV2028 @ SV139 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV904 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1572 ) @ SV2028 ) @ SV139 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV139 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6856]) ).
thf(6902,plain,
! [SV1643: $i,SV251: $i,SV2061: $i,SV1005: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1005 @ SV2061 @ SV251 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV251 ) @ SV1005 @ SV251 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1643 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1005 @ SV1643 @ SV251 ) @ ( c_Power_Opower__class_Opower @ SV2061 @ SV1643 @ SV251 ) @ SV251 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6858]) ).
thf(6903,plain,
! [SV2291: $i,SV2081: $i,SV1673: $i,SV1039: $i,SV2542: $i,SV2530: $i,SV2502: $i,SV2459: $i,SV2401: $i,SV285: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV285 @ SV2401 @ SV2459 @ SV2502 @ SV2530 @ SV2542 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV1673 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV2081 ) @ SV2291 ) )
= ( hAPP @ ( hAPP @ SV285 @ ( hAPP @ ( hAPP @ SV285 @ SV1039 ) @ SV2081 ) ) @ ( hAPP @ ( hAPP @ SV285 @ SV1673 ) @ SV2291 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6867]) ).
thf(6904,plain,
! [SV2296: $i,SV2086: $i,SV1678: $i,SV1044: $i,SV2543: $i,SV2535: $i,SV2507: $i,SV2464: $i,SV290: $i,SV2406: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2406 @ SV290 @ SV2464 @ SV2507 @ SV2535 @ SV2543 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ SV2296 ) )
= ( hAPP @ ( hAPP @ SV290 @ SV2086 ) @ ( hAPP @ ( hAPP @ SV290 @ ( hAPP @ ( hAPP @ SV290 @ SV1044 ) @ SV1678 ) ) @ SV2296 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6872]) ).
thf(6905,plain,
! [SV2297: $i,SV2087: $i,SV1679: $i,SV1045: $i,SV2544: $i,SV2536: $i,SV2508: $i,SV2465: $i,SV291: $i,SV2407: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2407 @ SV291 @ SV2465 @ SV2508 @ SV2536 @ SV2544 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV291 @ ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ SV1679 ) ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) )
= ( hAPP @ ( hAPP @ SV291 @ SV1045 ) @ ( hAPP @ ( hAPP @ SV291 @ SV1679 ) @ ( hAPP @ ( hAPP @ SV291 @ SV2087 ) @ SV2297 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6873]) ).
thf(6906,plain,
! [SV2298: $i,SV2088: $i,SV1680: $i,SV1046: $i,SV2545: $i,SV2537: $i,SV2509: $i,SV2466: $i,SV292: $i,SV2408: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2408 @ SV292 @ SV2466 @ SV2509 @ SV2537 @ SV2545 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV1680 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV2088 ) @ SV2298 ) )
= ( hAPP @ ( hAPP @ SV292 @ ( hAPP @ ( hAPP @ SV292 @ SV1046 ) @ SV2088 ) ) @ ( hAPP @ ( hAPP @ SV292 @ SV1680 ) @ SV2298 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6874]) ).
thf(6907,plain,
! [SV647: $i,SV1899: $i,SV1364: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $true )
| ( ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $true )
| ( ( class_Power_Opower @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6883]) ).
thf(6908,plain,
! [SV1906: $i,SV2220: $i,SV1375: $i,SV659: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV1375 @ SV659 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV659 ) @ SV2220 @ SV659 )
= $false )
| ( ( SV1375 = SV2220 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1375 @ ( c_Suc @ SV1906 ) @ SV659 )
= ( c_Power_Opower__class_Opower @ SV2220 @ ( c_Suc @ SV1906 ) @ SV659 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV659 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6884]) ).
thf(6909,plain,
! [SV660: $i,SV2486: $i,SV1907: $i,SV2361: $i,SV1376: $i,SV2221: $i,SV2439: $i] :
( ( ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6885]) ).
thf(6910,plain,
! [SV2547: $i,SV2546: $i,SV2540: $i,SV2519: $i,SV2487: $i,SV2440: $i,SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
!= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SV2440 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SV2487 @ SV2519 @ SV2540 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SV2546 @ SV2519 @ SV2547 ) @ SV2440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6886]) ).
thf(6911,plain,
! [SV1459: $i,SV2489: $i,SV1975: $i,SV2378: $i,SV750: $i,SV2257: $i,SV2442: $i] :
( ( ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6892]) ).
thf(6912,plain,
! [SV1981: $i,SV1466: $i,SV2259: $i,SV757: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
= $false )
| ( ( SV1466 = SV2259 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6894]) ).
thf(6913,plain,
! [SV647: $i,SV1899: $i,SV1364: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1364 @ SV1899 @ SV647 )
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $false )
| ( ( SV1364
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $true )
| ( ( class_Power_Opower @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV647 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6907]) ).
thf(6914,plain,
! [SV660: $i,SV2486: $i,SV1907: $i,SV1376: $i,SV2361: $i,SV2439: $i,SV2221: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6909]) ).
thf(6915,plain,
! [SV2547: $i,SV2546: $i,SV2540: $i,SV2519: $i,SV2487: $i,SV2440: $i,SV2363: $i,SV2224: $i,SV1918: $i,SV1388: $i,SV673: $i] :
( ( ( ( hAPP @ SV673 @ ( hAPP @ SV1388 @ SV1918 ) )
= ( hAPP @ SV2224 @ ( hAPP @ SV2363 @ SV2440 ) ) )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV673 @ SV1388 @ SV2487 @ SV2519 @ SV2540 ) @ SV1918 )
= ( hAPP @ ( c_Fun_Ocomp @ SV2224 @ SV2363 @ SV2546 @ SV2519 @ SV2547 ) @ SV2440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6910]) ).
thf(6916,plain,
! [SV1459: $i,SV2489: $i,SV1975: $i,SV750: $i,SV2378: $i,SV2442: $i,SV2257: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6911]) ).
thf(6917,plain,
! [SV1981: $i,SV1466: $i,SV2259: $i,SV757: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
= $false )
| ( ( SV1466 = SV2259 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6912]) ).
thf(6918,plain,
! [SV660: $i,SV2486: $i,SV1907: $i,SV1376: $i,SV2361: $i,SV2439: $i,SV2221: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6914]) ).
thf(6919,plain,
! [SV1459: $i,SV2489: $i,SV1975: $i,SV750: $i,SV2378: $i,SV2442: $i,SV2257: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6916]) ).
thf(6920,plain,
! [SV1981: $i,SV2259: $i,SV1466: $i,SV757: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV1466 @ SV757 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV757 ) @ SV2259 @ SV757 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1981 @ tc_nat )
= $false )
| ( ( SV1466 = SV2259 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1466 @ SV1981 @ SV757 )
= ( c_Power_Opower__class_Opower @ SV2259 @ SV1981 @ SV757 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV757 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6917]) ).
thf(6921,plain,
! [SV660: $i,SV2221: $i,SV2486: $i,SV1907: $i,SV1376: $i,SV2361: $i,SV2439: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
= $false )
| ( ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6918]) ).
thf(6922,plain,
! [SV1459: $i,SV2257: $i,SV2489: $i,SV1975: $i,SV750: $i,SV2378: $i,SV2442: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
= $false )
| ( ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6919]) ).
thf(6923,plain,
! [SV660: $i,SV2221: $i,SV2486: $i,SV1907: $i,SV1376: $i,SV2361: $i,SV2439: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
= $false )
| ( ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6921]) ).
thf(6924,plain,
! [SV1459: $i,SV2257: $i,SV2489: $i,SV1975: $i,SV750: $i,SV2378: $i,SV2442: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
= $false )
| ( ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6922]) ).
thf(6925,plain,
! [SV660: $i,SV2221: $i,SV2486: $i,SV1376: $i,SV2361: $i,SV2439: $i,SV1907: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1907 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV2439 @ SV2361 @ SV1376 @ tc_Type_Otype ) @ SV1907 @ SV2486 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2221 ) )
= $false )
| ( ( c_Type_Otyping @ SV2439 @ SV2221 @ SV1376 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1907 ) @ SV2221 ) @ SV2361 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV660 ) @ SV1376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6923]) ).
thf(6926,plain,
! [SV1459: $i,SV2257: $i,SV2489: $i,SV750: $i,SV2378: $i,SV2442: $i,SV1975: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1975 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV2442 @ SV2378 @ SV750 @ tc_Type_Otype ) @ SV1975 @ SV2489 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV2257 ) )
= $false )
| ( ( c_Type_Otyping @ SV2442 @ SV2257 @ SV750 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1975 ) @ SV2257 ) @ SV2378 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV750 ) @ SV1459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6924]) ).
thf(6927,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1648,6926,6925,6920,6915,6913,6908,6906,6905,6904,6903,6902,6901,6900,6899,6898,6897,6896,6895,6893,6891,6890,6889,6888,6887,6882,6881,6880,6879,6878,6877,6876,6875,6871,6870,6869,6868,6866,6865,6864,6863,6862,6861,6860,6859,6857,6855,6839,6836,6833,6832,6831,6828,6827,6826,6825,6824,6823,6820,6819,6818,6817,6816,6815,6814,6813,6812,6811,6810,6809,6808,6805,6804,6803,6790,6787,6785,6781,6779,6778,6776,6775,6769,6768,6767,6766,6760,6756,6754,6753,6750,6745,6738,6737,6732,6718,6717,6711,6709,6708,6707,6703,6702,6701,6698,6697,6696,6695,6681,6678,6677,6672,6671,6669,6668,6667,6666,6665,6664,6663,6662,6658,6657,6652,6651,6649,6639,6638,6633,6632,6628,6626,6622,6620,6617,6609,6601,6600,6599,6598,6597,6596,6595,6594,6593,6592,6591,6590,6589,6580,6579,6578,6577,6576,6575,6562,6556,6555,6554,6553,6552,6551,6549,6505,6501,6497,6496,6495,6494,6493,6492,6491,6490,6487,6486,6485,6484,6483,6477,6476,6475,6469,6460,6457,6455,6452,6450,6445,6438,6436,6434,6431,6430,6428,6427,6425,6424,6422,6410,6409,6407,6405,6403,6402,6399,6398,6397,6383,6382,6377,6365,6352,6345,6338,6337,6336,6335,6334,6333,6331,6330,6327,6326,6325,6324,6321,6319,6318,6283,6280,6274,6273,6269,6268,6265,6263,6239,6238,6237,6232,6228,6220,6219,6217,6216,6213,6212,6211,6207,6204,6197,6189,6188,6185,6184,6179,6176,6175,6167,6164,6163,6153,6152,6149,6146,6143,6142,6140,6133,6130,6129,6126,6125,6124,6123,6121,6118,6107,6106,6086,6085,6084,6083,6077,6076,6075,6074,6073,6068,6067,6061,6060,6053,6040,6024,6023,5982,5978,5977,5955,5954,5953,5952,5951,5950,5949,5942,5935,5933,5930,5929,5928,5927,5926,5925,5924,5923,5922,5921,5920,5912,5909,5908,5905,5903,5893,5892,5890,5883,5882,5879,5873,5872,5870,5866,5865,5861,5858,5857,5856,5854,5850,5844,5841,5840,5839,5834,5832,5829,5826,5823,5821,5815,5813,5812,5811,5803,5801,5798,5797,5795,5792,5791,5782,5780,5771,5765,5760,5759,5758,5757,5755,5753,5752,5751,5749,5748,5747,5746,5744,5743,5740,5739,5733,5726,5725,5724,5721,5719,5718,5704,5703,5702,5695,5694,5692,5691,5684,5679,5678,5677,5673,5671,5670,5669,5662,5661,5657,5656,5653,5652,5648,5647,5640,5639,5638,5626,5610,5609,5608,5607,5606,5605,5604,5603,5564,5563,5562,5554,5545,5544,5542,5541,5540,5538,5537,5536,5533,5532,5531,5530,5529,5526,5522,5521,5512,5506,5492,5491,5488,5482,5478,5477,5476,5475,5474,5473,5472,5455,5451,5450,5449,5448,5444,5441,5440,5439,5437,5436,5435,5434,5433,5428,5427,5426,5425,5412,5398,5388,5384,5383,5382,5376,5372,5371,5363,5344,5343,5333,5332,5323,5322,5316,5313,5312,5310,5308,5304,5303,5302,5291,5284,5282,5275,5274,5273,5270,5268,5257,5256,5246,5244,5243,5236,5234,5219,5218,5217,5216,5215,5214,5201,5196,5195,5194,5193,5192,5184,5183,5162,5161,5160,5159,5158,5156,5155,5154,5153,5152,5151,5147,5146,5145,5144,5143,5139,5138,5132,5130,5129,5128,5124,5118,5117,5116,5115,5113,5101,5100,5095,5092,5091,5088,5087,5085,5082,5076,5075,5074,5052,5051,5050,5047,5042,5037,5036,5035,5034,4986,4985,4979,4977,4976,4967,4961,4958,4957,4951,4939,4938,4936,4916,4915,4904,4902,4894,4884,4882,4875,4858,4856,4855,4854,4842,4835,4828,4827,4826,4825,4818,4804,4801,4789,4775,4659,4653,4649,4647,4640,4629,4623,4617,4608,4605,4598,4576,4571,4539,4537,4536,4534,4524,4502,4499,4493,4488,4485,4481,4462,4452,4433,4417,4405,4404,4384,4380,4379,4378,4376,4339,4335,4331,4330,4329,4325,4323,4315,4306,4301,4300,4293,4289,4285,4248,4241,4240,4236,4235,4233,4225,4215,4211,4210,4203,4201,4192,4191,4179,4174,4171,4168,4159,4154,4139,4115,4112,4086,4081,4077,4048,4043,3996,3973,3955,3934,3909,3907,3906,3891,3872,3834,3833,3807,3798,3797,3784,3778,3773,3769,3756,3739,3669,3607,3606,3589,3588,3587,3586,3582,3576,3575,3573,3556,3524,3518,3514,3507,3455,3429,3409,3408,3407,3403,3402,3401,3400,3399,3391,3390,3389,3386,3385,3382,3375,3369,3230,3166,3165,3164,3163,3162,3160,3159,3157,3137,3113,3102,3100,3078,3077,3073,3035,3028,2950,2949,2940,2914,2789,2759,2749,2748,2654,2598,2597,2592,2451,2450,2449,2448,2447,2446,2445,2444,2443,2442,2441,2440,2439,2438,2437,2436,2435,2434,2433,2432,2431,2430,2429,2428,2424,2417,2415,2414,2412,2404,2399,2397,2396,2395,2373,2328,2324,2267,2208,1896,1841,1837,1792]) ).
thf(6928,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[6927]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL815-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 12:32:30 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 238.79/40.06 ......
% 238.79/40.06
% 238.79/40.06 No.of.Axioms: 817
% 238.79/40.06
% 238.79/40.06 Length.of.Defs: 0
% 238.79/40.06
% 238.79/40.06 Contains.Choice.Funs: false
% 238.79/40.06 .............................................................................................................................................................................................................................................................
% 238.79/40.06
% 238.79/40.06 ********************************
% 238.79/40.06 * All subproblems solved! *
% 238.79/40.06 ********************************
% 238.79/40.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:817,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:295,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6927,loop_count:0,foatp_calls:1,translation:fof_full)
% 238.79/40.06
% 238.79/40.06 %**** Beginning of derivation protocol ****
% 238.79/40.06 % SZS output start CNFRefutation
% See solution above
% 238.79/40.10
% 238.79/40.10 %**** End of derivation protocol ****
% 238.79/40.10 %**** no. of clauses in derivation: 6928 ****
% 238.79/40.10 %**** clause counter: 6927 ****
% 238.79/40.10
% 238.79/40.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:817,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:295,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6927,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------