%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL827-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 10:30:51 AM UTC 2026
% Result : Unsatisfiable 198.12s 33.26s
% Output : CNFRefutation 198.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 394
% Syntax : Number of formulae : 3014 (1996 unt; 0 typ; 0 def)
% Number of atoms : 14295 (5854 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 50191 (3188 ~;3869 |; 0 &;43134 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 99 ( 96 usr; 28 con; 0-5 aty)
% Number of variables : 8849 ( 0 ^;8849 !; 0 ?;8849 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_All,type,
c_All: $i > $i ).
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i ).
thf(tp_c_COMBS,type,
c_COMBS: $i > $i > $i > $i ).
thf(tp_c_Ex,type,
c_Ex: $i > $i ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
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 ).
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_OdB_OdB__size,type,
c_Lambda_OdB_OdB__size: $i > $i ).
thf(tp_c_Lambda_Olift,type,
c_Lambda_Olift: $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i ).
thf(tp_c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(tp_c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
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_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(tp_c_List_Omap,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(tp_c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tp_c_Predicate_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(tp_c_Type_Oshift,type,
c_Type_Oshift: $i > $i ).
thf(tp_c_Type_Osko__Type__Xabs__typeE__1__1,type,
c_Type_Osko__Type__Xabs__typeE__1__1: $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xabs__typeE__1__2,type,
c_Type_Osko__Type__Xabs__typeE__1__2: $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xlist__app__typeD__1__1,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xlist__app__typeE__1__1,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__2__1,type,
c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__3__1,type,
c_Type_Osko__Type__Xtyping__elims__3__1: $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__3__2,type,
c_Type_Osko__Type__Xtyping__elims__3__2: $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xvar__app__typesE__1__1,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xvar__app__types__1__1,type,
c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
thf(tp_c_Type_Otype_Otype__size,type,
c_Type_Otype_Otype__size: $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i ).
thf(tp_c_Type_Otypings,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(tp_c_and,type,
c_and: $i ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_c_implies,type,
c_implies: $i ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_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_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__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_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_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_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_Type_Otype,type,
tc_Type_Otype: $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_T_H____,type,
v_T_H____: $i ).
thf(tp_v_T_Ha______,type,
v_T_Ha______: $i ).
thf(tp_v_T____,type,
v_T____: $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_ea______,type,
v_ea______: $i ).
thf(tp_v_i____,type,
v_i____: $i ).
thf(tp_v_ia______,type,
v_ia______: $i ).
thf(tp_v_n____,type,
v_n____: $i ).
thf(tp_v_rs____,type,
v_rs____: $i ).
thf(tp_v_sko__CHAINED__1,type,
v_sko__CHAINED__1: $i > $i > $i > $i > $i ).
thf(tp_v_sko__local__XCons__1__1,type,
v_sko__local__XCons__1__1: $i > $i > $i > $i > $i ).
thf(tp_v_sko__local__XCons__Xhyps__1__1,type,
v_sko__local__XCons__Xhyps__1__1: $i > $i > $i > $i > $i ).
thf(tp_v_thesis____,type,
v_thesis____: $o ).
thf(tp_v_u____,type,
v_u____: $i ).
thf(tp_v_ua______,type,
v_ua______: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(4,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(6,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(8,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(9,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(10,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(11,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(12,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(13,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(14,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(15,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(16,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(17,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(18,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(19,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(20,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(21,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(22,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(23,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(24,axiom,
! [V_u: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_u ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_u ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
thf(25,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__CHAINED__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
thf(26,axiom,
c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) ) ) @ v_as____ @ tc_Lambda_OdB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(27,axiom,
c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ c_Lambda_Osubst ) @ v_u____ ) ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(28,axiom,
! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e_H ) @ V_u ) @ V_U ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e_H ) @ V_i ) @ V_U ) ) @ V_t ) @ V_T ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e_H ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(29,axiom,
! [V_env: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( c_Lambda_OdB_OVar @ V_x ) ) @ ( hAPP @ V_env @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(30,axiom,
! [V_U: $i] :
( v_thesis____
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ V_U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
thf(31,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_T_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).
thf(32,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__local__XCons__Xhyps__1__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_Ohyps_I1_J_1) ).
thf(33,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_ea______ ) @ v_ua______ ) @ v_T____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
thf(34,axiom,
v_n____ != v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_False_0) ).
thf(35,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__local__XCons__1__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_1) ).
thf(36,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(37,axiom,
! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_env ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T ) ) @ V_t ) @ V_U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(38,axiom,
! [T_a: $i,V_e: $i,V_x: $i,V_T: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_x ) @ V_T ) @ V_x )
= V_T ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(39,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ V_T1 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_T1 ) ) @ V_t ) @ V_Ta ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(40,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ V_T2 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_T2 ) ) @ V_t ) @ V_Ta ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(41,axiom,
! [T_a: $i,V_e: $i,V_i: $i,V_T: $i,V_j: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_T ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(42,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t_H ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(43,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_e____ ) @ v_u____ ) @ v_T____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
thf(44,axiom,
! [V_u: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_u ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_u ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).
thf(45,axiom,
! [V_ua: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_ua ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_ua ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_ua ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_I_0) ).
thf(46,axiom,
! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_U ) ) @ ( c_Lambda_Olift @ V_t @ V_i ) ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(47,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(48,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(49,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(50,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(52,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(53,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(54,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(55,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(56,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(57,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(59,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(60,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(63,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(64,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(65,axiom,
! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(66,axiom,
! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_U ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ V_t ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ V_s ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
thf(67,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(68,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(69,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(70,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(71,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(72,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(73,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(74,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(75,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(76,axiom,
! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(77,axiom,
! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(78,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(79,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(80,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(81,axiom,
! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ 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/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(82,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(83,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(84,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(85,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(86,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(87,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(88,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(89,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(90,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(91,axiom,
! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(92,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(94,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(95,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(96,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(97,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(99,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(100,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(101,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(102,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(103,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(105,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(106,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(108,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(109,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(110,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(111,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) ) @ V_s ) @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(112,axiom,
! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(113,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(115,axiom,
! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(116,axiom,
! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(117,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(118,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_ea______ ) @ v_ia______ ) @ v_T____ ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_T_Ha______ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(120,axiom,
! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(121,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(122,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(123,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
thf(124,axiom,
! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(125,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 ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(126,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 ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(127,axiom,
! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(128,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_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(129,axiom,
! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(130,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(131,axiom,
! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(132,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(133,axiom,
! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
thf(134,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(135,axiom,
! [V_e: $i,V_t: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) ) ) @ V_t ) @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__typeE_0) ).
thf(136,axiom,
! [V_e: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) ) @ V_t ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).
thf(137,axiom,
! [T_a: $i,V_e: $i,V_i: $i,V_U: $i,V_T: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_U ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T ) ) @ ( c_Suc @ V_i ) ) @ V_U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).
thf(138,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(139,axiom,
! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(140,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(141,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_i: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
thf(142,axiom,
! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ V_e @ V_us @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).
thf(143,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t_H ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(144,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 ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(145,axiom,
! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
thf(146,axiom,
! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(147,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(148,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(149,axiom,
! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(150,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(151,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(152,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(153,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(154,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(155,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(156,axiom,
! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(157,axiom,
! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(158,axiom,
! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(159,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(160,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(161,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(163,axiom,
! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Suc @ V_k ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).
thf(164,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(165,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(166,axiom,
! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(167,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(168,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(169,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(170,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 ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).
thf(171,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(172,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(173,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(174,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(175,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(176,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(177,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(178,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(179,axiom,
! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(180,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(181,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(182,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_Suc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(184,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(185,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(186,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(187,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(188,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(189,axiom,
! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(190,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(191,axiom,
! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(192,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(193,axiom,
! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(194,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(195,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(196,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(197,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(198,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(199,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(200,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(201,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(202,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(203,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(204,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(205,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(206,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(207,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(210,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(211,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(212,axiom,
! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(213,axiom,
! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(214,axiom,
! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(215,axiom,
! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(216,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(217,axiom,
! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(218,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(219,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_Suc @ V_n ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(220,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ V_m ) ) @ V_n )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(221,axiom,
! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(222,axiom,
! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(223,axiom,
! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_m ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(224,axiom,
! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_i ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(225,axiom,
! [V_m: $i,V_x: $i] : ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_x ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(226,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(227,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(228,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(229,axiom,
! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(230,axiom,
! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(231,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(232,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(233,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(234,axiom,
! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(235,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(236,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(237,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(238,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(239,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(240,axiom,
! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(241,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(242,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(243,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(244,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(245,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(246,axiom,
! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(247,axiom,
! [V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ V_dB1 ) ) @ ( c_Lambda_OdB_OdB__size @ V_dB2 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).
thf(248,axiom,
! [V_dB1: $i,V_dB2: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_dB1 @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ V_dB2 @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).
thf(249,axiom,
! [V_dB: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ V_dB ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ V_dB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).
thf(250,axiom,
! [V_dB: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ V_dB ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_dB @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).
thf(251,axiom,
! [V_n: $i] :
( ( V_n
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
thf(252,axiom,
! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
thf(254,axiom,
! [V_type1: $i,V_type2: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ tc_Type_Otype )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_type1 @ tc_Type_Otype ) ) @ ( c_Nat_Osize__class_Osize @ V_type2 @ tc_Type_Otype ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I4_J_0) ).
thf(255,axiom,
! [V_type1: $i,V_type2: $i] :
( ( c_Type_Otype_Otype__size @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Type_Otype_Otype__size @ V_type1 ) ) @ ( c_Type_Otype_Otype__size @ V_type2 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I2_J_0) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).
thf(258,axiom,
! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(259,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(260,axiom,
! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(261,axiom,
! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(262,axiom,
! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(263,axiom,
! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(264,axiom,
! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(265,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(266,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(267,axiom,
! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(268,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(269,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(270,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(271,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(272,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(273,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(274,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(275,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(276,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(277,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(278,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(279,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(280,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(281,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(282,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(283,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(284,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(285,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(286,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(287,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(288,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(289,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(290,axiom,
! [V_U: $i,V_T: $i,V_e: $i,V_us: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( V_U
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).
thf(291,axiom,
! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
thf(292,axiom,
! [V_i: $i,V_k: $i] :
( ( ( 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/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(293,axiom,
! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_i ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(294,axiom,
! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(295,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(296,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(297,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(298,axiom,
! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(299,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(300,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(301,axiom,
! [V_s: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(302,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(303,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(304,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(305,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(306,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(307,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(308,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(309,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(310,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(311,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(312,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(313,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(314,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(315,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(316,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(317,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(318,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(319,axiom,
! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(320,axiom,
! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(321,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(323,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(324,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(325,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(326,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(327,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(328,axiom,
! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(329,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(330,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(331,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(332,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(333,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(334,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(335,axiom,
! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(336,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(337,axiom,
! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(338,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(339,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(340,axiom,
! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(341,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(342,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(343,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(344,axiom,
! [T_a: $i,V_e: $i,V_i: $i,V_T: $i,V_j: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_T ) @ 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/sandbox/benchmark/theBenchmark.p',cls_shift__lt_0) ).
thf(345,axiom,
! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(346,axiom,
! [V_n: $i,V_i: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ V_i ) @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(347,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_b @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(348,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_n @ tc_nat )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(349,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_n @ tc_nat )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(350,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(351,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) @ ( c_Suc @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(352,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(353,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(354,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(355,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(356,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(357,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(358,axiom,
! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(359,axiom,
! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(360,axiom,
! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(361,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(362,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(363,axiom,
! [V_m: $i,V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_Suc @ V_m ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(364,axiom,
! [V_P: $i,V_b: $i,V_d: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_b ) @ V_d ) @ V_b @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
thf(365,axiom,
! [V_P: $i,V_b: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_b ) @ V_x ) @ V_b @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
thf(366,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) ) @ V_b )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(367,axiom,
! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(368,axiom,
! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(369,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(370,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(371,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(372,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(373,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(374,axiom,
! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ V_m @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(375,axiom,
! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(376,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(377,axiom,
! [V_j: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(378,axiom,
! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(379,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(380,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(381,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(382,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(383,axiom,
! [V_n: $i,V_m: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
= V_m )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(384,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(385,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(386,axiom,
! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
thf(387,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(388,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(389,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(390,axiom,
! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
thf(391,axiom,
! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
thf(392,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(393,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[392]) ).
thf(394,negated_conjecture,
! [V_x: $i] :
( v_thesis____
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(395,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(396,plain,
$false = $false,
inference(unfold_def,[status(thm)],[393]) ).
thf(397,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(398,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(399,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(400,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(401,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(402,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(403,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(404,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(405,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(406,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(407,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(408,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(409,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(410,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(411,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(412,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(413,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(414,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(415,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(416,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(417,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(418,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)],[22]) ).
thf(419,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)],[23]) ).
thf(420,plain,
( ( ! [V_u: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_u ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_u ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(421,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__CHAINED__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(422,plain,
( ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) ) ) @ v_as____ @ tc_Lambda_OdB )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(423,plain,
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ c_Lambda_Osubst ) @ v_u____ ) ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(424,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e_H ) @ V_u ) @ V_U ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e_H ) @ V_i ) @ V_U ) ) @ V_t ) @ V_T ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[28]) ).
thf(425,plain,
( ( ! [V_env: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( c_Lambda_OdB_OVar @ V_x ) ) @ ( hAPP @ V_env @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(426,plain,
( ( ! [V_U: $i] :
( v_thesis____
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ V_U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(427,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_T_H____ ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(428,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__local__XCons__Xhyps__1__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(429,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_ea______ ) @ v_ua______ ) @ v_T____ ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(430,plain,
( ( v_n____ != v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(431,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__local__XCons__1__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(432,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(433,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_env ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T ) ) @ V_t ) @ V_U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(434,plain,
( ( ! [T_a: $i,V_e: $i,V_x: $i,V_T: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_x ) @ V_T ) @ V_x )
= V_T ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(435,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ V_T1 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_T1 ) ) @ V_t ) @ V_Ta ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(436,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ V_T2 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_T2 ) ) @ V_t ) @ V_Ta ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(437,plain,
( ( ! [T_a: $i,V_e: $i,V_i: $i,V_T: $i,V_j: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_T ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(438,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t_H ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(439,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_e____ ) @ v_u____ ) @ v_T____ ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(440,plain,
( ( ! [V_u: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_u ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_u ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(441,plain,
( ( ! [V_ua: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_ua ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_ua ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_ua ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(442,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_U ) ) @ ( c_Lambda_Olift @ V_t @ V_i ) ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(443,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)],[47]) ).
thf(444,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)],[48]) ).
thf(445,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)],[49]) ).
thf(446,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)],[50]) ).
thf(447,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)],[51]) ).
thf(448,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)],[52]) ).
thf(449,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)],[53]) ).
thf(450,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)],[54]) ).
thf(451,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)],[55]) ).
thf(452,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)],[56]) ).
thf(453,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)],[57]) ).
thf(454,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)],[58]) ).
thf(455,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)],[59]) ).
thf(456,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)],[60]) ).
thf(457,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)],[61]) ).
thf(458,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)],[62]) ).
thf(459,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)],[63]) ).
thf(460,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)],[64]) ).
thf(461,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(462,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_U ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ V_t ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ V_s ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(463,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)],[67]) ).
thf(464,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)],[68]) ).
thf(465,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)],[69]) ).
thf(466,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)],[70]) ).
thf(467,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)],[71]) ).
thf(468,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)],[72]) ).
thf(469,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)],[73]) ).
thf(470,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)],[74]) ).
thf(471,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)],[75]) ).
thf(472,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[76]) ).
thf(473,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)],[77]) ).
thf(474,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)],[78]) ).
thf(475,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)],[79]) ).
thf(476,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)],[80]) ).
thf(477,plain,
( ( ! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ 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)],[81]) ).
thf(478,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)],[82]) ).
thf(479,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)],[83]) ).
thf(480,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)],[84]) ).
thf(481,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(482,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(483,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(484,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)],[88]) ).
thf(485,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)],[89]) ).
thf(486,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)],[90]) ).
thf(487,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)],[91]) ).
thf(488,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(489,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)],[93]) ).
thf(490,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)],[94]) ).
thf(491,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(492,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(493,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(494,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)],[98]) ).
thf(495,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(496,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)],[100]) ).
thf(497,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)],[101]) ).
thf(498,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)],[102]) ).
thf(499,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)],[103]) ).
thf(500,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)],[104]) ).
thf(501,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)],[105]) ).
thf(502,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)],[106]) ).
thf(503,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)],[107]) ).
thf(504,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(505,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(506,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(507,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) ) @ V_s ) @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(508,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(509,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(510,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)],[114]) ).
thf(511,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)],[115]) ).
thf(512,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(513,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)],[117]) ).
thf(514,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_ea______ ) @ v_ia______ ) @ v_T____ ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_T_Ha______ ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(515,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)],[119]) ).
thf(516,plain,
( ( ! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(517,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)],[121]) ).
thf(518,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)],[122]) ).
thf(519,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(520,plain,
( ( ! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(521,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 ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(522,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 ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(523,plain,
( ( ! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(524,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_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(525,plain,
( ( ! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(526,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(527,plain,
( ( ! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(528,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(529,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[133]) ).
thf(530,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(531,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) ) ) @ V_t ) @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(532,plain,
( ( ! [V_e: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) ) @ V_t ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(533,plain,
( ( ! [T_a: $i,V_e: $i,V_i: $i,V_U: $i,V_T: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_U ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T ) ) @ ( c_Suc @ V_i ) ) @ V_U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(534,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(535,plain,
( ( ! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[139]) ).
thf(536,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(537,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_i: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[141]) ).
thf(538,plain,
( ( ! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ V_e @ V_us @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(539,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t_H ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(540,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 ) @ ( 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)],[144]) ).
thf(541,plain,
( ( ! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(542,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(543,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)],[147]) ).
thf(544,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)],[148]) ).
thf(545,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)],[149]) ).
thf(546,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)],[150]) ).
thf(547,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)],[151]) ).
thf(548,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)],[152]) ).
thf(549,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)],[153]) ).
thf(550,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)],[154]) ).
thf(551,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)],[155]) ).
thf(552,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)],[156]) ).
thf(553,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)],[157]) ).
thf(554,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)],[158]) ).
thf(555,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)],[159]) ).
thf(556,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)],[160]) ).
thf(557,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(558,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)],[162]) ).
thf(559,plain,
( ( ! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Suc @ V_k ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( 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)],[163]) ).
thf(560,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)],[164]) ).
thf(561,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)],[165]) ).
thf(562,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)],[166]) ).
thf(563,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)],[167]) ).
thf(564,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)],[168]) ).
thf(565,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)],[169]) ).
thf(566,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 ) @ ( 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)],[170]) ).
thf(567,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)],[171]) ).
thf(568,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)],[172]) ).
thf(569,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)],[173]) ).
thf(570,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)],[174]) ).
thf(571,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)],[175]) ).
thf(572,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)],[176]) ).
thf(573,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)],[177]) ).
thf(574,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)],[178]) ).
thf(575,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)],[179]) ).
thf(576,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(577,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(578,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)],[182]) ).
thf(579,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)],[183]) ).
thf(580,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)],[184]) ).
thf(581,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)],[185]) ).
thf(582,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)],[186]) ).
thf(583,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)],[187]) ).
thf(584,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)],[188]) ).
thf(585,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)],[189]) ).
thf(586,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)],[190]) ).
thf(587,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(588,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(589,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(590,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(591,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)],[195]) ).
thf(592,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)],[196]) ).
thf(593,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)],[197]) ).
thf(594,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)],[198]) ).
thf(595,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)],[199]) ).
thf(596,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)],[200]) ).
thf(597,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)],[201]) ).
thf(598,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)],[202]) ).
thf(599,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)],[203]) ).
thf(600,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)],[204]) ).
thf(601,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)],[205]) ).
thf(602,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)],[206]) ).
thf(603,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)],[207]) ).
thf(604,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)],[208]) ).
thf(605,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)],[209]) ).
thf(606,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)],[210]) ).
thf(607,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)],[211]) ).
thf(608,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(609,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(610,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(611,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(612,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(613,plain,
( ( ! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(614,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(615,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)],[219]) ).
thf(616,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)],[220]) ).
thf(617,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(618,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(619,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)],[223]) ).
thf(620,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)],[224]) ).
thf(621,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)],[225]) ).
thf(622,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)],[226]) ).
thf(623,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)],[227]) ).
thf(624,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)],[228]) ).
thf(625,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)],[229]) ).
thf(626,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)],[230]) ).
thf(627,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)],[231]) ).
thf(628,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)],[232]) ).
thf(629,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)],[233]) ).
thf(630,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)],[234]) ).
thf(631,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)],[235]) ).
thf(632,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)],[236]) ).
thf(633,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)],[237]) ).
thf(634,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)],[238]) ).
thf(635,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)],[239]) ).
thf(636,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)],[240]) ).
thf(637,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)],[241]) ).
thf(638,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)],[242]) ).
thf(639,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)],[243]) ).
thf(640,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)],[244]) ).
thf(641,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)],[245]) ).
thf(642,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)],[246]) ).
thf(643,plain,
( ( ! [V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ V_dB1 ) ) @ ( c_Lambda_OdB_OdB__size @ V_dB2 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(644,plain,
( ( ! [V_dB1: $i,V_dB2: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_dB1 @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ V_dB2 @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(645,plain,
( ( ! [V_dB: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ V_dB ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ V_dB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(646,plain,
( ( ! [V_dB: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ V_dB ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_dB @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(647,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)],[251]) ).
thf(648,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)],[252]) ).
thf(649,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)],[253]) ).
thf(650,plain,
( ( ! [V_type1: $i,V_type2: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ tc_Type_Otype )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_type1 @ tc_Type_Otype ) ) @ ( c_Nat_Osize__class_Osize @ V_type2 @ tc_Type_Otype ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(651,plain,
( ( ! [V_type1: $i,V_type2: $i] :
( ( c_Type_Otype_Otype__size @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Type_Otype_Otype__size @ V_type1 ) ) @ ( c_Type_Otype_Otype__size @ V_type2 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(652,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)],[256]) ).
thf(653,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)],[257]) ).
thf(654,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(655,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(656,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(657,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(658,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(659,plain,
( ( ! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(660,plain,
( ( ! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(661,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(662,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(663,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)],[267]) ).
thf(664,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)],[268]) ).
thf(665,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)],[269]) ).
thf(666,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)],[270]) ).
thf(667,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)],[271]) ).
thf(668,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)],[272]) ).
thf(669,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)],[273]) ).
thf(670,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)],[274]) ).
thf(671,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)],[275]) ).
thf(672,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)],[276]) ).
thf(673,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)],[277]) ).
thf(674,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)],[278]) ).
thf(675,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)],[279]) ).
thf(676,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)],[280]) ).
thf(677,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)],[281]) ).
thf(678,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)],[282]) ).
thf(679,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)],[283]) ).
thf(680,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)],[284]) ).
thf(681,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)],[285]) ).
thf(682,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)],[286]) ).
thf(683,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)],[287]) ).
thf(684,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)],[288]) ).
thf(685,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)],[289]) ).
thf(686,plain,
( ( ! [V_U: $i,V_T: $i,V_e: $i,V_us: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( V_U
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(687,plain,
( ( ! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(688,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( 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)],[292]) ).
thf(689,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_i ) ) @ ( 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)],[293]) ).
thf(690,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( 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)],[294]) ).
thf(691,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(692,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(693,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(694,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(695,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(696,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(697,plain,
( ( ! [V_s: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(698,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)],[302]) ).
thf(699,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)],[303]) ).
thf(700,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)],[304]) ).
thf(701,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)],[305]) ).
thf(702,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)],[306]) ).
thf(703,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)],[307]) ).
thf(704,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)],[308]) ).
thf(705,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)],[309]) ).
thf(706,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)],[310]) ).
thf(707,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)],[311]) ).
thf(708,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)],[312]) ).
thf(709,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)],[313]) ).
thf(710,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)],[314]) ).
thf(711,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)],[315]) ).
thf(712,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)],[316]) ).
thf(713,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(714,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(715,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)],[319]) ).
thf(716,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)],[320]) ).
thf(717,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(718,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)],[322]) ).
thf(719,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)],[323]) ).
thf(720,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)],[324]) ).
thf(721,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(722,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(723,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(724,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(725,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)],[329]) ).
thf(726,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)],[330]) ).
thf(727,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)],[331]) ).
thf(728,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)],[332]) ).
thf(729,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)],[333]) ).
thf(730,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)],[334]) ).
thf(731,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(732,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)],[336]) ).
thf(733,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)],[337]) ).
thf(734,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)],[338]) ).
thf(735,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)],[339]) ).
thf(736,plain,
( ( ! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(737,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(738,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(739,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(740,plain,
( ( ! [T_a: $i,V_e: $i,V_i: $i,V_T: $i,V_j: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_T ) @ 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)],[344]) ).
thf(741,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)],[345]) ).
thf(742,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)],[346]) ).
thf(743,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)],[347]) ).
thf(744,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)],[348]) ).
thf(745,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)],[349]) ).
thf(746,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)],[350]) ).
thf(747,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)],[351]) ).
thf(748,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)],[352]) ).
thf(749,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)],[353]) ).
thf(750,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)],[354]) ).
thf(751,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)],[355]) ).
thf(752,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)],[356]) ).
thf(753,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)],[357]) ).
thf(754,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)],[358]) ).
thf(755,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)],[359]) ).
thf(756,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)],[360]) ).
thf(757,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)],[361]) ).
thf(758,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)],[362]) ).
thf(759,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)],[363]) ).
thf(760,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)],[364]) ).
thf(761,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)],[365]) ).
thf(762,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)],[366]) ).
thf(763,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)],[367]) ).
thf(764,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)],[368]) ).
thf(765,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)],[369]) ).
thf(766,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)],[370]) ).
thf(767,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)],[371]) ).
thf(768,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)],[372]) ).
thf(769,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)],[373]) ).
thf(770,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)],[374]) ).
thf(771,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)],[375]) ).
thf(772,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)],[376]) ).
thf(773,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)],[377]) ).
thf(774,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)],[378]) ).
thf(775,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)],[379]) ).
thf(776,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)],[380]) ).
thf(777,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)],[381]) ).
thf(778,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)],[382]) ).
thf(779,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)],[383]) ).
thf(780,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)],[384]) ).
thf(781,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)],[385]) ).
thf(782,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)],[386]) ).
thf(783,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)],[387]) ).
thf(784,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)],[388]) ).
thf(785,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)],[389]) ).
thf(786,plain,
( ( ! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(787,plain,
( ( ! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(788,plain,
( ( ! [V_x: $i] :
( v_thesis____
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(789,plain,
( ( ~ v_thesis____ ) = $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(790,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[396]) ).
thf(791,plain,
( ( ~ v_thesis____ ) = $true ),
inference(copy,[status(thm)],[789]) ).
thf(792,plain,
( ( ! [V_x: $i] :
( v_thesis____
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(793,plain,
( ( ! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(794,plain,
( ( ! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(795,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)],[785]) ).
thf(796,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)],[784]) ).
thf(797,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)],[783]) ).
thf(798,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)],[782]) ).
thf(799,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)],[781]) ).
thf(800,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)],[780]) ).
thf(801,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)],[779]) ).
thf(802,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)],[778]) ).
thf(803,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)],[777]) ).
thf(804,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)],[776]) ).
thf(805,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)],[775]) ).
thf(806,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)],[774]) ).
thf(807,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)],[773]) ).
thf(808,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)],[772]) ).
thf(809,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)],[771]) ).
thf(810,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)],[770]) ).
thf(811,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)],[769]) ).
thf(812,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)],[768]) ).
thf(813,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)],[767]) ).
thf(814,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)],[766]) ).
thf(815,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)],[765]) ).
thf(816,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)],[764]) ).
thf(817,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)],[763]) ).
thf(818,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)],[762]) ).
thf(819,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)],[761]) ).
thf(820,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)],[760]) ).
thf(821,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)],[759]) ).
thf(822,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)],[758]) ).
thf(823,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)],[757]) ).
thf(824,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)],[756]) ).
thf(825,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)],[755]) ).
thf(826,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)],[754]) ).
thf(827,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)],[753]) ).
thf(828,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)],[752]) ).
thf(829,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)],[751]) ).
thf(830,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)],[750]) ).
thf(831,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)],[749]) ).
thf(832,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)],[748]) ).
thf(833,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)],[747]) ).
thf(834,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)],[746]) ).
thf(835,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)],[745]) ).
thf(836,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)],[744]) ).
thf(837,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)],[743]) ).
thf(838,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)],[742]) ).
thf(839,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)],[741]) ).
thf(840,plain,
( ( ! [T_a: $i,V_e: $i,V_i: $i,V_T: $i,V_j: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_T ) @ 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)],[740]) ).
thf(841,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(842,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(843,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(844,plain,
( ( ! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(845,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)],[735]) ).
thf(846,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)],[734]) ).
thf(847,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)],[733]) ).
thf(848,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)],[732]) ).
thf(849,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(850,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)],[730]) ).
thf(851,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)],[729]) ).
thf(852,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)],[728]) ).
thf(853,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)],[727]) ).
thf(854,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)],[726]) ).
thf(855,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)],[725]) ).
thf(856,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(857,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(858,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(859,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(860,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)],[720]) ).
thf(861,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)],[719]) ).
thf(862,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)],[718]) ).
thf(863,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(864,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)],[716]) ).
thf(865,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)],[715]) ).
thf(866,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(867,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(868,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)],[712]) ).
thf(869,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)],[711]) ).
thf(870,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)],[710]) ).
thf(871,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)],[709]) ).
thf(872,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)],[708]) ).
thf(873,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)],[707]) ).
thf(874,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)],[706]) ).
thf(875,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)],[705]) ).
thf(876,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)],[704]) ).
thf(877,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)],[703]) ).
thf(878,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)],[702]) ).
thf(879,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)],[701]) ).
thf(880,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)],[700]) ).
thf(881,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)],[699]) ).
thf(882,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)],[698]) ).
thf(883,plain,
( ( ! [V_s: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(884,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(885,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(886,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(887,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(888,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(889,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(890,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( 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)],[690]) ).
thf(891,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_i ) ) @ ( 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)],[689]) ).
thf(892,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( 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)],[688]) ).
thf(893,plain,
( ( ! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(894,plain,
( ( ! [V_U: $i,V_T: $i,V_e: $i,V_us: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( V_U
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(895,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)],[685]) ).
thf(896,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)],[684]) ).
thf(897,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)],[683]) ).
thf(898,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)],[682]) ).
thf(899,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)],[681]) ).
thf(900,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)],[680]) ).
thf(901,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)],[679]) ).
thf(902,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)],[678]) ).
thf(903,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)],[677]) ).
thf(904,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)],[676]) ).
thf(905,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)],[675]) ).
thf(906,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)],[674]) ).
thf(907,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)],[673]) ).
thf(908,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)],[672]) ).
thf(909,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)],[671]) ).
thf(910,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)],[670]) ).
thf(911,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)],[669]) ).
thf(912,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)],[668]) ).
thf(913,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)],[667]) ).
thf(914,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)],[666]) ).
thf(915,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)],[665]) ).
thf(916,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)],[664]) ).
thf(917,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)],[663]) ).
thf(918,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(919,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(920,plain,
( ( ! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(921,plain,
( ( ! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(922,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(923,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(924,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(925,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(926,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(927,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)],[653]) ).
thf(928,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)],[652]) ).
thf(929,plain,
( ( ! [V_type1: $i,V_type2: $i] :
( ( c_Type_Otype_Otype__size @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Type_Otype_Otype__size @ V_type1 ) ) @ ( c_Type_Otype_Otype__size @ V_type2 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(930,plain,
( ( ! [V_type1: $i,V_type2: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ tc_Type_Otype )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_type1 @ tc_Type_Otype ) ) @ ( c_Nat_Osize__class_Osize @ V_type2 @ tc_Type_Otype ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(931,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)],[649]) ).
thf(932,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)],[648]) ).
thf(933,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)],[647]) ).
thf(934,plain,
( ( ! [V_dB: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ V_dB ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_dB @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(935,plain,
( ( ! [V_dB: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ V_dB ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ V_dB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(936,plain,
( ( ! [V_dB1: $i,V_dB2: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_dB1 @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ V_dB2 @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(937,plain,
( ( ! [V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ V_dB1 ) ) @ ( c_Lambda_OdB_OdB__size @ V_dB2 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(938,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)],[642]) ).
thf(939,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)],[641]) ).
thf(940,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(941,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)],[639]) ).
thf(942,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)],[638]) ).
thf(943,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)],[637]) ).
thf(944,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)],[636]) ).
thf(945,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)],[635]) ).
thf(946,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)],[634]) ).
thf(947,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)],[633]) ).
thf(948,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)],[632]) ).
thf(949,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)],[631]) ).
thf(950,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)],[630]) ).
thf(951,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)],[629]) ).
thf(952,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)],[628]) ).
thf(953,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)],[627]) ).
thf(954,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)],[626]) ).
thf(955,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)],[625]) ).
thf(956,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)],[624]) ).
thf(957,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)],[623]) ).
thf(958,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)],[622]) ).
thf(959,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)],[621]) ).
thf(960,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)],[620]) ).
thf(961,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)],[619]) ).
thf(962,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(963,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(964,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)],[616]) ).
thf(965,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)],[615]) ).
thf(966,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(967,plain,
( ( ! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(968,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(969,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(970,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(971,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(972,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(973,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)],[607]) ).
thf(974,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)],[606]) ).
thf(975,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)],[605]) ).
thf(976,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)],[604]) ).
thf(977,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)],[603]) ).
thf(978,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)],[602]) ).
thf(979,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)],[601]) ).
thf(980,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)],[600]) ).
thf(981,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)],[599]) ).
thf(982,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)],[598]) ).
thf(983,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)],[597]) ).
thf(984,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)],[596]) ).
thf(985,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)],[595]) ).
thf(986,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)],[594]) ).
thf(987,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)],[593]) ).
thf(988,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)],[592]) ).
thf(989,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)],[591]) ).
thf(990,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(991,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(992,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(993,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(994,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)],[586]) ).
thf(995,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)],[585]) ).
thf(996,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)],[584]) ).
thf(997,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)],[583]) ).
thf(998,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)],[582]) ).
thf(999,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)],[581]) ).
thf(1000,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)],[580]) ).
thf(1001,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)],[579]) ).
thf(1002,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)],[578]) ).
thf(1003,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(1004,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(1005,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)],[575]) ).
thf(1006,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)],[574]) ).
thf(1007,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)],[573]) ).
thf(1008,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)],[572]) ).
thf(1009,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)],[571]) ).
thf(1010,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)],[570]) ).
thf(1011,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)],[569]) ).
thf(1012,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)],[568]) ).
thf(1013,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)],[567]) ).
thf(1014,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 ) @ ( 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)],[566]) ).
thf(1015,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)],[565]) ).
thf(1016,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)],[564]) ).
thf(1017,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)],[563]) ).
thf(1018,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)],[562]) ).
thf(1019,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)],[561]) ).
thf(1020,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)],[560]) ).
thf(1021,plain,
( ( ! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Suc @ V_k ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( 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)],[559]) ).
thf(1022,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)],[558]) ).
thf(1023,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1024,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)],[556]) ).
thf(1025,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)],[555]) ).
thf(1026,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)],[554]) ).
thf(1027,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)],[553]) ).
thf(1028,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)],[552]) ).
thf(1029,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)],[551]) ).
thf(1030,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)],[550]) ).
thf(1031,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)],[549]) ).
thf(1032,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)],[548]) ).
thf(1033,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)],[547]) ).
thf(1034,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)],[546]) ).
thf(1035,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)],[545]) ).
thf(1036,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)],[544]) ).
thf(1037,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)],[543]) ).
thf(1038,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(1039,plain,
( ( ! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(1040,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 ) @ ( 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)],[540]) ).
thf(1041,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t_H ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(1042,plain,
( ( ! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ V_e @ V_us @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(1043,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_i: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[537]) ).
thf(1044,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1045,plain,
( ( ! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[535]) ).
thf(1046,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(1047,plain,
( ( ! [T_a: $i,V_e: $i,V_i: $i,V_U: $i,V_T: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_U ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T ) ) @ ( c_Suc @ V_i ) ) @ V_U ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1048,plain,
( ( ! [V_e: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) ) @ V_t ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1049,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) ) ) @ V_t ) @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(1050,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(1051,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[529]) ).
thf(1052,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(1053,plain,
( ( ! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1054,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(1055,plain,
( ( ! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(1056,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_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(1057,plain,
( ( ! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(1058,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 ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(1059,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 ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(1060,plain,
( ( ! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(1061,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(1062,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)],[518]) ).
thf(1063,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)],[517]) ).
thf(1064,plain,
( ( ! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(1065,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)],[515]) ).
thf(1066,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_ea______ ) @ v_ia______ ) @ v_T____ ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_T_Ha______ ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(1067,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)],[513]) ).
thf(1068,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(1069,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)],[511]) ).
thf(1070,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)],[510]) ).
thf(1071,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(1072,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(1073,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) ) @ V_s ) @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(1074,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(1075,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(1076,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(1077,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)],[503]) ).
thf(1078,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)],[502]) ).
thf(1079,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)],[501]) ).
thf(1080,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)],[500]) ).
thf(1081,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)],[499]) ).
thf(1082,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)],[498]) ).
thf(1083,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)],[497]) ).
thf(1084,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)],[496]) ).
thf(1085,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(1086,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)],[494]) ).
thf(1087,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(1088,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(1089,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(1090,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)],[490]) ).
thf(1091,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)],[489]) ).
thf(1092,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(1093,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)],[487]) ).
thf(1094,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)],[486]) ).
thf(1095,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)],[485]) ).
thf(1096,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)],[484]) ).
thf(1097,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(1098,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(1099,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1100,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)],[480]) ).
thf(1101,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)],[479]) ).
thf(1102,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)],[478]) ).
thf(1103,plain,
( ( ! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ 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)],[477]) ).
thf(1104,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)],[476]) ).
thf(1105,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)],[475]) ).
thf(1106,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)],[474]) ).
thf(1107,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)],[473]) ).
thf(1108,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[472]) ).
thf(1109,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)],[471]) ).
thf(1110,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)],[470]) ).
thf(1111,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)],[469]) ).
thf(1112,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)],[468]) ).
thf(1113,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)],[467]) ).
thf(1114,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)],[466]) ).
thf(1115,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)],[465]) ).
thf(1116,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)],[464]) ).
thf(1117,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)],[463]) ).
thf(1118,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_U ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ V_t ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ V_s ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(1119,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(1120,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)],[460]) ).
thf(1121,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)],[459]) ).
thf(1122,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)],[458]) ).
thf(1123,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)],[457]) ).
thf(1124,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)],[456]) ).
thf(1125,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)],[455]) ).
thf(1126,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)],[454]) ).
thf(1127,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)],[453]) ).
thf(1128,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)],[452]) ).
thf(1129,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)],[451]) ).
thf(1130,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)],[450]) ).
thf(1131,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)],[449]) ).
thf(1132,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)],[448]) ).
thf(1133,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)],[447]) ).
thf(1134,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)],[446]) ).
thf(1135,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)],[445]) ).
thf(1136,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)],[444]) ).
thf(1137,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)],[443]) ).
thf(1138,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_U ) ) @ ( c_Lambda_Olift @ V_t @ V_i ) ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(1139,plain,
( ( ! [V_ua: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_ua ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_ua ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_ua ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(1140,plain,
( ( ! [V_u: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_u ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_u ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(1141,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_e____ ) @ v_u____ ) @ v_T____ ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(1142,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t_H ) @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_t ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(1143,plain,
( ( ! [T_a: $i,V_e: $i,V_i: $i,V_T: $i,V_j: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_i ) @ V_T ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(1144,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ V_T2 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_T2 ) ) @ V_t ) @ V_Ta ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(1145,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ V_u ) @ V_T1 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e ) @ V_i ) @ V_T1 ) ) @ V_t ) @ V_Ta ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(1146,plain,
( ( ! [T_a: $i,V_e: $i,V_x: $i,V_T: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ T_a ) @ V_e ) @ V_x ) @ V_T ) @ V_x )
= V_T ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(1147,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_env ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_T ) ) @ V_t ) @ V_U ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(1148,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(1149,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__local__XCons__1__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(1150,plain,
( ( v_n____ != v_i____ )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(1151,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_ea______ ) @ v_ua______ ) @ v_T____ ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(1152,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__local__XCons__Xhyps__1__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(1153,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_T_H____ ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(1154,plain,
( ( ! [V_U: $i] :
( v_thesis____
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ V_U ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(1155,plain,
( ( ! [V_env: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_env ) @ ( c_Lambda_OdB_OVar @ V_x ) ) @ ( hAPP @ V_env @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(1156,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_e_H ) @ V_u ) @ V_U ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_e_H ) @ V_i ) @ V_U ) ) @ V_t ) @ V_T ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ 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)],[424]) ).
thf(1157,plain,
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ c_Lambda_Osubst ) @ v_u____ ) ) @ v_i____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(1158,plain,
( ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) ) ) @ v_as____ @ tc_Lambda_OdB )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(1159,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ ( v_sko__CHAINED__1 @ v_T____ @ v_a____ @ v_e____ @ v_i____ ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(1160,plain,
( ( ! [V_u: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ V_u ) @ V_ia ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ V_ea ) @ V_u ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ V_ea ) @ V_ia ) @ v_T____ ) ) @ v_a____ ) @ V_T_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(1161,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)],[419]) ).
thf(1162,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)],[418]) ).
thf(1163,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(1164,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(1165,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(1166,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(1167,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(1168,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(1169,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(1170,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(1171,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(1172,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(1173,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(1174,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(1175,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(1176,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(1177,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(1178,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(1179,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(1180,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(1181,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(1182,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(1183,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(1184,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[790]) ).
thf(1185,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)],[1078]) ).
thf(1186,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)],[1000]) ).
thf(1187,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)],[1008]) ).
thf(1188,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)],[848]) ).
thf(1189,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)],[825]) ).
thf(1190,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)],[1096]) ).
thf(1191,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)],[881]) ).
thf(1192,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)],[947]) ).
thf(1193,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)],[882]) ).
thf(1194,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)],[831]) ).
thf(1195,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)],[1079]) ).
thf(1196,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)],[941]) ).
thf(1197,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(1198,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1130]) ).
thf(1199,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)],[999]) ).
thf(1200,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)],[1128]) ).
thf(1201,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[963]) ).
thf(1202,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[856]) ).
thf(1203,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1094]) ).
thf(1204,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)],[1010]) ).
thf(1205,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)],[1116]) ).
thf(1206,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)],[1009]) ).
thf(1207,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)],[998]) ).
thf(1208,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)],[1125]) ).
thf(1209,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)],[806]) ).
thf(1210,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[867]) ).
thf(1211,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)],[945]) ).
thf(1212,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[857]) ).
thf(1213,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)],[950]) ).
thf(1214,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 ) )
| ( SX2
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1059]) ).
thf(1215,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)],[846]) ).
thf(1216,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)],[943]) ).
thf(1217,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)],[829]) ).
thf(1218,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1090]) ).
thf(1219,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)],[946]) ).
thf(1220,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)],[1113]) ).
thf(1221,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)],[1067]) ).
thf(1222,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)],[1095]) ).
thf(1223,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)],[1129]) ).
thf(1224,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)],[942]) ).
thf(1225,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SX5 ) @ SX3 ) @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SX5 ) @ SX4 ) @ SX0 ) ) @ SX2 ) @ SX6 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1145]) ).
thf(1226,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)],[802]) ).
thf(1227,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)],[1015]) ).
thf(1228,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)],[1012]) ).
thf(1229,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)],[994]) ).
thf(1230,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)],[830]) ).
thf(1231,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[866]) ).
thf(1232,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)],[1093]) ).
thf(1233,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)],[845]) ).
thf(1234,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SX5 ) @ SX3 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SX5 ) @ SX4 ) @ SX1 ) ) @ SX2 ) @ SX6 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1144]) ).
thf(1235,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)],[1114]) ).
thf(1236,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[962]) ).
thf(1237,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)],[944]) ).
thf(1238,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)],[1117]) ).
thf(1239,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)],[1124]) ).
thf(1240,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 ) )
| ( SX2
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1058]) ).
thf(1241,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)],[1069]) ).
thf(1242,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)],[1011]) ).
thf(1243,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)],[1115]) ).
thf(1244,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)],[1131]) ).
thf(1245,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)],[803]) ).
thf(1246,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)],[1007]) ).
thf(1247,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(1248,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)],[1127]) ).
thf(1249,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 ) )
| ( SX1
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1056]) ).
thf(1250,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)],[824]) ).
thf(1251,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)],[1013]) ).
thf(1252,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)],[1016]) ).
thf(1253,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(1254,plain,
( ( v_n____ != v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[1150]) ).
thf(1255,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1132]) ).
thf(1256,plain,
v_thesis____ = $false,
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(1257,plain,
! [SV1: $i] :
( ( v_thesis____
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1258,plain,
! [SV2: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ SV2 ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1259,plain,
! [SV3: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ SV3 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1260,plain,
! [SV4: $i] :
( ( ! [SY977: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SY977 @ tc_nat ) @ SV4 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV4 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY977 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1261,plain,
! [SV5: $i] :
( ( ! [SY978: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV5 @ SY978 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY978 @ SV5 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1262,plain,
! [SV6: $i] :
( ( ! [SY979: $i] :
( ( c_HOL_Oord__class_Oless @ SV6 @ SY979 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY979 @ SV6 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1263,plain,
! [SV7: $i] :
( ( ! [SY980: $i,SY981: $i] :
( ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY980 @ SY981 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ominus__class_Ominus @ SY980 @ SY981 @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1264,plain,
! [SV8: $i] :
( ( ! [SY982: $i,SY983: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV8 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY982 @ SY983 @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SY982 @ SY983 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1265,plain,
! [SV9: $i] :
( ( ! [SY984: $i,SY985: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV9 )
| ( c_HOL_Oord__class_Oless @ SY984 @ SY985 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY984 @ SY985 @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1266,plain,
! [SV10: $i] :
( ( ! [SY986: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV10 ) @ ( c_HOL_Ominus__class_Ominus @ SY986 @ SV10 @ tc_nat ) )
= SY986 )
| ( c_HOL_Oord__class_Oless @ SY986 @ SV10 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1267,plain,
! [SV11: $i] :
( ( ! [SY987: $i,SY988: $i] :
( ( c_HOL_Oord__class_Oless @ SV11 @ ( c_HOL_Ominus__class_Ominus @ SY987 @ SY988 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV11 ) @ SY988 ) @ SY987 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1268,plain,
! [SV12: $i] :
( ( ! [SY989: $i,SY990: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV12 ) @ SY989 ) @ SY990 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_HOL_Ominus__class_Ominus @ SY990 @ SY989 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1269,plain,
! [SV13: $i] :
( ( ! [SY991: $i,SY992: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ SY991 @ tc_nat ) @ SY992 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SY992 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1270,plain,
! [SV14: $i] :
( ( ! [SY993: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV14 ) @ ( c_Suc @ SY993 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV14 @ SY993 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1271,plain,
! [SV15: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV15 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1272,plain,
! [SV16: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV16 @ SV16 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1273,plain,
! [SV17: $i] :
( ( ! [SY994: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV17 )
| ~ ( class_Int_Onumber__ring @ SV17 )
| ( ( c_HOL_Ominus__class_Ominus @ SY994 @ SY994 @ SV17 )
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1274,plain,
! [SV18: $i] :
( ( ! [SY995: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV18 )
| ( ( c_HOL_Ominus__class_Ominus @ SY995 @ SY995 @ SV18 )
= ( c_HOL_Ozero__class_Ozero @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1275,plain,
! [SV19: $i] :
( ( ! [SY996: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV19 )
| ( ( c_HOL_Ominus__class_Ominus @ SY996 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= SY996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1276,plain,
! [SV20: $i] :
( ( ! [SY997: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV20 )
| ( ( c_HOL_Ominus__class_Ominus @ SY997 @ SY997 @ SV20 )
= ( c_HOL_Ozero__class_Ozero @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1277,plain,
! [SV21: $i] :
( ( ! [SY998: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV21 )
| ( ( c_HOL_Ominus__class_Ominus @ SY998 @ SY998 @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1278,plain,
! [SV22: $i] :
( ( ! [SY999: $i,SY1000: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SY999 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SY1000 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1000 @ SV22 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1000 @ SY999 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1279,plain,
! [SV23: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV23 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1280,plain,
! [SV24: $i] :
( ( ! [SY1001: $i,SY1002: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV24 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ominus__class_Ominus @ SY1001 @ SY1002 @ SV24 ) ) @ SY1002 )
= SY1001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1281,plain,
! [SV25: $i] :
( ( ! [SY1003: $i,SY1004: $i] :
( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1003 ) @ SY1004 ) @ SY1003 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV25 @ SY1004 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1282,plain,
! [SV26: $i] :
( ( ! [SY1005: $i,SY1006: $i] :
( ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1005 ) @ SY1006 ) @ SY1005 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV26 @ SY1006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1283,plain,
! [SV27: $i] :
( ( ! [SY1007: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV27 @ SY1007 @ tc_nat ) @ ( c_Suc @ SV27 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1284,plain,
! [SV28: $i] :
( ( ! [SY1008: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV28 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV28 ) @ SY1008 ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1285,plain,
! [SV29: $i] :
( ( ! [SY1009: $i,SY1010: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV29 @ SY1009 @ tc_nat ) @ SY1010 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV29 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1009 ) @ SY1010 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1286,plain,
! [SV30: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV30 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1287,plain,
! [SV31: $i] :
( ( ! [SY1011: $i,SY1012: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV31 ) @ SY1011 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1012 ) @ SY1011 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV31 @ SY1012 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1288,plain,
! [SV32: $i] :
( ( ! [SY1013: $i,SY1014: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV32 ) @ SY1013 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV32 ) @ SY1014 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY1013 @ SY1014 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1289,plain,
! [SV33: $i] :
( ( ! [SY1015: $i,SY1016: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ SY1015 @ tc_nat ) @ SY1016 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ SY1016 @ tc_nat ) @ SY1015 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1290,plain,
! [SV34: $i] :
( ( ! [SY1017: $i,SY1018: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV34 ) @ SY1017 @ tc_nat ) @ ( c_Suc @ SY1018 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SY1017 @ tc_nat ) @ SY1018 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1291,plain,
! [SV35: $i] :
( ( ! [SY1019: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV35 @ ( c_Suc @ SY1019 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV35 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY1019 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1292,plain,
! [SV36: $i] :
( ( ! [SY1020: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV36 ) @ SY1020 ) @ SY1020 @ tc_nat )
= SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1293,plain,
! [SV37: $i] :
( ( ! [SY1021: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV37 ) @ SY1021 ) @ SV37 @ tc_nat )
= SY1021 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1294,plain,
! [SV38: $i] :
( ( ! [SY1022: $i,SY1023: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV38 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY1022 ) @ SY1023 ) @ SY1023 @ SV38 )
= SY1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1295,plain,
! [SV39: $i] :
( ( ! [SY1024: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV39 @ ( c_Suc @ SY1024 ) @ tc_nat ) @ SV39 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV39 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1296,plain,
! [SV40: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV40 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV40 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV40 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1297,plain,
! [SV41: $i] :
( ( ! [SY1025: $i,SY1026: $i,SY1027: $i,SY1028: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV41 ) @ SY1025 ) @ SY1026 ) @ SY1027 ) @ SY1028 )
= ( hAPP @ SY1025 @ ( c_HOL_Ominus__class_Ominus @ SY1028 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1026 @ SY1028 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1298,plain,
! [SV42: $i] :
( ( ! [SY1029: $i,SY1030: $i,SY1031: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV42 @ SY1029 ) @ SY1030 ) @ SY1031 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV42 @ SY1030 ) @ SY1031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1299,plain,
! [SV43: $i] :
( ( ! [SY1032: $i,SY1033: $i] :
~ ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_ONil @ SY1032 ) @ SY1033 @ SY1032 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1300,plain,
! [SV44: $i] :
( ( ! [SY1034: $i,SY1035: $i] :
~ ( c_ListOrder_Ostep1 @ SV44 @ SY1034 @ ( c_List_Olist_ONil @ SY1035 ) @ SY1035 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1301,plain,
! [SV45: $i] :
( ( ! [SY1036: $i,SY1037: $i,SY1038: $i] :
( ( c_List_Ofoldl @ SV45 @ SY1036 @ ( c_List_Olist_ONil @ SY1037 ) @ SY1038 @ SY1037 )
= SY1036 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1302,plain,
! [SV46: $i] :
( ( ( c_Predicate_Oconversep @ ( c_fequal @ SV46 ) @ SV46 @ SV46 )
= ( c_fequal @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1303,plain,
! [SV47: $i] :
( ( ! [SY1039: $i] :
( ( SV47 = SY1039 )
| ( c_HOL_Oord__class_Oless @ SV47 @ SY1039 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV47 @ ( c_Suc @ SY1039 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1304,plain,
! [SV48: $i] :
( ( ! [SY1040: $i] :
( ( SV48 = SY1040 )
| ~ ( c_HOL_Oord__class_Oless @ SY1040 @ ( c_Suc @ SV48 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1040 @ SV48 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1305,plain,
! [SV49: $i] :
( ( ! [SY1041: $i] :
( ( SV49 = SY1041 )
| ~ ( c_HOL_Oord__class_Oless @ SV49 @ ( c_Suc @ SY1041 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV49 @ SY1041 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1306,plain,
! [SV50: $i] :
( ( ! [SY1042: $i,SY1043: $i,SY1044: $i,SY1045: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SY1042 ) @ SY1043 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SY1044 ) @ SY1045 ) @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SY1043 @ SY1045 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SY1042 @ SY1044 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1307,plain,
! [SV51: $i] :
( ( ! [SY1046: $i,SY1047: $i,SY1048: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SY1046 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1047 ) @ SY1048 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1046 @ SY1048 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV51 @ SY1047 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1308,plain,
! [SV52: $i] :
( ( c_HOL_Oord__class_Oless @ SV52 @ ( c_Suc @ SV52 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1309,plain,
! [SV53: $i] :
( ( c_HOL_Oord__class_Oless @ SV53 @ ( c_Suc @ SV53 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1310,plain,
! [SV54: $i] :
( ( ! [SY1049: $i,SY1050: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV54 ) @ SY1049 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1050 @ SY1049 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY1050 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1311,plain,
! [SV55: $i] :
( ( ! [SY1051: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV55 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SY1051 @ SV55 @ SV55 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SY1051 @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1312,plain,
! [SV56: $i] :
( ( ! [SY1052: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV56 )
| ( c_HOL_Oord__class_Oless @ SY1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SY1052 ) @ ( c_HOL_Oone__class_Oone @ SV56 ) ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1313,plain,
! [SV57: $i] :
( ( ! [SY1053: $i,SY1054: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV57 @ SY1053 @ SY1054 ) @ SY1054 @ SY1053 )
= SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1314,plain,
! [SV58: $i] :
( ( ! [SY1055: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SY1055 ) @ SV58 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1315,plain,
! [SV59: $i] :
( ( ! [SY1056: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV59 ) @ SY1056 ) @ SY1056 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1316,plain,
! [SV60: $i] :
( ( ! [SY1057: $i,SY1058: $i,SY1059: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV60 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1057 ) @ SY1058 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1059 ) @ SY1058 ) @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SY1057 @ SY1059 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1317,plain,
! [SV61: $i] :
( ( ! [SY1060: $i,SY1061: $i,SY1062: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV61 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1060 ) @ SY1061 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1062 ) @ SY1061 ) @ SV61 )
| ~ ( c_HOL_Oord__class_Oless @ SY1060 @ SY1062 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1318,plain,
! [SV62: $i] :
( ( ! [SY1063: $i,SY1064: $i,SY1065: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV62 )
| ( c_HOL_Oord__class_Oless @ SY1063 @ SY1064 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SY1063 ) @ SY1065 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SY1064 ) @ SY1065 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1319,plain,
! [SV63: $i] :
( ( ! [SY1066: $i,SY1067: $i,SY1068: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV63 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SY1066 ) @ SY1067 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SY1066 ) @ SY1068 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY1067 @ SY1068 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1320,plain,
! [SV64: $i] :
( ( ! [SY1069: $i,SY1070: $i,SY1071: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SY1069 ) @ SY1070 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SY1069 ) @ SY1071 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SY1070 @ SY1071 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1321,plain,
! [SV65: $i] :
( ( ! [SY1072: $i,SY1073: $i,SY1074: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV65 )
| ( c_HOL_Oord__class_Oless @ SY1072 @ SY1073 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY1074 ) @ SY1072 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY1074 ) @ SY1073 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1322,plain,
! [SV66: $i] :
( ( ! [SY1075: $i,SY1076: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV66 ) @ SY1075 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1076 ) @ SY1075 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV66 @ SY1076 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1323,plain,
! [SV67: $i] :
( ( ! [SY1077: $i,SY1078: $i] :
( ( c_HOL_Oord__class_Oless @ SV67 @ SY1077 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1078 ) @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1078 ) @ SY1077 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1324,plain,
! [SV68: $i] :
( ( ! [SY1079: $i,SY1080: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SY1079 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SY1080 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1079 @ SY1080 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1325,plain,
! [SV69: $i] :
( ( ! [SY1081: $i] :
( ( c_HOL_Oord__class_Oless @ SV69 @ SY1081 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV69 ) @ SY1081 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1326,plain,
! [SV70: $i] :
( ( ! [SY1082: $i] :
( ( c_HOL_Oord__class_Oless @ SV70 @ ( c_Suc @ SY1082 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV70 @ SY1082 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1327,plain,
! [SV71: $i] :
( ( ! [SY1083: $i,SY1084: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV71 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1083 ) @ SY1084 ) @ SV71 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1083 @ SV71 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1084 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1328,plain,
! [SV72: $i] :
( ( ! [SY1085: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ SV72 ) @ SY1085 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ SV72 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1085 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1329,plain,
! [SV73: $i] :
( ( ! [SY1086: $i,SY1087: $i,SY1088: $i,SY1089: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SY1086 ) @ SY1087 ) @ SY1088 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SY1086 ) @ SY1089 ) @ SY1088 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SY1087 ) @ SY1089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1330,plain,
! [SV74: $i] :
( ( ! [SY1090: $i,SY1091: $i,SY1092: $i,SY1093: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SY1090 ) @ SY1091 ) @ SY1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SY1093 ) @ SY1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SY1090 ) @ SY1091 ) @ SY1093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1331,plain,
! [SV75: $i] :
( ( ! [SY1094: $i,SY1095: $i,SY1096: $i] :
( ( c_Wellfounded_Oaccp @ SV75 @ SY1094 @ SY1095 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV75 @ SY1094 ) @ SY1096 ) )
| ~ ( c_Wellfounded_Oaccp @ SV75 @ SY1096 @ SY1095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1332,plain,
! [SV76: $i] :
( ( ! [SY1097: $i,SY1098: $i,SY1099: $i] :
( ( c_Wellfounded_Oaccp @ SV76 @ SY1097 @ SY1098 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SY1097 ) @ SY1099 ) )
| ~ ( c_Wellfounded_Oaccp @ SV76 @ SY1099 @ SY1098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1333,plain,
! [SV77: $i] :
( ( ! [SY1100: $i,SY1101: $i,SY1102: $i] :
( ( c_Type_Otypings @ SV77 @ SY1100 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1101 @ SV77 @ SY1102 @ SY1100 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV77 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1102 @ SY1100 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1334,plain,
! [SV78: $i] :
( ( ! [SY1103: $i,SY1104: $i,SY1105: $i] :
( ( c_Type_Otypings @ SV78 @ SY1103 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1104 @ SV78 @ SY1105 @ SY1103 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV78 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1105 @ SY1103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1335,plain,
! [SV79: $i] :
( ( ! [SY1106: $i,SY1107: $i,SY1108: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV79 ) @ SY1106 ) @ SY1107 ) @ SY1108 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV79 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1108 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( c_Lambda_Olift @ SY1106 @ SY1108 ) ) @ SY1107 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1107 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1108 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1336,plain,
! [SV80: $i] :
( ( ! [SY1109: $i,SY1110: $i,SY1111: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV80 ) @ SY1109 ) @ SY1110 ) @ SY1111 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV80 @ SY1111 ) ) @ ( c_Lambda_Olift @ SY1109 @ SY1111 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1110 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1111 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1110 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1337,plain,
! [SV81: $i] :
( ( ! [SY1112: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV81 ) @ SY1112 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV81 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ SV81 @ SY1112 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1338,plain,
! [SV82: $i] :
( ( ! [SY1113: $i,SY1114: $i] :
( ( SV82
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV82 @ SY1113 @ SY1114 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV82 @ SY1113 @ SY1114 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1113 ) @ ( c_Lambda_OdB_OAbs @ SY1114 ) ) @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1339,plain,
! [SV83: $i] :
( ( ! [SY1115: $i,SY1116: $i,SY1117: $i,SY1118: $i,SY1119: $i,SY1120: $i] :
( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1115 @ SV83 @ SY1116 @ SY1117 ) @ SY1115 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1116 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1118 ) @ SY1119 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
| ~ ( c_Type_Otypings @ SY1116 @ SY1119 @ SY1120 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1116 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1118 ) @ SY1119 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1117 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1340,plain,
! [SV84: $i] :
( ( ! [SY1121: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV84 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SY1121 ) @ SY1121 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SY1121 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1341,plain,
! [SV85: $i] :
( ( ! [SY1122: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV85 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SY1122 @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SY1122 ) @ SY1122 ) @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1342,plain,
! [SV86: $i] :
( ( ! [SY1123: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1123 @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1343,plain,
! [SV87: $i] :
( ( ! [SY1124: $i,SY1125: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SY1124 ) @ SY1125 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SY1125 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SY1124 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1344,plain,
! [SV88: $i] :
( ( ! [SY1126: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV88 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SY1126 ) @ SY1126 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SY1126 @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1345,plain,
! [SV89: $i] :
( ( ! [SY1127: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV89 )
| ( c_HOL_Oord__class_Oless @ SY1127 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SY1127 ) @ SY1127 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1346,plain,
! [SV90: $i] :
( ( ! [SY1128: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV90 )
| ( c_HOL_Oord__class_Oless @ SY1128 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SY1128 ) @ SY1128 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1347,plain,
! [SV91: $i] :
( ( ! [SY1129: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV91 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ SY1129 ) @ SY1129 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY1129 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1348,plain,
! [SV92: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV92 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1349,plain,
! [SV93: $i] :
( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY1130 ) @ SY1131 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SY1131 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SY1130 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1350,plain,
! [SV94: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV94 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( c_HOL_Oone__class_Oone @ SV94 ) @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1351,plain,
! [SV95: $i] :
( ( ! [SY1132: $i,SY1133: $i,SY1134: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV95 )
| ( c_HOL_Oord__class_Oless @ SY1132 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY1133 ) @ SY1134 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SY1132 @ SY1134 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SY1133 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1352,plain,
! [SV96: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV96 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV96 )
= ( c_HOL_Ozero__class_Ozero @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1353,plain,
! [SV97: $i] :
( ( ! [SY1135: $i,SY1136: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV97 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1135 @ SV97 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1136 @ SV97 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SY1135 @ SY1136 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1354,plain,
! [SV98: $i] :
( ( ! [SY1137: $i,SY1138: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV98 )
| ( c_HOL_Oord__class_Oless @ SY1137 @ SY1138 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1137 @ SV98 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1138 @ SV98 ) @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1355,plain,
! [SV99: $i] :
( ( ! [SY1139: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV99 ) @ SY1139 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV99 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1356,plain,
! [SV100: $i] :
( ( ! [SY1140: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV100 ) @ SY1140 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1140 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1357,plain,
! [SV101: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV101 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1358,plain,
! [SV102: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV102 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1359,plain,
! [SV103: $i] :
( ( ! [SY1141: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV103 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1141 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1141 ) @ SV103 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1360,plain,
! [SV104: $i] :
( ( ( SV104
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1361,plain,
! [SV105: $i] :
( ( ! [SY1142: $i,SY1143: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SY1142 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SY1143 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SY1142 @ SY1143 @ SV105 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1362,plain,
! [SV106: $i] :
( ( ! [SY1144: $i,SY1145: $i,SY1146: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV106 ) @ SY1144 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1145 ) @ SY1146 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1144 ) @ SY1146 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV106 ) @ SY1145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1363,plain,
! [SV107: $i] :
( ( ! [SY1147: $i,SY1148: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV107 ) @ SY1147 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1148 ) @ SY1147 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV107 ) @ SY1148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1364,plain,
! [SV108: $i] :
( ( ! [SY1149: $i,SY1150: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SY1149 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SY1150 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1149 ) @ SY1150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1365,plain,
! [SV109: $i] :
( ( ! [SY1151: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV109 ) ) @ ( c_Lambda_OdB_OAbs @ SY1151 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SY1151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1366,plain,
! [SV110: $i] :
( ( ! [SY1152: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV110 ) @ SY1152 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV110 ) @ SY1152 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1367,plain,
! [SV111: $i] :
( ( ! [SY1153: $i,SY1154: $i,SY1155: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SY1153 ) @ SY1154 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SY1155 ) @ SY1154 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1153 ) @ SY1155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1368,plain,
! [SV112: $i] :
( ( ! [SY1156: $i,SY1157: $i,SY1158: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV112 ) @ SY1156 ) @ SY1157 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1158 ) @ SY1156 ) @ SY1157 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV112 ) @ SY1158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1369,plain,
! [SV113: $i] :
( ( ! [SY1159: $i,SY1160: $i,SY1161: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SY1159 ) @ SY1160 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SY1161 ) @ SY1160 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1159 ) @ SY1161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1370,plain,
! [SV114: $i] :
( ( ! [SY1162: $i,SY1163: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV114 ) ) @ SY1162 ) @ SY1163 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1163 @ SV114 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1371,plain,
! [SV115: $i] :
( ( ! [SY1164: $i,SY1165: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV115 ) ) @ SY1164 ) @ SY1165 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV115 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1165 @ SV115 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1372,plain,
! [SV116: $i] :
( ( ! [SY1166: $i] :
( ( c_Type_Otype_Otype__size @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV116 ) @ SY1166 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Type_Otype_Otype__size @ SV116 ) ) @ ( c_Type_Otype_Otype__size @ SY1166 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1373,plain,
! [SV117: $i] :
( ( ! [SY1167: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV117 ) @ SY1167 ) @ tc_Type_Otype )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV117 @ tc_Type_Otype ) ) @ ( c_Nat_Osize__class_Osize @ SY1167 @ tc_Type_Otype ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1374,plain,
! [SV118: $i] :
( ( ! [SY1168: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV118 ) @ SY1168 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV118 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ SY1168 ) ) )
| ( SV118
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1375,plain,
! [SV119: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV119 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV119 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1376,plain,
! [SV120: $i] :
( ( ( SV120
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV120 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1377,plain,
! [SV121: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ SV121 ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV121 @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1378,plain,
! [SV122: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ SV122 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ SV122 ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1379,plain,
! [SV123: $i] :
( ( ! [SY1169: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SY1169 ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV123 @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ SY1169 @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1380,plain,
! [SV124: $i] :
( ( ! [SY1170: $i] :
( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SY1170 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ SV124 ) ) @ ( c_Lambda_OdB_OdB__size @ SY1170 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1381,plain,
! [SV125: $i] :
( ( ! [SY1171: $i,SY1172: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV125 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SY1171 @ SY1172 @ SV125 @ SV125 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SY1172 @ SY1171 @ SV125 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1382,plain,
! [SV126: $i] :
( ( ! [SY1173: $i,SY1174: $i,SY1175: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV126 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SY1173 ) @ SY1174 ) @ SY1175 @ SV126 @ SV126 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SY1173 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SY1174 @ SY1175 @ SV126 @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1383,plain,
! [SV127: $i] :
( ( ! [SY1176: $i,SY1177: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SY1176 ) @ SY1177 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SY1177 ) @ SY1176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1384,plain,
! [SV128: $i] :
( ( ! [SY1178: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV128 ) @ SY1178 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1178 ) @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1385,plain,
! [SV129: $i] :
( ( ! [SY1179: $i,SY1180: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV129 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SY1179 ) @ SY1180 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SY1180 ) @ SY1179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1386,plain,
! [SV130: $i] :
( ( ! [SY1181: $i,SY1182: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SY1181 ) @ SY1182 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SY1182 ) @ SY1181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1387,plain,
! [SV131: $i] :
( ( ! [SY1183: $i,SY1184: $i] :
( ( c_HOL_Oord__class_Oless @ SV131 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1183 ) @ SY1184 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV131 @ SY1184 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1388,plain,
! [SV132: $i] :
( ( ! [SY1185: $i,SY1186: $i] :
( ( c_HOL_Oord__class_Oless @ SV132 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1185 ) @ SY1186 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV132 @ SY1185 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1389,plain,
! [SV133: $i] :
( ( ! [SY1187: $i,SY1188: $i] :
( ( c_HOL_Oord__class_Oless @ SV133 @ SY1187 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV133 ) @ SY1188 ) @ SY1187 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1390,plain,
! [SV134: $i] :
( ( ! [SY1189: $i,SY1190: $i] :
( ( c_HOL_Oord__class_Oless @ SV134 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1189 ) @ SY1190 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV134 @ SY1190 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1391,plain,
! [SV135: $i] :
( ( ! [SY1191: $i,SY1192: $i] :
( ( c_HOL_Oord__class_Oless @ SV135 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1191 ) @ SY1192 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV135 @ SY1191 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1392,plain,
! [SV136: $i] :
( ( ! [SY1193: $i] : ( c_HOL_Oord__class_Oless @ SV136 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV136 ) @ SY1193 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1393,plain,
! [SV137: $i] :
( ( ! [SY1194: $i] : ( c_HOL_Oord__class_Oless @ SV137 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1194 ) @ SV137 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1394,plain,
! [SV138: $i] :
( ( ! [SY1195: $i] : ( c_HOL_Oord__class_Oless @ SV138 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV138 ) @ SY1195 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1395,plain,
! [SV139: $i] :
( ( ! [SY1196: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV139 ) ) @ SY1196 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV139 ) @ SY1196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1396,plain,
! [SV140: $i] :
( ( ! [SY1197: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV140 ) @ ( c_Suc @ SY1197 ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV140 ) @ SY1197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1397,plain,
! [SV141: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV141 ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV141 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1398,plain,
! [SV142: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1399,plain,
! [SV143: $i] :
( ( ! [SY1198: $i,SY1199: $i,SY1200: $i,SY1201: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SY1198 ) @ SY1199 ) @ SY1200 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SY1198 ) @ SY1201 ) @ SY1200 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SY1198 ) @ SY1199 ) @ SY1201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1400,plain,
! [SV144: $i] :
( ( ! [SY1202: $i,SY1203: $i,SY1204: $i] :
( ( c_Wellfounded_Oaccp @ SV144 @ SY1202 @ SY1203 )
| ~ ( c_Wellfounded_Oaccp @ SV144 @ SY1204 @ SY1203 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV144 @ SY1203 ) @ SY1202 ) @ SY1204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1401,plain,
! [SV145: $i] :
( ( ! [SY1205: $i,SY1206: $i,SY1207: $i] :
( ( c_Wellfounded_Oaccp @ SV145 @ SY1205 @ SY1206 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SY1206 ) @ SY1205 ) @ SY1207 ) )
| ~ ( c_Wellfounded_Oaccp @ SV145 @ SY1207 @ SY1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1402,plain,
! [SV146: $i] :
( ( ! [SY1208: $i,SY1209: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV146 @ SY1208 ) @ SY1209 ) @ SY1209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1403,plain,
! [SV147: $i] :
( ( ! [SY1210: $i,SY1211: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV147 @ SY1210 ) @ SY1211 ) @ SY1211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1404,plain,
! [SV148: $i] :
( ( ! [SY1212: $i] : ( c_List_Olistsp @ SV148 @ ( c_List_Olist_ONil @ SY1212 ) @ SY1212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1405,plain,
! [SV149: $i] :
( ( ( c_Suc @ SV149 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1406,plain,
! [SV150: $i] :
( ( ( c_Suc @ SV150 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1407,plain,
! [SV151: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV151 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= ( c_HOL_Ozero__class_Ozero @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1408,plain,
! [SV152: $i] :
( ( ! [SY1213: $i,SY1214: $i,SY1215: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1213 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1214 ) @ SY1215 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1213 ) @ SY1214 ) ) @ SY1215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1409,plain,
! [SV153: $i] :
( ( ! [SY1216: $i,SY1217: $i,SY1218: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1216 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1217 ) @ SY1218 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1217 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1216 ) @ SY1218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1410,plain,
! [SV154: $i] :
( ( ! [SY1219: $i,SY1220: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1219 ) @ SY1220 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1219 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ SY1220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1411,plain,
! [SV155: $i] :
( ( ! [SY1221: $i,SY1222: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SY1221 ) ) @ SY1222 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1221 ) @ SY1222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1412,plain,
! [SV156: $i] :
( ( ! [SY1223: $i,SY1224: $i,SY1225: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY1223 ) @ SY1224 ) ) @ SY1225 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY1223 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY1224 ) @ SY1225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1413,plain,
! [SV157: $i] :
( ( ! [SY1226: $i,SY1227: $i,SY1228: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1226 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1227 ) @ SY1228 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1226 ) @ SY1228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1414,plain,
! [SV158: $i] :
( ( ! [SY1229: $i,SY1230: $i,SY1231: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY1229 ) @ SY1230 ) ) @ SY1231 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY1229 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY1230 ) @ SY1231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1415,plain,
! [SV159: $i] :
( ( ! [SY1232: $i,SY1233: $i,SY1234: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SY1232 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SY1233 ) @ SY1234 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SY1232 ) @ SY1233 ) ) @ SY1234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1416,plain,
! [SV160: $i] :
( ( ! [SY1235: $i,SY1236: $i,SY1237: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SY1235 ) @ SY1236 ) ) @ SY1237 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SY1235 ) @ SY1237 ) ) @ SY1236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1417,plain,
! [SV161: $i] :
( ( ! [SY1238: $i,SY1239: $i,SY1240: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY1238 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY1239 ) @ SY1240 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY1239 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY1238 ) @ SY1240 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1418,plain,
! [SV162: $i] :
( ( ! [SY1241: $i,SY1242: $i,SY1243: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SY1241 ) @ SY1242 ) ) @ SY1243 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SY1241 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SY1242 ) @ SY1243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1419,plain,
! [SV163: $i] :
( ( ! [SY1244: $i,SY1245: $i,SY1246: $i,SY1247: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV163 @ SY1244 @ SY1245 ) @ SY1246 ) @ SY1247 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV163 @ SY1247 ) @ SY1246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1420,plain,
! [SV164: $i] :
( ( ! [SY1248: $i,SY1249: $i,SY1250: $i,SY1251: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV164 @ SY1248 ) @ SY1249 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV164 @ SY1250 @ SY1251 ) @ SY1249 ) @ SY1248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1421,plain,
! [SV165: $i] :
( ( ! [SY1252: $i,SY1253: $i,SY1254: $i,SY1255: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV165 @ SY1252 @ SY1253 ) @ SY1254 ) @ SY1255 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV165 @ SY1255 ) @ SY1254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1422,plain,
! [SV166: $i] :
( ( ! [SY1256: $i,SY1257: $i,SY1258: $i,SY1259: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SY1256 ) @ SY1257 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV166 @ SY1258 @ SY1259 ) @ SY1257 ) @ SY1256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1423,plain,
! [SV167: $i] :
( ( ! [SY1260: $i,SY1261: $i,SY1262: $i] :
( ( c_List_Ofoldr @ SV167 @ ( c_List_Olist_ONil @ SY1260 ) @ SY1261 @ SY1260 @ SY1262 )
= SY1261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1424,plain,
! [SV168: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV168 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV168 )
= ( c_HOL_Oone__class_Oone @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1425,plain,
! [SV169: $i] :
( ( ! [SY1263: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV169 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SY1263 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ ( c_HOL_Oone__class_Oone @ SV169 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1263 @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1426,plain,
! [SV170: $i] :
( ( ! [SY1264: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV170 ) ) @ SY1264 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ ( c_Suc @ SY1264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1427,plain,
! [SV171: $i] :
( ( ! [SY1265: $i,SY1266: $i,SY1267: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV171 @ SY1265 ) @ SY1266 ) @ SY1267 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV171 @ SY1265 @ SY1265 ) @ SY1265 ) @ SY1267 ) @ SY1266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1428,plain,
! [SV172: $i] :
( ( ! [SY1268: $i,SY1269: $i,SY1270: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV172 @ SY1268 @ SY1268 ) @ SY1268 ) @ SY1269 ) @ SY1270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV172 @ SY1268 ) @ SY1270 ) @ SY1269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1429,plain,
! [SV173: $i] :
( ( ! [SY1271: $i,SY1272: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV173 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SY1271 @ SY1272 @ SV173 @ SV173 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SY1271 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SY1272 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 @ SV173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1430,plain,
! [SV174: $i] :
( ( ! [SY1273: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV174 ) @ SY1273 @ tc_nat )
| ( ( c_Suc @ SV174 )
= SY1273 )
| ~ ( c_HOL_Oord__class_Oless @ SV174 @ SY1273 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1431,plain,
! [SV175: $i] :
( ( ! [SY1274: $i,SY1275: $i,SY1276: $i,SY1277: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ ( c_Lambda_Olift @ SY1274 @ SY1275 ) ) @ ( c_Suc @ SY1276 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1277 ) @ SY1274 ) @ SY1276 ) ) @ SY1275 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SY1277 ) @ SY1275 ) ) @ SY1274 ) @ SY1276 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1275 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1276 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1432,plain,
! [SV176: $i] :
( ( ! [SY1278: $i,SY1279: $i,SY1280: $i,SY1281: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV176 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SY1278 ) @ SY1279 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SY1280 ) @ SY1281 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SY1278 ) @ SY1280 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SY1279 ) @ SY1281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1433,plain,
! [SV177: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV177 @ SV177 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV177 @ ( c_Suc @ SV177 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1434,plain,
! [SV178: $i] :
( ( ! [SY1282: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV178 @ SY1282 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1282 @ ( c_Suc @ SV178 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1435,plain,
! [SV179: $i] :
( ( ! [SY1283: $i] :
( ( c_HOL_Oord__class_Oless @ SV179 @ ( c_Suc @ SY1283 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1283 @ SV179 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1436,plain,
! [SV180: $i] :
( ( ! [SY1284: $i,SY1285: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SY1284 ) @ ( c_Suc @ SY1285 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SY1285 ) @ SY1284 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1284 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1285 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1437,plain,
! [SV181: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV181 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ ( c_HOL_Oone__class_Oone @ SV181 ) ) @ ( c_HOL_Oone__class_Oone @ SV181 ) ) @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1438,plain,
! [SV182: $i] :
( ( ! [SY1286: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV182 @ SY1286 ) @ SY1286 )
= ( c_Transitive__Closure_Ortranclp @ SV182 @ SY1286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1439,plain,
! [SV183: $i] :
( ( ! [SY1287: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) ) @ SY1287 )
= SY1287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1440,plain,
! [SV184: $i] :
( ( ! [SY1288: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV184 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( c_HOL_Ozero__class_Ozero @ SV184 ) ) @ SY1288 )
= SY1288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1441,plain,
! [SV185: $i] :
( ( SV185
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV185 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1442,plain,
! [SV186: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV186 )
= SV186 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1443,plain,
! [SV187: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV187 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV187 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1444,plain,
! [SV188: $i] :
( ( ! [SY1289: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV188 )
| ~ ( class_Int_Onumber__ring @ SV188 )
| ( SY1289
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SY1289 ) @ ( c_HOL_Ozero__class_Ozero @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1445,plain,
! [SV189: $i] :
( ( ! [SY1290: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV189 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV189 ) @ SY1290 ) @ ( c_HOL_Ozero__class_Ozero @ SV189 ) )
= SY1290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1446,plain,
! [SV190: $i] :
( ( ! [SY1291: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV190 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ ( c_HOL_Ozero__class_Ozero @ SV190 ) ) @ SY1291 )
= SY1291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1447,plain,
! [SV191: $i] :
( ( ! [SY1292: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV191 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV191 ) @ SY1292 ) @ ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= SY1292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1448,plain,
! [SV192: $i] :
( ( ! [SY1293: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV192 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SY1293 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) )
= SY1293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1449,plain,
! [SV193: $i] :
( ( ! [SY1294: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV193 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV193 ) @ ( c_HOL_Ozero__class_Ozero @ SV193 ) ) @ SY1294 )
= SY1294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1450,plain,
! [SV194: $i] :
( ( ! [SY1295: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV194 ) @ ( c_Suc @ SY1295 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV194 @ SY1295 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1451,plain,
! [SV195: $i] :
( ( ! [SY1296: $i] :
( ( c_HOL_Oord__class_Oless @ SV195 @ SY1296 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV195 ) @ ( c_Suc @ SY1296 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1452,plain,
! [SV196: $i] :
( ( ! [SY1297: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV196 ) @ ( c_Suc @ SY1297 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV196 @ SY1297 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1453,plain,
! [SV197: $i] :
( ( ! [SY1298: $i,SY1299: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV197 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1298 @ SV197 @ SY1299 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1298 ) @ SV197 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1454,plain,
! [SV198: $i] :
( ( ! [SY1300: $i,SY1301: $i,SY1302: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ SY1300 ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1301 @ SV198 @ SY1302 @ SY1300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1302 ) @ SY1300 ) ) @ SY1301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1455,plain,
! [SV199: $i] :
( ( ! [SY1303: $i,SY1304: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV199 ) ) @ SY1303 ) @ SY1304 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV199 ) @ ( c_Lambda_Olift @ SY1303 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1304 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1456,plain,
! [SV200: $i] :
( ( ! [SY1305: $i,SY1306: $i,SY1307: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SY1305 ) @ SY1306 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SY1307 ) @ SY1306 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1307 ) @ SY1305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1457,plain,
! [SV201: $i] :
( ( ! [SY1308: $i,SY1309: $i,SY1310: $i,SY1311: $i,SY1312: $i,SY1313: $i] :
( ( c_Type_Otypings @ SV201 @ SY1308 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1309 @ SY1310 @ SV201 @ SY1308 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1311 ) @ SY1312 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1310 ) )
| ~ ( c_Type_Otypings @ SV201 @ SY1312 @ SY1313 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1311 ) @ SY1312 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1458,plain,
! [SV202: $i] :
( ( ! [SY1314: $i,SY1315: $i,SY1316: $i] :
( ( c_Type_Otypings @ SV202 @ SY1314 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1315 @ SV202 @ SY1316 @ SY1314 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV202 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1316 ) @ SY1314 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1459,plain,
! [SV203: $i] :
( ( ! [SY1317: $i,SY1318: $i,SY1319: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ SY1317 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1318 @ SV203 @ SY1317 @ SY1319 ) @ SY1318 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1317 @ SY1319 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1460,plain,
! [SV204: $i] :
( ( ! [SY1320: $i,SY1321: $i,SY1322: $i,SY1323: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1320 @ SY1321 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1322 ) )
| ~ ( c_Type_Otypings @ SV204 @ SY1321 @ SY1323 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SY1320 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1323 @ SY1322 @ tc_Type_Otype @ tc_Type_Otype ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1461,plain,
! [SV205: $i] :
( ( ! [SY1324: $i,SY1325: $i,SY1326: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ SY1324 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1325 @ SV205 @ SY1324 @ SY1326 ) @ SY1325 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1324 @ SY1326 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1462,plain,
! [SV206: $i] :
( ( ! [SY1327: $i,SY1328: $i,SY1329: $i,SY1330: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SY1327 ) @ SY1328 ) @ SY1329 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1330 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SY1327 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1330 ) ) @ ( c_Suc @ SY1328 ) ) @ SY1329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1463,plain,
! [SV207: $i] :
( ( ! [SY1331: $i,SY1332: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV207 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SY1331 @ SV207 @ SY1332 ) ) ) @ SY1332 ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SY1331 @ SV207 @ SY1332 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV207 ) @ ( c_Lambda_OdB_OAbs @ SY1332 ) ) @ SY1331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1464,plain,
! [SV208: $i] :
( ( ! [SY1333: $i,SY1334: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV208 @ SY1333 ) ) ) @ SY1333 ) @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV208 @ SY1333 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV208 ) @ ( c_Lambda_OdB_OAbs @ SY1333 ) ) @ SY1334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1465,plain,
! [SV209: $i] :
( ( ! [SY1335: $i,SY1336: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV209 @ SY1335 ) ) @ ( c_Lambda_Olift @ SY1336 @ SY1335 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV209 ) @ SY1336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1466,plain,
! [SV210: $i] :
( ( ! [SY1337: $i,SY1338: $i,SY1339: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_Lambda_OdB_OVar @ SY1337 ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1338 @ SV210 @ SY1337 @ SY1339 ) @ SY1338 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1337 ) @ SY1339 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1467,plain,
! [SV211: $i] :
( ( ! [SY1340: $i,SY1341: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV211 ) @ SY1340 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1340 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV211 ) ) @ SY1340 ) @ SY1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1468,plain,
! [SV212: $i] :
( ( ! [SY1342: $i,SY1343: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SY1342 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SY1343 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY1342 @ SY1343 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1469,plain,
! [SV213: $i] :
( ( ! [SY1344: $i,SY1345: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SY1344 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1345 @ SY1344 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV213 ) @ SY1345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1470,plain,
! [SV214: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV214 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1471,plain,
! [SV215: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV215 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV215 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1472,plain,
! [SV216: $i] :
( ( ( c_Lambda_OdB_OVar @ SV216 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV216 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1473,plain,
! [SV217: $i] :
( ( ! [SY1346: $i,SY1347: $i,SY1348: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ SY1346 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1347 @ SV217 @ SY1346 @ SY1348 ) ) @ SY1347 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1346 ) @ SY1348 ) ) @ SY1347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1474,plain,
! [SV218: $i] :
( ( ! [SY1349: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV218 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1349 @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1349 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1475,plain,
! [SV219: $i] :
( ( ! [SY1350: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1350 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1350 @ SV219 ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1476,plain,
! [SV220: $i] :
( ( ! [SY1351: $i,SY1352: $i] :
( ( SV220
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1351 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1351 @ SY1352 @ SV220 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1351 ) @ SY1352 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1477,plain,
! [SV221: $i] :
( ( ! [SY1353: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV221 ) @ SY1353 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY1353 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1478,plain,
! [SV222: $i] :
( ( ! [SY1354: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV222 ) ) @ ( c_Lambda_OdB_OAbs @ SY1354 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SY1354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1479,plain,
! [SV223: $i] :
( ( ! [SY1355: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV223 ) @ ( c_Lambda_OdB_OVar @ SY1355 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1480,plain,
! [SV224: $i] :
( ( ! [SY1356: $i,SY1357: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV224 @ SY1356 ) ) @ ( c_Lambda_Olift @ SY1357 @ SY1356 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV224 ) @ SY1357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1481,plain,
! [SV225: $i] :
( ( ! [SY1358: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV225 ) @ SY1358 )
= ( c_Lambda_OdB_OVar @ SV225 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV225 @ SY1358 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1482,plain,
! [SV226: $i] :
( ( ! [SY1359: $i,SY1360: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV226 @ SY1359 ) ) @ SY1360 ) @ SY1359 )
= SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1483,plain,
! [SV227: $i] :
( ( ! [SY1361: $i,SY1362: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV227 ) @ SY1361 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1362 ) @ SY1361 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV227 ) @ SY1362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1484,plain,
! [SV228: $i] :
( ( ! [SY1363: $i,SY1364: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SY1363 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SY1364 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1363 ) @ SY1364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1485,plain,
! [SV229: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV229 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1486,plain,
! [SV230: $i] :
( ( ! [SY1365: $i] :
( ( c_HOL_Oord__class_Oless @ SV230 @ SV230 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV230 ) ) @ SY1365 ) @ SV230 )
= SY1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1487,plain,
! [SV231: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV231 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1488,plain,
! [SV232: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV232 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1489,plain,
! [SV233: $i] :
( ( ! [SY1366: $i,SY1367: $i,SY1368: $i] :
( ~ ( class_Orderings_Oorder @ SV233 )
| ( c_HOL_Oord__class_Oless @ SY1366 @ SY1367 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SY1366 @ SY1368 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SY1368 @ SY1367 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1490,plain,
! [SV234: $i] :
( ( ! [SY1369: $i,SY1370: $i,SY1371: $i] :
( ~ ( class_Orderings_Opreorder @ SV234 )
| ( c_HOL_Oord__class_Oless @ SY1369 @ SY1370 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY1371 @ SY1370 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY1369 @ SY1371 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1491,plain,
! [SV235: $i] :
( ( ! [SY1372: $i,SY1373: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV235 ) ) @ SY1372 ) @ SY1373 )
= ( c_Lambda_OdB_OVar @ SV235 ) )
| ( SV235 = SY1373 )
| ( c_HOL_Oord__class_Oless @ SY1373 @ SV235 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1492,plain,
! [SV236: $i] :
( ( ! [SY1374: $i,SY1375: $i,SY1376: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV236 ) @ SY1374 ) @ SY1375 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1376 ) @ SY1374 ) @ SY1375 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV236 ) @ SY1376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1493,plain,
! [SV237: $i] :
( ( ! [SY1377: $i,SY1378: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV237 ) @ SY1377 ) @ SY1378 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV237 @ SY1378 ) ) @ ( c_Lambda_Olift @ SY1377 @ SY1378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1494,plain,
! [SV238: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1495,plain,
! [SV239: $i] :
( ( ! [SY1379: $i,SY1380: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) ) @ SY1379 ) @ SY1380 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1379 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV239 ) @ SY1379 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1380 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1496,plain,
! [SV240: $i] :
( ( ! [SY1381: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV240 @ SY1381 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1497,plain,
! [SV241: $i] :
( ( ! [SY1382: $i,SY1383: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV241 @ SY1382 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1383 @ SY1382 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV241 ) @ SY1383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1498,plain,
! [SV242: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV242 @ SV242 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1499,plain,
! [SV243: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV243 @ SV243 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1500,plain,
! [SV244: $i] :
( ( ! [SY1384: $i] :
( ~ ( class_Orderings_Oorder @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ SY1384 @ SY1384 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1501,plain,
! [SV245: $i] :
( ( ! [SY1385: $i] :
( ~ ( class_Orderings_Olinorder @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ SY1385 @ SY1385 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1502,plain,
! [SV246: $i] :
( ( ! [SY1386: $i] :
( ~ ( class_Orderings_Opreorder @ SV246 )
| ~ ( c_HOL_Oord__class_Oless @ SY1386 @ SY1386 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1503,plain,
! [SV247: $i] :
( ( ! [SY1387: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV247 ) ) @ SY1387 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV247 ) @ SY1387 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1504,plain,
! [SV248: $i] :
( ( ! [SY1388: $i,SY1389: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV248 )
| ( c_HOL_Oord__class_Oless @ SY1388 @ SY1389 @ SV248 )
| ( c_HOL_Oord__class_Oless @ SY1389 @ SY1388 @ SV248 )
| ( SY1389 = SY1388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1505,plain,
! [SV249: $i] :
( ( ! [SY1390: $i,SY1391: $i] :
( ~ ( class_Orderings_Olinorder @ SV249 )
| ( SY1390 = SY1391 )
| ( c_HOL_Oord__class_Oless @ SY1391 @ SY1390 @ SV249 )
| ( c_HOL_Oord__class_Oless @ SY1390 @ SY1391 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1506,plain,
! [SV250: $i] :
( ( ! [SY1392: $i] :
( ( c_HOL_Oord__class_Oless @ SV250 @ SY1392 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1392 @ SV250 @ tc_nat )
| ( SY1392 = SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1507,plain,
! [SV251: $i] :
( ( ! [SY1393: $i,SY1394: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV251 @ SY1393 ) @ SY1394 ) )
| ( c_HOL_Oord__class_Oless @ SY1393 @ SY1394 @ tc_nat )
| ( SY1394 = SY1393 )
| ( c_HOL_Oord__class_Oless @ SY1394 @ SY1393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1508,plain,
! [SV252: $i] :
( ( ! [SY1395: $i,SY1396: $i,SY1397: $i,SY1398: $i] :
( ( SV252 = SY1395 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1396 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1397 ) @ SY1398 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1395 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1396 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1397 ) @ SY1398 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1509,plain,
! [SV253: $i] :
( ( ! [SY1399: $i] :
( ( c_HOL_Oord__class_Oless @ SV253 @ SY1399 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1399 @ SV253 @ tc_nat )
| ( SY1399 = SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1510,plain,
! [SV254: $i] :
( ( ! [SY1400: $i,SY1401: $i] :
( ~ ( class_Orderings_Olinorder @ SV254 )
| ( c_HOL_Oord__class_Oless @ SY1400 @ SY1401 @ SV254 )
| ( c_HOL_Oord__class_Oless @ SY1401 @ SY1400 @ SV254 )
| ( SY1401 = SY1400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1511,plain,
! [SV255: $i] :
( ( ! [SY1402: $i,SY1403: $i] :
( ~ ( class_Orderings_Olinorder @ SV255 )
| ( c_HOL_Oord__class_Oless @ SY1402 @ SY1403 @ SV255 )
| ( SY1403 = SY1402 )
| ( c_HOL_Oord__class_Oless @ SY1403 @ SY1402 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1512,plain,
! [SV256: $i] :
( ( ! [SY1404: $i,SY1405: $i] :
( ~ ( class_Orderings_Olinorder @ SV256 )
| ( SY1404 = SY1405 )
| ( c_HOL_Oord__class_Oless @ SY1404 @ SY1405 @ SV256 )
| ( c_HOL_Oord__class_Oless @ SY1405 @ SY1404 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1513,plain,
! [SV257: $i] :
( ( ! [SY1406: $i,SY1407: $i,SY1408: $i,SY1409: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1406 ) @ SY1407 ) ) @ SY1408 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SY1407 ) @ SY1409 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SY1406 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1409 ) @ SY1408 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1514,plain,
! [SV258: $i] :
( ( ! [SY1410: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV258 ) ) @ SY1410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1515,plain,
! [SV259: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV259 @ tc_nat )
| ( SV259
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1516,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)],[1121]) ).
thf(1517,plain,
! [SV260: $i] :
( ( ! [SY1411: $i,SY1412: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV260 ) ) @ SY1411 ) @ SY1412 )
= ( c_Lambda_OdB_OVar @ SV260 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV260 @ SY1412 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1518,plain,
! [SV261: $i] :
( ( ! [SY1413: $i,SY1414: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV261 ) @ ( c_Lambda_OdB_OVar @ SY1413 ) ) @ SY1414 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1519,plain,
! [SV262: $i] :
( ( ! [SY1415: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV262 ) ) @ SY1415 ) @ SV262 )
= SY1415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1520,plain,
! [SV263: $i] :
( ( ! [SY1416: $i,SY1417: $i,SY1418: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV263 ) @ SY1416 ) ) @ SY1417 ) @ SY1418 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV263 ) @ SY1417 ) @ SY1418 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1416 ) @ SY1417 ) @ SY1418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1521,plain,
! [SV264: $i] :
( ( ! [SY1419: $i,SY1420: $i] :
( ~ ( class_Orderings_Oorder @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SY1419 @ SY1420 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SY1420 @ SY1419 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1522,plain,
! [SV265: $i] :
( ( ! [SY1421: $i,SY1422: $i] :
( ~ ( class_Orderings_Olinorder @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SY1421 @ SY1422 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SY1422 @ SY1421 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1523,plain,
! [SV266: $i] :
( ( ! [SY1423: $i,SY1424: $i] :
( ~ ( class_Orderings_Opreorder @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SY1423 @ SY1424 @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SY1424 @ SY1423 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1524,plain,
! [SV267: $i] :
( ( ! [SY1425: $i,SY1426: $i] :
( ~ ( class_Orderings_Opreorder @ SV267 )
| ~ ( c_HOL_Oord__class_Oless @ SY1425 @ SY1426 @ SV267 )
| ~ ( c_HOL_Oord__class_Oless @ SY1426 @ SY1425 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1525,plain,
! [SV268: $i] :
( ( ! [SY1427: $i,SY1428: $i,SY1429: $i,SY1430: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV268 ) @ SY1427 ) @ SY1428 ) ) @ ( c_Lambda_Olift @ SY1429 @ SY1427 ) ) @ SY1430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV268 ) @ SY1429 ) @ SY1430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1526,plain,
! [SV269: $i] :
( ( ! [SY1431: $i,SY1432: $i,SY1433: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SY1431 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1432 ) @ SV269 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1432 ) @ SY1431 ) @ v_T____ ) ) @ v_a____ ) @ SY1433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1527,plain,
! [SV270: $i] :
( ( ! [SY1434: $i,SY1435: $i,SY1436: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SY1434 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1435 ) @ SV270 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1435 ) @ SY1434 ) @ v_T____ ) ) @ v_a____ ) @ SY1436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1528,plain,
! [SV271: $i] :
( ( ! [SY1437: $i,SY1438: $i,SY1439: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SY1437 ) @ SY1438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1439 ) @ SY1437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SY1439 ) @ SY1438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1529,plain,
! [SV272: $i] :
( ( ! [SY1440: $i,SY1441: $i,SY1442: $i,SY1443: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV272 ) @ SY1440 ) @ SY1441 ) @ SY1442 ) @ SY1443 )
= ( hAPP @ SY1440 @ SY1443 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1443 @ SY1441 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1530,plain,
! [SV273: $i] :
( ( ! [SY1444: $i,SY1445: $i,SY1446: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV273 ) @ SY1444 ) @ SY1445 ) @ SY1446 ) @ SY1445 )
= SY1446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1531,plain,
! [SV274: $i] :
( ( ! [SY1447: $i,SY1448: $i,SY1449: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV274 ) @ ( c_Lambda_OdB_OAbs @ SY1447 ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1448 ) @ SY1449 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1448 ) ) @ SY1447 ) @ SY1449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1532,plain,
! [SV275: $i] :
( ( ! [SY1450: $i,SY1451: $i] :
( ( ( hAPP @ SV275 @ SY1450 )
= SY1451 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV275 ) @ ( c_Lambda_OdB_OVar @ SY1450 ) ) @ SY1451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1533,plain,
! [SV276: $i] :
( ( v_thesis____
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1534,plain,
! [SV277: $i] :
( ( ! [SY1452: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV277 ) @ ( c_Lambda_OdB_OVar @ SY1452 ) ) @ ( hAPP @ SV277 @ SY1452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1535,plain,
! [SV278: $i] :
( ( ! [SY1453: $i,SY1454: $i,SY1455: $i,SY1456: $i,SY1457: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SY1453 ) @ SY1454 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SY1455 ) @ SY1454 ) ) @ SY1456 ) @ SY1457 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1456 ) @ SY1453 ) @ SY1455 ) ) @ SY1457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1536,plain,
! [SV279: $i] :
( ( ! [SY1458: $i,SY1459: $i,SY1460: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SY1458 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1459 ) @ SV279 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1459 ) @ SY1458 ) @ v_T____ ) ) @ v_a____ ) @ SY1460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1537,plain,
! [SV280: $i] :
( ( ! [SY1461: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV280 @ SY1461 ) )
| ~ ( class_Orderings_Opreorder @ SY1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1538,plain,
! [SV281: $i] :
( ( ! [SY1462: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV281 @ SY1462 ) )
| ~ ( class_Orderings_Oorder @ SY1462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1539,plain,
! [SV282: $i] :
( ( ! [SY1463: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV282 ) @ SY1463 ) @ SY1463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1540,plain,
! [SV283: $i] :
( ( ! [SY1464: $i,SY1465: $i] :
( ( SV283 = SY1464 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1465 ) @ SV283 ) @ SY1464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1541,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1542,plain,
! [SV284: $i] :
( ( ! [SY1466: $i,SY1467: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SY1466 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1467 @ SY1466 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV284 = SY1467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1543,plain,
! [SV285: $i] :
( ( ! [SY1468: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV285 ) @ SY1468 ) )
| ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV285
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1544,plain,
! [SV286: $i] :
( ( ! [SY1469: $i,SY1470: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV286 ) @ SY1469 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1470 ) @ SY1469 ) )
| ( SV286 = SY1470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1545,plain,
! [SV287: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV287 )
| ( ( c_HOL_Oone__class_Oone @ SV287 )
!= ( c_HOL_Ozero__class_Ozero @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1546,plain,
! [SV288: $i] :
( ( ! [SY1471: $i,SY1472: $i,SY1473: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1471 @ SY1471 @ SV288 )
!= ( c_HOL_Ominus__class_Ominus @ SY1472 @ SY1473 @ SV288 ) )
| ( SY1472 = SY1473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1547,plain,
! [SV289: $i] :
( ( ! [SY1474: $i,SY1475: $i] :
( ( ( c_Lambda_OdB_OVar @ SV289 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1474 @ SY1475 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV289 )
= SY1474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1548,plain,
! [SV290: $i] :
( ( ! [SY1476: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV290 ) @ SY1476 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1476
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV290
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1549,plain,
! [SV291: $i] :
( ( ! [SY1477: $i,SY1478: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV291 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY1477 @ SV291 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1478 @ SV291 ) )
| ( SY1477 = SY1478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1550,plain,
! [SV292: $i] :
( ( ! [SY1479: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV292 ) @ SY1479 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1479
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1551,plain,
! [SV293: $i] :
( ( ! [SY1480: $i,SY1481: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV293 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1480 @ SY1481 @ SV293 )
!= ( c_HOL_Ozero__class_Ozero @ SV293 ) )
| ( SY1480 = SY1481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1552,plain,
! [SV294: $i] :
( ( ! [SY1482: $i,SY1483: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV294 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1482 @ SY1483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV294 )
= SY1482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1553,plain,
! [SV295: $i] :
( ( ! [SY1484: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV295 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV295 ) @ SY1484 ) @ SY1484 )
!= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
| ( SY1484
= ( c_HOL_Ozero__class_Ozero @ SV295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1554,plain,
! [SV296: $i] :
( ( ! [SY1485: $i] :
( ( ( c_Suc @ SV296 )
!= ( c_Suc @ SY1485 ) )
| ( SV296 = SY1485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1555,plain,
! [SV297: $i] :
( ( ! [SY1486: $i] :
( ( ( c_Lambda_OdB_OVar @ SV297 )
!= ( c_Lambda_OdB_OVar @ SY1486 ) )
| ( SV297 = SY1486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1556,plain,
! [SV298: $i] :
( ( ! [SY1487: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV298 ) @ SY1487 ) )
| ( SY1487
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1487
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1557,plain,
! [SV299: $i] :
( ( ! [SY1488: $i,SY1489: $i,SY1490: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV299 ) @ SY1488 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1489 ) @ SY1490 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV299 = SY1489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1558,plain,
! [SV300: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1559,plain,
! [SV301: $i] :
( ( ( c_Suc @ SV301 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1560,plain,
! [SV302: $i] :
( ( ! [SY1491: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV302 )
!= ( c_Lambda_OdB_OAbs @ SY1491 ) )
| ( SV302 = SY1491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1561,plain,
! [SV303: $i] :
( ( ! [SY1492: $i,SY1493: $i,SY1494: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV303 )
| ~ ( class_Int_Onumber__ring @ SV303 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SY1492 ) @ SY1493 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SY1492 ) @ SY1494 ) )
| ( SY1493 = SY1494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1562,plain,
! [SV304: $i] :
( ( ! [SY1495: $i,SY1496: $i,SY1497: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV304 ) @ SY1495 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1496 ) @ SY1497 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV304 = SY1496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1563,plain,
! [SV305: $i] :
( ( ! [SY1498: $i,SY1499: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SY1498 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SY1499 ) )
| ( SY1498 = SY1499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1564,plain,
! [SV306: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV306 )
| ( ( c_HOL_Ozero__class_Ozero @ SV306 )
!= ( c_HOL_Oone__class_Oone @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1565,plain,
! [SV307: $i] :
( ( ! [SY1500: $i,SY1501: $i,SY1502: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV307 ) @ SY1500 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1501 ) @ SY1502 ) )
| ( SV307 = SY1501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1566,plain,
! [SV308: $i] :
( ( ! [SY1503: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV308 @ SY1503 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SY1503 @ SV308 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1503 = SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1567,plain,
! [SV309: $i] :
( ( SV309
!= ( c_Suc @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1568,plain,
! [SV310: $i] :
( ( ! [SY1504: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SY1504 )
!= SV310 )
| ( SY1504
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1569,plain,
! [SV311: $i] :
( ( ( c_Suc @ SV311 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1570,plain,
! [SV312: $i] :
( ( ! [SY1505: $i,SY1506: $i,SY1507: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV312 ) @ SY1505 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1506 ) @ SY1507 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1506 @ SY1505 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV312 @ SY1507 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1571,plain,
! [SV313: $i] :
( ( ! [SY1508: $i,SY1509: $i] :
( ( ( c_Lambda_OdB_OVar @ SV313 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1508 @ SY1509 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1509
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1572,plain,
! [SV314: $i] :
( ( ! [SY1510: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV314 ) @ SY1510 ) )
| ( SV314
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1510
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1573,plain,
! [SV315: $i] :
( ( ! [SY1511: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV315 ) @ SY1511 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1574,plain,
! [SV316: $i] :
( ( ! [SY1512: $i,SY1513: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV316 )
| ~ ( class_Int_Onumber__ring @ SV316 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1512 @ SY1513 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SY1512 = SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1575,plain,
! [SV317: $i] :
( ( ! [SY1514: $i] :
( ( c_Lambda_OdB_OVar @ SV317 )
!= ( c_Lambda_OdB_OAbs @ SY1514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1576,plain,
! [SV318: $i] :
( ( ! [SY1515: $i,SY1516: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV318 )
| ~ ( class_Int_Onumber__ring @ SV318 )
| ( SY1515
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SY1515 ) @ SY1516 ) )
| ( SY1516
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1577,plain,
! [SV319: $i] :
( ( ! [SY1517: $i,SY1518: $i,SY1519: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SY1517 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1518 ) @ SY1519 ) )
| ( SY1517 = SY1519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1578,plain,
! [SV320: $i] :
( ( ! [SY1520: $i,SY1521: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV320 ) @ SY1520 )
!= ( c_Lambda_OdB_OVar @ SY1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1579,plain,
! [SV321: $i] :
( ( ! [SY1522: $i,SY1523: $i] :
( ( c_Lambda_OdB_OVar @ SV321 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1522 ) @ SY1523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1580,plain,
! [SV322: $i] :
( ( ! [SY1524: $i,SY1525: $i] :
( ( c_Lambda_OdB_OAbs @ SV322 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1524 ) @ SY1525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1581,plain,
! [SV323: $i] :
( ( ! [SY1526: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SY1526 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1526
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1582,plain,
! [SV324: $i] :
( ( ! [SY1527: $i,SY1528: $i,SY1529: $i,SY1530: $i,SY1531: $i,SY1532: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SY1527 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1528 ) @ SY1529 ) @ SY1530 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1531 ) @ SY1529 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1531 ) @ SY1530 ) @ SV324 ) ) @ SY1528 ) @ SY1532 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1583,plain,
! [SV325: $i] :
( ( ! [SY1533: $i,SY1534: $i,SY1535: $i,SY1536: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1533 @ SY1534 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY1535 @ SY1536 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SY1533 @ SY1534 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SY1535 @ SY1536 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1584,plain,
! [SV326: $i] :
( ( ! [SY1537: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV326 ) @ SY1537 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1537
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1537
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1585,plain,
! [SV327: $i] :
( ( ! [SY1538: $i,SY1539: $i,SY1540: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SY1538 ) @ SY1539 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SY1538 ) @ SY1540 ) )
| ( SY1539 = SY1540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1586,plain,
! [SV328: $i] :
( ( ! [SY1541: $i,SY1542: $i,SY1543: $i,SY1544: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV328 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SY1541 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SY1542 ) @ SY1543 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SY1542 ) @ SY1544 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SY1541 ) @ SY1543 )
= SY1544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1587,plain,
! [SV329: $i] :
( ( ! [SY1545: $i,SY1546: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV329 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1545 @ SY1546 @ SV329 )
!= ( c_HOL_Ozero__class_Ozero @ SV329 ) )
| ( SY1545 = SY1546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1588,plain,
! [SV330: $i] :
( ( ( c_Suc @ SV330 )
!= SV330 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1589,plain,
! [SV331: $i] :
( ( ! [SY1547: $i,SY1548: $i,SY1549: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV331 ) @ SY1547 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1548 ) @ SY1549 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1590,plain,
! [SV332: $i] :
( ( ! [SY1550: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV332 ) @ SY1550 ) )
| ( SY1550
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV332
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1591,plain,
! [SV333: $i] :
( ( ! [SY1551: $i,SY1552: $i,SY1553: $i,SY1554: $i,SY1555: $i,SY1556: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SY1551 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1552 ) @ SY1553 ) @ SY1554 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1555 ) @ SY1553 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1555 ) @ SY1554 ) @ SY1551 ) ) @ SY1552 ) @ SY1556 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1592,plain,
! [SV334: $i] :
( ( ! [SY1557: $i,SY1558: $i,SY1559: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SY1557 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1558 ) @ SY1559 ) )
| ( SV334 = SY1558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1593,plain,
! [SV335: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1594,plain,
! [SV336: $i] :
( ( ! [SY1560: $i] :
( ( SV336
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV336 ) @ SY1560 ) )
| ( SY1560
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1595,plain,
! [SV337: $i] :
( ( ! [SY1561: $i,SY1562: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV337 @ SY1561 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1562 ) )
| ( SV337
= ( c_Lambda_OdB_OAbs @ SY1562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1596,plain,
! [SV338: $i] :
( ( ! [SY1563: $i,SY1564: $i,SY1565: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV338 ) @ SY1563 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1564 ) @ SY1565 ) )
| ( SY1563 = SY1565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1597,plain,
! [SV339: $i] :
( ( ! [SY1566: $i,SY1567: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV339 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1566 @ SY1567 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1567
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1598,plain,
! [SV340: $i] :
( ( ! [SY1568: $i,SY1569: $i,SY1570: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV340 ) ) @ SY1568 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1569 ) @ SY1570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1599,plain,
! [SV341: $i] :
( ( ! [SY1571: $i,SY1572: $i,SY1573: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV341 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SY1571 ) @ SY1572 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SY1571 ) @ SY1573 ) )
| ( SY1572 = SY1573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1600,plain,
! [SV342: $i] :
( ( ! [SY1574: $i,SY1575: $i,SY1576: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV342 ) @ SY1574 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1575 ) @ SY1576 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1574 = SY1576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1601,plain,
! [SV343: $i] :
( ( ! [SY1577: $i,SY1578: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV343 ) @ SY1577 )
!= ( c_Lambda_OdB_OAbs @ SY1578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1602,plain,
! [SV344: $i] :
( ( ! [SY1579: $i,SY1580: $i,SY1581: $i,SY1582: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1579 @ SY1580 @ SV344 )
!= ( c_HOL_Ominus__class_Ominus @ SY1581 @ SY1582 @ SV344 ) )
| ( c_HOL_Oord__class_Oless @ SY1581 @ SY1582 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SY1579 @ SY1580 @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1603,plain,
! [SV345: $i] :
( ( ! [SY1583: $i,SY1584: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SY1583 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SY1584 ) )
| ( SY1583 = SY1584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1604,plain,
! [SV346: $i] :
( ( ! [SY1585: $i] :
( ( ( c_Suc @ SV346 )
!= ( c_Suc @ SY1585 ) )
| ( SV346 = SY1585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1605,plain,
! [SV347: $i] :
( ( ! [SY1586: $i,SY1587: $i,SY1588: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV347 ) @ SY1586 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1587 ) @ SY1588 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1586 = SY1588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1606,plain,
! [SV348: $i] :
( ( ! [SY1589: $i,SY1590: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV348 @ SY1589 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1590 ) )
| ( SY1589
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1607,plain,
! [SV349: $i] :
( ( ! [SY1591: $i,SY1592: $i,SY1593: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV349 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1591 @ SY1592 @ SV349 )
!= ( c_HOL_Ominus__class_Ominus @ SY1593 @ SY1593 @ SV349 ) )
| ( SY1591 = SY1592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1608,plain,
! [SV350: $i] :
( ( ! [SY1594: $i,SY1595: $i,SY1596: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SY1594 ) @ SY1595 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SY1596 ) @ SY1595 ) )
| ( SY1594 = SY1596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1609,plain,
! [SV351: $i] :
( ( ! [SY1597: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV351 ) @ SY1597 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV351
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV351
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1610,plain,
! [SV352: $i] :
( ( ! [SY1598: $i,SY1599: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SY1598 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1599 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SY1598 )
= SY1599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1611,plain,
( ( v_n____ = v_i____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1612,plain,
! [SV353: $i] :
( ( ! [SY1600: $i] :
( ( c_Lambda_OdB_OAbs @ SV353 )
!= ( c_Lambda_OdB_OVar @ SY1600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1613,plain,
! [SV1: $i] :
( ( v_thesis____ = $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1614,plain,
! [SV354: $i,SV4: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV354 @ tc_nat ) @ SV4 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV4 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1615,plain,
! [SV355: $i,SV5: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV5 @ SV355 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV355 @ SV5 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1616,plain,
! [SV356: $i,SV6: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV6 @ SV356 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV356 @ SV6 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1617,plain,
! [SV357: $i,SV7: $i] :
( ( ! [SY1601: $i] :
( ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV357 @ SY1601 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ominus__class_Ominus @ SV357 @ SY1601 @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1618,plain,
! [SV358: $i,SV8: $i] :
( ( ! [SY1602: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV8 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SY1602 @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SV358 @ SY1602 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1619,plain,
! [SV359: $i,SV9: $i] :
( ( ! [SY1603: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV9 )
| ( c_HOL_Oord__class_Oless @ SV359 @ SY1603 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SY1603 @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1620,plain,
! [SV360: $i,SV10: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV10 ) @ ( c_HOL_Ominus__class_Ominus @ SV360 @ SV10 @ tc_nat ) )
= SV360 )
| ( c_HOL_Oord__class_Oless @ SV360 @ SV10 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1621,plain,
! [SV361: $i,SV11: $i] :
( ( ! [SY1604: $i] :
( ( c_HOL_Oord__class_Oless @ SV11 @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SY1604 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV11 ) @ SY1604 ) @ SV361 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1622,plain,
! [SV362: $i,SV12: $i] :
( ( ! [SY1605: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV12 ) @ SV362 ) @ SY1605 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_HOL_Ominus__class_Ominus @ SY1605 @ SV362 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1623,plain,
! [SV363: $i,SV13: $i] :
( ( ! [SY1606: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ SV363 @ tc_nat ) @ SY1606 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SY1606 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1624,plain,
! [SV364: $i,SV14: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV14 ) @ ( c_Suc @ SV364 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV14 @ SV364 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1625,plain,
! [SV365: $i,SV17: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV17 )
| ~ ( class_Int_Onumber__ring @ SV17 )
| ( ( c_HOL_Ominus__class_Ominus @ SV365 @ SV365 @ SV17 )
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1626,plain,
! [SV366: $i,SV18: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV18 )
| ( ( c_HOL_Ominus__class_Ominus @ SV366 @ SV366 @ SV18 )
= ( c_HOL_Ozero__class_Ozero @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1627,plain,
! [SV367: $i,SV19: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV19 )
| ( ( c_HOL_Ominus__class_Ominus @ SV367 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= SV367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1628,plain,
! [SV368: $i,SV20: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV20 )
| ( ( c_HOL_Ominus__class_Ominus @ SV368 @ SV368 @ SV20 )
= ( c_HOL_Ozero__class_Ozero @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1629,plain,
! [SV369: $i,SV21: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV21 )
| ( ( c_HOL_Ominus__class_Ominus @ SV369 @ SV369 @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1630,plain,
! [SV370: $i,SV22: $i] :
( ( ! [SY1607: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV370 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SY1607 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1607 @ SV22 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1607 @ SV370 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1631,plain,
! [SV371: $i,SV24: $i] :
( ( ! [SY1608: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV24 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ominus__class_Ominus @ SV371 @ SY1608 @ SV24 ) ) @ SY1608 )
= SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1632,plain,
! [SV372: $i,SV25: $i] :
( ( ! [SY1609: $i] :
( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV372 ) @ SY1609 ) @ SV372 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV25 @ SY1609 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1633,plain,
! [SV373: $i,SV26: $i] :
( ( ! [SY1610: $i] :
( ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV373 ) @ SY1610 ) @ SV373 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV26 @ SY1610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1634,plain,
! [SV374: $i,SV27: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV27 @ SV374 @ tc_nat ) @ ( c_Suc @ SV27 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1635,plain,
! [SV375: $i,SV28: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV28 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV28 ) @ SV375 ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1636,plain,
! [SV376: $i,SV29: $i] :
( ( ! [SY1611: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV29 @ SV376 @ tc_nat ) @ SY1611 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV29 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV376 ) @ SY1611 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1637,plain,
! [SV377: $i,SV31: $i] :
( ( ! [SY1612: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV31 ) @ SV377 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1612 ) @ SV377 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV31 @ SY1612 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1638,plain,
! [SV378: $i,SV32: $i] :
( ( ! [SY1613: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV32 ) @ SV378 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV32 ) @ SY1613 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV378 @ SY1613 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1639,plain,
! [SV379: $i,SV33: $i] :
( ( ! [SY1614: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ SV379 @ tc_nat ) @ SY1614 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ SY1614 @ tc_nat ) @ SV379 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1640,plain,
! [SV380: $i,SV34: $i] :
( ( ! [SY1615: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV34 ) @ SV380 @ tc_nat ) @ ( c_Suc @ SY1615 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SV380 @ tc_nat ) @ SY1615 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1641,plain,
! [SV381: $i,SV35: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV35 @ ( c_Suc @ SV381 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV35 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV381 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1642,plain,
! [SV382: $i,SV36: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV36 ) @ SV382 ) @ SV382 @ tc_nat )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1643,plain,
! [SV383: $i,SV37: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV37 ) @ SV383 ) @ SV37 @ tc_nat )
= SV383 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1644,plain,
! [SV384: $i,SV38: $i] :
( ( ! [SY1616: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV38 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV384 ) @ SY1616 ) @ SY1616 @ SV38 )
= SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1645,plain,
! [SV385: $i,SV39: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV39 @ ( c_Suc @ SV385 ) @ tc_nat ) @ SV39 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV39 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1646,plain,
! [SV40: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV40 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV40 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV40 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1647,plain,
! [SV386: $i,SV41: $i] :
( ( ! [SY1617: $i,SY1618: $i,SY1619: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV41 ) @ SV386 ) @ SY1617 ) @ SY1618 ) @ SY1619 )
= ( hAPP @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SY1619 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1617 @ SY1619 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1648,plain,
! [SV387: $i,SV42: $i] :
( ( ! [SY1620: $i,SY1621: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV42 @ SV387 ) @ SY1620 ) @ SY1621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV42 @ SY1620 ) @ SY1621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1649,plain,
! [SV388: $i,SV43: $i] :
( ( ! [SY1622: $i] :
~ ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_ONil @ SV388 ) @ SY1622 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1650,plain,
! [SV389: $i,SV44: $i] :
( ( ! [SY1623: $i] :
~ ( c_ListOrder_Ostep1 @ SV44 @ SV389 @ ( c_List_Olist_ONil @ SY1623 ) @ SY1623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1651,plain,
! [SV390: $i,SV45: $i] :
( ( ! [SY1624: $i,SY1625: $i] :
( ( c_List_Ofoldl @ SV45 @ SV390 @ ( c_List_Olist_ONil @ SY1624 ) @ SY1625 @ SY1624 )
= SV390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1652,plain,
! [SV391: $i,SV47: $i] :
( ( ( SV47 = SV391 )
| ( c_HOL_Oord__class_Oless @ SV47 @ SV391 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV47 @ ( c_Suc @ SV391 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1653,plain,
! [SV392: $i,SV48: $i] :
( ( ( SV48 = SV392 )
| ~ ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SV48 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV392 @ SV48 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1654,plain,
! [SV393: $i,SV49: $i] :
( ( ( SV49 = SV393 )
| ~ ( c_HOL_Oord__class_Oless @ SV49 @ ( c_Suc @ SV393 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV49 @ SV393 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1655,plain,
! [SV394: $i,SV50: $i] :
( ( ! [SY1626: $i,SY1627: $i,SY1628: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SY1626 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SY1627 ) @ SY1628 ) @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SY1626 @ SY1628 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ SY1627 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1656,plain,
! [SV395: $i,SV51: $i] :
( ( ! [SY1629: $i,SY1630: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV395 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1629 ) @ SY1630 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV395 @ SY1630 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV51 @ SY1629 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1657,plain,
! [SV396: $i,SV54: $i] :
( ( ! [SY1631: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV54 ) @ SV396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1631 @ SV396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY1631 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1658,plain,
! [SV397: $i,SV55: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV55 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV397 @ SV55 @ SV55 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV397 @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1659,plain,
! [SV398: $i,SV56: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV398 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV398 ) @ ( c_HOL_Oone__class_Oone @ SV56 ) ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1660,plain,
! [SV399: $i,SV57: $i] :
( ( ! [SY1632: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV57 @ SV399 @ SY1632 ) @ SY1632 @ SV399 )
= SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1661,plain,
! [SV400: $i,SV58: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SV400 ) @ SV58 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1662,plain,
! [SV401: $i,SV59: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV59 ) @ SV401 ) @ SV401 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1663,plain,
! [SV402: $i,SV60: $i] :
( ( ! [SY1633: $i,SY1634: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV60 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV402 ) @ SY1633 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1634 ) @ SY1633 ) @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV402 @ SY1634 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1664,plain,
! [SV403: $i,SV61: $i] :
( ( ! [SY1635: $i,SY1636: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV61 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV403 ) @ SY1635 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1636 ) @ SY1635 ) @ SV61 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SY1636 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1665,plain,
! [SV404: $i,SV62: $i] :
( ( ! [SY1637: $i,SY1638: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV62 )
| ( c_HOL_Oord__class_Oless @ SV404 @ SY1637 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV404 ) @ SY1638 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SY1637 ) @ SY1638 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1666,plain,
! [SV405: $i,SV63: $i] :
( ( ! [SY1639: $i,SY1640: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV63 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SY1639 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SY1640 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY1639 @ SY1640 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1667,plain,
! [SV406: $i,SV64: $i] :
( ( ! [SY1641: $i,SY1642: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SY1641 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SY1642 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SY1641 @ SY1642 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1668,plain,
! [SV407: $i,SV65: $i] :
( ( ! [SY1643: $i,SY1644: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV65 )
| ( c_HOL_Oord__class_Oless @ SV407 @ SY1643 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY1644 ) @ SV407 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY1644 ) @ SY1643 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1669,plain,
! [SV408: $i,SV66: $i] :
( ( ! [SY1645: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV66 ) @ SV408 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1645 ) @ SV408 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV66 @ SY1645 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1670,plain,
! [SV409: $i,SV67: $i] :
( ( ! [SY1646: $i] :
( ( c_HOL_Oord__class_Oless @ SV67 @ SV409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1646 ) @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1646 ) @ SV409 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1671,plain,
! [SV410: $i,SV68: $i] :
( ( ! [SY1647: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SY1647 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV410 @ SY1647 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1672,plain,
! [SV411: $i,SV69: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV69 @ SV411 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV69 ) @ SV411 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1673,plain,
! [SV412: $i,SV70: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV70 @ ( c_Suc @ SV412 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV70 @ SV412 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1674,plain,
! [SV413: $i,SV71: $i] :
( ( ! [SY1648: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV71 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SY1648 ) @ SV71 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV413 @ SV71 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1648 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1675,plain,
! [SV414: $i,SV72: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ SV72 ) @ SV414 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ SV72 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV414 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1676,plain,
! [SV415: $i,SV73: $i] :
( ( ! [SY1649: $i,SY1650: $i,SY1651: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SY1649 ) @ SY1650 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SY1651 ) @ SY1650 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SY1649 ) @ SY1651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1677,plain,
! [SV416: $i,SV74: $i] :
( ( ! [SY1652: $i,SY1653: $i,SY1654: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SY1652 ) @ SY1653 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SY1654 ) @ SY1653 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SY1652 ) @ SY1654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1678,plain,
! [SV417: $i,SV75: $i] :
( ( ! [SY1655: $i,SY1656: $i] :
( ( c_Wellfounded_Oaccp @ SV75 @ SV417 @ SY1655 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV75 @ SV417 ) @ SY1656 ) )
| ~ ( c_Wellfounded_Oaccp @ SV75 @ SY1656 @ SY1655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1679,plain,
! [SV418: $i,SV76: $i] :
( ( ! [SY1657: $i,SY1658: $i] :
( ( c_Wellfounded_Oaccp @ SV76 @ SV418 @ SY1657 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV418 ) @ SY1658 ) )
| ~ ( c_Wellfounded_Oaccp @ SV76 @ SY1658 @ SY1657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1680,plain,
! [SV419: $i,SV77: $i] :
( ( ! [SY1659: $i,SY1660: $i] :
( ( c_Type_Otypings @ SV77 @ SV419 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1659 @ SV77 @ SY1660 @ SV419 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV77 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1660 @ SV419 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1681,plain,
! [SV420: $i,SV78: $i] :
( ( ! [SY1661: $i,SY1662: $i] :
( ( c_Type_Otypings @ SV78 @ SV420 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1661 @ SV78 @ SY1662 @ SV420 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV78 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1662 @ SV420 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1682,plain,
! [SV421: $i,SV79: $i] :
( ( ! [SY1663: $i,SY1664: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV79 ) @ SV421 ) @ SY1663 ) @ SY1664 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV79 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1664 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( c_Lambda_Olift @ SV421 @ SY1664 ) ) @ SY1663 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1663 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1664 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1683,plain,
! [SV422: $i,SV80: $i] :
( ( ! [SY1665: $i,SY1666: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV80 ) @ SV422 ) @ SY1665 ) @ SY1666 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV80 @ SY1666 ) ) @ ( c_Lambda_Olift @ SV422 @ SY1666 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1665 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1666 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1665 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1684,plain,
! [SV423: $i,SV81: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV81 ) @ SV423 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV81 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ SV81 @ SV423 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1685,plain,
! [SV424: $i,SV82: $i] :
( ( ! [SY1667: $i] :
( ( SV82
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV82 @ SV424 @ SY1667 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV82 @ SV424 @ SY1667 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV424 ) @ ( c_Lambda_OdB_OAbs @ SY1667 ) ) @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1686,plain,
! [SV425: $i,SV83: $i] :
( ( ! [SY1668: $i,SY1669: $i,SY1670: $i,SY1671: $i,SY1672: $i] :
( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SY1668 @ SY1669 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1668 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1670 ) @ SY1671 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
| ~ ( c_Type_Otypings @ SY1668 @ SY1671 @ SY1672 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1668 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1670 ) @ SY1671 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1669 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1687,plain,
! [SV426: $i,SV84: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV84 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV426 ) @ SV426 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV426 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1688,plain,
! [SV427: $i,SV85: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV85 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV427 @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV427 ) @ SV427 ) @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1689,plain,
! [SV428: $i,SV86: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV428 @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1690,plain,
! [SV429: $i,SV87: $i] :
( ( ! [SY1673: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV429 ) @ SY1673 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SY1673 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1691,plain,
! [SV430: $i,SV88: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV88 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SV430 ) @ SV430 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SV430 @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1692,plain,
! [SV431: $i,SV89: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV431 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV431 ) @ SV431 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1693,plain,
! [SV432: $i,SV90: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV90 )
| ( c_HOL_Oord__class_Oless @ SV432 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV432 ) @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1694,plain,
! [SV433: $i,SV91: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV91 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ SV433 ) @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV433 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1695,plain,
! [SV92: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV92 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1696,plain,
! [SV434: $i,SV93: $i] :
( ( ! [SY1674: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV434 ) @ SY1674 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SY1674 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV434 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1697,plain,
! [SV94: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV94 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( c_HOL_Oone__class_Oone @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1698,plain,
! [SV435: $i,SV95: $i] :
( ( ! [SY1675: $i,SY1676: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY1675 ) @ SY1676 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV435 @ SY1676 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SY1675 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1699,plain,
! [SV96: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV96 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV96 )
= ( c_HOL_Ozero__class_Ozero @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1700,plain,
! [SV436: $i,SV97: $i] :
( ( ! [SY1677: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV97 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV436 @ SV97 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1677 @ SV97 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV436 @ SY1677 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1701,plain,
! [SV437: $i,SV98: $i] :
( ( ! [SY1678: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV98 )
| ( c_HOL_Oord__class_Oless @ SV437 @ SY1678 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV437 @ SV98 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1678 @ SV98 ) @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1702,plain,
! [SV438: $i,SV99: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV99 ) @ SV438 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV99 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1703,plain,
! [SV439: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV100 ) @ SV439 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV439 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1704,plain,
! [SV440: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV103 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV440 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SV103 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1705,plain,
! [SV104: $i] :
( ( ( SV104
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV104 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1706,plain,
! [SV441: $i,SV105: $i] :
( ( ! [SY1679: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV441 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SY1679 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV441 @ SY1679 @ SV105 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1707,plain,
! [SV442: $i,SV106: $i] :
( ( ! [SY1680: $i,SY1681: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV106 ) @ SV442 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1680 ) @ SY1681 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV442 ) @ SY1681 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV106 ) @ SY1680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1708,plain,
! [SV443: $i,SV107: $i] :
( ( ! [SY1682: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV107 ) @ SV443 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1682 ) @ SV443 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV107 ) @ SY1682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1709,plain,
! [SV444: $i,SV108: $i] :
( ( ! [SY1683: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SV444 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SY1683 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV444 ) @ SY1683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1710,plain,
! [SV445: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV109 ) ) @ ( c_Lambda_OdB_OAbs @ SV445 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1711,plain,
! [SV446: $i,SV110: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV110 ) @ SV446 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV110 ) @ SV446 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1712,plain,
! [SV447: $i,SV111: $i] :
( ( ! [SY1684: $i,SY1685: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SV447 ) @ SY1684 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SY1685 ) @ SY1684 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV447 ) @ SY1685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1713,plain,
! [SV448: $i,SV112: $i] :
( ( ! [SY1686: $i,SY1687: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV112 ) @ SV448 ) @ SY1686 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1687 ) @ SV448 ) @ SY1686 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV112 ) @ SY1687 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1714,plain,
! [SV449: $i,SV113: $i] :
( ( ! [SY1688: $i,SY1689: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SV449 ) @ SY1688 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SY1689 ) @ SY1688 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV449 ) @ SY1689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1715,plain,
! [SV450: $i,SV114: $i] :
( ( ! [SY1690: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV114 ) ) @ SV450 ) @ SY1690 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1690 @ SV114 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1716,plain,
! [SV451: $i,SV115: $i] :
( ( ! [SY1691: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV115 ) ) @ SV451 ) @ SY1691 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV115 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1691 @ SV115 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1717,plain,
! [SV452: $i,SV116: $i] :
( ( ( c_Type_Otype_Otype__size @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV116 ) @ SV452 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Type_Otype_Otype__size @ SV116 ) ) @ ( c_Type_Otype_Otype__size @ SV452 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1718,plain,
! [SV453: $i,SV117: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV117 ) @ SV453 ) @ tc_Type_Otype )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV117 @ tc_Type_Otype ) ) @ ( c_Nat_Osize__class_Osize @ SV453 @ tc_Type_Otype ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1719,plain,
! [SV454: $i,SV118: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV118 ) @ SV454 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV118 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ SV454 ) ) )
| ( SV118
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1720,plain,
! [SV119: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV119 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV119 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV119 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1721,plain,
! [SV120: $i] :
( ( ( SV120
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV120 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1722,plain,
! [SV455: $i,SV123: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV455 ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV123 @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ SV455 @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1723,plain,
! [SV456: $i,SV124: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV456 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ SV124 ) ) @ ( c_Lambda_OdB_OdB__size @ SV456 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1724,plain,
! [SV457: $i,SV125: $i] :
( ( ! [SY1692: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV125 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SV457 @ SY1692 @ SV125 @ SV125 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SY1692 @ SV457 @ SV125 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1725,plain,
! [SV458: $i,SV126: $i] :
( ( ! [SY1693: $i,SY1694: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV126 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ SY1693 ) @ SY1694 @ SV126 @ SV126 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SY1693 @ SY1694 @ SV126 @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1726,plain,
! [SV459: $i,SV127: $i] :
( ( ! [SY1695: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SV459 ) @ SY1695 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SY1695 ) @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1727,plain,
! [SV460: $i,SV128: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV128 ) @ SV460 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV460 ) @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1728,plain,
! [SV461: $i,SV129: $i] :
( ( ! [SY1696: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV129 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV461 ) @ SY1696 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SY1696 ) @ SV461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1729,plain,
! [SV462: $i,SV130: $i] :
( ( ! [SY1697: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV462 ) @ SY1697 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SY1697 ) @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1730,plain,
! [SV463: $i,SV131: $i] :
( ( ! [SY1698: $i] :
( ( c_HOL_Oord__class_Oless @ SV131 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV463 ) @ SY1698 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV131 @ SY1698 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1731,plain,
! [SV464: $i,SV132: $i] :
( ( ! [SY1699: $i] :
( ( c_HOL_Oord__class_Oless @ SV132 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV464 ) @ SY1699 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV132 @ SV464 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1732,plain,
! [SV465: $i,SV133: $i] :
( ( ! [SY1700: $i] :
( ( c_HOL_Oord__class_Oless @ SV133 @ SV465 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV133 ) @ SY1700 ) @ SV465 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1733,plain,
! [SV466: $i,SV134: $i] :
( ( ! [SY1701: $i] :
( ( c_HOL_Oord__class_Oless @ SV134 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV466 ) @ SY1701 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV134 @ SY1701 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1734,plain,
! [SV467: $i,SV135: $i] :
( ( ! [SY1702: $i] :
( ( c_HOL_Oord__class_Oless @ SV135 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV467 ) @ SY1702 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV135 @ SV467 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1735,plain,
! [SV468: $i,SV136: $i] :
( ( c_HOL_Oord__class_Oless @ SV136 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV136 ) @ SV468 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1736,plain,
! [SV469: $i,SV137: $i] :
( ( c_HOL_Oord__class_Oless @ SV137 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV469 ) @ SV137 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1737,plain,
! [SV470: $i,SV138: $i] :
( ( c_HOL_Oord__class_Oless @ SV138 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV138 ) @ SV470 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1738,plain,
! [SV471: $i,SV139: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV139 ) ) @ SV471 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV139 ) @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1739,plain,
! [SV472: $i,SV140: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV140 ) @ ( c_Suc @ SV472 ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV140 ) @ SV472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1740,plain,
! [SV141: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV141 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV141 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1741,plain,
! [SV142: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1742,plain,
! [SV473: $i,SV143: $i] :
( ( ! [SY1703: $i,SY1704: $i,SY1705: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SY1703 ) @ SY1704 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SY1705 ) @ SY1704 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SY1703 ) @ SY1705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1743,plain,
! [SV474: $i,SV144: $i] :
( ( ! [SY1706: $i,SY1707: $i] :
( ( c_Wellfounded_Oaccp @ SV144 @ SV474 @ SY1706 )
| ~ ( c_Wellfounded_Oaccp @ SV144 @ SY1707 @ SY1706 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV144 @ SY1706 ) @ SV474 ) @ SY1707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1744,plain,
! [SV475: $i,SV145: $i] :
( ( ! [SY1708: $i,SY1709: $i] :
( ( c_Wellfounded_Oaccp @ SV145 @ SV475 @ SY1708 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SY1708 ) @ SV475 ) @ SY1709 ) )
| ~ ( c_Wellfounded_Oaccp @ SV145 @ SY1709 @ SY1708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1745,plain,
! [SV476: $i,SV146: $i] :
( ( ! [SY1710: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV146 @ SV476 ) @ SY1710 ) @ SY1710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1746,plain,
! [SV477: $i,SV147: $i] :
( ( ! [SY1711: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV147 @ SV477 ) @ SY1711 ) @ SY1711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1747,plain,
! [SV478: $i,SV148: $i] :
( ( c_List_Olistsp @ SV148 @ ( c_List_Olist_ONil @ SV478 ) @ SV478 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1748,plain,
! [SV151: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV151 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1749,plain,
! [SV479: $i,SV152: $i] :
( ( ! [SY1712: $i,SY1713: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY1712 ) @ SY1713 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ SY1712 ) ) @ SY1713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1750,plain,
! [SV480: $i,SV153: $i] :
( ( ! [SY1714: $i,SY1715: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1714 ) @ SY1715 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SY1714 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ SY1715 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1751,plain,
! [SV481: $i,SV154: $i] :
( ( ! [SY1716: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SY1716 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ SY1716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1752,plain,
! [SV482: $i,SV155: $i] :
( ( ! [SY1717: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SV482 ) ) @ SY1717 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV482 ) @ SY1717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1753,plain,
! [SV483: $i,SV156: $i] :
( ( ! [SY1718: $i,SY1719: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ SY1718 ) ) @ SY1719 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY1718 ) @ SY1719 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1754,plain,
! [SV484: $i,SV157: $i] :
( ( ! [SY1720: $i,SY1721: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1720 ) @ SY1721 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY1720 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ SY1721 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1755,plain,
! [SV485: $i,SV158: $i] :
( ( ! [SY1722: $i,SY1723: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ SY1722 ) ) @ SY1723 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY1722 ) @ SY1723 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1756,plain,
! [SV486: $i,SV159: $i] :
( ( ! [SY1724: $i,SY1725: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SY1724 ) @ SY1725 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ SY1724 ) ) @ SY1725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1757,plain,
! [SV487: $i,SV160: $i] :
( ( ! [SY1726: $i,SY1727: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SY1726 ) ) @ SY1727 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SY1727 ) ) @ SY1726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1758,plain,
! [SV488: $i,SV161: $i] :
( ( ! [SY1728: $i,SY1729: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY1728 ) @ SY1729 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY1728 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ SY1729 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1759,plain,
! [SV489: $i,SV162: $i] :
( ( ! [SY1730: $i,SY1731: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ SY1730 ) ) @ SY1731 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SY1730 ) @ SY1731 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1760,plain,
! [SV490: $i,SV163: $i] :
( ( ! [SY1732: $i,SY1733: $i,SY1734: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV163 @ SV490 @ SY1732 ) @ SY1733 ) @ SY1734 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV163 @ SY1734 ) @ SY1733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1761,plain,
! [SV491: $i,SV164: $i] :
( ( ! [SY1735: $i,SY1736: $i,SY1737: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV164 @ SV491 ) @ SY1735 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV164 @ SY1736 @ SY1737 ) @ SY1735 ) @ SV491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1762,plain,
! [SV492: $i,SV165: $i] :
( ( ! [SY1738: $i,SY1739: $i,SY1740: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV165 @ SV492 @ SY1738 ) @ SY1739 ) @ SY1740 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV165 @ SY1740 ) @ SY1739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1763,plain,
! [SV493: $i,SV166: $i] :
( ( ! [SY1741: $i,SY1742: $i,SY1743: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV493 ) @ SY1741 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV166 @ SY1742 @ SY1743 ) @ SY1741 ) @ SV493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1764,plain,
! [SV494: $i,SV167: $i] :
( ( ! [SY1744: $i,SY1745: $i] :
( ( c_List_Ofoldr @ SV167 @ ( c_List_Olist_ONil @ SV494 ) @ SY1744 @ SV494 @ SY1745 )
= SY1744 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1765,plain,
! [SV168: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV168 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV168 )
= ( c_HOL_Oone__class_Oone @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1766,plain,
! [SV495: $i,SV169: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV169 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV495 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ ( c_HOL_Oone__class_Oone @ SV169 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV495 @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1767,plain,
! [SV496: $i,SV170: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV170 ) ) @ SV496 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV170 ) @ ( c_Suc @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1768,plain,
! [SV497: $i,SV171: $i] :
( ( ! [SY1746: $i,SY1747: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV171 @ SV497 ) @ SY1746 ) @ SY1747 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV171 @ SV497 @ SV497 ) @ SV497 ) @ SY1747 ) @ SY1746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1769,plain,
! [SV498: $i,SV172: $i] :
( ( ! [SY1748: $i,SY1749: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV172 @ SV498 @ SV498 ) @ SV498 ) @ SY1748 ) @ SY1749 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV172 @ SV498 ) @ SY1749 ) @ SY1748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1770,plain,
! [SV499: $i,SV173: $i] :
( ( ! [SY1750: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV173 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV499 @ SY1750 @ SV173 @ SV173 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV499 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SY1750 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 @ SV173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1771,plain,
! [SV500: $i,SV174: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV174 ) @ SV500 @ tc_nat )
| ( ( c_Suc @ SV174 )
= SV500 )
| ~ ( c_HOL_Oord__class_Oless @ SV174 @ SV500 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1772,plain,
! [SV501: $i,SV175: $i] :
( ( ! [SY1751: $i,SY1752: $i,SY1753: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ ( c_Lambda_Olift @ SV501 @ SY1751 ) ) @ ( c_Suc @ SY1752 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1753 ) @ SV501 ) @ SY1752 ) ) @ SY1751 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SY1753 ) @ SY1751 ) ) @ SV501 ) @ SY1752 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1751 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1752 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1773,plain,
! [SV502: $i,SV176: $i] :
( ( ! [SY1754: $i,SY1755: $i,SY1756: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV176 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SY1754 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SY1755 ) @ SY1756 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SY1755 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SY1754 ) @ SY1756 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1774,plain,
! [SV177: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV177 @ SV177 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV177 @ ( c_Suc @ SV177 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1775,plain,
! [SV503: $i,SV178: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV178 @ SV503 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV503 @ ( c_Suc @ SV178 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1776,plain,
! [SV504: $i,SV179: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV179 @ ( c_Suc @ SV504 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV504 @ SV179 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1777,plain,
! [SV505: $i,SV180: $i] :
( ( ! [SY1757: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SV505 ) @ ( c_Suc @ SY1757 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SY1757 ) @ SV505 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV505 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1757 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1778,plain,
! [SV181: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV181 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ ( c_HOL_Oone__class_Oone @ SV181 ) ) @ ( c_HOL_Oone__class_Oone @ SV181 ) ) @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1779,plain,
! [SV506: $i,SV182: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV182 @ SV506 ) @ SV506 )
= ( c_Transitive__Closure_Ortranclp @ SV182 @ SV506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1780,plain,
! [SV507: $i,SV183: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) ) @ SV507 )
= SV507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1781,plain,
! [SV508: $i,SV184: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV184 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( c_HOL_Ozero__class_Ozero @ SV184 ) ) @ SV508 )
= SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1782,plain,
! [SV509: $i,SV188: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV188 )
| ~ ( class_Int_Onumber__ring @ SV188 )
| ( SV509
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV509 ) @ ( c_HOL_Ozero__class_Ozero @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1783,plain,
! [SV510: $i,SV189: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV189 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV189 ) @ SV510 ) @ ( c_HOL_Ozero__class_Ozero @ SV189 ) )
= SV510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1784,plain,
! [SV511: $i,SV190: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV190 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ ( c_HOL_Ozero__class_Ozero @ SV190 ) ) @ SV511 )
= SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1785,plain,
! [SV512: $i,SV191: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV191 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV191 ) @ SV512 ) @ ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1786,plain,
! [SV513: $i,SV192: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV192 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV513 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) )
= SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1787,plain,
! [SV514: $i,SV193: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV193 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV193 ) @ ( c_HOL_Ozero__class_Ozero @ SV193 ) ) @ SV514 )
= SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1788,plain,
! [SV515: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV194 ) @ ( c_Suc @ SV515 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV194 @ SV515 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1789,plain,
! [SV516: $i,SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV195 @ SV516 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV195 ) @ ( c_Suc @ SV516 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1790,plain,
! [SV517: $i,SV196: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV196 ) @ ( c_Suc @ SV517 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV196 @ SV517 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1791,plain,
! [SV518: $i,SV197: $i] :
( ( ! [SY1758: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV197 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV518 @ SV197 @ SY1758 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV518 ) @ SV197 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1792,plain,
! [SV519: $i,SV198: $i] :
( ( ! [SY1759: $i,SY1760: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ SV519 ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1759 @ SV198 @ SY1760 @ SV519 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1760 ) @ SV519 ) ) @ SY1759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1793,plain,
! [SV520: $i,SV199: $i] :
( ( ! [SY1761: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV199 ) ) @ SV520 ) @ SY1761 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV199 ) @ ( c_Lambda_Olift @ SV520 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1761 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1794,plain,
! [SV521: $i,SV200: $i] :
( ( ! [SY1762: $i,SY1763: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV521 ) @ SY1762 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SY1763 ) @ SY1762 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1763 ) @ SV521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1795,plain,
! [SV522: $i,SV201: $i] :
( ( ! [SY1764: $i,SY1765: $i,SY1766: $i,SY1767: $i,SY1768: $i] :
( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1764 @ SY1765 @ SV201 @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1766 ) @ SY1767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1765 ) )
| ~ ( c_Type_Otypings @ SV201 @ SY1767 @ SY1768 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1766 ) @ SY1767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1796,plain,
! [SV523: $i,SV202: $i] :
( ( ! [SY1769: $i,SY1770: $i] :
( ( c_Type_Otypings @ SV202 @ SV523 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1769 @ SV202 @ SY1770 @ SV523 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV202 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1770 ) @ SV523 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1797,plain,
! [SV524: $i,SV203: $i] :
( ( ! [SY1771: $i,SY1772: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ SV524 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1771 @ SV203 @ SV524 @ SY1772 ) @ SY1771 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV524 @ SY1772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1798,plain,
! [SV525: $i,SV204: $i] :
( ( ! [SY1773: $i,SY1774: $i,SY1775: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV525 @ SY1773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1774 ) )
| ~ ( c_Type_Otypings @ SV204 @ SY1773 @ SY1775 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SV525 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1775 @ SY1774 @ tc_Type_Otype @ tc_Type_Otype ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1799,plain,
! [SV526: $i,SV205: $i] :
( ( ! [SY1776: $i,SY1777: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ SV526 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1776 @ SV205 @ SV526 @ SY1777 ) @ SY1776 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV526 @ SY1777 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1800,plain,
! [SV527: $i,SV206: $i] :
( ( ! [SY1778: $i,SY1779: $i,SY1780: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SV527 ) @ SY1778 ) @ SY1779 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1780 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SV527 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1780 ) ) @ ( c_Suc @ SY1778 ) ) @ SY1779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1801,plain,
! [SV528: $i,SV207: $i] :
( ( ! [SY1781: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV207 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV528 @ SV207 @ SY1781 ) ) ) @ SY1781 ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV528 @ SV207 @ SY1781 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV207 ) @ ( c_Lambda_OdB_OAbs @ SY1781 ) ) @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1802,plain,
! [SV529: $i,SV208: $i] :
( ( ! [SY1782: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV208 @ SV529 ) ) ) @ SV529 ) @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV208 @ SV529 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV208 ) @ ( c_Lambda_OdB_OAbs @ SV529 ) ) @ SY1782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1803,plain,
! [SV530: $i,SV209: $i] :
( ( ! [SY1783: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV209 @ SV530 ) ) @ ( c_Lambda_Olift @ SY1783 @ SV530 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV209 ) @ SY1783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1804,plain,
! [SV531: $i,SV210: $i] :
( ( ! [SY1784: $i,SY1785: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_Lambda_OdB_OVar @ SV531 ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1784 @ SV210 @ SV531 @ SY1785 ) @ SY1784 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV531 ) @ SY1785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1805,plain,
! [SV532: $i,SV211: $i] :
( ( ! [SY1786: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV211 ) @ SV532 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1786 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV532 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV211 ) ) @ SV532 ) @ SY1786 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1806,plain,
! [SV533: $i,SV212: $i] :
( ( ! [SY1787: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SV533 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SY1787 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV533 @ SY1787 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1807,plain,
! [SV534: $i,SV213: $i] :
( ( ! [SY1788: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1788 @ SV534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV213 ) @ SY1788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1808,plain,
! [SV535: $i,SV217: $i] :
( ( ! [SY1789: $i,SY1790: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ SV535 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1789 @ SV217 @ SV535 @ SY1790 ) ) @ SY1789 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ SY1790 ) ) @ SY1789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1809,plain,
! [SV536: $i,SV218: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV218 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV536 @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV536 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1810,plain,
! [SV537: $i,SV219: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV537 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV537 @ SV219 ) @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1811,plain,
! [SV538: $i,SV220: $i] :
( ( ! [SY1791: $i] :
( ( SV220
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV538 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV538 @ SY1791 @ SV220 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV538 ) @ SY1791 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1812,plain,
! [SV539: $i,SV221: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV221 ) @ SV539 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV539 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1813,plain,
! [SV540: $i,SV222: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV222 ) ) @ ( c_Lambda_OdB_OAbs @ SV540 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SV540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1814,plain,
! [SV541: $i,SV223: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV223 ) @ ( c_Lambda_OdB_OVar @ SV541 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1815,plain,
! [SV542: $i,SV224: $i] :
( ( ! [SY1792: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV224 @ SV542 ) ) @ ( c_Lambda_Olift @ SY1792 @ SV542 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV224 ) @ SY1792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1816,plain,
! [SV543: $i,SV225: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV225 ) @ SV543 )
= ( c_Lambda_OdB_OVar @ SV225 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV225 @ SV543 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1817,plain,
! [SV544: $i,SV226: $i] :
( ( ! [SY1793: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV226 @ SV544 ) ) @ SY1793 ) @ SV544 )
= SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1818,plain,
! [SV545: $i,SV227: $i] :
( ( ! [SY1794: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV227 ) @ SV545 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1794 ) @ SV545 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV227 ) @ SY1794 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1819,plain,
! [SV546: $i,SV228: $i] :
( ( ! [SY1795: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SV546 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SY1795 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV546 ) @ SY1795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1820,plain,
! [SV229: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV229 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1821,plain,
! [SV547: $i,SV230: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV230 @ SV230 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV230 ) ) @ SV547 ) @ SV230 )
= SV547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1822,plain,
! [SV231: $i] :
( ( c_HOL_Oord__class_Oless @ SV231 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1823,plain,
! [SV232: $i] :
( ( c_HOL_Oord__class_Oless @ SV232 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1824,plain,
! [SV548: $i,SV233: $i] :
( ( ! [SY1796: $i,SY1797: $i] :
( ~ ( class_Orderings_Oorder @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV548 @ SY1796 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV548 @ SY1797 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SY1797 @ SY1796 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1825,plain,
! [SV549: $i,SV234: $i] :
( ( ! [SY1798: $i,SY1799: $i] :
( ~ ( class_Orderings_Opreorder @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV549 @ SY1798 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY1799 @ SY1798 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV549 @ SY1799 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1826,plain,
! [SV550: $i,SV235: $i] :
( ( ! [SY1800: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV235 ) ) @ SV550 ) @ SY1800 )
= ( c_Lambda_OdB_OVar @ SV235 ) )
| ( SV235 = SY1800 )
| ( c_HOL_Oord__class_Oless @ SY1800 @ SV235 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1827,plain,
! [SV551: $i,SV236: $i] :
( ( ! [SY1801: $i,SY1802: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV236 ) @ SV551 ) @ SY1801 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1802 ) @ SV551 ) @ SY1801 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV236 ) @ SY1802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1828,plain,
! [SV552: $i,SV237: $i] :
( ( ! [SY1803: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV237 ) @ SV552 ) @ SY1803 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV237 @ SY1803 ) ) @ ( c_Lambda_Olift @ SV552 @ SY1803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1829,plain,
! [SV553: $i,SV239: $i] :
( ( ! [SY1804: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) ) @ SV553 ) @ SY1804 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV239 ) @ SV553 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1804 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1830,plain,
! [SV554: $i,SV240: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV240 @ SV554 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1831,plain,
! [SV555: $i,SV241: $i] :
( ( ! [SY1805: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV241 @ SV555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1805 @ SV555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV241 ) @ SY1805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1832,plain,
! [SV242: $i] :
( ( c_HOL_Oord__class_Oless @ SV242 @ SV242 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1833,plain,
! [SV243: $i] :
( ( c_HOL_Oord__class_Oless @ SV243 @ SV243 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1834,plain,
! [SV556: $i,SV244: $i] :
( ( ~ ( class_Orderings_Oorder @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ SV556 @ SV556 @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1835,plain,
! [SV557: $i,SV245: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV557 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1836,plain,
! [SV558: $i,SV246: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV246 )
| ~ ( c_HOL_Oord__class_Oless @ SV558 @ SV558 @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1837,plain,
! [SV559: $i,SV247: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV247 ) ) @ SV559 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV247 ) @ SV559 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1838,plain,
! [SV560: $i,SV248: $i] :
( ( ! [SY1806: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV560 @ SY1806 @ SV248 )
| ( c_HOL_Oord__class_Oless @ SY1806 @ SV560 @ SV248 )
| ( SY1806 = SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1839,plain,
! [SV561: $i,SV249: $i] :
( ( ! [SY1807: $i] :
( ~ ( class_Orderings_Olinorder @ SV249 )
| ( SV561 = SY1807 )
| ( c_HOL_Oord__class_Oless @ SY1807 @ SV561 @ SV249 )
| ( c_HOL_Oord__class_Oless @ SV561 @ SY1807 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1840,plain,
! [SV562: $i,SV250: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV250 @ SV562 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV562 @ SV250 @ tc_nat )
| ( SV562 = SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1841,plain,
! [SV563: $i,SV251: $i] :
( ( ! [SY1808: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV251 @ SV563 ) @ SY1808 ) )
| ( c_HOL_Oord__class_Oless @ SV563 @ SY1808 @ tc_nat )
| ( SY1808 = SV563 )
| ( c_HOL_Oord__class_Oless @ SY1808 @ SV563 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1842,plain,
! [SV564: $i,SV252: $i] :
( ( ! [SY1809: $i,SY1810: $i,SY1811: $i] :
( ( SV252 = SV564 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1809 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1810 ) @ SY1811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1809 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1810 ) @ SY1811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1843,plain,
! [SV565: $i,SV253: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV253 @ SV565 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV565 @ SV253 @ tc_nat )
| ( SV565 = SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1844,plain,
! [SV566: $i,SV254: $i] :
( ( ! [SY1812: $i] :
( ~ ( class_Orderings_Olinorder @ SV254 )
| ( c_HOL_Oord__class_Oless @ SV566 @ SY1812 @ SV254 )
| ( c_HOL_Oord__class_Oless @ SY1812 @ SV566 @ SV254 )
| ( SY1812 = SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1845,plain,
! [SV567: $i,SV255: $i] :
( ( ! [SY1813: $i] :
( ~ ( class_Orderings_Olinorder @ SV255 )
| ( c_HOL_Oord__class_Oless @ SV567 @ SY1813 @ SV255 )
| ( SY1813 = SV567 )
| ( c_HOL_Oord__class_Oless @ SY1813 @ SV567 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1846,plain,
! [SV568: $i,SV256: $i] :
( ( ! [SY1814: $i] :
( ~ ( class_Orderings_Olinorder @ SV256 )
| ( SV568 = SY1814 )
| ( c_HOL_Oord__class_Oless @ SV568 @ SY1814 @ SV256 )
| ( c_HOL_Oord__class_Oless @ SY1814 @ SV568 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1847,plain,
! [SV569: $i,SV257: $i] :
( ( ! [SY1815: $i,SY1816: $i,SY1817: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV569 ) @ SY1815 ) ) @ SY1816 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SY1815 ) @ SY1817 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV569 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1817 ) @ SY1816 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1848,plain,
! [SV570: $i,SV258: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV258 ) ) @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1849,plain,
! [SV259: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV259 @ tc_nat )
= $true )
| ( ( SV259
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1850,plain,
! [SV571: $i,SV260: $i] :
( ( ! [SY1818: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV260 ) ) @ SV571 ) @ SY1818 )
= ( c_Lambda_OdB_OVar @ SV260 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV260 @ SY1818 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1851,plain,
! [SV572: $i,SV261: $i] :
( ( ! [SY1819: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV261 ) @ ( c_Lambda_OdB_OVar @ SV572 ) ) @ SY1819 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1852,plain,
! [SV573: $i,SV262: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV262 ) ) @ SV573 ) @ SV262 )
= SV573 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1853,plain,
! [SV574: $i,SV263: $i] :
( ( ! [SY1820: $i,SY1821: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV263 ) @ SV574 ) ) @ SY1820 ) @ SY1821 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV263 ) @ SY1820 ) @ SY1821 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV574 ) @ SY1820 ) @ SY1821 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1854,plain,
! [SV575: $i,SV264: $i] :
( ( ! [SY1822: $i] :
( ~ ( class_Orderings_Oorder @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV575 @ SY1822 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SY1822 @ SV575 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1855,plain,
! [SV576: $i,SV265: $i] :
( ( ! [SY1823: $i] :
( ~ ( class_Orderings_Olinorder @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV576 @ SY1823 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SY1823 @ SV576 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1856,plain,
! [SV577: $i,SV266: $i] :
( ( ! [SY1824: $i] :
( ~ ( class_Orderings_Opreorder @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV577 @ SY1824 @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SY1824 @ SV577 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1857,plain,
! [SV578: $i,SV267: $i] :
( ( ! [SY1825: $i] :
( ~ ( class_Orderings_Opreorder @ SV267 )
| ~ ( c_HOL_Oord__class_Oless @ SV578 @ SY1825 @ SV267 )
| ~ ( c_HOL_Oord__class_Oless @ SY1825 @ SV578 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1858,plain,
! [SV579: $i,SV268: $i] :
( ( ! [SY1826: $i,SY1827: $i,SY1828: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV268 ) @ SV579 ) @ SY1826 ) ) @ ( c_Lambda_Olift @ SY1827 @ SV579 ) ) @ SY1828 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV268 ) @ SY1827 ) @ SY1828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1859,plain,
! [SV580: $i,SV269: $i] :
( ( ! [SY1829: $i,SY1830: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1829 ) @ SV269 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1829 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SY1830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1860,plain,
! [SV581: $i,SV270: $i] :
( ( ! [SY1831: $i,SY1832: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1831 ) @ SV270 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1831 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SY1832 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1861,plain,
! [SV582: $i,SV271: $i] :
( ( ! [SY1833: $i,SY1834: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV582 ) @ SY1833 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1834 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SY1834 ) @ SY1833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1862,plain,
! [SV583: $i,SV272: $i] :
( ( ! [SY1835: $i,SY1836: $i,SY1837: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV272 ) @ SV583 ) @ SY1835 ) @ SY1836 ) @ SY1837 )
= ( hAPP @ SV583 @ SY1837 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1837 @ SY1835 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1863,plain,
! [SV584: $i,SV273: $i] :
( ( ! [SY1838: $i,SY1839: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV273 ) @ SV584 ) @ SY1838 ) @ SY1839 ) @ SY1838 )
= SY1839 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1864,plain,
! [SV585: $i,SV274: $i] :
( ( ! [SY1840: $i,SY1841: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV274 ) @ ( c_Lambda_OdB_OAbs @ SV585 ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1840 ) @ SY1841 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1840 ) ) @ SV585 ) @ SY1841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1865,plain,
! [SV586: $i,SV275: $i] :
( ( ! [SY1842: $i] :
( ( ( hAPP @ SV275 @ SV586 )
= SY1842 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV275 ) @ ( c_Lambda_OdB_OVar @ SV586 ) ) @ SY1842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1866,plain,
! [SV276: $i] :
( ( v_thesis____ = $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ SV276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1867,plain,
! [SV587: $i,SV277: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV277 ) @ ( c_Lambda_OdB_OVar @ SV587 ) ) @ ( hAPP @ SV277 @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1868,plain,
! [SV588: $i,SV278: $i] :
( ( ! [SY1843: $i,SY1844: $i,SY1845: $i,SY1846: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SY1843 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SY1844 ) @ SY1843 ) ) @ SY1845 ) @ SY1846 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1845 ) @ SV588 ) @ SY1844 ) ) @ SY1846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1869,plain,
! [SV589: $i,SV279: $i] :
( ( ! [SY1847: $i,SY1848: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1847 ) @ SV279 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1847 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SY1848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1870,plain,
! [SV590: $i,SV280: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV280 @ SV590 ) )
| ~ ( class_Orderings_Opreorder @ SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1871,plain,
! [SV591: $i,SV281: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV281 @ SV591 ) )
| ~ ( class_Orderings_Oorder @ SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1872,plain,
! [SV592: $i,SV282: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV282 ) @ SV592 ) @ SV592 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1873,plain,
! [SV593: $i,SV283: $i] :
( ( ! [SY1849: $i] :
( ( SV283 = SV593 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1849 ) @ SV283 ) @ SV593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1874,plain,
! [SV594: $i,SV284: $i] :
( ( ! [SY1850: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1850 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV284 = SY1850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1875,plain,
! [SV595: $i,SV285: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV285 ) @ SV595 ) )
| ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV285
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1876,plain,
! [SV596: $i,SV286: $i] :
( ( ! [SY1851: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV286 ) @ SV596 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1851 ) @ SV596 ) )
| ( SV286 = SY1851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1877,plain,
! [SV287: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV287 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV287 )
!= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1878,plain,
! [SV597: $i,SV288: $i] :
( ( ! [SY1852: $i,SY1853: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( c_HOL_Ominus__class_Ominus @ SV597 @ SV597 @ SV288 )
!= ( c_HOL_Ominus__class_Ominus @ SY1852 @ SY1853 @ SV288 ) )
| ( SY1852 = SY1853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1879,plain,
! [SV598: $i,SV289: $i] :
( ( ! [SY1854: $i] :
( ( ( c_Lambda_OdB_OVar @ SV289 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV598 @ SY1854 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV289 )
= SV598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1880,plain,
! [SV599: $i,SV290: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV290 ) @ SV599 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV599
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV290
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1881,plain,
! [SV600: $i,SV291: $i] :
( ( ! [SY1855: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV291 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV600 @ SV291 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1855 @ SV291 ) )
| ( SV600 = SY1855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1882,plain,
! [SV601: $i,SV292: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV292 ) @ SV601 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV601
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1883,plain,
! [SV602: $i,SV293: $i] :
( ( ! [SY1856: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV293 )
| ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SY1856 @ SV293 )
!= ( c_HOL_Ozero__class_Ozero @ SV293 ) )
| ( SV602 = SY1856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1884,plain,
! [SV603: $i,SV294: $i] :
( ( ! [SY1857: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV294 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV603 @ SY1857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV294 )
= SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1885,plain,
! [SV604: $i,SV295: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV295 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV295 ) @ SV604 ) @ SV604 )
!= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
| ( SV604
= ( c_HOL_Ozero__class_Ozero @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1886,plain,
! [SV605: $i,SV296: $i] :
( ( ( ( c_Suc @ SV296 )
!= ( c_Suc @ SV605 ) )
| ( SV296 = SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1887,plain,
! [SV606: $i,SV297: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV297 )
!= ( c_Lambda_OdB_OVar @ SV606 ) )
| ( SV297 = SV606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1888,plain,
! [SV607: $i,SV298: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV298 ) @ SV607 ) )
| ( SV607
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV607
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1889,plain,
! [SV608: $i,SV299: $i] :
( ( ! [SY1858: $i,SY1859: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV299 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1858 ) @ SY1859 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV299 = SY1858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1890,plain,
! [SV300: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV300 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1891,plain,
! [SV301: $i] :
( ( ( c_Suc @ SV301 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1892,plain,
! [SV609: $i,SV302: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV302 )
!= ( c_Lambda_OdB_OAbs @ SV609 ) )
| ( SV302 = SV609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1893,plain,
! [SV610: $i,SV303: $i] :
( ( ! [SY1860: $i,SY1861: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV303 )
| ~ ( class_Int_Onumber__ring @ SV303 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SY1860 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SY1861 ) )
| ( SY1860 = SY1861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1894,plain,
! [SV611: $i,SV304: $i] :
( ( ! [SY1862: $i,SY1863: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV304 ) @ SV611 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1862 ) @ SY1863 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV304 = SY1862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1895,plain,
! [SV612: $i,SV305: $i] :
( ( ! [SY1864: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SV612 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SY1864 ) )
| ( SV612 = SY1864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1896,plain,
! [SV306: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV306 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV306 )
!= ( c_HOL_Oone__class_Oone @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1897,plain,
! [SV613: $i,SV307: $i] :
( ( ! [SY1865: $i,SY1866: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV307 ) @ SV613 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1865 ) @ SY1866 ) )
| ( SV307 = SY1865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1898,plain,
! [SV614: $i,SV308: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV308 @ SV614 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV614 @ SV308 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV614 = SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1899,plain,
! [SV309: $i] :
( ( SV309
= ( c_Suc @ SV309 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1900,plain,
! [SV615: $i,SV310: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV615 )
!= SV310 )
| ( SV615
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1901,plain,
! [SV311: $i] :
( ( ( c_Suc @ SV311 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1902,plain,
! [SV616: $i,SV312: $i] :
( ( ! [SY1867: $i,SY1868: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV312 ) @ SV616 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1867 ) @ SY1868 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1867 @ SV616 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV312 @ SY1868 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1903,plain,
! [SV617: $i,SV313: $i] :
( ( ! [SY1869: $i] :
( ( ( c_Lambda_OdB_OVar @ SV313 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV617 @ SY1869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1869
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1904,plain,
! [SV618: $i,SV314: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV314 ) @ SV618 ) )
| ( SV314
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1905,plain,
! [SV619: $i,SV315: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV315 ) @ SV619 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1906,plain,
! [SV620: $i,SV316: $i] :
( ( ! [SY1870: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV316 )
| ~ ( class_Int_Onumber__ring @ SV316 )
| ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SY1870 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV620 = SY1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1907,plain,
! [SV621: $i,SV317: $i] :
( ( ( c_Lambda_OdB_OVar @ SV317 )
!= ( c_Lambda_OdB_OAbs @ SV621 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1908,plain,
! [SV622: $i,SV318: $i] :
( ( ! [SY1871: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV318 )
| ~ ( class_Int_Onumber__ring @ SV318 )
| ( SV622
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV622 ) @ SY1871 ) )
| ( SY1871
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1909,plain,
! [SV623: $i,SV319: $i] :
( ( ! [SY1872: $i,SY1873: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV623 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1872 ) @ SY1873 ) )
| ( SV623 = SY1873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1910,plain,
! [SV624: $i,SV320: $i] :
( ( ! [SY1874: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV320 ) @ SV624 )
!= ( c_Lambda_OdB_OVar @ SY1874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1911,plain,
! [SV625: $i,SV321: $i] :
( ( ! [SY1875: $i] :
( ( c_Lambda_OdB_OVar @ SV321 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV625 ) @ SY1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1912,plain,
! [SV626: $i,SV322: $i] :
( ( ! [SY1876: $i] :
( ( c_Lambda_OdB_OAbs @ SV322 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV626 ) @ SY1876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1913,plain,
! [SV627: $i,SV323: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV627 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1914,plain,
! [SV628: $i,SV324: $i] :
( ( ! [SY1877: $i,SY1878: $i,SY1879: $i,SY1880: $i,SY1881: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1877 ) @ SY1878 ) @ SY1879 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1880 ) @ SY1878 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1880 ) @ SY1879 ) @ SV324 ) ) @ SY1877 ) @ SY1881 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1915,plain,
! [SV629: $i,SV325: $i] :
( ( ! [SY1882: $i,SY1883: $i,SY1884: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SY1882 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY1883 @ SY1884 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV629 @ SY1882 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SY1883 @ SY1884 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1916,plain,
! [SV630: $i,SV326: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV326 ) @ SV630 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV630
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV630
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1917,plain,
! [SV631: $i,SV327: $i] :
( ( ! [SY1885: $i,SY1886: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SY1885 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SY1886 ) )
| ( SY1885 = SY1886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1918,plain,
! [SV632: $i,SV328: $i] :
( ( ! [SY1887: $i,SY1888: $i,SY1889: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV328 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SY1887 ) @ SY1888 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SY1887 ) @ SY1889 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ SY1888 )
= SY1889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1919,plain,
! [SV633: $i,SV329: $i] :
( ( ! [SY1890: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV329 )
| ( ( c_HOL_Ominus__class_Ominus @ SV633 @ SY1890 @ SV329 )
!= ( c_HOL_Ozero__class_Ozero @ SV329 ) )
| ( SV633 = SY1890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1920,plain,
! [SV330: $i] :
( ( ( c_Suc @ SV330 )
= SV330 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1921,plain,
! [SV634: $i,SV331: $i] :
( ( ! [SY1891: $i,SY1892: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV331 ) @ SV634 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1891 ) @ SY1892 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1922,plain,
! [SV635: $i,SV332: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV332 ) @ SV635 ) )
| ( SV635
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV332
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1923,plain,
! [SV636: $i,SV333: $i] :
( ( ! [SY1893: $i,SY1894: $i,SY1895: $i,SY1896: $i,SY1897: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1893 ) @ SY1894 ) @ SY1895 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY1896 ) @ SY1894 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1894 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY1896 ) @ SY1895 ) @ SV636 ) ) @ SY1893 ) @ SY1897 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1924,plain,
! [SV637: $i,SV334: $i] :
( ( ! [SY1898: $i,SY1899: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SV637 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1898 ) @ SY1899 ) )
| ( SV334 = SY1898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1925,plain,
! [SV335: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV335 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1926,plain,
! [SV638: $i,SV336: $i] :
( ( ( SV336
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV336 ) @ SV638 ) )
| ( SV638
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1927,plain,
! [SV639: $i,SV337: $i] :
( ( ! [SY1900: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV337 @ SV639 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1900 ) )
| ( SV337
= ( c_Lambda_OdB_OAbs @ SY1900 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1928,plain,
! [SV640: $i,SV338: $i] :
( ( ! [SY1901: $i,SY1902: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV338 ) @ SV640 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1901 ) @ SY1902 ) )
| ( SV640 = SY1902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1929,plain,
! [SV641: $i,SV339: $i] :
( ( ! [SY1903: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV339 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV641 @ SY1903 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1903
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1930,plain,
! [SV642: $i,SV340: $i] :
( ( ! [SY1904: $i,SY1905: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV340 ) ) @ SV642 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1904 ) @ SY1905 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1931,plain,
! [SV643: $i,SV341: $i] :
( ( ! [SY1906: $i,SY1907: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV341 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SY1906 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SY1907 ) )
| ( SY1906 = SY1907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1932,plain,
! [SV644: $i,SV342: $i] :
( ( ! [SY1908: $i,SY1909: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV342 ) @ SV644 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1908 ) @ SY1909 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV644 = SY1909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1933,plain,
! [SV645: $i,SV343: $i] :
( ( ! [SY1910: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV343 ) @ SV645 )
!= ( c_Lambda_OdB_OAbs @ SY1910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1934,plain,
! [SV646: $i,SV344: $i] :
( ( ! [SY1911: $i,SY1912: $i,SY1913: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
| ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SY1911 @ SV344 )
!= ( c_HOL_Ominus__class_Ominus @ SY1912 @ SY1913 @ SV344 ) )
| ( c_HOL_Oord__class_Oless @ SY1912 @ SY1913 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SV646 @ SY1911 @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1935,plain,
! [SV647: $i,SV345: $i] :
( ( ! [SY1914: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SV647 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SY1914 ) )
| ( SV647 = SY1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1936,plain,
! [SV648: $i,SV346: $i] :
( ( ( ( c_Suc @ SV346 )
!= ( c_Suc @ SV648 ) )
| ( SV346 = SV648 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1937,plain,
! [SV649: $i,SV347: $i] :
( ( ! [SY1915: $i,SY1916: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV347 ) @ SV649 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1915 ) @ SY1916 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV649 = SY1916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1938,plain,
! [SV650: $i,SV348: $i] :
( ( ! [SY1917: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV348 @ SV650 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1917 ) )
| ( SV650
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1939,plain,
! [SV651: $i,SV349: $i] :
( ( ! [SY1918: $i,SY1919: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV349 )
| ( ( c_HOL_Ominus__class_Ominus @ SV651 @ SY1918 @ SV349 )
!= ( c_HOL_Ominus__class_Ominus @ SY1919 @ SY1919 @ SV349 ) )
| ( SV651 = SY1918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1940,plain,
! [SV652: $i,SV350: $i] :
( ( ! [SY1920: $i,SY1921: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV652 ) @ SY1920 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SY1921 ) @ SY1920 ) )
| ( SV652 = SY1921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1941,plain,
! [SV653: $i,SV351: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV351 ) @ SV653 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV351
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV351
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1942,plain,
! [SV654: $i,SV352: $i] :
( ( ! [SY1922: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV654 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1922 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV654 )
= SY1922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1943,plain,
! [SV655: $i,SV353: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV353 )
!= ( c_Lambda_OdB_OVar @ SV655 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1944,plain,
! [SV1: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ SV1 ) )
= $false )
| ( v_thesis____ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1945,plain,
! [SV354: $i,SV4: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV354 @ tc_nat ) @ SV4 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV4 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1946,plain,
! [SV355: $i,SV5: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV5 @ SV355 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV355 @ SV5 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1947,plain,
! [SV356: $i,SV6: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV6 @ SV356 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV356 @ SV6 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1948,plain,
! [SV656: $i,SV357: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV357 @ SV656 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ominus__class_Ominus @ SV357 @ SV656 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1949,plain,
! [SV657: $i,SV358: $i,SV8: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV8 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV657 @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SV358 @ SV657 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1950,plain,
! [SV658: $i,SV359: $i,SV9: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV9 )
| ( c_HOL_Oord__class_Oless @ SV359 @ SV658 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV658 @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1951,plain,
! [SV360: $i,SV10: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV10 ) @ ( c_HOL_Ominus__class_Ominus @ SV360 @ SV10 @ tc_nat ) )
= SV360 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV360 @ SV10 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1952,plain,
! [SV659: $i,SV361: $i,SV11: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV11 @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV659 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV11 ) @ SV659 ) @ SV361 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1953,plain,
! [SV660: $i,SV362: $i,SV12: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV12 ) @ SV362 ) @ SV660 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_HOL_Ominus__class_Ominus @ SV660 @ SV362 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1954,plain,
! [SV661: $i,SV363: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ SV363 @ tc_nat ) @ SV661 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SV661 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1955,plain,
! [SV365: $i,SV17: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV17 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV17 )
| ( ( c_HOL_Ominus__class_Ominus @ SV365 @ SV365 @ SV17 )
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1956,plain,
! [SV366: $i,SV18: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV18 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV366 @ SV366 @ SV18 )
= ( c_HOL_Ozero__class_Ozero @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1957,plain,
! [SV367: $i,SV19: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV19 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV367 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= SV367 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1958,plain,
! [SV368: $i,SV20: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV20 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV368 @ SV368 @ SV20 )
= ( c_HOL_Ozero__class_Ozero @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1959,plain,
! [SV369: $i,SV21: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV21 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV369 @ SV369 @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1960,plain,
! [SV662: $i,SV370: $i,SV22: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV370 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV662 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV22 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV370 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1961,plain,
! [SV663: $i,SV371: $i,SV24: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV24 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ominus__class_Ominus @ SV371 @ SV663 @ SV24 ) ) @ SV663 )
= SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1962,plain,
! [SV664: $i,SV372: $i,SV25: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV372 ) @ SV664 ) @ SV372 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV25 @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1963,plain,
! [SV665: $i,SV373: $i,SV26: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV373 ) @ SV665 ) @ SV373 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV26 @ SV665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1964,plain,
! [SV666: $i,SV376: $i,SV29: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV29 @ SV376 @ tc_nat ) @ SV666 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV29 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV376 ) @ SV666 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1965,plain,
! [SV667: $i,SV377: $i,SV31: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV31 ) @ SV377 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV667 ) @ SV377 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV31 @ SV667 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1966,plain,
! [SV668: $i,SV378: $i,SV32: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV32 ) @ SV378 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV32 ) @ SV668 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV378 @ SV668 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1967,plain,
! [SV669: $i,SV379: $i,SV33: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ SV379 @ tc_nat ) @ SV669 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ SV669 @ tc_nat ) @ SV379 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1968,plain,
! [SV670: $i,SV380: $i,SV34: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV34 ) @ SV380 @ tc_nat ) @ ( c_Suc @ SV670 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SV380 @ tc_nat ) @ SV670 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1969,plain,
! [SV671: $i,SV384: $i,SV38: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV38 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV384 ) @ SV671 ) @ SV671 @ SV38 )
= SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1970,plain,
! [SV385: $i,SV39: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV39 @ ( c_Suc @ SV385 ) @ tc_nat ) @ SV39 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV39 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1971,plain,
! [SV40: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV40 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV40 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1972,plain,
! [SV672: $i,SV386: $i,SV41: $i] :
( ( ! [SY1923: $i,SY1924: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV41 ) @ SV386 ) @ SV672 ) @ SY1923 ) @ SY1924 )
= ( hAPP @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SY1924 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV672 @ SY1924 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1973,plain,
! [SV673: $i,SV387: $i,SV42: $i] :
( ( ! [SY1925: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV42 @ SV387 ) @ SV673 ) @ SY1925 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV42 @ SV673 ) @ SY1925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1974,plain,
! [SV674: $i,SV388: $i,SV43: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_ONil @ SV388 ) @ SV674 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1975,plain,
! [SV675: $i,SV389: $i,SV44: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV44 @ SV389 @ ( c_List_Olist_ONil @ SV675 ) @ SV675 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1976,plain,
! [SV676: $i,SV390: $i,SV45: $i] :
( ( ! [SY1926: $i] :
( ( c_List_Ofoldl @ SV45 @ SV390 @ ( c_List_Olist_ONil @ SV676 ) @ SY1926 @ SV676 )
= SV390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1977,plain,
! [SV391: $i,SV47: $i] :
( ( ( SV47 = SV391 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV47 @ SV391 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV47 @ ( c_Suc @ SV391 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1978,plain,
! [SV392: $i,SV48: $i] :
( ( ( SV48 = SV392 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SV48 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV392 @ SV48 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1979,plain,
! [SV393: $i,SV49: $i] :
( ( ( SV49 = SV393 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV49 @ ( c_Suc @ SV393 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV49 @ SV393 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1980,plain,
! [SV677: $i,SV394: $i,SV50: $i] :
( ( ! [SY1927: $i,SY1928: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SY1927 ) @ SY1928 ) @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SY1928 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ SY1927 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1981,plain,
! [SV678: $i,SV395: $i,SV51: $i] :
( ( ! [SY1929: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV395 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV678 ) @ SY1929 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV395 @ SY1929 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV51 @ SV678 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1982,plain,
! [SV679: $i,SV396: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV54 ) @ SV396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV679 @ SV396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV679 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1983,plain,
! [SV397: $i,SV55: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV55 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV397 @ SV55 @ SV55 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV397 @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1984,plain,
! [SV398: $i,SV56: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV56 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV398 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV398 ) @ ( c_HOL_Oone__class_Oone @ SV56 ) ) @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1985,plain,
! [SV680: $i,SV399: $i,SV57: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV57 @ SV399 @ SV680 ) @ SV680 @ SV399 )
= SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1986,plain,
! [SV400: $i,SV58: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SV400 ) @ SV58 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1987,plain,
! [SV401: $i,SV59: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV59 ) @ SV401 ) @ SV401 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1988,plain,
! [SV681: $i,SV402: $i,SV60: $i] :
( ( ! [SY1930: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV60 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV402 ) @ SV681 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1930 ) @ SV681 ) @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV402 @ SY1930 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1989,plain,
! [SV682: $i,SV403: $i,SV61: $i] :
( ( ! [SY1931: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV61 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV403 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1931 ) @ SV682 ) @ SV61 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SY1931 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(1990,plain,
! [SV683: $i,SV404: $i,SV62: $i] :
( ( ! [SY1932: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV62 )
| ( c_HOL_Oord__class_Oless @ SV404 @ SV683 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV404 ) @ SY1932 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV683 ) @ SY1932 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1991,plain,
! [SV684: $i,SV405: $i,SV63: $i] :
( ( ! [SY1933: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV63 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV684 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SY1933 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV684 @ SY1933 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1992,plain,
! [SV685: $i,SV406: $i,SV64: $i] :
( ( ! [SY1934: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV685 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SY1934 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV685 @ SY1934 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1993,plain,
! [SV686: $i,SV407: $i,SV65: $i] :
( ( ! [SY1935: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV65 )
| ( c_HOL_Oord__class_Oless @ SV407 @ SV686 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY1935 ) @ SV407 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SY1935 ) @ SV686 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1994,plain,
! [SV687: $i,SV408: $i,SV66: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV66 ) @ SV408 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV687 ) @ SV408 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV66 @ SV687 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1995,plain,
! [SV688: $i,SV409: $i,SV67: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV67 @ SV409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV409 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1996,plain,
! [SV689: $i,SV410: $i,SV68: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SV689 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV410 @ SV689 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1997,plain,
! [SV411: $i,SV69: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV69 @ SV411 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV69 ) @ SV411 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1998,plain,
! [SV412: $i,SV70: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV70 @ ( c_Suc @ SV412 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV70 @ SV412 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1999,plain,
! [SV690: $i,SV413: $i,SV71: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV71 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SV690 ) @ SV71 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV413 @ SV71 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV690 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2000,plain,
! [SV691: $i,SV415: $i,SV73: $i] :
( ( ! [SY1936: $i,SY1937: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV691 ) @ SY1936 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SY1937 ) @ SY1936 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SV691 ) @ SY1937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2001,plain,
! [SV692: $i,SV416: $i,SV74: $i] :
( ( ! [SY1938: $i,SY1939: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SY1938 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SY1939 ) @ SY1938 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SY1939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2002,plain,
! [SV693: $i,SV417: $i,SV75: $i] :
( ( ! [SY1940: $i] :
( ( c_Wellfounded_Oaccp @ SV75 @ SV417 @ SV693 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV75 @ SV417 ) @ SY1940 ) )
| ~ ( c_Wellfounded_Oaccp @ SV75 @ SY1940 @ SV693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2003,plain,
! [SV694: $i,SV418: $i,SV76: $i] :
( ( ! [SY1941: $i] :
( ( c_Wellfounded_Oaccp @ SV76 @ SV418 @ SV694 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV418 ) @ SY1941 ) )
| ~ ( c_Wellfounded_Oaccp @ SV76 @ SY1941 @ SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2004,plain,
! [SV695: $i,SV419: $i,SV77: $i] :
( ( ! [SY1942: $i] :
( ( c_Type_Otypings @ SV77 @ SV419 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV695 @ SV77 @ SY1942 @ SV419 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV77 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1942 @ SV419 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV695 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2005,plain,
! [SV696: $i,SV420: $i,SV78: $i] :
( ( ! [SY1943: $i] :
( ( c_Type_Otypings @ SV78 @ SV420 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV696 @ SV78 @ SY1943 @ SV420 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV78 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1943 @ SV420 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2006,plain,
! [SV697: $i,SV421: $i,SV79: $i] :
( ( ! [SY1944: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV79 ) @ SV421 ) @ SV697 ) @ SY1944 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV79 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1944 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( c_Lambda_Olift @ SV421 @ SY1944 ) ) @ SV697 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV697 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1944 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2007,plain,
! [SV698: $i,SV422: $i,SV80: $i] :
( ( ! [SY1945: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV80 ) @ SV422 ) @ SV698 ) @ SY1945 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV80 @ SY1945 ) ) @ ( c_Lambda_Olift @ SV422 @ SY1945 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV698 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1945 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV698 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2008,plain,
! [SV423: $i,SV81: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV81 ) @ SV423 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV81 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV81 @ SV423 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(2009,plain,
! [SV699: $i,SV424: $i,SV82: $i] :
( ( ( SV82
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV82 @ SV424 @ SV699 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV82 @ SV424 @ SV699 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV424 ) @ ( c_Lambda_OdB_OAbs @ SV699 ) ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2010,plain,
! [SV700: $i,SV425: $i,SV83: $i] :
( ( ! [SY1946: $i,SY1947: $i,SY1948: $i,SY1949: $i] :
( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SY1946 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1947 ) @ SY1948 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
| ~ ( c_Type_Otypings @ SV700 @ SY1948 @ SY1949 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1947 ) @ SY1948 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1946 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2011,plain,
! [SV426: $i,SV84: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV84 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV426 ) @ SV426 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV426 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(2012,plain,
! [SV427: $i,SV85: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV85 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV427 @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV427 ) @ SV427 ) @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(2013,plain,
! [SV428: $i,SV86: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV86 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV428 @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(2014,plain,
! [SV701: $i,SV429: $i,SV87: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV429 ) @ SV701 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV701 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2015,plain,
! [SV430: $i,SV88: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV88 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SV430 ) @ SV430 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SV430 @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(2016,plain,
! [SV431: $i,SV89: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV89 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV431 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV431 ) @ SV431 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(2017,plain,
! [SV432: $i,SV90: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV90 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV432 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV432 ) @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(2018,plain,
! [SV433: $i,SV91: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV91 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ SV433 ) @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV433 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(2019,plain,
! [SV92: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV92 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(2020,plain,
! [SV702: $i,SV434: $i,SV93: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV434 ) @ SV702 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV702 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV434 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2021,plain,
! [SV94: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV94 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ ( c_HOL_Oone__class_Oone @ SV94 ) @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(2022,plain,
! [SV703: $i,SV435: $i,SV95: $i] :
( ( ! [SY1950: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV703 ) @ SY1950 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV435 @ SY1950 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV703 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2023,plain,
! [SV96: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV96 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV96 )
= ( c_HOL_Ozero__class_Ozero @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(2024,plain,
! [SV704: $i,SV436: $i,SV97: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV97 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV436 @ SV97 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV704 @ SV97 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV436 @ SV704 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2025,plain,
! [SV705: $i,SV437: $i,SV98: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV98 )
| ( c_HOL_Oord__class_Oless @ SV437 @ SV705 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV437 @ SV98 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV705 @ SV98 ) @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2026,plain,
! [SV438: $i,SV99: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV99 ) @ SV438 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV99 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(2027,plain,
! [SV439: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV100 ) @ SV439 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV439 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(2028,plain,
! [SV440: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV103 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV440 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SV103 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(2029,plain,
! [SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV104
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(2030,plain,
! [SV706: $i,SV441: $i,SV105: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV105 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV441 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV706 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV441 @ SV706 @ SV105 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2031,plain,
! [SV707: $i,SV442: $i,SV106: $i] :
( ( ! [SY1951: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV106 ) @ SV442 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV707 ) @ SY1951 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV442 ) @ SY1951 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV106 ) @ SV707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2032,plain,
! [SV708: $i,SV443: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV107 ) @ SV443 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV708 ) @ SV443 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV107 ) @ SV708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2033,plain,
! [SV709: $i,SV444: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SV444 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SV709 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV444 ) @ SV709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2034,plain,
! [SV445: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV109 ) ) @ ( c_Lambda_OdB_OAbs @ SV445 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SV445 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(2035,plain,
! [SV710: $i,SV447: $i,SV111: $i] :
( ( ! [SY1952: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SV447 ) @ SV710 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SY1952 ) @ SV710 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV447 ) @ SY1952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2036,plain,
! [SV711: $i,SV448: $i,SV112: $i] :
( ( ! [SY1953: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV112 ) @ SV448 ) @ SV711 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1953 ) @ SV448 ) @ SV711 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV112 ) @ SY1953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2037,plain,
! [SV712: $i,SV449: $i,SV113: $i] :
( ( ! [SY1954: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SV449 ) @ SV712 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SY1954 ) @ SV712 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV449 ) @ SY1954 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2038,plain,
! [SV713: $i,SV450: $i,SV114: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV114 ) ) @ SV450 ) @ SV713 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV713 @ SV114 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2039,plain,
! [SV714: $i,SV451: $i,SV115: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV115 ) ) @ SV451 ) @ SV714 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV115 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV714 @ SV115 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2040,plain,
! [SV454: $i,SV118: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV118 ) @ SV454 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV118 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ SV454 ) ) )
= $true )
| ( ( SV118
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(2041,plain,
! [SV119: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV119 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV119 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(2042,plain,
! [SV120: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat )
= $false )
| ( ( SV120
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV120 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(2043,plain,
! [SV715: $i,SV457: $i,SV125: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV125 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SV457 @ SV715 @ SV125 @ SV125 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SV715 @ SV457 @ SV125 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2044,plain,
! [SV716: $i,SV458: $i,SV126: $i] :
( ( ! [SY1955: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV126 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ SV716 ) @ SY1955 @ SV126 @ SV126 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV716 @ SY1955 @ SV126 @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2045,plain,
! [SV717: $i,SV459: $i,SV127: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SV459 ) @ SV717 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SV717 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2046,plain,
! [SV718: $i,SV461: $i,SV129: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV129 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV461 ) @ SV718 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV718 ) @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2047,plain,
! [SV719: $i,SV462: $i,SV130: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV462 ) @ SV719 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV719 ) @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2048,plain,
! [SV720: $i,SV463: $i,SV131: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV131 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV463 ) @ SV720 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV131 @ SV720 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2049,plain,
! [SV721: $i,SV464: $i,SV132: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV132 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV464 ) @ SV721 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV132 @ SV464 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2050,plain,
! [SV722: $i,SV465: $i,SV133: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV133 @ SV465 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV133 ) @ SV722 ) @ SV465 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2051,plain,
! [SV723: $i,SV466: $i,SV134: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV134 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV466 ) @ SV723 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV134 @ SV723 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2052,plain,
! [SV724: $i,SV467: $i,SV135: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV135 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV467 ) @ SV724 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV135 @ SV467 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2053,plain,
! [SV141: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV141 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(2054,plain,
! [SV142: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV142 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV142 @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(2055,plain,
! [SV725: $i,SV473: $i,SV143: $i] :
( ( ! [SY1956: $i,SY1957: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SY1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SY1957 ) @ SY1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SY1957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2056,plain,
! [SV726: $i,SV474: $i,SV144: $i] :
( ( ! [SY1958: $i] :
( ( c_Wellfounded_Oaccp @ SV144 @ SV474 @ SV726 )
| ~ ( c_Wellfounded_Oaccp @ SV144 @ SY1958 @ SV726 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV144 @ SV726 ) @ SV474 ) @ SY1958 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2057,plain,
! [SV727: $i,SV475: $i,SV145: $i] :
( ( ! [SY1959: $i] :
( ( c_Wellfounded_Oaccp @ SV145 @ SV475 @ SV727 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SV727 ) @ SV475 ) @ SY1959 ) )
| ~ ( c_Wellfounded_Oaccp @ SV145 @ SY1959 @ SV727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2058,plain,
! [SV728: $i,SV476: $i,SV146: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV146 @ SV476 ) @ SV728 ) @ SV728 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2059,plain,
! [SV729: $i,SV477: $i,SV147: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV147 @ SV477 ) @ SV729 ) @ SV729 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2060,plain,
! [SV151: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV151 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(2061,plain,
! [SV730: $i,SV479: $i,SV152: $i] :
( ( ! [SY1960: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV730 ) @ SY1960 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ SV730 ) ) @ SY1960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2062,plain,
! [SV731: $i,SV480: $i,SV153: $i] :
( ( ! [SY1961: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV731 ) @ SY1961 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ SY1961 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2063,plain,
! [SV732: $i,SV481: $i,SV154: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV732 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV154 ) @ SV732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2064,plain,
! [SV733: $i,SV482: $i,SV155: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ SV482 ) ) @ SV733 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV155 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV482 ) @ SV733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2065,plain,
! [SV734: $i,SV483: $i,SV156: $i] :
( ( ! [SY1962: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ SV734 ) ) @ SY1962 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV734 ) @ SY1962 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2066,plain,
! [SV735: $i,SV484: $i,SV157: $i] :
( ( ! [SY1963: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV735 ) @ SY1963 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ SY1963 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2067,plain,
! [SV736: $i,SV485: $i,SV158: $i] :
( ( ! [SY1964: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ SV736 ) ) @ SY1964 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV736 ) @ SY1964 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2068,plain,
! [SV737: $i,SV486: $i,SV159: $i] :
( ( ! [SY1965: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV737 ) @ SY1965 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ SV737 ) ) @ SY1965 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2069,plain,
! [SV738: $i,SV487: $i,SV160: $i] :
( ( ! [SY1966: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SV738 ) ) @ SY1966 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SY1966 ) ) @ SV738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2070,plain,
! [SV739: $i,SV488: $i,SV161: $i] :
( ( ! [SY1967: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV739 ) @ SY1967 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV739 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ SY1967 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2071,plain,
! [SV740: $i,SV489: $i,SV162: $i] :
( ( ! [SY1968: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ SV740 ) ) @ SY1968 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV740 ) @ SY1968 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2072,plain,
! [SV741: $i,SV490: $i,SV163: $i] :
( ( ! [SY1969: $i,SY1970: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV163 @ SV490 @ SV741 ) @ SY1969 ) @ SY1970 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV163 @ SY1970 ) @ SY1969 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2073,plain,
! [SV742: $i,SV491: $i,SV164: $i] :
( ( ! [SY1971: $i,SY1972: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV164 @ SV491 ) @ SV742 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV164 @ SY1971 @ SY1972 ) @ SV742 ) @ SV491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2074,plain,
! [SV743: $i,SV492: $i,SV165: $i] :
( ( ! [SY1973: $i,SY1974: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV165 @ SV492 @ SV743 ) @ SY1973 ) @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV165 @ SY1974 ) @ SY1973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2075,plain,
! [SV744: $i,SV493: $i,SV166: $i] :
( ( ! [SY1975: $i,SY1976: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV493 ) @ SV744 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV166 @ SY1975 @ SY1976 ) @ SV744 ) @ SV493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2076,plain,
! [SV745: $i,SV494: $i,SV167: $i] :
( ( ! [SY1977: $i] :
( ( c_List_Ofoldr @ SV167 @ ( c_List_Olist_ONil @ SV494 ) @ SV745 @ SV494 @ SY1977 )
= SV745 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2077,plain,
! [SV168: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV168 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV168 )
= ( c_HOL_Oone__class_Oone @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(2078,plain,
! [SV495: $i,SV169: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV169 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV495 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ ( c_HOL_Oone__class_Oone @ SV169 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV495 @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(2079,plain,
! [SV746: $i,SV497: $i,SV171: $i] :
( ( ! [SY1978: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV171 @ SV497 ) @ SV746 ) @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV171 @ SV497 @ SV497 ) @ SV497 ) @ SY1978 ) @ SV746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2080,plain,
! [SV747: $i,SV498: $i,SV172: $i] :
( ( ! [SY1979: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV172 @ SV498 @ SV498 ) @ SV498 ) @ SV747 ) @ SY1979 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV172 @ SV498 ) @ SY1979 ) @ SV747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2081,plain,
! [SV748: $i,SV499: $i,SV173: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV173 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV499 @ SV748 @ SV173 @ SV173 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV499 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2082,plain,
! [SV500: $i,SV174: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV174 ) @ SV500 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV174 )
= SV500 )
| ~ ( c_HOL_Oord__class_Oless @ SV174 @ SV500 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(2083,plain,
! [SV749: $i,SV501: $i,SV175: $i] :
( ( ! [SY1980: $i,SY1981: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ ( c_Lambda_Olift @ SV501 @ SV749 ) ) @ ( c_Suc @ SY1980 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1981 ) @ SV501 ) @ SY1980 ) ) @ SV749 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SY1981 ) @ SV749 ) ) @ SV501 ) @ SY1980 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV749 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1980 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2084,plain,
! [SV750: $i,SV502: $i,SV176: $i] :
( ( ! [SY1982: $i,SY1983: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV176 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV750 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SY1982 ) @ SY1983 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SY1982 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV750 ) @ SY1983 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2085,plain,
! [SV503: $i,SV178: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV178 @ SV503 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV503 @ ( c_Suc @ SV178 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(2086,plain,
! [SV504: $i,SV179: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV179 @ ( c_Suc @ SV504 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV504 @ SV179 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1776]) ).
thf(2087,plain,
! [SV751: $i,SV505: $i,SV180: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SV505 ) @ ( c_Suc @ SV751 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SV751 ) @ SV505 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV505 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV751 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2088,plain,
! [SV181: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV181 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV181 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV181 ) @ ( c_HOL_Oone__class_Oone @ SV181 ) ) @ ( c_HOL_Oone__class_Oone @ SV181 ) ) @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(2089,plain,
! [SV507: $i,SV183: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) ) @ SV507 )
= SV507 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(2090,plain,
! [SV508: $i,SV184: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV184 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( c_HOL_Ozero__class_Ozero @ SV184 ) ) @ SV508 )
= SV508 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(2091,plain,
! [SV509: $i,SV188: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV188 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV188 )
| ( SV509
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV509 ) @ ( c_HOL_Ozero__class_Ozero @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(2092,plain,
! [SV510: $i,SV189: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV189 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV189 ) @ SV510 ) @ ( c_HOL_Ozero__class_Ozero @ SV189 ) )
= SV510 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(2093,plain,
! [SV511: $i,SV190: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV190 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ ( c_HOL_Ozero__class_Ozero @ SV190 ) ) @ SV511 )
= SV511 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(2094,plain,
! [SV512: $i,SV191: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV191 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV191 ) @ SV512 ) @ ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= SV512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(2095,plain,
! [SV513: $i,SV192: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV192 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV513 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) )
= SV513 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(2096,plain,
! [SV514: $i,SV193: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV193 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV193 ) @ ( c_HOL_Ozero__class_Ozero @ SV193 ) ) @ SV514 )
= SV514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(2097,plain,
! [SV515: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV194 ) @ ( c_Suc @ SV515 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV194 @ SV515 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(2098,plain,
! [SV516: $i,SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV195 @ SV516 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV195 ) @ ( c_Suc @ SV516 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(2099,plain,
! [SV517: $i,SV196: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV196 ) @ ( c_Suc @ SV517 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV196 @ SV517 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2100,plain,
! [SV752: $i,SV518: $i,SV197: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV197 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV518 @ SV197 @ SV752 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV518 ) @ SV197 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2101,plain,
! [SV753: $i,SV519: $i,SV198: $i] :
( ( ! [SY1984: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ SV519 ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV753 @ SV198 @ SY1984 @ SV519 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1984 ) @ SV519 ) ) @ SV753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2102,plain,
! [SV754: $i,SV520: $i,SV199: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV199 ) ) @ SV520 ) @ SV754 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV199 ) @ ( c_Lambda_Olift @ SV520 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV754 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2103,plain,
! [SV755: $i,SV521: $i,SV200: $i] :
( ( ! [SY1985: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV521 ) @ SV755 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SY1985 ) @ SV755 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1985 ) @ SV521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2104,plain,
! [SV756: $i,SV522: $i,SV201: $i] :
( ( ! [SY1986: $i,SY1987: $i,SY1988: $i,SY1989: $i] :
( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SY1986 @ SV201 @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1987 ) @ SY1988 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1986 ) )
| ~ ( c_Type_Otypings @ SV201 @ SY1988 @ SY1989 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1987 ) @ SY1988 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2105,plain,
! [SV757: $i,SV523: $i,SV202: $i] :
( ( ! [SY1990: $i] :
( ( c_Type_Otypings @ SV202 @ SV523 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV757 @ SV202 @ SY1990 @ SV523 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV202 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1990 ) @ SV523 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2106,plain,
! [SV758: $i,SV524: $i,SV203: $i] :
( ( ! [SY1991: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ SV524 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV758 @ SV203 @ SV524 @ SY1991 ) @ SV758 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV524 @ SY1991 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2107,plain,
! [SV759: $i,SV525: $i,SV204: $i] :
( ( ! [SY1992: $i,SY1993: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV525 @ SV759 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1992 ) )
| ~ ( c_Type_Otypings @ SV204 @ SV759 @ SY1993 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SV525 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1993 @ SY1992 @ tc_Type_Otype @ tc_Type_Otype ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2108,plain,
! [SV760: $i,SV526: $i,SV205: $i] :
( ( ! [SY1994: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ SV526 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV760 @ SV205 @ SV526 @ SY1994 ) @ SV760 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV526 @ SY1994 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2109,plain,
! [SV761: $i,SV527: $i,SV206: $i] :
( ( ! [SY1995: $i,SY1996: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SV527 ) @ SV761 ) @ SY1995 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1996 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SV527 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1996 ) ) @ ( c_Suc @ SV761 ) ) @ SY1995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2110,plain,
! [SV762: $i,SV528: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV207 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV528 @ SV207 @ SV762 ) ) ) @ SV762 ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV528 @ SV207 @ SV762 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV207 ) @ ( c_Lambda_OdB_OAbs @ SV762 ) ) @ SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2111,plain,
! [SV763: $i,SV529: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV208 @ SV529 ) ) ) @ SV529 ) @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV208 @ SV529 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV208 ) @ ( c_Lambda_OdB_OAbs @ SV529 ) ) @ SV763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2112,plain,
! [SV764: $i,SV530: $i,SV209: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV209 @ SV530 ) ) @ ( c_Lambda_Olift @ SV764 @ SV530 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV209 ) @ SV764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2113,plain,
! [SV765: $i,SV531: $i,SV210: $i] :
( ( ! [SY1997: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_Lambda_OdB_OVar @ SV531 ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV765 @ SV210 @ SV531 @ SY1997 ) @ SV765 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV531 ) @ SY1997 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2114,plain,
! [SV766: $i,SV532: $i,SV211: $i] :
( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV211 ) @ SV532 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV532 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV211 ) ) @ SV532 ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2115,plain,
! [SV767: $i,SV533: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SV533 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SV767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV533 @ SV767 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2116,plain,
! [SV768: $i,SV534: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV768 @ SV534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV213 ) @ SV768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2117,plain,
! [SV769: $i,SV535: $i,SV217: $i] :
( ( ! [SY1998: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ SV535 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV769 @ SV217 @ SV535 @ SY1998 ) ) @ SV769 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ SY1998 ) ) @ SV769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2118,plain,
! [SV536: $i,SV218: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV218 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV536 @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV536 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(2119,plain,
! [SV537: $i,SV219: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV219 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV537 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV537 @ SV219 ) @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(2120,plain,
! [SV770: $i,SV538: $i,SV220: $i] :
( ( ( SV220
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV538 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV538 @ SV770 @ SV220 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV538 ) @ SV770 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2121,plain,
! [SV539: $i,SV221: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV221 ) @ SV539 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV539 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(2122,plain,
! [SV540: $i,SV222: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV222 ) ) @ ( c_Lambda_OdB_OAbs @ SV540 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SV540 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(2123,plain,
! [SV541: $i,SV223: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV223 ) @ ( c_Lambda_OdB_OVar @ SV541 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(2124,plain,
! [SV771: $i,SV542: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV224 @ SV542 ) ) @ ( c_Lambda_Olift @ SV771 @ SV542 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV224 ) @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2125,plain,
! [SV543: $i,SV225: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV225 ) @ SV543 )
= ( c_Lambda_OdB_OVar @ SV225 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV225 @ SV543 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(2126,plain,
! [SV772: $i,SV544: $i,SV226: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV226 @ SV544 ) ) @ SV772 ) @ SV544 )
= SV226 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2127,plain,
! [SV773: $i,SV545: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV227 ) @ SV545 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV773 ) @ SV545 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV227 ) @ SV773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2128,plain,
! [SV774: $i,SV546: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SV546 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SV774 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV546 ) @ SV774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2129,plain,
! [SV229: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV229 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(2130,plain,
! [SV547: $i,SV230: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV230 @ SV230 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV230 ) ) @ SV547 ) @ SV230 )
= SV547 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2131,plain,
! [SV775: $i,SV548: $i,SV233: $i] :
( ( ! [SY1999: $i] :
( ~ ( class_Orderings_Oorder @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV548 @ SV775 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV548 @ SY1999 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SY1999 @ SV775 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2132,plain,
! [SV776: $i,SV549: $i,SV234: $i] :
( ( ! [SY2000: $i] :
( ~ ( class_Orderings_Opreorder @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV549 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY2000 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV549 @ SY2000 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2133,plain,
! [SV777: $i,SV550: $i,SV235: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV235 ) ) @ SV550 ) @ SV777 )
= ( c_Lambda_OdB_OVar @ SV235 ) )
| ( SV235 = SV777 )
| ( c_HOL_Oord__class_Oless @ SV777 @ SV235 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2134,plain,
! [SV778: $i,SV551: $i,SV236: $i] :
( ( ! [SY2001: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV236 ) @ SV551 ) @ SV778 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2001 ) @ SV551 ) @ SV778 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV236 ) @ SY2001 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2135,plain,
! [SV779: $i,SV552: $i,SV237: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV237 ) @ SV552 ) @ SV779 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV237 @ SV779 ) ) @ ( c_Lambda_Olift @ SV552 @ SV779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2136,plain,
! [SV780: $i,SV553: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) ) @ SV553 ) @ SV780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV239 ) @ SV553 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2137,plain,
! [SV554: $i,SV240: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV240 @ SV554 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2138,plain,
! [SV781: $i,SV555: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV241 @ SV555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV781 @ SV555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV241 ) @ SV781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2139,plain,
! [SV556: $i,SV244: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV244 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV556 @ SV556 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2140,plain,
! [SV557: $i,SV245: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV245 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV557 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2141,plain,
! [SV558: $i,SV246: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV246 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV558 @ SV558 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2142,plain,
! [SV782: $i,SV560: $i,SV248: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV560 @ SV782 @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV782 @ SV560 @ SV248 )
| ( SV782 = SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2143,plain,
! [SV783: $i,SV561: $i,SV249: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV249 )
| ( SV561 = SV783 )
| ( c_HOL_Oord__class_Oless @ SV783 @ SV561 @ SV249 )
| ( c_HOL_Oord__class_Oless @ SV561 @ SV783 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2144,plain,
! [SV562: $i,SV250: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV250 @ SV562 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV562 @ SV250 @ tc_nat )
| ( SV562 = SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(2145,plain,
! [SV784: $i,SV563: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV251 @ SV563 ) @ SV784 ) )
| ( c_HOL_Oord__class_Oless @ SV563 @ SV784 @ tc_nat )
| ( SV784 = SV563 )
| ( c_HOL_Oord__class_Oless @ SV784 @ SV563 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2146,plain,
! [SV785: $i,SV564: $i,SV252: $i] :
( ( ! [SY2002: $i,SY2003: $i] :
( ( SV252 = SV564 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2002 ) @ SY2003 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2002 ) @ SY2003 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2147,plain,
! [SV565: $i,SV253: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV253 @ SV565 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV565 @ SV253 @ tc_nat )
| ( SV565 = SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2148,plain,
! [SV786: $i,SV566: $i,SV254: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV254 )
| ( c_HOL_Oord__class_Oless @ SV566 @ SV786 @ SV254 )
| ( c_HOL_Oord__class_Oless @ SV786 @ SV566 @ SV254 )
| ( SV786 = SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2149,plain,
! [SV787: $i,SV567: $i,SV255: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV255 )
| ( c_HOL_Oord__class_Oless @ SV567 @ SV787 @ SV255 )
| ( SV787 = SV567 )
| ( c_HOL_Oord__class_Oless @ SV787 @ SV567 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2150,plain,
! [SV788: $i,SV568: $i,SV256: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV256 )
| ( SV568 = SV788 )
| ( c_HOL_Oord__class_Oless @ SV568 @ SV788 @ SV256 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SV568 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2151,plain,
! [SV789: $i,SV569: $i,SV257: $i] :
( ( ! [SY2004: $i,SY2005: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV569 ) @ SV789 ) ) @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV789 ) @ SY2005 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV569 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2005 ) @ SY2004 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2152,plain,
! [SV570: $i,SV258: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV258 ) ) @ SV570 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(2153,plain,
! [SV790: $i,SV571: $i,SV260: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV260 ) ) @ SV571 ) @ SV790 )
= ( c_Lambda_OdB_OVar @ SV260 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV260 @ SV790 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2154,plain,
! [SV791: $i,SV572: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV261 ) @ ( c_Lambda_OdB_OVar @ SV572 ) ) @ SV791 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2155,plain,
! [SV792: $i,SV574: $i,SV263: $i] :
( ( ! [SY2006: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV263 ) @ SV574 ) ) @ SV792 ) @ SY2006 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV263 ) @ SV792 ) @ SY2006 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV574 ) @ SV792 ) @ SY2006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2156,plain,
! [SV793: $i,SV575: $i,SV264: $i] :
( ( ~ ( class_Orderings_Oorder @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV793 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV575 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2157,plain,
! [SV794: $i,SV576: $i,SV265: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV794 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV576 @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2158,plain,
! [SV795: $i,SV577: $i,SV266: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV795 @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV795 @ SV577 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2159,plain,
! [SV796: $i,SV578: $i,SV267: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV267 )
| ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV796 @ SV267 )
| ~ ( c_HOL_Oord__class_Oless @ SV796 @ SV578 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2160,plain,
! [SV797: $i,SV579: $i,SV268: $i] :
( ( ! [SY2007: $i,SY2008: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV268 ) @ SV579 ) @ SV797 ) ) @ ( c_Lambda_Olift @ SY2007 @ SV579 ) ) @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV268 ) @ SY2007 ) @ SY2008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2161,plain,
! [SV798: $i,SV580: $i,SV269: $i] :
( ( ! [SY2009: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV798 ) @ SV269 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV798 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SY2009 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2162,plain,
! [SV799: $i,SV581: $i,SV270: $i] :
( ( ! [SY2010: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV799 ) @ SV270 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV799 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SY2010 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2163,plain,
! [SV800: $i,SV582: $i,SV271: $i] :
( ( ! [SY2011: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV582 ) @ SV800 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2011 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SY2011 ) @ SV800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2164,plain,
! [SV801: $i,SV583: $i,SV272: $i] :
( ( ! [SY2012: $i,SY2013: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV272 ) @ SV583 ) @ SV801 ) @ SY2012 ) @ SY2013 )
= ( hAPP @ SV583 @ SY2013 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2013 @ SV801 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2165,plain,
! [SV802: $i,SV584: $i,SV273: $i] :
( ( ! [SY2014: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV273 ) @ SV584 ) @ SV802 ) @ SY2014 ) @ SV802 )
= SY2014 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2166,plain,
! [SV803: $i,SV585: $i,SV274: $i] :
( ( ! [SY2015: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV274 ) @ ( c_Lambda_OdB_OAbs @ SV585 ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV803 ) @ SY2015 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV803 ) ) @ SV585 ) @ SY2015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2167,plain,
! [SV804: $i,SV586: $i,SV275: $i] :
( ( ( ( hAPP @ SV275 @ SV586 )
= SV804 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV275 ) @ ( c_Lambda_OdB_OVar @ SV586 ) ) @ SV804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2168,plain,
! [SV276: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ v_a____ ) @ SV276 ) )
= $false )
| ( v_thesis____ = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(2169,plain,
! [SV805: $i,SV588: $i,SV278: $i] :
( ( ! [SY2016: $i,SY2017: $i,SY2018: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SV805 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SY2016 ) @ SV805 ) ) @ SY2017 ) @ SY2018 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2017 ) @ SV588 ) @ SY2016 ) ) @ SY2018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2170,plain,
! [SV806: $i,SV589: $i,SV279: $i] :
( ( ! [SY2019: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV806 ) @ SV279 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV806 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SY2019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2171,plain,
! [SV590: $i,SV280: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV280 @ SV590 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(2172,plain,
! [SV591: $i,SV281: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV281 @ SV591 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2173,plain,
! [SV807: $i,SV593: $i,SV283: $i] :
( ( ( SV283 = SV593 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV807 ) @ SV283 ) @ SV593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2174,plain,
! [SV808: $i,SV594: $i,SV284: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV808 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV284 = SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2175,plain,
! [SV595: $i,SV285: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV285 ) @ SV595 ) )
= $true )
| ( ( ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV285
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2176,plain,
! [SV809: $i,SV596: $i,SV286: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV286 ) @ SV596 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV809 ) @ SV596 ) )
| ( SV286 = SV809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2177,plain,
! [SV287: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV287 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV287 )
!= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(2178,plain,
! [SV810: $i,SV597: $i,SV288: $i] :
( ( ! [SY2020: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( c_HOL_Ominus__class_Ominus @ SV597 @ SV597 @ SV288 )
!= ( c_HOL_Ominus__class_Ominus @ SV810 @ SY2020 @ SV288 ) )
| ( SV810 = SY2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2179,plain,
! [SV811: $i,SV598: $i,SV289: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV289 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV598 @ SV811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV289 )
= SV598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2180,plain,
! [SV599: $i,SV290: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV290 ) @ SV599 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV599
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV290
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2181,plain,
! [SV812: $i,SV600: $i,SV291: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV291 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV600 @ SV291 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV812 @ SV291 ) )
| ( SV600 = SV812 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2182,plain,
! [SV601: $i,SV292: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV292 ) @ SV601 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV601
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2183,plain,
! [SV813: $i,SV602: $i,SV293: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV293 )
| ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV813 @ SV293 )
!= ( c_HOL_Ozero__class_Ozero @ SV293 ) )
| ( SV602 = SV813 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2184,plain,
! [SV814: $i,SV603: $i,SV294: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV294 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV603 @ SV814 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV294 )
= SV603 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2185,plain,
! [SV604: $i,SV295: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV295 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV295 ) @ SV604 ) @ SV604 )
!= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
| ( SV604
= ( c_HOL_Ozero__class_Ozero @ SV295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2186,plain,
! [SV605: $i,SV296: $i] :
( ( ( ( c_Suc @ SV296 )
!= ( c_Suc @ SV605 ) )
= $true )
| ( ( SV296 = SV605 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(2187,plain,
! [SV606: $i,SV297: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV297 )
!= ( c_Lambda_OdB_OVar @ SV606 ) )
= $true )
| ( ( SV297 = SV606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2188,plain,
! [SV607: $i,SV298: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV298 ) @ SV607 ) )
= $true )
| ( ( ( SV607
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV607
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2189,plain,
! [SV815: $i,SV608: $i,SV299: $i] :
( ( ! [SY2021: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV299 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV815 ) @ SY2021 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV299 = SV815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2190,plain,
! [SV609: $i,SV302: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV302 )
!= ( c_Lambda_OdB_OAbs @ SV609 ) )
= $true )
| ( ( SV302 = SV609 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2191,plain,
! [SV816: $i,SV610: $i,SV303: $i] :
( ( ! [SY2022: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV303 )
| ~ ( class_Int_Onumber__ring @ SV303 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV816 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SY2022 ) )
| ( SV816 = SY2022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2192,plain,
! [SV817: $i,SV611: $i,SV304: $i] :
( ( ! [SY2023: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV304 ) @ SV611 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV817 ) @ SY2023 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV304 = SV817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2193,plain,
! [SV818: $i,SV612: $i,SV305: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SV612 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SV818 ) )
| ( SV612 = SV818 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2194,plain,
! [SV306: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV306 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV306 )
!= ( c_HOL_Oone__class_Oone @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(2195,plain,
! [SV819: $i,SV613: $i,SV307: $i] :
( ( ! [SY2024: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV307 ) @ SV613 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV819 ) @ SY2024 ) )
| ( SV307 = SV819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2196,plain,
! [SV614: $i,SV308: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV308 @ SV614 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV614 @ SV308 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV614 = SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2197,plain,
! [SV615: $i,SV310: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV615 )
!= SV310 )
= $true )
| ( ( SV615
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2198,plain,
! [SV820: $i,SV616: $i,SV312: $i] :
( ( ! [SY2025: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV312 ) @ SV616 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV820 ) @ SY2025 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV820 @ SV616 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV312 @ SY2025 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2199,plain,
! [SV821: $i,SV617: $i,SV313: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV313 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV617 @ SV821 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV821
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2200,plain,
! [SV618: $i,SV314: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV314 ) @ SV618 ) )
= $true )
| ( ( ( SV314
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2201,plain,
! [SV619: $i,SV315: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV315 ) @ SV619 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2202,plain,
! [SV822: $i,SV620: $i,SV316: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV316 )
| ~ ( class_Int_Onumber__ring @ SV316 )
| ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV822 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV620 = SV822 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2203,plain,
! [SV621: $i,SV317: $i] :
( ( ( c_Lambda_OdB_OVar @ SV317 )
= ( c_Lambda_OdB_OAbs @ SV621 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(2204,plain,
! [SV823: $i,SV622: $i,SV318: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV318 )
| ~ ( class_Int_Onumber__ring @ SV318 )
| ( SV622
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV622 ) @ SV823 ) )
| ( SV823
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2205,plain,
! [SV824: $i,SV623: $i,SV319: $i] :
( ( ! [SY2026: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV623 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV824 ) @ SY2026 ) )
| ( SV623 = SY2026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2206,plain,
! [SV825: $i,SV624: $i,SV320: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV320 ) @ SV624 )
!= ( c_Lambda_OdB_OVar @ SV825 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2207,plain,
! [SV826: $i,SV625: $i,SV321: $i] :
( ( ( c_Lambda_OdB_OVar @ SV321 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV625 ) @ SV826 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2208,plain,
! [SV827: $i,SV626: $i,SV322: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV322 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV626 ) @ SV827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2209,plain,
! [SV627: $i,SV323: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV627 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(2210,plain,
! [SV828: $i,SV628: $i,SV324: $i] :
( ( ! [SY2027: $i,SY2028: $i,SY2029: $i,SY2030: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SY2027 ) @ SY2028 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY2029 ) @ SY2027 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY2029 ) @ SY2028 ) @ SV324 ) ) @ SV828 ) @ SY2030 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2211,plain,
! [SV829: $i,SV629: $i,SV325: $i] :
( ( ! [SY2031: $i,SY2032: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY2031 @ SY2032 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SY2031 @ SY2032 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2212,plain,
! [SV630: $i,SV326: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV326 ) @ SV630 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV630
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV630
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2213,plain,
! [SV830: $i,SV631: $i,SV327: $i] :
( ( ! [SY2033: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV830 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SY2033 ) )
| ( SV830 = SY2033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2214,plain,
! [SV831: $i,SV632: $i,SV328: $i] :
( ( ! [SY2034: $i,SY2035: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV328 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SY2034 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SY2035 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ SY2034 )
= SY2035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2215,plain,
! [SV832: $i,SV633: $i,SV329: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV329 )
| ( ( c_HOL_Ominus__class_Ominus @ SV633 @ SV832 @ SV329 )
!= ( c_HOL_Ozero__class_Ozero @ SV329 ) )
| ( SV633 = SV832 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2216,plain,
! [SV833: $i,SV634: $i,SV331: $i] :
( ( ! [SY2036: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV331 ) @ SV634 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV833 ) @ SY2036 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2217,plain,
! [SV635: $i,SV332: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV332 ) @ SV635 ) )
= $true )
| ( ( ( SV635
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV332
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2218,plain,
! [SV834: $i,SV636: $i,SV333: $i] :
( ( ! [SY2037: $i,SY2038: $i,SY2039: $i,SY2040: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SY2037 ) @ SY2038 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY2039 ) @ SY2037 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2037 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY2039 ) @ SY2038 ) @ SV636 ) ) @ SV834 ) @ SY2040 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2219,plain,
! [SV835: $i,SV637: $i,SV334: $i] :
( ( ! [SY2041: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SV637 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV835 ) @ SY2041 ) )
| ( SV334 = SV835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2220,plain,
! [SV638: $i,SV336: $i] :
( ( ( SV336
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV336 ) @ SV638 ) )
= $true )
| ( ( SV638
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2221,plain,
! [SV836: $i,SV639: $i,SV337: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV337 @ SV639 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV836 ) )
| ( SV337
= ( c_Lambda_OdB_OAbs @ SV836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2222,plain,
! [SV837: $i,SV640: $i,SV338: $i] :
( ( ! [SY2042: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV338 ) @ SV640 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV837 ) @ SY2042 ) )
| ( SV640 = SY2042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2223,plain,
! [SV838: $i,SV641: $i,SV339: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV339 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV641 @ SV838 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV838
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2224,plain,
! [SV839: $i,SV642: $i,SV340: $i] :
( ( ! [SY2043: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV340 ) ) @ SV642 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV839 ) @ SY2043 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2225,plain,
! [SV840: $i,SV643: $i,SV341: $i] :
( ( ! [SY2044: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV341 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV840 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SY2044 ) )
| ( SV840 = SY2044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2226,plain,
! [SV841: $i,SV644: $i,SV342: $i] :
( ( ! [SY2045: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV342 ) @ SV644 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV841 ) @ SY2045 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV644 = SY2045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2227,plain,
! [SV842: $i,SV645: $i,SV343: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV343 ) @ SV645 )
!= ( c_Lambda_OdB_OAbs @ SV842 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2228,plain,
! [SV843: $i,SV646: $i,SV344: $i] :
( ( ! [SY2046: $i,SY2047: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
| ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
!= ( c_HOL_Ominus__class_Ominus @ SY2046 @ SY2047 @ SV344 ) )
| ( c_HOL_Oord__class_Oless @ SY2046 @ SY2047 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2229,plain,
! [SV844: $i,SV647: $i,SV345: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SV647 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SV844 ) )
| ( SV647 = SV844 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2230,plain,
! [SV648: $i,SV346: $i] :
( ( ( ( c_Suc @ SV346 )
!= ( c_Suc @ SV648 ) )
= $true )
| ( ( SV346 = SV648 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2231,plain,
! [SV845: $i,SV649: $i,SV347: $i] :
( ( ! [SY2048: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV347 ) @ SV649 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV845 ) @ SY2048 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV649 = SY2048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2232,plain,
! [SV846: $i,SV650: $i,SV348: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV348 @ SV650 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV846 ) )
| ( SV650
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2233,plain,
! [SV847: $i,SV651: $i,SV349: $i] :
( ( ! [SY2049: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV349 )
| ( ( c_HOL_Ominus__class_Ominus @ SV651 @ SV847 @ SV349 )
!= ( c_HOL_Ominus__class_Ominus @ SY2049 @ SY2049 @ SV349 ) )
| ( SV651 = SV847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2234,plain,
! [SV848: $i,SV652: $i,SV350: $i] :
( ( ! [SY2050: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV652 ) @ SV848 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SY2050 ) @ SV848 ) )
| ( SV652 = SY2050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2235,plain,
! [SV653: $i,SV351: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV351 ) @ SV653 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV351
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV351
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2236,plain,
! [SV849: $i,SV654: $i,SV352: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV654 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV849 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV654 )
= SV849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2237,plain,
! [SV655: $i,SV353: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV353 )
= ( c_Lambda_OdB_OVar @ SV655 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2238,plain,
! [SV354: $i,SV4: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV4 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV354 @ tc_nat ) @ SV4 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2239,plain,
! [SV5: $i,SV355: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV355 @ SV5 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV5 @ SV355 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2240,plain,
! [SV6: $i,SV356: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV356 @ SV6 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV6 @ SV356 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2241,plain,
! [SV656: $i,SV357: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV357 @ SV656 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ominus__class_Ominus @ SV357 @ SV656 @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2242,plain,
! [SV657: $i,SV358: $i,SV8: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV8 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV657 @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SV358 @ SV657 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2243,plain,
! [SV658: $i,SV359: $i,SV9: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV9 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV359 @ SV658 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV658 @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2244,plain,
! [SV659: $i,SV361: $i,SV11: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV11 @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV659 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV11 ) @ SV659 ) @ SV361 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1952]) ).
thf(2245,plain,
! [SV660: $i,SV362: $i,SV12: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV12 ) @ SV362 ) @ SV660 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_HOL_Ominus__class_Ominus @ SV660 @ SV362 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2246,plain,
! [SV661: $i,SV363: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ SV363 @ tc_nat ) @ SV661 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV13 @ SV661 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2247,plain,
! [SV365: $i,SV17: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV17 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV17 )
| ( ( c_HOL_Ominus__class_Ominus @ SV365 @ SV365 @ SV17 )
= ( c_HOL_Ozero__class_Ozero @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2248,plain,
! [SV366: $i,SV18: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV18 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV366 @ SV366 @ SV18 )
= ( c_HOL_Ozero__class_Ozero @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2249,plain,
! [SV367: $i,SV19: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV19 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV367 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= SV367 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2250,plain,
! [SV368: $i,SV20: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV20 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV368 @ SV368 @ SV20 )
= ( c_HOL_Ozero__class_Ozero @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2251,plain,
! [SV369: $i,SV21: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV21 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV369 @ SV369 @ SV21 )
= ( c_HOL_Ozero__class_Ozero @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2252,plain,
! [SV662: $i,SV370: $i,SV22: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV370 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV662 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV22 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV370 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2253,plain,
! [SV663: $i,SV371: $i,SV24: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV24 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ominus__class_Ominus @ SV371 @ SV663 @ SV24 ) ) @ SV663 )
= SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2254,plain,
! [SV664: $i,SV372: $i,SV25: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV372 ) @ SV664 ) @ SV372 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV664 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2255,plain,
! [SV665: $i,SV373: $i,SV26: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV373 ) @ SV665 ) @ SV373 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV26 @ SV665 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2256,plain,
! [SV671: $i,SV384: $i,SV38: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV38 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV384 ) @ SV671 ) @ SV671 @ SV38 )
= SV384 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2257,plain,
! [SV385: $i,SV39: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV39 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV39 @ ( c_Suc @ SV385 ) @ tc_nat ) @ SV39 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2258,plain,
! [SV850: $i,SV672: $i,SV386: $i,SV41: $i] :
( ( ! [SY2051: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV41 ) @ SV386 ) @ SV672 ) @ SV850 ) @ SY2051 )
= ( hAPP @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SY2051 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV672 @ SY2051 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2259,plain,
! [SV851: $i,SV673: $i,SV387: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV42 @ SV387 ) @ SV673 ) @ SV851 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV42 @ SV673 ) @ SV851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2260,plain,
! [SV674: $i,SV388: $i,SV43: $i] :
( ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_ONil @ SV388 ) @ SV674 @ SV388 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2261,plain,
! [SV675: $i,SV389: $i,SV44: $i] :
( ( c_ListOrder_Ostep1 @ SV44 @ SV389 @ ( c_List_Olist_ONil @ SV675 ) @ SV675 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2262,plain,
! [SV852: $i,SV676: $i,SV390: $i,SV45: $i] :
( ( ( c_List_Ofoldl @ SV45 @ SV390 @ ( c_List_Olist_ONil @ SV676 ) @ SV852 @ SV676 )
= SV390 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2263,plain,
! [SV391: $i,SV47: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV47 @ SV391 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV47 @ ( c_Suc @ SV391 ) @ tc_nat ) )
= $true )
| ( ( SV47 = SV391 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1977]) ).
thf(2264,plain,
! [SV48: $i,SV392: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SV48 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV392 @ SV48 @ tc_nat )
= $true )
| ( ( SV48 = SV392 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2265,plain,
! [SV393: $i,SV49: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV49 @ ( c_Suc @ SV393 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV49 @ SV393 @ tc_nat )
= $true )
| ( ( SV49 = SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2266,plain,
! [SV853: $i,SV677: $i,SV394: $i,SV50: $i] :
( ( ! [SY2052: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV853 ) @ SY2052 ) @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SY2052 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ SV853 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2267,plain,
! [SV854: $i,SV678: $i,SV395: $i,SV51: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV395 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV678 ) @ SV854 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV395 @ SV854 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV51 @ SV678 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2268,plain,
! [SV679: $i,SV396: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV54 ) @ SV396 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV679 @ SV396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV679 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2269,plain,
! [SV397: $i,SV55: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV55 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV397 @ SV55 @ SV55 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV397 @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV55 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2270,plain,
! [SV398: $i,SV56: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV56 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV398 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV398 ) @ ( c_HOL_Oone__class_Oone @ SV56 ) ) @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2271,plain,
! [SV855: $i,SV681: $i,SV402: $i,SV60: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV60 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV402 ) @ SV681 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV855 ) @ SV681 ) @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV402 @ SV855 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2272,plain,
! [SV856: $i,SV682: $i,SV403: $i,SV61: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV61 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV403 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV856 ) @ SV682 ) @ SV61 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV856 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2273,plain,
! [SV857: $i,SV683: $i,SV404: $i,SV62: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV62 )
| ( c_HOL_Oord__class_Oless @ SV404 @ SV683 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV404 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV683 ) @ SV857 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2274,plain,
! [SV858: $i,SV684: $i,SV405: $i,SV63: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV63 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV684 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV858 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV684 @ SV858 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2275,plain,
! [SV859: $i,SV685: $i,SV406: $i,SV64: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV685 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV859 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV685 @ SV859 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2276,plain,
! [SV860: $i,SV686: $i,SV407: $i,SV65: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV65 )
| ( c_HOL_Oord__class_Oless @ SV407 @ SV686 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV407 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV686 ) @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2277,plain,
! [SV687: $i,SV408: $i,SV66: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV66 ) @ SV408 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV687 ) @ SV408 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV66 @ SV687 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2278,plain,
! [SV688: $i,SV409: $i,SV67: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV67 @ SV409 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV409 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2279,plain,
! [SV689: $i,SV410: $i,SV68: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SV689 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV410 @ SV689 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2280,plain,
! [SV411: $i,SV69: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV69 ) @ SV411 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV69 @ SV411 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2281,plain,
! [SV412: $i,SV70: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV70 @ SV412 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV70 @ ( c_Suc @ SV412 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2282,plain,
! [SV690: $i,SV413: $i,SV71: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV71 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SV690 ) @ SV71 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV413 @ SV71 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV690 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1999]) ).
thf(2283,plain,
! [SV861: $i,SV691: $i,SV415: $i,SV73: $i] :
( ( ! [SY2053: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV691 ) @ SV861 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SY2053 ) @ SV861 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SV691 ) @ SY2053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2284,plain,
! [SV862: $i,SV692: $i,SV416: $i,SV74: $i] :
( ( ! [SY2054: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV862 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SY2054 ) @ SV862 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SY2054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2285,plain,
! [SV863: $i,SV693: $i,SV417: $i,SV75: $i] :
( ( ( c_Wellfounded_Oaccp @ SV75 @ SV417 @ SV693 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV75 @ SV417 ) @ SV863 ) )
| ~ ( c_Wellfounded_Oaccp @ SV75 @ SV863 @ SV693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2286,plain,
! [SV864: $i,SV694: $i,SV418: $i,SV76: $i] :
( ( ( c_Wellfounded_Oaccp @ SV76 @ SV418 @ SV694 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV418 ) @ SV864 ) )
| ~ ( c_Wellfounded_Oaccp @ SV76 @ SV864 @ SV694 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2287,plain,
! [SV865: $i,SV695: $i,SV419: $i,SV77: $i] :
( ( ( c_Type_Otypings @ SV77 @ SV419 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV695 @ SV77 @ SV865 @ SV419 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV77 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV865 @ SV419 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2288,plain,
! [SV866: $i,SV696: $i,SV420: $i,SV78: $i] :
( ( ( c_Type_Otypings @ SV78 @ SV420 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV696 @ SV78 @ SV866 @ SV420 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV78 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV866 @ SV420 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2289,plain,
! [SV867: $i,SV697: $i,SV421: $i,SV79: $i] :
( ( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV79 ) @ SV421 ) @ SV697 ) @ SV867 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV79 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV867 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( c_Lambda_Olift @ SV421 @ SV867 ) ) @ SV697 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV697 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV867 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2290,plain,
! [SV868: $i,SV698: $i,SV422: $i,SV80: $i] :
( ( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV80 ) @ SV422 ) @ SV698 ) @ SV868 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV80 @ SV868 ) ) @ ( c_Lambda_Olift @ SV422 @ SV868 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV698 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV868 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV698 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2291,plain,
! [SV699: $i,SV424: $i,SV82: $i] :
( ( ( SV82
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV82 @ SV424 @ SV699 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV82 @ SV424 @ SV699 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV424 ) @ ( c_Lambda_OdB_OAbs @ SV699 ) ) @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2292,plain,
! [SV869: $i,SV700: $i,SV425: $i,SV83: $i] :
( ( ! [SY2055: $i,SY2056: $i,SY2057: $i] :
( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2055 ) @ SY2056 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
| ~ ( c_Type_Otypings @ SV700 @ SY2056 @ SY2057 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2055 ) @ SY2056 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2293,plain,
! [SV426: $i,SV84: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV84 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV426 ) @ SV426 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV426 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2294,plain,
! [SV427: $i,SV85: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV85 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV427 @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV427 ) @ SV427 ) @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2295,plain,
! [SV428: $i,SV86: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV86 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV428 @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2296,plain,
! [SV701: $i,SV429: $i,SV87: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV429 ) @ SV701 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV701 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2297,plain,
! [SV430: $i,SV88: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV88 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SV430 ) @ SV430 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SV430 @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2298,plain,
! [SV431: $i,SV89: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV89 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV431 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV431 ) @ SV431 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2299,plain,
! [SV432: $i,SV90: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV90 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV432 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV432 ) @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2300,plain,
! [SV433: $i,SV91: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV91 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ SV433 ) @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV433 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2301,plain,
! [SV92: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV92 ) @ ( c_HOL_Ozero__class_Ozero @ SV92 ) @ SV92 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2302,plain,
! [SV702: $i,SV434: $i,SV93: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV434 ) @ SV702 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV702 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV434 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2303,plain,
! [SV870: $i,SV703: $i,SV435: $i,SV95: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV703 ) @ SV870 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV870 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV703 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2304,plain,
! [SV704: $i,SV436: $i,SV97: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV97 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV436 @ SV97 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV704 @ SV97 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV436 @ SV704 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2305,plain,
! [SV705: $i,SV437: $i,SV98: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV98 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV705 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV437 @ SV98 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV705 @ SV98 ) @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2306,plain,
! [SV438: $i,SV99: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV99 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV99 ) @ SV438 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2307,plain,
! [SV100: $i,SV439: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV439 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV100 ) @ SV439 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2308,plain,
! [SV103: $i,SV440: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV440 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SV103 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV103 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2309,plain,
! [SV706: $i,SV441: $i,SV105: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV105 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV441 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV706 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV441 @ SV706 @ SV105 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2310,plain,
! [SV871: $i,SV707: $i,SV442: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV106 ) @ SV442 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV707 ) @ SV871 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV442 ) @ SV871 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV106 ) @ SV707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2311,plain,
! [SV708: $i,SV443: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV107 ) @ SV443 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV708 ) @ SV443 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV107 ) @ SV708 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2312,plain,
! [SV709: $i,SV444: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SV444 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SV709 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV444 ) @ SV709 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2313,plain,
! [SV445: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SV445 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV109 ) ) @ ( c_Lambda_OdB_OAbs @ SV445 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2314,plain,
! [SV872: $i,SV710: $i,SV447: $i,SV111: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SV447 ) @ SV710 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SV872 ) @ SV710 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV447 ) @ SV872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2315,plain,
! [SV873: $i,SV711: $i,SV448: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV112 ) @ SV448 ) @ SV711 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV873 ) @ SV448 ) @ SV711 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV112 ) @ SV873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2316,plain,
! [SV874: $i,SV712: $i,SV449: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SV449 ) @ SV712 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SV874 ) @ SV712 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV449 ) @ SV874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2317,plain,
! [SV713: $i,SV450: $i,SV114: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV114 ) ) @ SV450 ) @ SV713 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV713 @ SV114 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2318,plain,
! [SV714: $i,SV451: $i,SV115: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV115 ) ) @ SV451 ) @ SV714 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV115 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV714 @ SV115 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2039]) ).
thf(2319,plain,
! [SV715: $i,SV457: $i,SV125: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV125 ) )
= $true )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SV457 @ SV715 @ SV125 @ SV125 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SV715 @ SV457 @ SV125 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2320,plain,
! [SV875: $i,SV716: $i,SV458: $i,SV126: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV126 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ SV716 ) @ SV875 @ SV126 @ SV126 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV716 @ SV875 @ SV126 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2321,plain,
! [SV717: $i,SV459: $i,SV127: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SV459 ) @ SV717 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SV717 ) @ SV459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2045]) ).
thf(2322,plain,
! [SV718: $i,SV461: $i,SV129: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV129 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV461 ) @ SV718 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV718 ) @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2323,plain,
! [SV719: $i,SV462: $i,SV130: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV462 ) @ SV719 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV719 ) @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2324,plain,
! [SV720: $i,SV463: $i,SV131: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV131 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV463 ) @ SV720 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV131 @ SV720 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2325,plain,
! [SV721: $i,SV464: $i,SV132: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV132 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV464 ) @ SV721 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV132 @ SV464 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2049]) ).
thf(2326,plain,
! [SV722: $i,SV465: $i,SV133: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV133 @ SV465 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV133 ) @ SV722 ) @ SV465 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2327,plain,
! [SV723: $i,SV466: $i,SV134: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV134 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV466 ) @ SV723 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV134 @ SV723 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2328,plain,
! [SV724: $i,SV467: $i,SV135: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV135 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV467 ) @ SV724 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV135 @ SV467 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2329,plain,
! [SV876: $i,SV725: $i,SV473: $i,SV143: $i] :
( ( ! [SY2058: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SY2058 ) @ SV876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SY2058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2330,plain,
! [SV877: $i,SV726: $i,SV474: $i,SV144: $i] :
( ( ( c_Wellfounded_Oaccp @ SV144 @ SV474 @ SV726 )
| ~ ( c_Wellfounded_Oaccp @ SV144 @ SV877 @ SV726 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV144 @ SV726 ) @ SV474 ) @ SV877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2331,plain,
! [SV878: $i,SV727: $i,SV475: $i,SV145: $i] :
( ( ( c_Wellfounded_Oaccp @ SV145 @ SV475 @ SV727 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SV727 ) @ SV475 ) @ SV878 ) )
| ~ ( c_Wellfounded_Oaccp @ SV145 @ SV878 @ SV727 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2332,plain,
! [SV879: $i,SV730: $i,SV479: $i,SV152: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV730 ) @ SV879 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ SV730 ) ) @ SV879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2333,plain,
! [SV880: $i,SV731: $i,SV480: $i,SV153: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV153 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV731 ) @ SV880 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ SV880 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2334,plain,
! [SV881: $i,SV734: $i,SV483: $i,SV156: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ SV734 ) ) @ SV881 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV734 ) @ SV881 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2335,plain,
! [SV882: $i,SV735: $i,SV484: $i,SV157: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV735 ) @ SV882 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ SV882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2336,plain,
! [SV883: $i,SV736: $i,SV485: $i,SV158: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ SV736 ) ) @ SV883 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV736 ) @ SV883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2337,plain,
! [SV884: $i,SV737: $i,SV486: $i,SV159: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV737 ) @ SV884 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ SV737 ) ) @ SV884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2338,plain,
! [SV885: $i,SV738: $i,SV487: $i,SV160: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SV738 ) ) @ SV885 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SV885 ) ) @ SV738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2339,plain,
! [SV886: $i,SV739: $i,SV488: $i,SV161: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV739 ) @ SV886 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV739 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ SV886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2340,plain,
! [SV887: $i,SV740: $i,SV489: $i,SV162: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ SV740 ) ) @ SV887 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV740 ) @ SV887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2341,plain,
! [SV888: $i,SV741: $i,SV490: $i,SV163: $i] :
( ( ! [SY2059: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV163 @ SV490 @ SV741 ) @ SV888 ) @ SY2059 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV163 @ SY2059 ) @ SV888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2342,plain,
! [SV889: $i,SV742: $i,SV491: $i,SV164: $i] :
( ( ! [SY2060: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV164 @ SV491 ) @ SV742 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV164 @ SV889 @ SY2060 ) @ SV742 ) @ SV491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2343,plain,
! [SV890: $i,SV743: $i,SV492: $i,SV165: $i] :
( ( ! [SY2061: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV165 @ SV492 @ SV743 ) @ SV890 ) @ SY2061 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV165 @ SY2061 ) @ SV890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2344,plain,
! [SV891: $i,SV744: $i,SV493: $i,SV166: $i] :
( ( ! [SY2062: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV493 ) @ SV744 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV166 @ SV891 @ SY2062 ) @ SV744 ) @ SV493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2345,plain,
! [SV892: $i,SV745: $i,SV494: $i,SV167: $i] :
( ( ( c_List_Ofoldr @ SV167 @ ( c_List_Olist_ONil @ SV494 ) @ SV745 @ SV494 @ SV892 )
= SV745 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2346,plain,
! [SV495: $i,SV169: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV169 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV495 ) @ SV169 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV169 ) @ ( c_HOL_Oone__class_Oone @ SV169 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV495 @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2347,plain,
! [SV893: $i,SV746: $i,SV497: $i,SV171: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV171 @ SV497 ) @ SV746 ) @ SV893 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV171 @ SV497 @ SV497 ) @ SV497 ) @ SV893 ) @ SV746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2348,plain,
! [SV894: $i,SV747: $i,SV498: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV172 @ SV498 @ SV498 ) @ SV498 ) @ SV747 ) @ SV894 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV172 @ SV498 ) @ SV894 ) @ SV747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2349,plain,
! [SV748: $i,SV499: $i,SV173: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV173 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV499 @ SV748 @ SV173 @ SV173 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV499 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2350,plain,
! [SV500: $i,SV174: $i] :
( ( ( ( c_Suc @ SV174 )
= SV500 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV174 @ SV500 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV174 ) @ SV500 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2351,plain,
! [SV895: $i,SV749: $i,SV501: $i,SV175: $i] :
( ( ! [SY2063: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ ( c_Lambda_Olift @ SV501 @ SV749 ) ) @ ( c_Suc @ SV895 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2063 ) @ SV501 ) @ SV895 ) ) @ SV749 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SY2063 ) @ SV749 ) ) @ SV501 ) @ SV895 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV749 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV895 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2352,plain,
! [SV896: $i,SV750: $i,SV502: $i,SV176: $i] :
( ( ! [SY2064: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV176 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV750 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV896 ) @ SY2064 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV896 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV750 ) @ SY2064 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2353,plain,
! [SV503: $i,SV178: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV178 @ SV503 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV503 @ ( c_Suc @ SV178 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2354,plain,
! [SV751: $i,SV505: $i,SV180: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SV505 ) @ ( c_Suc @ SV751 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SV751 ) @ SV505 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV505 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV751 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2355,plain,
! [SV507: $i,SV183: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV183 ) @ ( c_HOL_Ozero__class_Ozero @ SV183 ) ) @ SV507 )
= SV507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2356,plain,
! [SV508: $i,SV184: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV184 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV184 ) @ ( c_HOL_Ozero__class_Ozero @ SV184 ) ) @ SV508 )
= SV508 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2357,plain,
! [SV509: $i,SV188: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV188 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV188 )
| ( SV509
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV509 ) @ ( c_HOL_Ozero__class_Ozero @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2358,plain,
! [SV510: $i,SV189: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV189 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV189 ) @ SV510 ) @ ( c_HOL_Ozero__class_Ozero @ SV189 ) )
= SV510 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2359,plain,
! [SV511: $i,SV190: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV190 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ ( c_HOL_Ozero__class_Ozero @ SV190 ) ) @ SV511 )
= SV511 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2360,plain,
! [SV512: $i,SV191: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV191 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV191 ) @ SV512 ) @ ( c_HOL_Ozero__class_Ozero @ SV191 ) )
= SV512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2361,plain,
! [SV513: $i,SV192: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV192 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV513 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) )
= SV513 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2362,plain,
! [SV514: $i,SV193: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV193 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV193 ) @ ( c_HOL_Ozero__class_Ozero @ SV193 ) ) @ SV514 )
= SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2363,plain,
! [SV515: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV194 @ SV515 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV194 ) @ ( c_Suc @ SV515 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2364,plain,
! [SV516: $i,SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV195 ) @ ( c_Suc @ SV516 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV195 @ SV516 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2365,plain,
! [SV517: $i,SV196: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV196 @ SV517 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV196 ) @ ( c_Suc @ SV517 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2366,plain,
! [SV752: $i,SV518: $i,SV197: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV197 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV518 @ SV197 @ SV752 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV518 ) @ SV197 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV752 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2367,plain,
! [SV897: $i,SV753: $i,SV519: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ SV519 ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV753 @ SV198 @ SV897 @ SV519 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV897 ) @ SV519 ) ) @ SV753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2368,plain,
! [SV898: $i,SV755: $i,SV521: $i,SV200: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV521 ) @ SV755 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV898 ) @ SV755 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV898 ) @ SV521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2369,plain,
! [SV899: $i,SV756: $i,SV522: $i,SV201: $i] :
( ( ! [SY2065: $i,SY2066: $i,SY2067: $i] :
( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2065 ) @ SY2066 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
| ~ ( c_Type_Otypings @ SV201 @ SY2066 @ SY2067 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2065 ) @ SY2066 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2370,plain,
! [SV900: $i,SV757: $i,SV523: $i,SV202: $i] :
( ( ( c_Type_Otypings @ SV202 @ SV523 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV757 @ SV202 @ SV900 @ SV523 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV202 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV900 ) @ SV523 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2371,plain,
! [SV901: $i,SV758: $i,SV524: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ SV524 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV758 @ SV203 @ SV524 @ SV901 ) @ SV758 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV524 @ SV901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2372,plain,
! [SV902: $i,SV759: $i,SV525: $i,SV204: $i] :
( ( ! [SY2068: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV525 @ SV759 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV902 ) )
| ~ ( c_Type_Otypings @ SV204 @ SV759 @ SY2068 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SV525 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY2068 @ SV902 @ tc_Type_Otype @ tc_Type_Otype ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2373,plain,
! [SV903: $i,SV760: $i,SV526: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ SV526 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV760 @ SV205 @ SV526 @ SV903 ) @ SV760 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV526 @ SV903 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2374,plain,
! [SV904: $i,SV761: $i,SV527: $i,SV206: $i] :
( ( ! [SY2069: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SV527 ) @ SV761 ) @ SV904 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2069 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SV527 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2069 ) ) @ ( c_Suc @ SV761 ) ) @ SV904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2375,plain,
! [SV762: $i,SV528: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV207 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV528 @ SV207 @ SV762 ) ) ) @ SV762 ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV528 @ SV207 @ SV762 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV207 ) @ ( c_Lambda_OdB_OAbs @ SV762 ) ) @ SV528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2376,plain,
! [SV763: $i,SV529: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV208 @ SV529 ) ) ) @ SV529 ) @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV208 @ SV529 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV208 ) @ ( c_Lambda_OdB_OAbs @ SV529 ) ) @ SV763 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2377,plain,
! [SV764: $i,SV530: $i,SV209: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV209 @ SV530 ) ) @ ( c_Lambda_Olift @ SV764 @ SV530 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV209 ) @ SV764 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2378,plain,
! [SV905: $i,SV765: $i,SV531: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_Lambda_OdB_OVar @ SV531 ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV765 @ SV210 @ SV531 @ SV905 ) @ SV765 @ tc_Type_Otype @ tc_Type_Otype ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV531 ) @ SV905 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2379,plain,
! [SV766: $i,SV532: $i,SV211: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV211 ) @ SV532 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV532 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV211 ) ) @ SV532 ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2380,plain,
! [SV767: $i,SV533: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SV533 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SV767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV533 @ SV767 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2381,plain,
! [SV768: $i,SV534: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV768 @ SV534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV213 ) @ SV768 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2382,plain,
! [SV906: $i,SV769: $i,SV535: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ SV535 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV769 @ SV217 @ SV535 @ SV906 ) ) @ SV769 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ SV906 ) ) @ SV769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2383,plain,
! [SV536: $i,SV218: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV218 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV536 @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV536 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2384,plain,
! [SV537: $i,SV219: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV219 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV537 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV537 @ SV219 ) @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2385,plain,
! [SV770: $i,SV538: $i,SV220: $i] :
( ( ( SV220
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV538 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV538 @ SV770 @ SV220 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV538 ) @ SV770 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2386,plain,
! [SV221: $i,SV539: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV539 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV221 ) @ SV539 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2387,plain,
! [SV540: $i,SV222: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SV540 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV222 ) ) @ ( c_Lambda_OdB_OAbs @ SV540 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2388,plain,
! [SV541: $i,SV223: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV223 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV223 ) @ ( c_Lambda_OdB_OVar @ SV541 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2389,plain,
! [SV771: $i,SV542: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV224 @ SV542 ) ) @ ( c_Lambda_Olift @ SV771 @ SV542 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV224 ) @ SV771 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2390,plain,
! [SV543: $i,SV225: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV225 @ SV543 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV225 ) @ SV543 )
= ( c_Lambda_OdB_OVar @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2391,plain,
! [SV773: $i,SV545: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV227 ) @ SV545 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV773 ) @ SV545 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV227 ) @ SV773 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2127]) ).
thf(2392,plain,
! [SV774: $i,SV546: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SV546 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SV774 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV546 ) @ SV774 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2393,plain,
! [SV907: $i,SV775: $i,SV548: $i,SV233: $i] :
( ( ~ ( class_Orderings_Oorder @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV548 @ SV775 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV548 @ SV907 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV907 @ SV775 @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2394,plain,
! [SV908: $i,SV776: $i,SV549: $i,SV234: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV549 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV549 @ SV908 @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2395,plain,
! [SV777: $i,SV550: $i,SV235: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV235 ) ) @ SV550 ) @ SV777 )
= ( c_Lambda_OdB_OVar @ SV235 ) )
= $true )
| ( ( ( SV235 = SV777 )
| ( c_HOL_Oord__class_Oless @ SV777 @ SV235 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2396,plain,
! [SV909: $i,SV778: $i,SV551: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV236 ) @ SV551 ) @ SV778 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV909 ) @ SV551 ) @ SV778 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV236 ) @ SV909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2397,plain,
! [SV780: $i,SV553: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) ) @ SV553 ) @ SV780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV239 ) @ SV553 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2398,plain,
! [SV554: $i,SV240: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV240 @ SV554 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2399,plain,
! [SV781: $i,SV555: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV241 @ SV555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV781 @ SV555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV241 ) @ SV781 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2400,plain,
! [SV556: $i,SV244: $i] :
( ( ( class_Orderings_Oorder @ SV244 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV556 @ SV556 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2401,plain,
! [SV557: $i,SV245: $i] :
( ( ( class_Orderings_Olinorder @ SV245 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV557 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2402,plain,
! [SV558: $i,SV246: $i] :
( ( ( class_Orderings_Opreorder @ SV246 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV558 @ SV558 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2403,plain,
! [SV782: $i,SV560: $i,SV248: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV248 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV560 @ SV782 @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV782 @ SV560 @ SV248 )
| ( SV782 = SV560 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2404,plain,
! [SV783: $i,SV561: $i,SV249: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV249 ) )
= $true )
| ( ( ( SV561 = SV783 )
| ( c_HOL_Oord__class_Oless @ SV783 @ SV561 @ SV249 )
| ( c_HOL_Oord__class_Oless @ SV561 @ SV783 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2405,plain,
! [SV250: $i,SV562: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV562 @ SV250 @ tc_nat )
= $true )
| ( ( SV562 = SV250 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV250 @ SV562 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2406,plain,
! [SV784: $i,SV563: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV251 @ SV563 ) @ SV784 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV563 @ SV784 @ tc_nat )
| ( SV784 = SV563 )
| ( c_HOL_Oord__class_Oless @ SV784 @ SV563 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2407,plain,
! [SV910: $i,SV785: $i,SV564: $i,SV252: $i] :
( ( ! [SY2070: $i] :
( ( SV252 = SV564 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SY2070 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SY2070 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2408,plain,
! [SV253: $i,SV565: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV565 @ SV253 @ tc_nat )
= $true )
| ( ( SV565 = SV253 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV253 @ SV565 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2409,plain,
! [SV786: $i,SV566: $i,SV254: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV254 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV566 @ SV786 @ SV254 )
| ( c_HOL_Oord__class_Oless @ SV786 @ SV566 @ SV254 )
| ( SV786 = SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2410,plain,
! [SV787: $i,SV567: $i,SV255: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV255 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV567 @ SV787 @ SV255 )
| ( SV787 = SV567 )
| ( c_HOL_Oord__class_Oless @ SV787 @ SV567 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2411,plain,
! [SV788: $i,SV568: $i,SV256: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV256 ) )
= $true )
| ( ( ( SV568 = SV788 )
| ( c_HOL_Oord__class_Oless @ SV568 @ SV788 @ SV256 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SV568 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2412,plain,
! [SV911: $i,SV789: $i,SV569: $i,SV257: $i] :
( ( ! [SY2071: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV569 ) @ SV789 ) ) @ SV911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV789 ) @ SY2071 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV569 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2071 ) @ SV911 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2413,plain,
! [SV790: $i,SV571: $i,SV260: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV260 ) ) @ SV571 ) @ SV790 )
= ( c_Lambda_OdB_OVar @ SV260 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV260 @ SV790 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2414,plain,
! [SV791: $i,SV572: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV261 ) @ ( c_Lambda_OdB_OVar @ SV572 ) ) @ SV791 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV261 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2415,plain,
! [SV912: $i,SV792: $i,SV574: $i,SV263: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV263 ) @ SV574 ) ) @ SV792 ) @ SV912 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV263 ) @ SV792 ) @ SV912 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV574 ) @ SV792 ) @ SV912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2416,plain,
! [SV793: $i,SV575: $i,SV264: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV264 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV793 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV575 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2417,plain,
! [SV794: $i,SV576: $i,SV265: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV265 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV794 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV576 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2418,plain,
! [SV795: $i,SV577: $i,SV266: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV266 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV795 @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV795 @ SV577 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2419,plain,
! [SV796: $i,SV578: $i,SV267: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV267 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV796 @ SV267 )
| ~ ( c_HOL_Oord__class_Oless @ SV796 @ SV578 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2420,plain,
! [SV913: $i,SV797: $i,SV579: $i,SV268: $i] :
( ( ! [SY2072: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV268 ) @ SV579 ) @ SV797 ) ) @ ( c_Lambda_Olift @ SV913 @ SV579 ) ) @ SY2072 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV268 ) @ SV913 ) @ SY2072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2421,plain,
! [SV914: $i,SV798: $i,SV580: $i,SV269: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV798 ) @ SV269 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV798 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SV914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2422,plain,
! [SV915: $i,SV799: $i,SV581: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV799 ) @ SV270 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV799 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SV915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2423,plain,
! [SV916: $i,SV800: $i,SV582: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV582 ) @ SV800 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV916 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV916 ) @ SV800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2424,plain,
! [SV917: $i,SV801: $i,SV583: $i,SV272: $i] :
( ( ! [SY2073: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV272 ) @ SV583 ) @ SV801 ) @ SV917 ) @ SY2073 )
= ( hAPP @ SV583 @ SY2073 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2073 @ SV801 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2425,plain,
! [SV918: $i,SV802: $i,SV584: $i,SV273: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV273 ) @ SV584 ) @ SV802 ) @ SV918 ) @ SV802 )
= SV918 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2426,plain,
! [SV919: $i,SV803: $i,SV585: $i,SV274: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV274 ) @ ( c_Lambda_OdB_OAbs @ SV585 ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV803 ) @ SV919 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV803 ) ) @ SV585 ) @ SV919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2427,plain,
! [SV804: $i,SV586: $i,SV275: $i] :
( ( ( ( hAPP @ SV275 @ SV586 )
= SV804 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV275 ) @ ( c_Lambda_OdB_OVar @ SV586 ) ) @ SV804 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2428,plain,
! [SV920: $i,SV805: $i,SV588: $i,SV278: $i] :
( ( ! [SY2074: $i,SY2075: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SV805 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SV920 ) @ SV805 ) ) @ SY2074 ) @ SY2075 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2074 ) @ SV588 ) @ SV920 ) ) @ SY2075 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2429,plain,
! [SV921: $i,SV806: $i,SV589: $i,SV279: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV806 ) @ SV279 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV806 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SV921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2430,plain,
! [SV280: $i,SV590: $i] :
( ( ( class_Orderings_Opreorder @ SV590 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV280 @ SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2431,plain,
! [SV281: $i,SV591: $i] :
( ( ( class_Orderings_Oorder @ SV591 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV281 @ SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2432,plain,
! [SV807: $i,SV593: $i,SV283: $i] :
( ( ( SV283 = SV593 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV807 ) @ SV283 ) @ SV593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2433,plain,
! [SV808: $i,SV594: $i,SV284: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV808 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV284 = SV808 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2434,plain,
! [SV595: $i,SV285: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV285 ) @ SV595 ) )
= $false )
| ( ( ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV285
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2435,plain,
! [SV809: $i,SV596: $i,SV286: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV286 ) @ SV596 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV809 ) @ SV596 ) )
= $true )
| ( ( SV286 = SV809 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2436,plain,
! [SV287: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV287 )
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2437,plain,
! [SV922: $i,SV810: $i,SV597: $i,SV288: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV288 )
| ( ( c_HOL_Ominus__class_Ominus @ SV597 @ SV597 @ SV288 )
!= ( c_HOL_Ominus__class_Ominus @ SV810 @ SV922 @ SV288 ) )
| ( SV810 = SV922 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2438,plain,
! [SV811: $i,SV598: $i,SV289: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV289 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV598 @ SV811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV289 )
= SV598 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2179]) ).
thf(2439,plain,
! [SV599: $i,SV290: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV290 ) @ SV599 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV599
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV290
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2440,plain,
! [SV812: $i,SV600: $i,SV291: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV291 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV600 @ SV291 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV812 @ SV291 ) )
| ( SV600 = SV812 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2441,plain,
! [SV601: $i,SV292: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV292 ) @ SV601 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV601
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2442,plain,
! [SV813: $i,SV602: $i,SV293: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV293 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV813 @ SV293 )
!= ( c_HOL_Ozero__class_Ozero @ SV293 ) )
| ( SV602 = SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2443,plain,
! [SV814: $i,SV603: $i,SV294: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV294 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV603 @ SV814 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV294 )
= SV603 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2444,plain,
! [SV604: $i,SV295: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV295 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV295 ) @ SV604 ) @ SV604 )
!= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
| ( SV604
= ( c_HOL_Ozero__class_Ozero @ SV295 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2445,plain,
! [SV605: $i,SV296: $i] :
( ( ( ( c_Suc @ SV296 )
= ( c_Suc @ SV605 ) )
= $false )
| ( ( SV296 = SV605 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2446,plain,
! [SV606: $i,SV297: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV297 )
= ( c_Lambda_OdB_OVar @ SV606 ) )
= $false )
| ( ( SV297 = SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2447,plain,
! [SV607: $i,SV298: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV298 ) @ SV607 ) )
= $false )
| ( ( ( SV607
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV607
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2448,plain,
! [SV923: $i,SV815: $i,SV608: $i,SV299: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV299 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV815 ) @ SV923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV299 = SV815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2449,plain,
! [SV609: $i,SV302: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV302 )
= ( c_Lambda_OdB_OAbs @ SV609 ) )
= $false )
| ( ( SV302 = SV609 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2450,plain,
! [SV924: $i,SV816: $i,SV610: $i,SV303: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV303 )
| ~ ( class_Int_Onumber__ring @ SV303 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV816 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV924 ) )
| ( SV816 = SV924 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2451,plain,
! [SV925: $i,SV817: $i,SV611: $i,SV304: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV304 ) @ SV611 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV817 ) @ SV925 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV304 = SV817 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2452,plain,
! [SV818: $i,SV612: $i,SV305: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SV612 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SV818 ) )
= $true )
| ( ( SV612 = SV818 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2453,plain,
! [SV306: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV306 )
= ( c_HOL_Oone__class_Oone @ SV306 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2454,plain,
! [SV926: $i,SV819: $i,SV613: $i,SV307: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV307 ) @ SV613 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV819 ) @ SV926 ) )
| ( SV307 = SV819 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2455,plain,
! [SV614: $i,SV308: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV308 @ SV614 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV614 @ SV308 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV614 = SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2456,plain,
! [SV615: $i,SV310: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV310 ) @ SV615 )
= SV310 )
= $false )
| ( ( SV615
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2457,plain,
! [SV927: $i,SV820: $i,SV616: $i,SV312: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV312 ) @ SV616 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV820 ) @ SV927 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV820 @ SV616 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV312 @ SV927 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2458,plain,
! [SV821: $i,SV617: $i,SV313: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV313 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV617 @ SV821 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV821
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2459,plain,
! [SV618: $i,SV314: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV314 ) @ SV618 ) )
= $false )
| ( ( ( SV314
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2460,plain,
! [SV619: $i,SV315: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV315 ) @ SV619 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2461,plain,
! [SV822: $i,SV620: $i,SV316: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV316 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV316 )
| ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV822 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV620 = SV822 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2462,plain,
! [SV823: $i,SV622: $i,SV318: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV318 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV318 )
| ( SV622
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV622 ) @ SV823 ) )
| ( SV823
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2463,plain,
! [SV928: $i,SV824: $i,SV623: $i,SV319: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV623 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV824 ) @ SV928 ) )
| ( SV623 = SV928 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2464,plain,
! [SV825: $i,SV624: $i,SV320: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV320 ) @ SV624 )
= ( c_Lambda_OdB_OVar @ SV825 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2465,plain,
! [SV826: $i,SV625: $i,SV321: $i] :
( ( ( c_Lambda_OdB_OVar @ SV321 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV625 ) @ SV826 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2466,plain,
! [SV827: $i,SV626: $i,SV322: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV322 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV626 ) @ SV827 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2467,plain,
! [SV627: $i,SV323: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV323 ) @ SV627 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2468,plain,
! [SV929: $i,SV828: $i,SV628: $i,SV324: $i] :
( ( ! [SY2076: $i,SY2077: $i,SY2078: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SY2076 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY2077 ) @ SV929 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY2077 ) @ SY2076 ) @ SV324 ) ) @ SV828 ) @ SY2078 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2469,plain,
! [SV930: $i,SV829: $i,SV629: $i,SV325: $i] :
( ( ! [SY2079: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV930 @ SY2079 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SY2079 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2470,plain,
! [SV630: $i,SV326: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV326 ) @ SV630 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV630
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV630
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2471,plain,
! [SV931: $i,SV830: $i,SV631: $i,SV327: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV830 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV931 ) )
| ( SV830 = SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2472,plain,
! [SV932: $i,SV831: $i,SV632: $i,SV328: $i] :
( ( ! [SY2080: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV328 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV932 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SY2080 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ SV932 )
= SY2080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2473,plain,
! [SV832: $i,SV633: $i,SV329: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV329 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV633 @ SV832 @ SV329 )
!= ( c_HOL_Ozero__class_Ozero @ SV329 ) )
| ( SV633 = SV832 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2474,plain,
! [SV933: $i,SV833: $i,SV634: $i,SV331: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV331 ) @ SV634 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV833 ) @ SV933 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2475,plain,
! [SV635: $i,SV332: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV332 ) @ SV635 ) )
= $false )
| ( ( ( SV635
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV332
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2476,plain,
! [SV934: $i,SV834: $i,SV636: $i,SV333: $i] :
( ( ! [SY2081: $i,SY2082: $i,SY2083: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SY2081 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY2082 ) @ SV934 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY2082 ) @ SY2081 ) @ SV636 ) ) @ SV834 ) @ SY2083 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2477,plain,
! [SV935: $i,SV835: $i,SV637: $i,SV334: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SV637 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV835 ) @ SV935 ) )
| ( SV334 = SV835 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2478,plain,
! [SV638: $i,SV336: $i] :
( ( ( SV336
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV336 ) @ SV638 ) )
= $false )
| ( ( SV638
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2479,plain,
! [SV836: $i,SV639: $i,SV337: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV337 @ SV639 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV836 ) )
= $true )
| ( ( SV337
= ( c_Lambda_OdB_OAbs @ SV836 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2480,plain,
! [SV936: $i,SV837: $i,SV640: $i,SV338: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV338 ) @ SV640 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV837 ) @ SV936 ) )
| ( SV640 = SV936 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2481,plain,
! [SV838: $i,SV641: $i,SV339: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV339 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV641 @ SV838 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV838
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2482,plain,
! [SV937: $i,SV839: $i,SV642: $i,SV340: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV340 ) ) @ SV642 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV839 ) @ SV937 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2483,plain,
! [SV938: $i,SV840: $i,SV643: $i,SV341: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV341 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV840 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV938 ) )
| ( SV840 = SV938 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2484,plain,
! [SV939: $i,SV841: $i,SV644: $i,SV342: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV342 ) @ SV644 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV841 ) @ SV939 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV644 = SV939 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2485,plain,
! [SV842: $i,SV645: $i,SV343: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV343 ) @ SV645 )
= ( c_Lambda_OdB_OAbs @ SV842 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2486,plain,
! [SV940: $i,SV843: $i,SV646: $i,SV344: $i] :
( ( ! [SY2084: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
| ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
!= ( c_HOL_Ominus__class_Ominus @ SV940 @ SY2084 @ SV344 ) )
| ( c_HOL_Oord__class_Oless @ SV940 @ SY2084 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2487,plain,
! [SV844: $i,SV647: $i,SV345: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SV647 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SV844 ) )
= $true )
| ( ( SV647 = SV844 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2488,plain,
! [SV648: $i,SV346: $i] :
( ( ( ( c_Suc @ SV346 )
= ( c_Suc @ SV648 ) )
= $false )
| ( ( SV346 = SV648 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2489,plain,
! [SV941: $i,SV845: $i,SV649: $i,SV347: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV347 ) @ SV649 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV845 ) @ SV941 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV649 = SV941 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2490,plain,
! [SV846: $i,SV650: $i,SV348: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV348 @ SV650 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV846 ) )
= $true )
| ( ( SV650
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2491,plain,
! [SV942: $i,SV847: $i,SV651: $i,SV349: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV349 )
| ( ( c_HOL_Ominus__class_Ominus @ SV651 @ SV847 @ SV349 )
!= ( c_HOL_Ominus__class_Ominus @ SV942 @ SV942 @ SV349 ) )
| ( SV651 = SV847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2492,plain,
! [SV943: $i,SV848: $i,SV652: $i,SV350: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV652 ) @ SV848 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV943 ) @ SV848 ) )
| ( SV652 = SV943 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2493,plain,
! [SV653: $i,SV351: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV351 ) @ SV653 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV351
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV351
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2494,plain,
! [SV849: $i,SV654: $i,SV352: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV654 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV849 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV654 )
= SV849 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2495,plain,
! [SV354: $i,SV4: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV4 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV354 @ tc_nat ) @ SV4 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2496,plain,
! [SV7: $i,SV656: $i,SV357: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV357 @ SV656 @ tc_nat ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ominus__class_Ominus @ SV357 @ SV656 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2497,plain,
! [SV657: $i,SV358: $i,SV8: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV8 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV657 @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SV358 @ SV657 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2498,plain,
! [SV658: $i,SV359: $i,SV9: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV9 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV359 @ SV658 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV658 @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2499,plain,
! [SV361: $i,SV659: $i,SV11: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV11 ) @ SV659 ) @ SV361 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV11 @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV659 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2500,plain,
! [SV362: $i,SV660: $i,SV12: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV12 @ ( c_HOL_Ominus__class_Ominus @ SV660 @ SV362 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV12 ) @ SV362 ) @ SV660 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2501,plain,
! [SV363: $i,SV661: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV13 @ SV661 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ SV363 @ tc_nat ) @ SV661 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2502,plain,
! [SV365: $i,SV17: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV17 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV365 @ SV365 @ SV17 )
= ( c_HOL_Ozero__class_Ozero @ SV17 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2503,plain,
! [SV370: $i,SV22: $i,SV662: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV22 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV370 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV370 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV662 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2504,plain,
! [SV663: $i,SV371: $i,SV24: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV24 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ominus__class_Ominus @ SV371 @ SV663 @ SV24 ) ) @ SV663 )
= SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2505,plain,
! [SV664: $i,SV372: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV372 ) @ SV664 ) @ SV372 @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV664 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2506,plain,
! [SV665: $i,SV373: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ SV26 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV373 ) @ SV665 ) @ SV373 @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV26 @ SV665 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2507,plain,
! [SV671: $i,SV384: $i,SV38: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV38 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV384 ) @ SV671 ) @ SV671 @ SV38 )
= SV384 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2508,plain,
! [SV944: $i,SV850: $i,SV672: $i,SV386: $i,SV41: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV41 ) @ SV386 ) @ SV672 ) @ SV850 ) @ SV944 )
= ( hAPP @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SV944 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV672 @ SV944 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2509,plain,
! [SV851: $i,SV673: $i,SV387: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV42 @ SV387 ) @ SV673 ) @ SV851 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV42 @ SV673 ) @ SV851 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2510,plain,
! [SV391: $i,SV47: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV47 @ ( c_Suc @ SV391 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV47 @ SV391 @ tc_nat )
= $true )
| ( ( SV47 = SV391 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2511,plain,
! [SV48: $i,SV392: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SV48 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV392 @ SV48 @ tc_nat )
= $true )
| ( ( SV48 = SV392 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2512,plain,
! [SV393: $i,SV49: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV49 @ ( c_Suc @ SV393 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV49 @ SV393 @ tc_nat )
= $true )
| ( ( SV49 = SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2513,plain,
! [SV945: $i,SV853: $i,SV677: $i,SV394: $i,SV50: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV853 ) @ SV945 ) @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV945 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ SV853 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2514,plain,
! [SV854: $i,SV678: $i,SV395: $i,SV51: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV395 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV678 ) @ SV854 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV395 @ SV854 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV51 @ SV678 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2515,plain,
! [SV54: $i,SV396: $i,SV679: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV679 @ SV396 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV679 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV54 ) @ SV396 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2516,plain,
! [SV855: $i,SV681: $i,SV402: $i,SV60: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV60 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV402 ) @ SV681 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV855 ) @ SV681 ) @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV402 @ SV855 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2517,plain,
! [SV856: $i,SV682: $i,SV403: $i,SV61: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV61 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV403 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV856 ) @ SV682 ) @ SV61 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV856 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2518,plain,
! [SV857: $i,SV683: $i,SV404: $i,SV62: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV62 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV404 @ SV683 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV404 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV683 ) @ SV857 ) @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2519,plain,
! [SV858: $i,SV684: $i,SV405: $i,SV63: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV63 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV684 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV858 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV684 @ SV858 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2520,plain,
! [SV859: $i,SV685: $i,SV406: $i,SV64: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV64 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV685 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV859 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV685 @ SV859 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2521,plain,
! [SV860: $i,SV686: $i,SV407: $i,SV65: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV65 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV407 @ SV686 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV407 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV686 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2276]) ).
thf(2522,plain,
! [SV408: $i,SV687: $i,SV66: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV66 @ SV687 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV66 ) @ SV408 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV687 ) @ SV408 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2523,plain,
! [SV409: $i,SV67: $i,SV688: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV67 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV409 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV67 @ SV409 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2524,plain,
! [SV68: $i,SV689: $i,SV410: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV410 @ SV689 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SV410 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV68 ) @ SV689 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2525,plain,
! [SV690: $i,SV413: $i,SV71: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV71 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SV690 ) @ SV71 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV413 @ SV71 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV690 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2526,plain,
! [SV946: $i,SV861: $i,SV691: $i,SV415: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV691 ) @ SV861 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV946 ) @ SV861 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SV691 ) @ SV946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2527,plain,
! [SV947: $i,SV862: $i,SV692: $i,SV416: $i,SV74: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV862 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SV947 ) @ SV862 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2528,plain,
! [SV863: $i,SV693: $i,SV417: $i,SV75: $i] :
( ( ( c_Wellfounded_Oaccp @ SV75 @ SV417 @ SV693 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV75 @ SV417 ) @ SV863 ) )
| ~ ( c_Wellfounded_Oaccp @ SV75 @ SV863 @ SV693 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2529,plain,
! [SV864: $i,SV694: $i,SV418: $i,SV76: $i] :
( ( ( c_Wellfounded_Oaccp @ SV76 @ SV418 @ SV694 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV418 ) @ SV864 ) )
| ~ ( c_Wellfounded_Oaccp @ SV76 @ SV864 @ SV694 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2530,plain,
! [SV865: $i,SV695: $i,SV419: $i,SV77: $i] :
( ( ( c_Type_Otypings @ SV77 @ SV419 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV695 @ SV77 @ SV865 @ SV419 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV77 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV865 @ SV419 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV695 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2531,plain,
! [SV866: $i,SV696: $i,SV420: $i,SV78: $i] :
( ( ( c_Type_Otypings @ SV78 @ SV420 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV696 @ SV78 @ SV866 @ SV420 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV78 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV866 @ SV420 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV696 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2532,plain,
! [SV867: $i,SV697: $i,SV421: $i,SV79: $i] :
( ( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV79 ) @ SV421 ) @ SV697 ) @ SV867 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV79 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV867 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( c_Lambda_Olift @ SV421 @ SV867 ) ) @ SV697 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV697 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV867 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2533,plain,
! [SV868: $i,SV698: $i,SV422: $i,SV80: $i] :
( ( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV80 ) @ SV422 ) @ SV698 ) @ SV868 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV80 @ SV868 ) ) @ ( c_Lambda_Olift @ SV422 @ SV868 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV698 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV868 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV698 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2534,plain,
! [SV82: $i,SV699: $i,SV424: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV424 ) @ ( c_Lambda_OdB_OAbs @ SV699 ) ) @ SV82 ) )
= $false )
| ( ( SV82
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV82 @ SV424 @ SV699 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV82 @ SV424 @ SV699 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2535,plain,
! [SV948: $i,SV869: $i,SV700: $i,SV425: $i,SV83: $i] :
( ( ! [SY2085: $i,SY2086: $i] :
( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SY2085 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
| ~ ( c_Type_Otypings @ SV700 @ SY2085 @ SY2086 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SY2085 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2536,plain,
! [SV426: $i,SV84: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV426 ) @ SV426 ) @ SV84 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV426 @ SV84 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2537,plain,
! [SV427: $i,SV85: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV427 @ SV85 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV427 ) @ SV427 ) @ SV85 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2538,plain,
! [SV86: $i,SV428: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV428 @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2539,plain,
! [SV701: $i,SV429: $i,SV87: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV429 ) @ SV701 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV701 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2540,plain,
! [SV430: $i,SV88: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SV430 ) @ SV430 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV430 @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2541,plain,
! [SV89: $i,SV431: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV431 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV431 ) @ SV431 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2542,plain,
! [SV90: $i,SV432: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV432 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV432 ) @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2543,plain,
! [SV433: $i,SV91: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ SV433 ) @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV433 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2544,plain,
! [SV702: $i,SV434: $i,SV93: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV434 ) @ SV702 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV702 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV434 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2545,plain,
! [SV870: $i,SV703: $i,SV435: $i,SV95: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV95 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV703 ) @ SV870 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV870 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV703 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2546,plain,
! [SV704: $i,SV436: $i,SV97: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV97 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV436 @ SV97 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV704 @ SV97 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ SV436 @ SV704 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2547,plain,
! [SV705: $i,SV437: $i,SV98: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV98 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV705 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV437 @ SV98 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV705 @ SV98 ) @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2548,plain,
! [SV103: $i,SV440: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SV103 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV440 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV103 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2549,plain,
! [SV706: $i,SV441: $i,SV105: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV105 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV441 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV706 @ SV105 @ SV105 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV105 ) @ SV441 @ SV706 @ SV105 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2550,plain,
! [SV871: $i,SV707: $i,SV442: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV106 ) @ SV442 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV707 ) @ SV871 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV442 ) @ SV871 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV106 ) @ SV707 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2551,plain,
! [SV443: $i,SV708: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV107 ) @ SV708 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV107 ) @ SV443 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV708 ) @ SV443 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2552,plain,
! [SV108: $i,SV709: $i,SV444: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV444 ) @ SV709 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SV444 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV108 ) @ SV709 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2553,plain,
! [SV872: $i,SV710: $i,SV447: $i,SV111: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SV447 ) @ SV710 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SV872 ) @ SV710 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV447 ) @ SV872 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2554,plain,
! [SV873: $i,SV711: $i,SV448: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV112 ) @ SV448 ) @ SV711 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV873 ) @ SV448 ) @ SV711 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV112 ) @ SV873 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2555,plain,
! [SV874: $i,SV712: $i,SV449: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SV449 ) @ SV712 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SV874 ) @ SV712 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV449 ) @ SV874 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2556,plain,
! [SV450: $i,SV114: $i,SV713: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV713 @ SV114 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV114 ) ) @ SV450 ) @ SV713 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2557,plain,
! [SV451: $i,SV115: $i,SV714: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV714 @ SV115 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV115 ) ) @ SV451 ) @ SV714 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV115 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2558,plain,
! [SV715: $i,SV457: $i,SV125: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV125 )
= $false )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SV457 @ SV715 @ SV125 @ SV125 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV125 ) @ SV715 @ SV457 @ SV125 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2559,plain,
! [SV875: $i,SV716: $i,SV458: $i,SV126: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV126 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ SV716 ) @ SV875 @ SV126 @ SV126 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV716 @ SV875 @ SV126 @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2560,plain,
! [SV717: $i,SV459: $i,SV127: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SV459 ) @ SV717 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV127 ) @ SV717 ) @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2561,plain,
! [SV718: $i,SV461: $i,SV129: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV129 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV461 ) @ SV718 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV129 ) @ SV718 ) @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2562,plain,
! [SV719: $i,SV462: $i,SV130: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV462 ) @ SV719 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV130 ) @ SV719 ) @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2563,plain,
! [SV463: $i,SV720: $i,SV131: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV131 @ SV720 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV131 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV463 ) @ SV720 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2564,plain,
! [SV721: $i,SV464: $i,SV132: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV132 @ SV464 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV132 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV464 ) @ SV721 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2565,plain,
! [SV465: $i,SV722: $i,SV133: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV133 ) @ SV722 ) @ SV465 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV133 @ SV465 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2566,plain,
! [SV466: $i,SV723: $i,SV134: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV134 @ SV723 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV134 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV466 ) @ SV723 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2567,plain,
! [SV724: $i,SV467: $i,SV135: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV135 @ SV467 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV135 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV467 ) @ SV724 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2568,plain,
! [SV949: $i,SV876: $i,SV725: $i,SV473: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV949 ) @ SV876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2569,plain,
! [SV877: $i,SV726: $i,SV474: $i,SV144: $i] :
( ( ( c_Wellfounded_Oaccp @ SV144 @ SV474 @ SV726 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV144 @ SV877 @ SV726 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV144 @ SV726 ) @ SV474 ) @ SV877 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2570,plain,
! [SV878: $i,SV727: $i,SV475: $i,SV145: $i] :
( ( ( c_Wellfounded_Oaccp @ SV145 @ SV475 @ SV727 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SV727 ) @ SV475 ) @ SV878 ) )
| ~ ( c_Wellfounded_Oaccp @ SV145 @ SV878 @ SV727 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2571,plain,
! [SV879: $i,SV730: $i,SV479: $i,SV152: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV730 ) @ SV879 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ SV730 ) ) @ SV879 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2572,plain,
! [SV880: $i,SV731: $i,SV480: $i,SV153: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV153 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV731 ) @ SV880 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ SV880 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2573,plain,
! [SV881: $i,SV734: $i,SV483: $i,SV156: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ SV734 ) ) @ SV881 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV734 ) @ SV881 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2574,plain,
! [SV882: $i,SV735: $i,SV484: $i,SV157: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV735 ) @ SV882 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ SV882 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2575,plain,
! [SV883: $i,SV736: $i,SV485: $i,SV158: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ SV736 ) ) @ SV883 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV736 ) @ SV883 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2576,plain,
! [SV884: $i,SV737: $i,SV486: $i,SV159: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV737 ) @ SV884 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ SV737 ) ) @ SV884 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2577,plain,
! [SV885: $i,SV738: $i,SV487: $i,SV160: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SV738 ) ) @ SV885 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SV885 ) ) @ SV738 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2578,plain,
! [SV886: $i,SV739: $i,SV488: $i,SV161: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV739 ) @ SV886 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV739 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ SV886 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2579,plain,
! [SV887: $i,SV740: $i,SV489: $i,SV162: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ SV740 ) ) @ SV887 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV740 ) @ SV887 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2580,plain,
! [SV950: $i,SV888: $i,SV741: $i,SV490: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV163 @ SV490 @ SV741 ) @ SV888 ) @ SV950 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV163 @ SV950 ) @ SV888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2581,plain,
! [SV951: $i,SV889: $i,SV742: $i,SV491: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV164 @ SV491 ) @ SV742 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV164 @ SV889 @ SV951 ) @ SV742 ) @ SV491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2582,plain,
! [SV952: $i,SV890: $i,SV743: $i,SV492: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV165 @ SV492 @ SV743 ) @ SV890 ) @ SV952 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV165 @ SV952 ) @ SV890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2583,plain,
! [SV953: $i,SV891: $i,SV744: $i,SV493: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV493 ) @ SV744 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV166 @ SV891 @ SV953 ) @ SV744 ) @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2584,plain,
! [SV893: $i,SV746: $i,SV497: $i,SV171: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV171 @ SV497 ) @ SV746 ) @ SV893 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV171 @ SV497 @ SV497 ) @ SV497 ) @ SV893 ) @ SV746 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2585,plain,
! [SV894: $i,SV747: $i,SV498: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV172 @ SV498 @ SV498 ) @ SV498 ) @ SV747 ) @ SV894 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV172 @ SV498 ) @ SV894 ) @ SV747 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2586,plain,
! [SV748: $i,SV499: $i,SV173: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV173 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV499 @ SV748 @ SV173 @ SV173 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV499 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV173 ) @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 @ SV173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2587,plain,
! [SV500: $i,SV174: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV174 @ SV500 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV174 )
= SV500 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV174 ) @ SV500 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2588,plain,
! [SV954: $i,SV895: $i,SV749: $i,SV501: $i,SV175: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ ( c_Lambda_Olift @ SV501 @ SV749 ) ) @ ( c_Suc @ SV895 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV954 ) @ SV501 ) @ SV895 ) ) @ SV749 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SV954 ) @ SV749 ) ) @ SV501 ) @ SV895 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV749 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV895 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2589,plain,
! [SV955: $i,SV896: $i,SV750: $i,SV502: $i,SV176: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV176 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV750 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV896 ) @ SV955 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV896 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV750 ) @ SV955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2590,plain,
! [SV178: $i,SV503: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV503 @ ( c_Suc @ SV178 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV178 @ SV503 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2591,plain,
! [SV180: $i,SV751: $i,SV505: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV505 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV751 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SV505 ) @ ( c_Suc @ SV751 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV180 @ SV751 ) @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2592,plain,
! [SV509: $i,SV188: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV188 ) )
= $true )
| ( ( SV509
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV509 ) @ ( c_HOL_Ozero__class_Ozero @ SV188 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2593,plain,
! [SV752: $i,SV197: $i,SV518: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV518 ) @ SV197 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV752 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV197 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV518 @ SV197 @ SV752 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2594,plain,
! [SV897: $i,SV753: $i,SV519: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ SV519 ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV753 @ SV198 @ SV897 @ SV519 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV897 ) @ SV519 ) ) @ SV753 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2595,plain,
! [SV898: $i,SV755: $i,SV521: $i,SV200: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV521 ) @ SV755 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV898 ) @ SV755 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV898 ) @ SV521 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2596,plain,
! [SV956: $i,SV899: $i,SV756: $i,SV522: $i,SV201: $i] :
( ( ! [SY2087: $i,SY2088: $i] :
( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SY2087 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
| ~ ( c_Type_Otypings @ SV201 @ SY2087 @ SY2088 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SY2087 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2597,plain,
! [SV900: $i,SV757: $i,SV523: $i,SV202: $i] :
( ( ( c_Type_Otypings @ SV202 @ SV523 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV757 @ SV202 @ SV900 @ SV523 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV202 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV900 ) @ SV523 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV757 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2598,plain,
! [SV901: $i,SV758: $i,SV524: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ SV524 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV758 @ SV203 @ SV524 @ SV901 ) @ SV758 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV524 @ SV901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV758 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2599,plain,
! [SV957: $i,SV902: $i,SV759: $i,SV525: $i,SV204: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV525 @ SV759 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV902 ) )
| ~ ( c_Type_Otypings @ SV204 @ SV759 @ SV957 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SV525 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV957 @ SV902 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2600,plain,
! [SV903: $i,SV760: $i,SV526: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ SV526 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV760 @ SV205 @ SV526 @ SV903 ) @ SV760 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV526 @ SV903 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV760 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2601,plain,
! [SV958: $i,SV904: $i,SV761: $i,SV527: $i,SV206: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SV527 ) @ SV761 ) @ SV904 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV958 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV206 ) @ SV527 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV958 ) ) @ ( c_Suc @ SV761 ) ) @ SV904 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2602,plain,
! [SV528: $i,SV762: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV207 ) @ ( c_Lambda_OdB_OAbs @ SV762 ) ) @ SV528 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV207 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV528 @ SV207 @ SV762 ) ) ) @ SV762 ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV528 @ SV207 @ SV762 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2603,plain,
! [SV763: $i,SV529: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV208 ) @ ( c_Lambda_OdB_OAbs @ SV529 ) ) @ SV763 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV208 @ SV529 ) ) ) @ SV529 ) @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV208 @ SV529 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2604,plain,
! [SV530: $i,SV764: $i,SV209: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV209 ) @ SV764 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV209 @ SV530 ) ) @ ( c_Lambda_Olift @ SV764 @ SV530 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2605,plain,
! [SV905: $i,SV765: $i,SV531: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_Lambda_OdB_OVar @ SV531 ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV765 @ SV210 @ SV531 @ SV905 ) @ SV765 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV531 ) @ SV905 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV765 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2606,plain,
! [SV766: $i,SV532: $i,SV211: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV211 ) @ SV532 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV532 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV211 ) ) @ SV532 ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2379]) ).
thf(2607,plain,
! [SV212: $i,SV767: $i,SV533: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV533 @ SV767 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SV533 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV212 @ SV767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2608,plain,
! [SV534: $i,SV768: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV213 ) @ SV768 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV768 @ SV534 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2609,plain,
! [SV906: $i,SV769: $i,SV535: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ SV535 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV769 @ SV217 @ SV535 @ SV906 ) ) @ SV769 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ SV906 ) ) @ SV769 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2610,plain,
! [SV536: $i,SV218: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV536 @ SV218 ) @ SV218 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV536 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2611,plain,
! [SV219: $i,SV537: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV537 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV537 @ SV219 ) @ SV219 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2612,plain,
! [SV220: $i,SV770: $i,SV538: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV538 ) @ SV770 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV220 ) )
= $false )
| ( ( SV220
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV538 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV538 @ SV770 @ SV220 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2613,plain,
! [SV542: $i,SV771: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV224 ) @ SV771 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV224 @ SV542 ) ) @ ( c_Lambda_Olift @ SV771 @ SV542 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2614,plain,
! [SV545: $i,SV773: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV227 ) @ SV773 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV227 ) @ SV545 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV773 ) @ SV545 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2615,plain,
! [SV228: $i,SV774: $i,SV546: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV546 ) @ SV774 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SV546 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV228 ) @ SV774 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2616,plain,
! [SV907: $i,SV775: $i,SV548: $i,SV233: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV233 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV548 @ SV775 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV548 @ SV907 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV907 @ SV775 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2617,plain,
! [SV908: $i,SV776: $i,SV549: $i,SV234: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV234 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV549 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV549 @ SV908 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2618,plain,
! [SV550: $i,SV777: $i,SV235: $i] :
( ( ( SV235 = SV777 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV777 @ SV235 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV235 ) ) @ SV550 ) @ SV777 )
= ( c_Lambda_OdB_OVar @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2619,plain,
! [SV909: $i,SV778: $i,SV551: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV236 ) @ SV551 ) @ SV778 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV909 ) @ SV551 ) @ SV778 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV236 ) @ SV909 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2620,plain,
! [SV780: $i,SV239: $i,SV553: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV553 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV239 ) @ SV553 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV780 @ 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 @ SV239 ) ) @ SV553 ) @ SV780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(2621,plain,
! [SV555: $i,SV781: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV241 ) @ SV781 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV241 @ SV555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV781 @ SV555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2622,plain,
! [SV244: $i,SV556: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV556 @ SV556 @ SV244 )
= $false )
| ( ( class_Orderings_Oorder @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2623,plain,
! [SV245: $i,SV557: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV557 @ SV557 @ SV245 )
= $false )
| ( ( class_Orderings_Olinorder @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2624,plain,
! [SV246: $i,SV558: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV558 @ SV558 @ SV246 )
= $false )
| ( ( class_Orderings_Opreorder @ SV246 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2625,plain,
! [SV782: $i,SV560: $i,SV248: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV248 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV560 @ SV782 @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV782 @ SV560 @ SV248 )
| ( SV782 = SV560 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2626,plain,
! [SV783: $i,SV561: $i,SV249: $i] :
( ( ( class_Orderings_Olinorder @ SV249 )
= $false )
| ( ( ( SV561 = SV783 )
| ( c_HOL_Oord__class_Oless @ SV783 @ SV561 @ SV249 )
| ( c_HOL_Oord__class_Oless @ SV561 @ SV783 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2627,plain,
! [SV251: $i,SV784: $i,SV563: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV563 @ SV784 @ tc_nat )
= $true )
| ( ( ( SV784 = SV563 )
| ( c_HOL_Oord__class_Oless @ SV784 @ SV563 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV251 @ SV563 ) @ SV784 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2628,plain,
! [SV959: $i,SV910: $i,SV785: $i,SV564: $i,SV252: $i] :
( ( ( SV252 = SV564 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2629,plain,
! [SV786: $i,SV566: $i,SV254: $i] :
( ( ( class_Orderings_Olinorder @ SV254 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV566 @ SV786 @ SV254 )
| ( c_HOL_Oord__class_Oless @ SV786 @ SV566 @ SV254 )
| ( SV786 = SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2630,plain,
! [SV787: $i,SV567: $i,SV255: $i] :
( ( ( class_Orderings_Olinorder @ SV255 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV567 @ SV787 @ SV255 )
| ( SV787 = SV567 )
| ( c_HOL_Oord__class_Oless @ SV787 @ SV567 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2631,plain,
! [SV788: $i,SV568: $i,SV256: $i] :
( ( ( class_Orderings_Olinorder @ SV256 )
= $false )
| ( ( ( SV568 = SV788 )
| ( c_HOL_Oord__class_Oless @ SV568 @ SV788 @ SV256 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SV568 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2632,plain,
! [SV960: $i,SV911: $i,SV789: $i,SV569: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV569 ) @ SV789 ) ) @ SV911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV789 ) @ SV960 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV569 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV960 ) @ SV911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2633,plain,
! [SV571: $i,SV790: $i,SV260: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV260 @ SV790 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV260 ) ) @ SV571 ) @ SV790 )
= ( c_Lambda_OdB_OVar @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2634,plain,
! [SV791: $i,SV572: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV261 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV261 ) @ ( c_Lambda_OdB_OVar @ SV572 ) ) @ SV791 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2635,plain,
! [SV793: $i,SV575: $i,SV264: $i] :
( ( ( class_Orderings_Oorder @ SV264 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV793 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV575 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2636,plain,
! [SV794: $i,SV576: $i,SV265: $i] :
( ( ( class_Orderings_Olinorder @ SV265 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV794 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV576 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2637,plain,
! [SV795: $i,SV577: $i,SV266: $i] :
( ( ( class_Orderings_Opreorder @ SV266 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV795 @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV795 @ SV577 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2638,plain,
! [SV796: $i,SV578: $i,SV267: $i] :
( ( ( class_Orderings_Opreorder @ SV267 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV796 @ SV267 )
| ~ ( c_HOL_Oord__class_Oless @ SV796 @ SV578 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2639,plain,
! [SV961: $i,SV913: $i,SV797: $i,SV579: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV268 ) @ SV579 ) @ SV797 ) ) @ ( c_Lambda_Olift @ SV913 @ SV579 ) ) @ SV961 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV268 ) @ SV913 ) @ SV961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(2640,plain,
! [SV914: $i,SV798: $i,SV580: $i,SV269: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV798 ) @ SV269 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV798 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SV914 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2641,plain,
! [SV915: $i,SV799: $i,SV581: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV799 ) @ SV270 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV799 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SV915 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2642,plain,
! [SV916: $i,SV800: $i,SV582: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV582 ) @ SV800 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV916 ) @ SV582 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV916 ) @ SV800 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2643,plain,
! [SV962: $i,SV917: $i,SV801: $i,SV583: $i,SV272: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV272 ) @ SV583 ) @ SV801 ) @ SV917 ) @ SV962 )
= ( hAPP @ SV583 @ SV962 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV962 @ SV801 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2644,plain,
! [SV919: $i,SV803: $i,SV585: $i,SV274: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV274 ) @ ( c_Lambda_OdB_OAbs @ SV585 ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV803 ) @ SV919 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV803 ) ) @ SV585 ) @ SV919 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2645,plain,
! [SV804: $i,SV586: $i,SV275: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV275 ) @ ( c_Lambda_OdB_OVar @ SV586 ) ) @ SV804 ) )
= $false )
| ( ( ( hAPP @ SV275 @ SV586 )
= SV804 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2646,plain,
! [SV963: $i,SV920: $i,SV805: $i,SV588: $i,SV278: $i] :
( ( ! [SY2089: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SV805 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SV920 ) @ SV805 ) ) @ SV963 ) @ SY2089 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV963 ) @ SV588 ) @ SV920 ) ) @ SY2089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2647,plain,
! [SV921: $i,SV806: $i,SV589: $i,SV279: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV806 ) @ SV279 ) @ v_T____ ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV806 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SV921 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2648,plain,
! [SV593: $i,SV283: $i,SV807: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV807 ) @ SV283 ) @ SV593 ) )
= $false )
| ( ( SV283 = SV593 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2649,plain,
! [SV808: $i,SV594: $i,SV284: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV284 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV808 @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV284 = SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2650,plain,
! [SV595: $i,SV285: $i] :
( ( ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV285
= ( 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 ) @ SV285 ) @ SV595 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2651,plain,
! [SV809: $i,SV596: $i,SV286: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV286 ) @ SV596 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV809 ) @ SV596 ) )
= $false )
| ( ( SV286 = SV809 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2652,plain,
! [SV922: $i,SV810: $i,SV597: $i,SV288: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV288 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV597 @ SV597 @ SV288 )
!= ( c_HOL_Ominus__class_Ominus @ SV810 @ SV922 @ SV288 ) )
| ( SV810 = SV922 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2437]) ).
thf(2653,plain,
! [SV811: $i,SV598: $i,SV289: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV289 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV598 @ SV811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV289 )
= SV598 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2654,plain,
! [SV290: $i,SV599: $i] :
( ( ( SV599
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV290
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV290 ) @ SV599 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(2655,plain,
! [SV812: $i,SV600: $i,SV291: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV291 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV600 @ SV291 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV812 @ SV291 ) )
| ( SV600 = SV812 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2656,plain,
! [SV601: $i,SV292: $i] :
( ( ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV601
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV292 ) @ SV601 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2657,plain,
! [SV813: $i,SV602: $i,SV293: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV293 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV813 @ SV293 )
!= ( c_HOL_Ozero__class_Ozero @ SV293 ) )
| ( SV602 = SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2658,plain,
! [SV814: $i,SV603: $i,SV294: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV294 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV603 @ SV814 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV294 )
= SV603 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2659,plain,
! [SV604: $i,SV295: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV295 ) @ SV604 ) @ SV604 )
!= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
= $true )
| ( ( SV604
= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2660,plain,
! [SV298: $i,SV607: $i] :
( ( ( SV607
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV607
= ( 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 ) @ SV298 ) @ SV607 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2661,plain,
! [SV923: $i,SV815: $i,SV608: $i,SV299: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV299 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV815 ) @ SV923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV299 = SV815 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2662,plain,
! [SV924: $i,SV816: $i,SV610: $i,SV303: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV303 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV303 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV816 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV924 ) )
| ( SV816 = SV924 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(2663,plain,
! [SV925: $i,SV817: $i,SV611: $i,SV304: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV304 ) @ SV611 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV817 ) @ SV925 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV304 = SV817 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(2664,plain,
! [SV818: $i,SV612: $i,SV305: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SV612 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV305 ) @ SV818 ) )
= $false )
| ( ( SV612 = SV818 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2665,plain,
! [SV926: $i,SV819: $i,SV613: $i,SV307: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV307 ) @ SV613 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV819 ) @ SV926 ) )
= $true )
| ( ( SV307 = SV819 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2666,plain,
! [SV308: $i,SV614: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV614 @ SV308 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV614 = SV308 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV308 @ SV614 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2455]) ).
thf(2667,plain,
! [SV927: $i,SV820: $i,SV616: $i,SV312: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV312 ) @ SV616 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV820 ) @ SV927 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV820 @ SV616 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV312 @ SV927 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2668,plain,
! [SV821: $i,SV617: $i,SV313: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV313 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV617 @ SV821 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV821
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2669,plain,
! [SV618: $i,SV314: $i] :
( ( ( SV314
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV618
= ( 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 ) @ SV314 ) @ SV618 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2670,plain,
! [SV822: $i,SV620: $i,SV316: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV316 )
| ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV822 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV620 = SV822 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2671,plain,
! [SV823: $i,SV622: $i,SV318: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV318 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV318 )
| ( SV622
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV622 ) @ SV823 ) )
| ( SV823
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2672,plain,
! [SV928: $i,SV824: $i,SV623: $i,SV319: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV623 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV824 ) @ SV928 ) )
= $true )
| ( ( SV623 = SV928 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2673,plain,
! [SV964: $i,SV929: $i,SV828: $i,SV628: $i,SV324: $i] :
( ( ! [SY2090: $i,SY2091: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY2090 ) @ SV929 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY2090 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2674,plain,
! [SV965: $i,SV930: $i,SV829: $i,SV629: $i,SV325: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV930 @ SV965 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV965 @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2675,plain,
! [SV326: $i,SV630: $i] :
( ( ( SV630
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV630
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV326 ) @ SV630 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2676,plain,
! [SV931: $i,SV830: $i,SV631: $i,SV327: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV830 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV931 ) )
| ( SV830 = SV931 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2677,plain,
! [SV966: $i,SV932: $i,SV831: $i,SV632: $i,SV328: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV328 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV932 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV966 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ SV932 )
= SV966 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2678,plain,
! [SV832: $i,SV633: $i,SV329: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV329 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV633 @ SV832 @ SV329 )
!= ( c_HOL_Ozero__class_Ozero @ SV329 ) )
| ( SV633 = SV832 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2679,plain,
! [SV933: $i,SV833: $i,SV634: $i,SV331: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV331 ) @ SV634 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV833 ) @ SV933 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2680,plain,
! [SV332: $i,SV635: $i] :
( ( ( SV635
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV332
= ( 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 ) @ SV332 ) @ SV635 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2681,plain,
! [SV967: $i,SV934: $i,SV834: $i,SV636: $i,SV333: $i] :
( ( ! [SY2092: $i,SY2093: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SY2092 ) @ SV934 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SY2092 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2682,plain,
! [SV935: $i,SV835: $i,SV637: $i,SV334: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SV637 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV835 ) @ SV935 ) )
= $true )
| ( ( SV334 = SV835 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2683,plain,
! [SV836: $i,SV639: $i,SV337: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV337 @ SV639 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV836 ) )
= $false )
| ( ( SV337
= ( c_Lambda_OdB_OAbs @ SV836 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2684,plain,
! [SV936: $i,SV837: $i,SV640: $i,SV338: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV338 ) @ SV640 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV837 ) @ SV936 ) )
= $true )
| ( ( SV640 = SV936 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2685,plain,
! [SV838: $i,SV641: $i,SV339: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV339 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV641 @ SV838 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV838
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2686,plain,
! [SV937: $i,SV839: $i,SV642: $i,SV340: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV340 ) ) @ SV642 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV839 ) @ SV937 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2687,plain,
! [SV938: $i,SV840: $i,SV643: $i,SV341: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV341 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV840 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV938 ) )
| ( SV840 = SV938 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2688,plain,
! [SV939: $i,SV841: $i,SV644: $i,SV342: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV342 ) @ SV644 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV841 ) @ SV939 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV644 = SV939 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2689,plain,
! [SV968: $i,SV940: $i,SV843: $i,SV646: $i,SV344: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
| ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
!= ( c_HOL_Ominus__class_Ominus @ SV940 @ SV968 @ SV344 ) )
| ( c_HOL_Oord__class_Oless @ SV940 @ SV968 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2690,plain,
! [SV844: $i,SV647: $i,SV345: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SV647 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV345 ) @ SV844 ) )
= $false )
| ( ( SV647 = SV844 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2691,plain,
! [SV941: $i,SV845: $i,SV649: $i,SV347: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV347 ) @ SV649 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV845 ) @ SV941 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV649 = SV941 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2489]) ).
thf(2692,plain,
! [SV846: $i,SV650: $i,SV348: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV348 @ SV650 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV846 ) )
= $false )
| ( ( SV650
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2693,plain,
! [SV942: $i,SV847: $i,SV651: $i,SV349: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV349 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV651 @ SV847 @ SV349 )
!= ( c_HOL_Ominus__class_Ominus @ SV942 @ SV942 @ SV349 ) )
| ( SV651 = SV847 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2694,plain,
! [SV943: $i,SV848: $i,SV652: $i,SV350: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV350 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV652 ) @ SV848 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV943 ) @ SV848 ) )
| ( SV652 = SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2695,plain,
! [SV653: $i,SV351: $i] :
( ( ( SV351
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV351
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV351 ) @ SV653 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2696,plain,
! [SV849: $i,SV654: $i,SV352: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV654 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV849 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV654 )
= SV849 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2697,plain,
! [SV4: $i,SV354: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV4 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV354 @ tc_nat ) @ SV4 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2698,plain,
! [SV7: $i,SV656: $i,SV357: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV357 @ SV656 @ tc_nat )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ominus__class_Ominus @ SV357 @ SV656 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2699,plain,
! [SV8: $i,SV657: $i,SV358: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV657 @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV358 @ SV657 @ SV8 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2497]) ).
thf(2700,plain,
! [SV9: $i,SV658: $i,SV359: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV359 @ SV658 @ SV9 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV658 @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2701,plain,
! [SV365: $i,SV17: $i] :
( ( ( class_Int_Onumber__ring @ SV17 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV365 @ SV365 @ SV17 )
= ( c_HOL_Ozero__class_Ozero @ SV17 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2702,plain,
! [SV370: $i,SV22: $i,SV662: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV662 @ SV22 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV662 @ SV370 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV370 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV662 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2703,plain,
! [SV944: $i,SV850: $i,SV672: $i,SV386: $i,SV41: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV41 ) @ SV386 ) @ SV672 ) @ SV850 ) @ SV944 )
= ( hAPP @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SV944 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV672 @ SV944 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2704,plain,
! [SV387: $i,SV851: $i,SV673: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV42 @ SV673 ) @ SV851 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV42 @ SV387 ) @ SV673 ) @ SV851 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2509]) ).
thf(2705,plain,
! [SV945: $i,SV853: $i,SV677: $i,SV394: $i,SV50: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV853 ) @ SV945 ) @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV945 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ SV853 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2706,plain,
! [SV678: $i,SV51: $i,SV854: $i,SV395: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV395 @ SV854 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV51 @ SV678 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV395 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV678 ) @ SV854 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2707,plain,
! [SV54: $i,SV396: $i,SV679: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV679 @ SV396 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV679 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV54 ) @ SV396 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2708,plain,
! [SV855: $i,SV681: $i,SV402: $i,SV60: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV60 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV402 ) @ SV681 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV855 ) @ SV681 ) @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV402 @ SV855 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2709,plain,
! [SV856: $i,SV682: $i,SV403: $i,SV61: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV61 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV403 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV856 ) @ SV682 ) @ SV61 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV856 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2710,plain,
! [SV857: $i,SV683: $i,SV404: $i,SV62: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV62 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV404 @ SV683 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV404 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV683 ) @ SV857 ) @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2711,plain,
! [SV858: $i,SV684: $i,SV405: $i,SV63: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV63 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV684 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV858 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV684 @ SV858 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2712,plain,
! [SV859: $i,SV685: $i,SV406: $i,SV64: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV64 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV685 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV859 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV685 @ SV859 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2713,plain,
! [SV860: $i,SV686: $i,SV407: $i,SV65: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV65 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV407 @ SV686 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV407 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV686 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2714,plain,
! [SV946: $i,SV861: $i,SV691: $i,SV415: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV691 ) @ SV861 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV946 ) @ SV861 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SV691 ) @ SV946 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2715,plain,
! [SV947: $i,SV862: $i,SV692: $i,SV416: $i,SV74: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV862 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SV947 ) @ SV862 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV947 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2716,plain,
! [SV693: $i,SV863: $i,SV417: $i,SV75: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV75 @ SV417 ) @ SV863 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV75 @ SV863 @ SV693 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV75 @ SV417 @ SV693 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2717,plain,
! [SV694: $i,SV864: $i,SV418: $i,SV76: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV418 ) @ SV864 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV76 @ SV864 @ SV694 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV76 @ SV418 @ SV694 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2529]) ).
thf(2718,plain,
! [SV695: $i,SV419: $i,SV865: $i,SV77: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV77 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV865 @ SV419 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV695 ) )
= $false )
| ( ( c_Type_Otypings @ SV77 @ SV419 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV695 @ SV77 @ SV865 @ SV419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2719,plain,
! [SV696: $i,SV420: $i,SV866: $i,SV78: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV78 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV866 @ SV420 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV696 ) )
= $false )
| ( ( c_Type_Otypings @ SV78 @ SV420 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV696 @ SV78 @ SV866 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2720,plain,
! [SV421: $i,SV79: $i,SV867: $i,SV697: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV697 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV867 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV79 ) @ SV421 ) @ SV697 ) @ SV867 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV79 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV867 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( c_Lambda_Olift @ SV421 @ SV867 ) ) @ SV697 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2721,plain,
! [SV422: $i,SV80: $i,SV698: $i,SV868: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV868 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV698 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV80 ) @ SV422 ) @ SV698 ) @ SV868 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ SV80 @ SV868 ) ) @ ( c_Lambda_Olift @ SV422 @ SV868 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV698 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2722,plain,
! [SV969: $i,SV948: $i,SV869: $i,SV700: $i,SV425: $i,SV83: $i] :
( ( ! [SY2094: $i] :
( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
| ~ ( c_Type_Otypings @ SV700 @ SV969 @ SY2094 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(2723,plain,
! [SV426: $i,SV84: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV426 @ SV84 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV426 ) @ SV426 ) @ SV84 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2724,plain,
! [SV427: $i,SV85: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV427 ) @ SV427 ) @ SV85 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV427 @ SV85 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2725,plain,
! [SV701: $i,SV429: $i,SV87: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV429 ) @ SV701 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV701 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2726,plain,
! [SV88: $i,SV430: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV430 @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV88 ) @ SV430 ) @ SV430 ) @ ( c_HOL_Ozero__class_Ozero @ SV88 ) @ SV88 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2727,plain,
! [SV431: $i,SV89: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV431 ) @ SV431 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV431 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2728,plain,
! [SV432: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ SV432 ) @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV432 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2729,plain,
! [SV91: $i,SV433: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV433 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV91 ) @ SV433 ) @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2730,plain,
! [SV702: $i,SV434: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV434 ) @ SV702 ) @ SV93 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV702 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV434 @ SV93 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2731,plain,
! [SV870: $i,SV703: $i,SV435: $i,SV95: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV95 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV703 ) @ SV870 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV870 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV703 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2732,plain,
! [SV704: $i,SV97: $i,SV436: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV436 @ SV97 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV704 @ SV97 ) @ SV97 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV436 @ SV704 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2733,plain,
! [SV98: $i,SV705: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV705 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV437 @ SV98 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV705 @ SV98 ) @ SV98 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2734,plain,
! [SV707: $i,SV106: $i,SV871: $i,SV442: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV442 ) @ SV871 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV106 ) @ SV707 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV106 ) @ SV442 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV707 ) @ SV871 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2735,plain,
! [SV710: $i,SV111: $i,SV872: $i,SV447: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV447 ) @ SV872 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SV447 ) @ SV710 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV111 ) @ SV872 ) @ SV710 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2736,plain,
! [SV711: $i,SV448: $i,SV873: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV112 ) @ SV873 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV112 ) @ SV448 ) @ SV711 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV873 ) @ SV448 ) @ SV711 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2737,plain,
! [SV712: $i,SV113: $i,SV874: $i,SV449: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV449 ) @ SV874 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SV449 ) @ SV712 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV113 ) @ SV874 ) @ SV712 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2738,plain,
! [SV875: $i,SV716: $i,SV458: $i,SV126: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV126 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ SV716 ) @ SV875 @ SV126 @ SV126 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV458 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV126 ) @ SV716 @ SV875 @ SV126 @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2739,plain,
! [SV949: $i,SV876: $i,SV725: $i,SV473: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV876 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV949 ) @ SV876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV949 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2740,plain,
! [SV474: $i,SV726: $i,SV877: $i,SV144: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV144 @ SV877 @ SV726 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV144 @ SV726 ) @ SV474 ) @ SV877 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV144 @ SV474 @ SV726 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2569]) ).
thf(2741,plain,
! [SV878: $i,SV475: $i,SV727: $i,SV145: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SV727 ) @ SV475 ) @ SV878 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV145 @ SV878 @ SV727 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV145 @ SV475 @ SV727 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2570]) ).
thf(2742,plain,
! [SV879: $i,SV730: $i,SV479: $i,SV152: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV730 ) @ SV879 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV479 ) @ SV730 ) ) @ SV879 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2743,plain,
! [SV880: $i,SV731: $i,SV480: $i,SV153: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV153 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV731 ) @ SV880 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV153 ) @ SV480 ) @ SV880 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2744,plain,
! [SV881: $i,SV734: $i,SV483: $i,SV156: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ SV734 ) ) @ SV881 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV734 ) @ SV881 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2745,plain,
! [SV882: $i,SV735: $i,SV484: $i,SV157: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV735 ) @ SV882 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV735 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV484 ) @ SV882 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2746,plain,
! [SV883: $i,SV736: $i,SV485: $i,SV158: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ SV736 ) ) @ SV883 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV485 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV736 ) @ SV883 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2747,plain,
! [SV884: $i,SV737: $i,SV486: $i,SV159: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV737 ) @ SV884 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV486 ) @ SV737 ) ) @ SV884 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2748,plain,
! [SV885: $i,SV738: $i,SV487: $i,SV160: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SV738 ) ) @ SV885 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV487 ) @ SV885 ) ) @ SV738 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2577]) ).
thf(2749,plain,
! [SV886: $i,SV739: $i,SV488: $i,SV161: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV739 ) @ SV886 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV739 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV488 ) @ SV886 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2750,plain,
! [SV887: $i,SV740: $i,SV489: $i,SV162: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ SV740 ) ) @ SV887 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV740 ) @ SV887 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2751,plain,
! [SV950: $i,SV888: $i,SV741: $i,SV490: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV163 @ SV490 @ SV741 ) @ SV888 ) @ SV950 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV163 @ SV950 ) @ SV888 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2752,plain,
! [SV951: $i,SV889: $i,SV742: $i,SV491: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV164 @ SV491 ) @ SV742 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV164 @ SV889 @ SV951 ) @ SV742 ) @ SV491 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2753,plain,
! [SV952: $i,SV890: $i,SV743: $i,SV492: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV165 @ SV492 @ SV743 ) @ SV890 ) @ SV952 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV165 @ SV952 ) @ SV890 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2754,plain,
! [SV953: $i,SV891: $i,SV744: $i,SV493: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV493 ) @ SV744 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV166 @ SV891 @ SV953 ) @ SV744 ) @ SV493 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2755,plain,
! [SV746: $i,SV893: $i,SV497: $i,SV171: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV171 @ SV497 @ SV497 ) @ SV497 ) @ SV893 ) @ SV746 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV171 @ SV497 ) @ SV746 ) @ SV893 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2756,plain,
! [SV747: $i,SV894: $i,SV498: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV172 @ SV498 ) @ SV894 ) @ SV747 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV172 @ SV498 @ SV498 ) @ SV498 ) @ SV747 ) @ SV894 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2757,plain,
! [SV954: $i,SV895: $i,SV749: $i,SV501: $i,SV175: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ ( c_Lambda_Olift @ SV501 @ SV749 ) ) @ ( c_Suc @ SV895 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV954 ) @ SV501 ) @ SV895 ) ) @ SV749 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SV954 ) @ SV749 ) ) @ SV501 ) @ SV895 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV749 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV895 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2758,plain,
! [SV955: $i,SV896: $i,SV750: $i,SV502: $i,SV176: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV176 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV750 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV896 ) @ SV955 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV896 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV750 ) @ SV955 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2759,plain,
! [SV509: $i,SV188: $i] :
( ( ( class_Int_Onumber__ring @ SV188 )
= $false )
| ( ( SV509
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV509 ) @ ( c_HOL_Ozero__class_Ozero @ SV188 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2760,plain,
! [SV753: $i,SV519: $i,SV897: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV897 ) @ SV519 ) ) @ SV753 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV198 ) @ SV519 ) @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV753 @ SV198 @ SV897 @ SV519 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2761,plain,
! [SV521: $i,SV755: $i,SV898: $i,SV200: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV898 ) @ SV755 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV898 ) @ SV521 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV521 ) @ SV755 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2595]) ).
thf(2762,plain,
! [SV970: $i,SV956: $i,SV899: $i,SV756: $i,SV522: $i,SV201: $i] :
( ( ! [SY2095: $i] :
( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
| ~ ( c_Type_Otypings @ SV201 @ SV970 @ SY2095 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(2763,plain,
! [SV757: $i,SV523: $i,SV900: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV202 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV900 ) @ SV523 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV757 ) )
= $false )
| ( ( c_Type_Otypings @ SV202 @ SV523 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV757 @ SV202 @ SV900 @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2764,plain,
! [SV758: $i,SV901: $i,SV524: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV524 @ SV901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV758 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV203 ) @ SV524 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV758 @ SV203 @ SV524 @ SV901 ) @ SV758 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2765,plain,
! [SV957: $i,SV902: $i,SV759: $i,SV525: $i,SV204: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV525 @ SV759 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV902 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV204 @ SV759 @ SV957 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SV525 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV957 @ SV902 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2766,plain,
! [SV760: $i,SV903: $i,SV526: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV526 @ SV903 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV760 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV205 ) @ SV526 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV760 @ SV205 @ SV526 @ SV903 ) @ SV760 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2767,plain,
! [SV765: $i,SV905: $i,SV531: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV531 ) @ SV905 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV765 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV210 ) @ ( c_Lambda_OdB_OVar @ SV531 ) ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV765 @ SV210 @ SV531 @ SV905 ) @ SV765 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2768,plain,
! [SV766: $i,SV211: $i,SV532: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV532 @ tc_Lambda_OdB ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV211 ) ) @ SV532 ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV211 ) @ SV532 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2769,plain,
! [SV769: $i,SV906: $i,SV535: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ SV906 ) ) @ SV769 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV217 ) @ SV535 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV769 @ SV217 @ SV535 @ SV906 ) ) @ SV769 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2770,plain,
! [SV218: $i,SV536: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV536 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV536 @ SV218 ) @ SV218 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2771,plain,
! [SV537: $i,SV219: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV537 @ SV219 ) @ SV219 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV537 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2772,plain,
! [SV907: $i,SV775: $i,SV548: $i,SV233: $i] :
( ( ( class_Orderings_Oorder @ SV233 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV548 @ SV775 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV548 @ SV907 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV907 @ SV775 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2773,plain,
! [SV908: $i,SV776: $i,SV549: $i,SV234: $i] :
( ( ( class_Orderings_Opreorder @ SV234 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV549 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV549 @ SV908 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2774,plain,
! [SV778: $i,SV551: $i,SV909: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV236 ) @ SV909 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV236 ) @ SV551 ) @ SV778 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV909 ) @ SV551 ) @ SV778 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2775,plain,
! [SV780: $i,SV239: $i,SV553: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV553 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV239 ) @ SV553 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV780 @ 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 @ SV239 ) ) @ SV553 ) @ SV780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2776,plain,
! [SV248: $i,SV782: $i,SV560: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV560 @ SV782 @ SV248 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV782 @ SV560 @ SV248 )
| ( SV782 = SV560 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2777,plain,
! [SV249: $i,SV783: $i,SV561: $i] :
( ( ( SV561 = SV783 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV783 @ SV561 @ SV249 )
| ( c_HOL_Oord__class_Oless @ SV561 @ SV783 @ SV249 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2778,plain,
! [SV251: $i,SV563: $i,SV784: $i] :
( ( ( SV784 = SV563 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV784 @ SV563 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV563 @ SV784 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV251 @ SV563 ) @ SV784 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2627]) ).
thf(2779,plain,
! [SV959: $i,SV910: $i,SV785: $i,SV564: $i,SV252: $i] :
( ( ( SV252 = SV564 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2780,plain,
! [SV254: $i,SV786: $i,SV566: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV566 @ SV786 @ SV254 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV786 @ SV566 @ SV254 )
| ( SV786 = SV566 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2629]) ).
thf(2781,plain,
! [SV255: $i,SV787: $i,SV567: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV567 @ SV787 @ SV255 )
= $true )
| ( ( ( SV787 = SV567 )
| ( c_HOL_Oord__class_Oless @ SV787 @ SV567 @ SV255 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2782,plain,
! [SV256: $i,SV788: $i,SV568: $i] :
( ( ( SV568 = SV788 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV568 @ SV788 @ SV256 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SV568 @ SV256 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2631]) ).
thf(2783,plain,
! [SV960: $i,SV911: $i,SV789: $i,SV569: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV569 ) @ SV789 ) ) @ SV911 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV789 ) @ SV960 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV569 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV960 ) @ SV911 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2784,plain,
! [SV264: $i,SV793: $i,SV575: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV793 @ SV264 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV575 @ SV264 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2785,plain,
! [SV265: $i,SV794: $i,SV576: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV794 @ SV265 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV576 @ SV265 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2786,plain,
! [SV266: $i,SV795: $i,SV577: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV795 @ SV266 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV795 @ SV577 @ SV266 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV266 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2637]) ).
thf(2787,plain,
! [SV267: $i,SV796: $i,SV578: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV578 @ SV796 @ SV267 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV796 @ SV578 @ SV267 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2638]) ).
thf(2788,plain,
! [SV961: $i,SV913: $i,SV797: $i,SV579: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV268 ) @ SV579 ) @ SV797 ) ) @ ( c_Lambda_Olift @ SV913 @ SV579 ) ) @ SV961 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV268 ) @ SV913 ) @ SV961 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2789,plain,
! [SV914: $i,SV580: $i,SV269: $i,SV798: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV798 ) @ SV269 ) @ v_T____ ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV798 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SV914 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2790,plain,
! [SV915: $i,SV581: $i,SV270: $i,SV799: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV799 ) @ SV270 ) @ v_T____ ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV799 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SV915 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2641]) ).
thf(2791,plain,
! [SV800: $i,SV271: $i,SV582: $i,SV916: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV916 ) @ SV582 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV916 ) @ SV800 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV582 ) @ SV800 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2792,plain,
! [SV962: $i,SV917: $i,SV801: $i,SV583: $i,SV272: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV272 ) @ SV583 ) @ SV801 ) @ SV917 ) @ SV962 )
= ( hAPP @ SV583 @ SV962 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV962 @ SV801 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2793,plain,
! [SV919: $i,SV585: $i,SV803: $i,SV274: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV803 ) ) @ SV585 ) @ SV919 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV274 ) @ ( c_Lambda_OdB_OAbs @ SV585 ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV803 ) @ SV919 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2794,plain,
! [SV971: $i,SV963: $i,SV920: $i,SV805: $i,SV588: $i,SV278: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SV805 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SV920 ) @ SV805 ) ) @ SV963 ) @ SV971 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV963 ) @ SV588 ) @ SV920 ) ) @ SV971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(2795,plain,
! [SV921: $i,SV589: $i,SV279: $i,SV806: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV806 ) @ SV279 ) @ v_T____ ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV806 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SV921 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(2796,plain,
! [SV922: $i,SV810: $i,SV597: $i,SV288: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV288 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV597 @ SV597 @ SV288 )
!= ( c_HOL_Ominus__class_Ominus @ SV810 @ SV922 @ SV288 ) )
| ( SV810 = SV922 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2797,plain,
! [SV812: $i,SV291: $i,SV600: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV600 @ SV291 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV812 @ SV291 ) )
= $true )
| ( ( SV600 = SV812 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2798,plain,
! [SV293: $i,SV813: $i,SV602: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV813 @ SV293 )
!= ( c_HOL_Ozero__class_Ozero @ SV293 ) )
= $true )
| ( ( SV602 = SV813 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(2799,plain,
! [SV604: $i,SV295: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV295 ) @ SV604 ) @ SV604 )
= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
= $false )
| ( ( SV604
= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2800,plain,
! [SV923: $i,SV815: $i,SV608: $i,SV299: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV299 ) @ SV608 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV815 ) @ SV923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV299 = SV815 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2801,plain,
! [SV924: $i,SV816: $i,SV610: $i,SV303: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV303 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV303 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV816 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV924 ) )
| ( SV816 = SV924 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2802,plain,
! [SV925: $i,SV817: $i,SV611: $i,SV304: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV304 ) @ SV611 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV817 ) @ SV925 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV304 = SV817 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2803,plain,
! [SV926: $i,SV819: $i,SV613: $i,SV307: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV307 ) @ SV613 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV819 ) @ SV926 ) )
= $false )
| ( ( SV307 = SV819 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2804,plain,
! [SV308: $i,SV614: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV614 @ SV308 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV614 = SV308 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV308 @ SV614 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2805,plain,
! [SV927: $i,SV820: $i,SV616: $i,SV312: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV312 ) @ SV616 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV820 ) @ SV927 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV820 @ SV616 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV312 @ SV927 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2806,plain,
! [SV822: $i,SV620: $i,SV316: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV316 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV822 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV620 = SV822 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2807,plain,
! [SV823: $i,SV622: $i,SV318: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV318 ) )
= $true )
| ( ( ( SV622
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV622 ) @ SV823 ) )
| ( SV823
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2808,plain,
! [SV928: $i,SV824: $i,SV623: $i,SV319: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV319 ) @ SV623 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV824 ) @ SV928 ) )
= $false )
| ( ( SV623 = SV928 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2809,plain,
! [SV972: $i,SV964: $i,SV929: $i,SV828: $i,SV628: $i,SV324: $i] :
( ( ! [SY2096: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SY2096 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(2810,plain,
! [SV965: $i,SV930: $i,SV829: $i,SV629: $i,SV325: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV930 @ SV965 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV965 @ SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2811,plain,
! [SV931: $i,SV830: $i,SV631: $i,SV327: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV830 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV931 ) )
| ( SV830 = SV931 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2812,plain,
! [SV966: $i,SV932: $i,SV831: $i,SV632: $i,SV328: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV328 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV932 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV966 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ SV932 )
= SV966 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2677]) ).
thf(2813,plain,
! [SV329: $i,SV832: $i,SV633: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV633 @ SV832 @ SV329 )
!= ( c_HOL_Ozero__class_Ozero @ SV329 ) )
= $true )
| ( ( SV633 = SV832 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(2814,plain,
! [SV973: $i,SV967: $i,SV934: $i,SV834: $i,SV636: $i,SV333: $i] :
( ( ! [SY2097: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SY2097 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(2815,plain,
! [SV935: $i,SV835: $i,SV637: $i,SV334: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SV637 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV835 ) @ SV935 ) )
= $false )
| ( ( SV334 = SV835 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2816,plain,
! [SV936: $i,SV837: $i,SV640: $i,SV338: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV338 ) @ SV640 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV837 ) @ SV936 ) )
= $false )
| ( ( SV640 = SV936 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2817,plain,
! [SV938: $i,SV840: $i,SV643: $i,SV341: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV341 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV840 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV938 ) )
| ( SV840 = SV938 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2818,plain,
! [SV939: $i,SV841: $i,SV644: $i,SV342: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV342 ) @ SV644 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV841 ) @ SV939 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV644 = SV939 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2819,plain,
! [SV968: $i,SV940: $i,SV843: $i,SV646: $i,SV344: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV344 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
!= ( c_HOL_Ominus__class_Ominus @ SV940 @ SV968 @ SV344 ) )
| ( c_HOL_Oord__class_Oless @ SV940 @ SV968 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2689]) ).
thf(2820,plain,
! [SV941: $i,SV845: $i,SV649: $i,SV347: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV347 ) @ SV649 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV845 ) @ SV941 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV649 = SV941 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2821,plain,
! [SV942: $i,SV847: $i,SV651: $i,SV349: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV349 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV651 @ SV847 @ SV349 )
!= ( c_HOL_Ominus__class_Ominus @ SV942 @ SV942 @ SV349 ) )
| ( SV651 = SV847 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2822,plain,
! [SV943: $i,SV848: $i,SV652: $i,SV350: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV350 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV652 ) @ SV848 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV943 ) @ SV848 ) )
| ( SV652 = SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2823,plain,
! [SV656: $i,SV357: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ominus__class_Ominus @ SV357 @ SV656 @ tc_nat ) ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV357 @ SV656 @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV7 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2824,plain,
! [SV8: $i,SV657: $i,SV358: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV358 @ SV657 @ SV8 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV657 @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2825,plain,
! [SV9: $i,SV658: $i,SV359: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV658 @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV359 @ SV658 @ SV9 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2826,plain,
! [SV22: $i,SV370: $i,SV662: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV662 @ SV370 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV662 @ SV22 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV370 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV22 @ SV662 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2827,plain,
! [SV850: $i,SV386: $i,SV41: $i,SV944: $i,SV672: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV672 @ SV944 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV41 ) @ SV386 ) @ SV672 ) @ SV850 ) @ SV944 )
= ( hAPP @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SV944 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2828,plain,
! [SV945: $i,SV853: $i,SV677: $i,SV394: $i,SV50: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV853 ) @ SV945 ) @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV945 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ SV853 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2829,plain,
! [SV678: $i,SV51: $i,SV854: $i,SV395: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV395 @ SV854 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV51 @ SV678 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV395 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV678 ) @ SV854 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2830,plain,
! [SV396: $i,SV679: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV679 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV679 @ SV396 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV54 ) @ SV396 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2831,plain,
! [SV855: $i,SV681: $i,SV402: $i,SV60: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV402 ) @ SV681 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV855 ) @ SV681 ) @ SV60 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV402 @ SV855 @ SV60 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2832,plain,
! [SV856: $i,SV682: $i,SV403: $i,SV61: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV403 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV856 ) @ SV682 ) @ SV61 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV856 @ SV61 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(2833,plain,
! [SV857: $i,SV62: $i,SV683: $i,SV404: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV404 @ SV683 @ SV62 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV404 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV683 ) @ SV857 ) @ SV62 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2710]) ).
thf(2834,plain,
! [SV858: $i,SV684: $i,SV405: $i,SV63: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV684 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV858 ) @ SV63 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV684 @ SV858 @ SV63 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2711]) ).
thf(2835,plain,
! [SV859: $i,SV685: $i,SV406: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV685 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV859 ) @ SV64 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV685 @ SV859 @ SV64 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(2836,plain,
! [SV860: $i,SV65: $i,SV686: $i,SV407: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV407 @ SV686 @ SV65 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV407 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV686 ) @ SV65 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2837,plain,
! [SV691: $i,SV861: $i,SV946: $i,SV415: $i,SV73: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV946 ) @ SV861 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SV691 ) @ SV946 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV691 ) @ SV861 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(2838,plain,
! [SV692: $i,SV416: $i,SV862: $i,SV947: $i,SV74: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SV947 ) @ SV862 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV947 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV862 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(2839,plain,
! [SV693: $i,SV863: $i,SV417: $i,SV75: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV75 @ SV417 ) @ SV863 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV75 @ SV863 @ SV693 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV75 @ SV417 @ SV693 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2840,plain,
! [SV694: $i,SV864: $i,SV418: $i,SV76: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV418 ) @ SV864 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV76 @ SV864 @ SV694 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV76 @ SV418 @ SV694 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2841,plain,
! [SV974: $i,SV969: $i,SV948: $i,SV869: $i,SV700: $i,SV425: $i,SV83: $i] :
( ( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
| ~ ( c_Type_Otypings @ SV700 @ SV969 @ SV974 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(2842,plain,
! [SV429: $i,SV87: $i,SV701: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV701 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV429 ) @ SV701 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2843,plain,
! [SV434: $i,SV702: $i,SV93: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV702 @ SV93 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV434 @ SV93 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV434 ) @ SV702 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2844,plain,
! [SV870: $i,SV703: $i,SV95: $i,SV435: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV703 ) @ SV870 ) @ SV95 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV870 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV703 @ SV95 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2731]) ).
thf(2845,plain,
! [SV97: $i,SV704: $i,SV436: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV436 @ SV704 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV436 @ SV97 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV704 @ SV97 ) @ SV97 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2846,plain,
! [SV705: $i,SV98: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV437 @ SV98 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV705 @ SV98 ) @ SV98 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV437 @ SV705 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2847,plain,
! [SV707: $i,SV106: $i,SV871: $i,SV442: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV442 ) @ SV871 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV106 ) @ SV707 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV106 ) @ SV442 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV707 ) @ SV871 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2848,plain,
! [SV725: $i,SV876: $i,SV949: $i,SV473: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV949 ) @ SV876 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV949 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV876 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2849,plain,
! [SV474: $i,SV726: $i,SV877: $i,SV144: $i] :
( ( ( c_Wellfounded_Oaccp @ SV144 @ SV877 @ SV726 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV144 @ SV726 ) @ SV474 ) @ SV877 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV144 @ SV474 @ SV726 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2850,plain,
! [SV878: $i,SV475: $i,SV727: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SV727 ) @ SV475 ) @ SV878 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV145 @ SV878 @ SV727 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV145 @ SV475 @ SV727 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2851,plain,
! [SV741: $i,SV490: $i,SV888: $i,SV950: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV163 @ SV950 ) @ SV888 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV163 @ SV490 @ SV741 ) @ SV888 ) @ SV950 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2852,plain,
! [SV491: $i,SV742: $i,SV951: $i,SV889: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV164 @ SV889 @ SV951 ) @ SV742 ) @ SV491 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV164 @ SV491 ) @ SV742 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2853,plain,
! [SV743: $i,SV492: $i,SV890: $i,SV952: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV165 @ SV952 ) @ SV890 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV165 @ SV492 @ SV743 ) @ SV890 ) @ SV952 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2854,plain,
! [SV493: $i,SV744: $i,SV953: $i,SV891: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV166 @ SV891 @ SV953 ) @ SV744 ) @ SV493 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV493 ) @ SV744 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2855,plain,
! [SV954: $i,SV501: $i,SV175: $i,SV895: $i,SV749: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV749 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV895 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ ( c_Lambda_Olift @ SV501 @ SV749 ) ) @ ( c_Suc @ SV895 ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV954 ) @ SV501 ) @ SV895 ) ) @ SV749 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV175 ) @ SV954 ) @ SV749 ) ) @ SV501 ) @ SV895 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2856,plain,
! [SV955: $i,SV896: $i,SV750: $i,SV502: $i,SV176: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV176 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV750 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV896 ) @ SV955 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV502 ) @ SV896 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV176 ) @ SV750 ) @ SV955 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2857,plain,
! [SV521: $i,SV755: $i,SV898: $i,SV200: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV898 ) @ SV755 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV898 ) @ SV521 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV521 ) @ SV755 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2858,plain,
! [SV975: $i,SV970: $i,SV956: $i,SV899: $i,SV756: $i,SV522: $i,SV201: $i] :
( ( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
| ~ ( c_Type_Otypings @ SV201 @ SV970 @ SV975 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(2859,plain,
! [SV902: $i,SV525: $i,SV957: $i,SV759: $i,SV204: $i] :
( ( ( ~ ( c_Type_Otypings @ SV204 @ SV759 @ SV957 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SV525 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV957 @ SV902 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV525 @ SV759 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV902 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2860,plain,
! [SV766: $i,SV211: $i,SV532: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV532 @ tc_Lambda_OdB )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV211 ) ) @ SV532 ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV211 ) @ SV532 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV766 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(2861,plain,
! [SV907: $i,SV233: $i,SV775: $i,SV548: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV548 @ SV775 @ SV233 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV548 @ SV907 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV907 @ SV775 @ SV233 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(2862,plain,
! [SV908: $i,SV234: $i,SV776: $i,SV549: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV549 @ SV776 @ SV234 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV908 @ SV776 @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV549 @ SV908 @ SV234 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2863,plain,
! [SV780: $i,SV553: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV239 ) @ SV553 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV553 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV239 ) ) @ SV553 ) @ SV780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(2864,plain,
! [SV248: $i,SV560: $i,SV782: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV782 @ SV560 @ SV248 )
= $true )
| ( ( SV782 = SV560 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV560 @ SV782 @ SV248 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2865,plain,
! [SV249: $i,SV561: $i,SV783: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV783 @ SV561 @ SV249 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV561 @ SV783 @ SV249 )
= $true )
| ( ( SV561 = SV783 )
= $true )
| ( ( class_Orderings_Olinorder @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2866,plain,
! [SV252: $i,SV564: $i,SV959: $i,SV910: $i,SV785: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV564 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) ) )
= $true )
| ( ( SV252 = SV564 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2867,plain,
! [SV254: $i,SV566: $i,SV786: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV786 @ SV566 @ SV254 )
= $true )
| ( ( SV786 = SV566 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV566 @ SV786 @ SV254 )
= $true )
| ( ( class_Orderings_Olinorder @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2780]) ).
thf(2868,plain,
! [SV255: $i,SV567: $i,SV787: $i] :
( ( ( SV787 = SV567 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV787 @ SV567 @ SV255 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV567 @ SV787 @ SV255 )
= $true )
| ( ( class_Orderings_Olinorder @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(2869,plain,
! [SV256: $i,SV788: $i,SV568: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV568 @ SV788 @ SV256 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV788 @ SV568 @ SV256 )
= $true )
| ( ( SV568 = SV788 )
= $true )
| ( ( class_Orderings_Olinorder @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2870,plain,
! [SV911: $i,SV569: $i,SV960: $i,SV789: $i,SV257: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV789 ) @ SV960 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV569 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV960 ) @ SV911 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV569 ) @ SV789 ) ) @ SV911 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(2871,plain,
! [SV264: $i,SV793: $i,SV575: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV575 @ SV793 @ SV264 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV575 @ SV264 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2872,plain,
! [SV265: $i,SV794: $i,SV576: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV576 @ SV794 @ SV265 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV576 @ SV265 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(2873,plain,
! [SV266: $i,SV795: $i,SV577: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV577 @ SV795 @ SV266 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV795 @ SV577 @ SV266 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2874,plain,
! [SV267: $i,SV796: $i,SV578: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV578 @ SV796 @ SV267 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV796 @ SV578 @ SV267 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2875,plain,
! [SV797: $i,SV579: $i,SV961: $i,SV913: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV268 ) @ SV913 ) @ SV961 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV268 ) @ SV579 ) @ SV797 ) ) @ ( c_Lambda_Olift @ SV913 @ SV579 ) ) @ SV961 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(2876,plain,
! [SV914: $i,SV580: $i,SV269: $i,SV798: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV798 ) @ SV269 ) @ v_T____ ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV798 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SV914 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2877,plain,
! [SV915: $i,SV581: $i,SV270: $i,SV799: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV799 ) @ SV270 ) @ v_T____ ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV799 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SV915 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(2878,plain,
! [SV800: $i,SV271: $i,SV582: $i,SV916: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV916 ) @ SV582 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV916 ) @ SV800 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV582 ) @ SV800 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2879,plain,
! [SV917: $i,SV583: $i,SV272: $i,SV801: $i,SV962: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV962 @ SV801 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ SV272 ) @ SV583 ) @ SV801 ) @ SV917 ) @ SV962 )
= ( hAPP @ SV583 @ SV962 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2880,plain,
! [SV971: $i,SV963: $i,SV920: $i,SV805: $i,SV588: $i,SV278: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SV805 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SV920 ) @ SV805 ) ) @ SV963 ) @ SV971 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV963 ) @ SV588 ) @ SV920 ) ) @ SV971 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(2881,plain,
! [SV921: $i,SV589: $i,SV279: $i,SV806: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV806 ) @ SV279 ) @ v_T____ ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV806 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SV921 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(2882,plain,
! [SV922: $i,SV810: $i,SV288: $i,SV597: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV597 @ SV597 @ SV288 )
!= ( c_HOL_Ominus__class_Ominus @ SV810 @ SV922 @ SV288 ) )
= $true )
| ( ( SV810 = SV922 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(2883,plain,
! [SV812: $i,SV291: $i,SV600: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV600 @ SV291 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV812 @ SV291 ) )
= $false )
| ( ( SV600 = SV812 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(2884,plain,
! [SV293: $i,SV813: $i,SV602: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV813 @ SV293 )
= ( c_HOL_Ozero__class_Ozero @ SV293 ) )
= $false )
| ( ( SV602 = SV813 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2885,plain,
! [SV924: $i,SV816: $i,SV610: $i,SV303: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV303 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV816 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV924 ) )
| ( SV816 = SV924 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2801]) ).
thf(2886,plain,
! [SV927: $i,SV312: $i,SV616: $i,SV820: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV820 @ SV616 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV312 @ SV927 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV312 ) @ SV616 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV820 ) @ SV927 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(2887,plain,
! [SV822: $i,SV620: $i,SV316: $i] :
( ( ( class_Int_Onumber__ring @ SV316 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV822 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV620 = SV822 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2888,plain,
! [SV823: $i,SV622: $i,SV318: $i] :
( ( ( class_Int_Onumber__ring @ SV318 )
= $false )
| ( ( ( SV622
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV622 ) @ SV823 ) )
| ( SV823
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2889,plain,
! [SV976: $i,SV972: $i,SV964: $i,SV929: $i,SV828: $i,SV628: $i,SV324: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(2890,plain,
! [SV965: $i,SV930: $i,SV829: $i,SV629: $i,SV325: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV930 @ SV965 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV965 @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2891,plain,
! [SV931: $i,SV830: $i,SV631: $i,SV327: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV830 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV931 ) )
= $true )
| ( ( SV830 = SV931 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(2892,plain,
! [SV966: $i,SV932: $i,SV831: $i,SV632: $i,SV328: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV328 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV932 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV966 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ SV932 )
= SV966 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(2893,plain,
! [SV329: $i,SV832: $i,SV633: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV633 @ SV832 @ SV329 )
= ( c_HOL_Ozero__class_Ozero @ SV329 ) )
= $false )
| ( ( SV633 = SV832 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2894,plain,
! [SV977: $i,SV973: $i,SV967: $i,SV934: $i,SV834: $i,SV636: $i,SV333: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(2895,plain,
! [SV938: $i,SV840: $i,SV643: $i,SV341: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV840 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV938 ) )
= $true )
| ( ( SV840 = SV938 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV341 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2817]) ).
thf(2896,plain,
! [SV968: $i,SV940: $i,SV843: $i,SV646: $i,SV344: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
!= ( c_HOL_Ominus__class_Ominus @ SV940 @ SV968 @ SV344 ) )
| ( c_HOL_Oord__class_Oless @ SV940 @ SV968 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(2897,plain,
! [SV942: $i,SV349: $i,SV847: $i,SV651: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV651 @ SV847 @ SV349 )
!= ( c_HOL_Ominus__class_Ominus @ SV942 @ SV942 @ SV349 ) )
= $true )
| ( ( SV651 = SV847 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV349 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2821]) ).
thf(2898,plain,
! [SV943: $i,SV848: $i,SV652: $i,SV350: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV652 ) @ SV848 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV943 ) @ SV848 ) )
= $true )
| ( ( SV652 = SV943 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(2899,plain,
! [SV945: $i,SV853: $i,SV677: $i,SV394: $i,SV50: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV853 ) @ SV945 ) @ SV50 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV945 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ SV853 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2828]) ).
thf(2900,plain,
! [SV854: $i,SV395: $i,SV678: $i,SV51: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV51 @ SV678 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV395 @ SV854 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV395 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV678 ) @ SV854 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2901,plain,
! [SV681: $i,SV60: $i,SV855: $i,SV402: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV402 @ SV855 @ SV60 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV402 ) @ SV681 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV855 ) @ SV681 ) @ SV60 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(2902,plain,
! [SV682: $i,SV61: $i,SV856: $i,SV403: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV403 @ SV856 @ SV61 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV403 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV856 ) @ SV682 ) @ SV61 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(2903,plain,
! [SV683: $i,SV857: $i,SV404: $i,SV62: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV404 ) @ SV857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV683 ) @ SV857 ) @ SV62 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV404 @ SV683 @ SV62 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(2904,plain,
! [SV405: $i,SV63: $i,SV858: $i,SV684: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV684 @ SV858 @ SV63 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV684 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV63 ) @ SV405 ) @ SV858 ) @ SV63 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(2905,plain,
! [SV406: $i,SV64: $i,SV859: $i,SV685: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV685 @ SV859 @ SV64 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV685 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV406 ) @ SV859 ) @ SV64 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(2906,plain,
! [SV686: $i,SV407: $i,SV860: $i,SV65: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV407 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV65 ) @ SV860 ) @ SV686 ) @ SV65 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV407 @ SV686 @ SV65 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(2907,plain,
! [SV691: $i,SV861: $i,SV946: $i,SV415: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV946 ) @ SV861 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SV691 ) @ SV946 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV691 ) @ SV861 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2908,plain,
! [SV692: $i,SV416: $i,SV862: $i,SV947: $i,SV74: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SV947 ) @ SV862 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV947 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV862 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2909,plain,
! [SV417: $i,SV693: $i,SV863: $i,SV75: $i] :
( ( ( c_Wellfounded_Oaccp @ SV75 @ SV863 @ SV693 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV75 @ SV417 ) @ SV863 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV75 @ SV417 @ SV693 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2910,plain,
! [SV418: $i,SV694: $i,SV864: $i,SV76: $i] :
( ( ( c_Wellfounded_Oaccp @ SV76 @ SV864 @ SV694 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV76 @ SV418 ) @ SV864 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV76 @ SV418 @ SV694 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2911,plain,
! [SV974: $i,SV969: $i,SV948: $i,SV869: $i,SV700: $i,SV425: $i,SV83: $i] :
( ( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
| ~ ( c_Type_Otypings @ SV700 @ SV969 @ SV974 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2841]) ).
thf(2912,plain,
! [SV429: $i,SV87: $i,SV701: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV701 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV429 ) @ SV701 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2913,plain,
! [SV434: $i,SV702: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV702 @ SV93 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV434 @ SV93 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV434 ) @ SV702 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(2914,plain,
! [SV703: $i,SV95: $i,SV870: $i,SV435: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV435 @ SV870 @ SV95 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV703 @ SV95 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV703 ) @ SV870 ) @ SV95 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(2915,plain,
! [SV871: $i,SV442: $i,SV707: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV106 ) @ SV707 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV442 ) @ SV871 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV106 ) @ SV442 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV707 ) @ SV871 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(2916,plain,
! [SV725: $i,SV876: $i,SV949: $i,SV473: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV949 ) @ SV876 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV949 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV876 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2917,plain,
! [SV877: $i,SV474: $i,SV726: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV144 @ SV726 ) @ SV474 ) @ SV877 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV144 @ SV877 @ SV726 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV144 @ SV474 @ SV726 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(2918,plain,
! [SV475: $i,SV727: $i,SV878: $i,SV145: $i] :
( ( ( c_Wellfounded_Oaccp @ SV145 @ SV878 @ SV727 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV145 @ SV727 ) @ SV475 ) @ SV878 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV145 @ SV475 @ SV727 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2919,plain,
! [SV755: $i,SV200: $i,SV521: $i,SV898: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV898 ) @ SV521 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV898 ) @ SV755 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV200 ) @ SV521 ) @ SV755 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(2920,plain,
! [SV975: $i,SV970: $i,SV956: $i,SV899: $i,SV756: $i,SV522: $i,SV201: $i] :
( ( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
| ~ ( c_Type_Otypings @ SV201 @ SV970 @ SV975 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(2921,plain,
! [SV902: $i,SV525: $i,SV957: $i,SV759: $i,SV204: $i] :
( ( ( c_Type_Otypings @ SV204 @ SV759 @ SV957 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SV525 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV957 @ SV902 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV525 @ SV759 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV902 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(2922,plain,
! [SV775: $i,SV233: $i,SV907: $i,SV548: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV548 @ SV907 @ SV233 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV907 @ SV775 @ SV233 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV548 @ SV775 @ SV233 )
= $true )
| ( ( class_Orderings_Oorder @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(2923,plain,
! [SV549: $i,SV234: $i,SV776: $i,SV908: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV908 @ SV776 @ SV234 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV549 @ SV908 @ SV234 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV549 @ SV776 @ SV234 )
= $true )
| ( ( class_Orderings_Opreorder @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(2924,plain,
! [SV252: $i,SV564: $i,SV959: $i,SV910: $i,SV785: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV564 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) ) )
= $true )
| ( ( SV252 = SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(2925,plain,
! [SV911: $i,SV569: $i,SV960: $i,SV789: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV789 ) @ SV960 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV569 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV960 ) @ SV911 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV569 ) @ SV789 ) ) @ SV911 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2926,plain,
! [SV264: $i,SV575: $i,SV793: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV793 @ SV575 @ SV264 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV575 @ SV793 @ SV264 )
= $false )
| ( ( class_Orderings_Oorder @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(2927,plain,
! [SV265: $i,SV576: $i,SV794: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV794 @ SV576 @ SV265 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV576 @ SV794 @ SV265 )
= $false )
| ( ( class_Orderings_Olinorder @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(2928,plain,
! [SV266: $i,SV577: $i,SV795: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV795 @ SV577 @ SV266 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV577 @ SV795 @ SV266 )
= $false )
| ( ( class_Orderings_Opreorder @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(2929,plain,
! [SV267: $i,SV578: $i,SV796: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV796 @ SV578 @ SV267 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV578 @ SV796 @ SV267 )
= $false )
| ( ( class_Orderings_Opreorder @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2930,plain,
! [SV914: $i,SV580: $i,SV798: $i,SV269: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV798 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SV914 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV798 ) @ SV269 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(2931,plain,
! [SV915: $i,SV581: $i,SV799: $i,SV270: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV799 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SV915 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV799 ) @ SV270 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(2932,plain,
! [SV582: $i,SV800: $i,SV916: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV916 ) @ SV800 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV916 ) @ SV582 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV271 ) @ SV582 ) @ SV800 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2933,plain,
! [SV971: $i,SV963: $i,SV920: $i,SV805: $i,SV588: $i,SV278: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SV805 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SV920 ) @ SV805 ) ) @ SV963 ) @ SV971 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV963 ) @ SV588 ) @ SV920 ) ) @ SV971 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(2934,plain,
! [SV921: $i,SV589: $i,SV806: $i,SV279: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV806 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SV921 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV806 ) @ SV279 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(2935,plain,
! [SV922: $i,SV810: $i,SV288: $i,SV597: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV597 @ SV597 @ SV288 )
= ( c_HOL_Ominus__class_Ominus @ SV810 @ SV922 @ SV288 ) )
= $false )
| ( ( SV810 = SV922 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2936,plain,
! [SV924: $i,SV816: $i,SV610: $i,SV303: $i] :
( ( ( class_Int_Onumber__ring @ SV303 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV816 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV924 ) )
| ( SV816 = SV924 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(2937,plain,
! [SV927: $i,SV312: $i,SV616: $i,SV820: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV820 @ SV616 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV312 @ SV927 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV312 ) @ SV616 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV820 ) @ SV927 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(2938,plain,
! [SV316: $i,SV822: $i,SV620: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV822 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
= $true )
| ( ( SV620 = SV822 )
= $true )
| ( ( class_Int_Onumber__ring @ SV316 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(2939,plain,
! [SV823: $i,SV318: $i,SV622: $i] :
( ( ( SV622
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV622 ) @ SV823 ) )
= $true )
| ( ( SV823
= ( c_HOL_Ozero__class_Ozero @ SV318 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV318 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2888]) ).
thf(2940,plain,
! [SV976: $i,SV972: $i,SV964: $i,SV929: $i,SV828: $i,SV628: $i,SV324: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2889]) ).
thf(2941,plain,
! [SV965: $i,SV930: $i,SV325: $i,SV829: $i,SV629: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV930 @ SV965 @ SV325 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV965 @ SV325 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(2942,plain,
! [SV931: $i,SV830: $i,SV631: $i,SV327: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV830 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ SV631 ) @ SV931 ) )
= $false )
| ( ( SV830 = SV931 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2891]) ).
thf(2943,plain,
! [SV966: $i,SV932: $i,SV831: $i,SV632: $i,SV328: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV932 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV966 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ SV932 )
= SV966 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2892]) ).
thf(2944,plain,
! [SV977: $i,SV973: $i,SV967: $i,SV934: $i,SV834: $i,SV636: $i,SV333: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(2945,plain,
! [SV938: $i,SV840: $i,SV643: $i,SV341: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV840 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV341 ) @ SV643 ) @ SV938 ) )
= $false )
| ( ( SV840 = SV938 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV341 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(2946,plain,
! [SV968: $i,SV940: $i,SV344: $i,SV843: $i,SV646: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
!= ( c_HOL_Ominus__class_Ominus @ SV940 @ SV968 @ SV344 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV940 @ SV968 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(2947,plain,
! [SV942: $i,SV349: $i,SV847: $i,SV651: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV651 @ SV847 @ SV349 )
= ( c_HOL_Ominus__class_Ominus @ SV942 @ SV942 @ SV349 ) )
= $false )
| ( ( SV651 = SV847 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(2948,plain,
! [SV943: $i,SV848: $i,SV652: $i,SV350: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV652 ) @ SV848 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV943 ) @ SV848 ) )
= $false )
| ( ( SV652 = SV943 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(2949,plain,
! [SV853: $i,SV394: $i,SV50: $i,SV945: $i,SV677: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV945 @ SV50 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV394 @ SV853 @ SV50 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV853 ) @ SV945 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2899]) ).
thf(2950,plain,
! [SV861: $i,SV415: $i,SV946: $i,SV691: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV73 @ SV691 ) @ SV946 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV946 ) @ SV861 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV73 @ SV415 ) @ SV691 ) @ SV861 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(2951,plain,
! [SV862: $i,SV947: $i,SV692: $i,SV416: $i,SV74: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV947 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV74 @ SV947 ) @ SV862 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV74 @ SV416 ) @ SV692 ) @ SV862 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(2952,plain,
! [SV425: $i,SV869: $i,SV974: $i,SV83: $i,SV969: $i,SV948: $i,SV700: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV700 @ SV969 @ SV974 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) )
= $true )
| ( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(2953,plain,
! [SV701: $i,SV87: $i,SV429: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV429 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV701 @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV87 ) @ SV429 ) @ SV701 ) @ ( c_HOL_Ozero__class_Ozero @ SV87 ) @ SV87 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(2954,plain,
! [SV702: $i,SV434: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV434 @ SV93 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV702 @ SV93 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV434 ) @ SV702 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(2955,plain,
! [SV703: $i,SV95: $i,SV870: $i,SV435: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV435 @ SV870 @ SV95 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV703 @ SV95 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV703 ) @ SV870 ) @ SV95 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(2956,plain,
! [SV876: $i,SV949: $i,SV725: $i,SV473: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV949 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV949 ) @ SV876 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV143 @ SV473 ) @ SV725 ) @ SV876 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(2957,plain,
! [SV756: $i,SV522: $i,SV975: $i,SV899: $i,SV970: $i,SV956: $i,SV201: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV201 @ SV970 @ SV975 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) )
= $true )
| ( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(2958,plain,
! [SV759: $i,SV902: $i,SV957: $i,SV525: $i,SV204: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ SV525 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV957 @ SV902 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $false )
| ( ( c_Type_Otypings @ SV204 @ SV759 @ SV957 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV204 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV525 @ SV759 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV902 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(2959,plain,
! [SV775: $i,SV233: $i,SV907: $i,SV548: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV548 @ SV907 @ SV233 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV907 @ SV775 @ SV233 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV548 @ SV775 @ SV233 )
= $true )
| ( ( class_Orderings_Oorder @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(2960,plain,
! [SV549: $i,SV234: $i,SV776: $i,SV908: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV908 @ SV776 @ SV234 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV549 @ SV908 @ SV234 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV549 @ SV776 @ SV234 )
= $true )
| ( ( class_Orderings_Opreorder @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(2961,plain,
! [SV564: $i,SV252: $i,SV959: $i,SV910: $i,SV785: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV252 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV785 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV910 ) @ SV959 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV564 ) )
= $false )
| ( ( SV252 = SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(2962,plain,
! [SV789: $i,SV911: $i,SV960: $i,SV569: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV569 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV960 ) @ SV911 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ SV789 ) @ SV960 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV257 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV569 ) @ SV789 ) ) @ SV911 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(2963,plain,
! [SV914: $i,SV580: $i,SV798: $i,SV269: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV798 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SV914 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV798 ) @ SV269 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(2964,plain,
! [SV915: $i,SV581: $i,SV799: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV799 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SV915 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV799 ) @ SV270 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2931]) ).
thf(2965,plain,
! [SV588: $i,SV971: $i,SV963: $i,SV805: $i,SV920: $i,SV278: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SV920 ) @ SV805 ) ) @ SV963 ) @ SV971 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV963 ) @ SV588 ) @ SV920 ) ) @ SV971 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SV805 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2933]) ).
thf(2966,plain,
! [SV921: $i,SV589: $i,SV806: $i,SV279: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV806 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SV921 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV806 ) @ SV279 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(2967,plain,
! [SV924: $i,SV816: $i,SV610: $i,SV303: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV816 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV924 ) )
= $true )
| ( ( SV816 = SV924 )
= $true )
| ( ( class_Int_Onumber__ring @ SV303 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2936]) ).
thf(2968,plain,
! [SV316: $i,SV822: $i,SV620: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV822 @ SV316 )
= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
= $false )
| ( ( SV620 = SV822 )
= $true )
| ( ( class_Int_Onumber__ring @ SV316 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(2969,plain,
! [SV823: $i,SV318: $i,SV622: $i] :
( ( ( SV622
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV622 ) @ SV823 ) )
= $false )
| ( ( SV823
= ( c_HOL_Ozero__class_Ozero @ SV318 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV318 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(2970,plain,
! [SV976: $i,SV972: $i,SV964: $i,SV929: $i,SV828: $i,SV628: $i,SV324: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(2971,plain,
! [SV965: $i,SV930: $i,SV325: $i,SV829: $i,SV629: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV930 @ SV965 @ SV325 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV965 @ SV325 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(2972,plain,
! [SV966: $i,SV932: $i,SV831: $i,SV632: $i,SV328: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV932 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV831 ) @ SV966 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV328 ) @ SV632 ) @ SV932 )
= SV966 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(2973,plain,
! [SV977: $i,SV973: $i,SV967: $i,SV934: $i,SV834: $i,SV636: $i,SV333: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(2974,plain,
! [SV968: $i,SV940: $i,SV344: $i,SV843: $i,SV646: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ SV940 @ SV968 @ SV344 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV940 @ SV968 @ SV344 )
| ~ ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(2975,plain,
! [SV853: $i,SV394: $i,SV50: $i,SV945: $i,SV677: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV945 @ SV50 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV394 @ SV853 @ SV50 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV853 ) @ SV945 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(2976,plain,
! [SV425: $i,SV869: $i,SV974: $i,SV83: $i,SV969: $i,SV948: $i,SV700: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV700 @ SV969 @ SV974 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) )
= $true )
| ( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(2977,plain,
! [SV870: $i,SV435: $i,SV703: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV703 @ SV95 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV435 @ SV870 @ SV95 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV435 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV703 ) @ SV870 ) @ SV95 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(2978,plain,
! [SV756: $i,SV522: $i,SV975: $i,SV899: $i,SV970: $i,SV956: $i,SV201: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV201 @ SV970 @ SV975 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) )
= $true )
| ( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(2979,plain,
! [SV548: $i,SV233: $i,SV775: $i,SV907: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV907 @ SV775 @ SV233 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV548 @ SV907 @ SV233 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV548 @ SV775 @ SV233 )
= $true )
| ( ( class_Orderings_Oorder @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(2980,plain,
! [SV776: $i,SV234: $i,SV908: $i,SV549: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV549 @ SV908 @ SV234 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV908 @ SV776 @ SV234 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV549 @ SV776 @ SV234 )
= $true )
| ( ( class_Orderings_Opreorder @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(2981,plain,
! [SV269: $i,SV914: $i,SV580: $i,SV798: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV798 ) @ SV580 ) @ v_T____ ) ) @ v_a____ ) @ SV914 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV798 ) @ SV269 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV269 ) @ SV580 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(2982,plain,
! [SV270: $i,SV915: $i,SV581: $i,SV799: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV799 ) @ SV581 ) @ v_T____ ) ) @ v_a____ ) @ SV915 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV270 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV799 ) @ SV270 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV270 ) @ SV581 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(2983,plain,
! [SV588: $i,SV971: $i,SV963: $i,SV805: $i,SV920: $i,SV278: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV278 ) @ SV920 ) @ SV805 ) ) @ SV963 ) @ SV971 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV963 ) @ SV588 ) @ SV920 ) ) @ SV971 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV278 ) @ SV588 ) @ SV805 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(2984,plain,
! [SV279: $i,SV921: $i,SV589: $i,SV806: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV806 ) @ SV589 ) @ v_T____ ) ) @ v_a____ ) @ SV921 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV279 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV806 ) @ SV279 ) @ v_T____ ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ SV279 ) @ SV589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(2985,plain,
! [SV924: $i,SV816: $i,SV610: $i,SV303: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV816 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV303 ) @ SV610 ) @ SV924 ) )
= $false )
| ( ( SV816 = SV924 )
= $true )
| ( ( class_Int_Onumber__ring @ SV303 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(2986,plain,
! [SV628: $i,SV976: $i,SV324: $i,SV972: $i,SV964: $i,SV929: $i,SV828: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2970]) ).
thf(2987,plain,
! [SV965: $i,SV930: $i,SV325: $i,SV829: $i,SV629: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV965 @ SV325 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV930 @ SV965 @ SV325 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2971]) ).
thf(2988,plain,
! [SV333: $i,SV977: $i,SV636: $i,SV973: $i,SV967: $i,SV934: $i,SV834: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(2989,plain,
! [SV843: $i,SV646: $i,SV344: $i,SV968: $i,SV940: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV940 @ SV968 @ SV344 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ SV940 @ SV968 @ SV344 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(2990,plain,
! [SV945: $i,SV677: $i,SV50: $i,SV853: $i,SV394: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV394 @ SV853 @ SV50 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV677 @ SV945 @ SV50 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV394 ) @ SV677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV853 ) @ SV945 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(2991,plain,
! [SV83: $i,SV425: $i,SV869: $i,SV948: $i,SV974: $i,SV969: $i,SV700: $i] :
( ( ( ~ ( c_Type_Otypings @ SV700 @ SV969 @ SV974 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
= $false )
| ( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(2992,plain,
! [SV899: $i,SV756: $i,SV522: $i,SV956: $i,SV975: $i,SV970: $i,SV201: $i] :
( ( ( ~ ( c_Type_Otypings @ SV201 @ SV970 @ SV975 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
= $false )
| ( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(2993,plain,
! [SV628: $i,SV976: $i,SV828: $i,SV964: $i,SV324: $i,SV929: $i,SV972: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2986]) ).
thf(2994,plain,
! [SV829: $i,SV629: $i,SV325: $i,SV965: $i,SV930: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV930 @ SV965 @ SV325 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV629 @ SV829 @ SV325 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV629 @ SV829 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV930 @ SV965 @ SV325 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(2995,plain,
! [SV333: $i,SV977: $i,SV834: $i,SV967: $i,SV636: $i,SV934: $i,SV973: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2988]) ).
thf(2996,plain,
! [SV968: $i,SV940: $i,SV344: $i,SV843: $i,SV646: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV646 @ SV843 @ SV344 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV940 @ SV968 @ SV344 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV843 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ SV940 @ SV968 @ SV344 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(2997,plain,
! [SV83: $i,SV425: $i,SV869: $i,SV948: $i,SV974: $i,SV969: $i,SV700: $i] :
( ( ( c_Type_Otypings @ SV700 @ SV969 @ SV974 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
= $false )
| ( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(2998,plain,
! [SV899: $i,SV756: $i,SV522: $i,SV956: $i,SV975: $i,SV970: $i,SV201: $i] :
( ( ( c_Type_Otypings @ SV201 @ SV970 @ SV975 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
= $false )
| ( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2992]) ).
thf(2999,plain,
! [SV628: $i,SV976: $i,SV828: $i,SV964: $i,SV324: $i,SV929: $i,SV972: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3000,plain,
! [SV333: $i,SV977: $i,SV834: $i,SV967: $i,SV636: $i,SV934: $i,SV973: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3001,plain,
! [SV83: $i,SV974: $i,SV425: $i,SV869: $i,SV969: $i,SV948: $i,SV700: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV869 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV425 ) )
= $false )
| ( ( c_Type_Otypings @ SV700 @ SV969 @ SV974 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV700 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV948 ) @ SV969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV83 ) )
= $false )
| ( ( SV83
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV425 @ SV83 @ SV700 @ SV869 ) @ SV425 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2997]) ).
thf(3002,plain,
! [SV899: $i,SV975: $i,SV756: $i,SV522: $i,SV970: $i,SV956: $i,SV201: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV756 ) )
= $false )
| ( ( c_Type_Otypings @ SV201 @ SV970 @ SV975 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV201 ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV956 ) @ SV970 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV899 ) )
= $false )
| ( ( c_Type_Otypings @ SV201 @ SV522 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV756 @ SV899 @ SV201 @ SV522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3003,plain,
! [SV628: $i,SV976: $i,SV828: $i,SV324: $i,SV964: $i,SV972: $i,SV929: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2999]) ).
thf(3004,plain,
! [SV333: $i,SV977: $i,SV834: $i,SV636: $i,SV967: $i,SV973: $i,SV934: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3005,plain,
! [SV628: $i,SV976: $i,SV828: $i,SV324: $i,SV964: $i,SV972: $i,SV929: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3006,plain,
! [SV333: $i,SV977: $i,SV834: $i,SV636: $i,SV967: $i,SV973: $i,SV934: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3007,plain,
! [SV628: $i,SV929: $i,SV976: $i,SV828: $i,SV324: $i,SV964: $i,SV972: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3008,plain,
! [SV333: $i,SV934: $i,SV977: $i,SV834: $i,SV636: $i,SV967: $i,SV973: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3009,plain,
! [SV628: $i,SV929: $i,SV976: $i,SV828: $i,SV324: $i,SV964: $i,SV972: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3010,plain,
! [SV333: $i,SV934: $i,SV977: $i,SV834: $i,SV636: $i,SV967: $i,SV973: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3011,plain,
! [SV628: $i,SV929: $i,SV976: $i,SV324: $i,SV964: $i,SV972: $i,SV828: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV828 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV972 ) @ SV964 ) @ SV324 ) ) @ SV828 ) @ SV976 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV929 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV972 ) @ SV929 ) @ SV324 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV828 ) @ SV929 ) @ SV964 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV324 ) @ SV628 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3012,plain,
! [SV333: $i,SV934: $i,SV977: $i,SV636: $i,SV967: $i,SV973: $i,SV834: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV834 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ SV973 ) @ SV967 ) @ SV636 ) ) @ SV834 ) @ SV977 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV934 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ SV973 ) @ SV934 ) @ SV636 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV834 ) @ SV934 ) @ SV967 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV333 ) @ SV636 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3013,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[841,3012,3011,3002,3001,2996,2994,2990,2985,2984,2983,2982,2981,2980,2979,2977,2972,2969,2968,2962,2961,2958,2956,2954,2953,2951,2950,2948,2947,2945,2942,2937,2935,2932,2929,2928,2927,2926,2919,2918,2917,2915,2910,2909,2906,2905,2904,2903,2902,2901,2900,2893,2884,2883,2879,2875,2869,2868,2867,2865,2864,2863,2860,2856,2855,2854,2853,2852,2851,2846,2845,2830,2827,2826,2825,2824,2823,2820,2818,2816,2815,2808,2804,2803,2802,2800,2799,2793,2778,2774,2771,2770,2769,2767,2766,2764,2763,2760,2759,2756,2755,2750,2749,2748,2747,2746,2745,2744,2743,2742,2738,2737,2736,2735,2729,2728,2727,2726,2724,2723,2721,2720,2719,2718,2704,2701,2697,2696,2695,2692,2690,2686,2685,2683,2680,2679,2675,2669,2668,2664,2660,2658,2656,2654,2653,2651,2650,2649,2648,2645,2634,2633,2624,2623,2622,2621,2618,2615,2614,2613,2612,2608,2607,2604,2603,2602,2601,2593,2591,2590,2587,2586,2567,2566,2565,2564,2563,2562,2561,2560,2558,2557,2556,2552,2551,2549,2548,2538,2534,2525,2524,2523,2522,2512,2511,2510,2507,2506,2505,2504,2501,2500,2499,2488,2485,2478,2467,2466,2465,2464,2460,2456,2453,2449,2446,2445,2436,2431,2430,2425,2415,2408,2405,2398,2390,2388,2387,2386,2365,2364,2363,2362,2361,2360,2359,2358,2356,2355,2346,2345,2313,2307,2306,2301,2281,2280,2270,2269,2262,2261,2260,2257,2251,2250,2249,2248,2240,2239,2237,2203,2168,2152,2135,2130,2129,2126,2102,2088,2086,2077,2064,2063,2060,2059,2058,2054,2053,2042,2041,2040,2029,2023,2021,2008,1987,1986,1985,1971,1968,1967,1966,1965,1964,1951,1944,1925,1920,1901,1899,1891,1890,1872,1867,1852,1849,1837,1833,1832,1823,1822,1779,1774,1767,1747,1739,1738,1737,1736,1735,1727,1723,1722,1718,1717,1711,1675,1643,1642,1641,1635,1634,1624,1611,1541,1516,1494,1472,1471,1470,1443,1442,1441,1406,1405,1378,1377,1358,1357,1309,1308,1302,1286,1279,1272,1271,1259,1258,1256,1181,1180,1179,1178,1177,1176,1175,1174,1173,1172,1171,1170,1169,1168,1167,1166,1165,1164,1163,1159,1158,1157,1153,1152,1151,1149,1141,1085,1074,1066,996,978,974,916,877,853]) ).
thf(3014,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3013]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL827-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 12:37:24 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 198.12/33.26 ..
% 198.12/33.26
% 198.12/33.26 No.of.Axioms: 393
% 198.12/33.26
% 198.12/33.26 Length.of.Defs: 0
% 198.12/33.26
% 198.12/33.26 Contains.Choice.Funs: false
% 198.12/33.26 ..............................................................................................................
% 198.12/33.26
% 198.12/33.26 ********************************
% 198.12/33.26 * All subproblems solved! *
% 198.12/33.26 ********************************
% 198.12/33.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:393,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:278,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3013,loop_count:0,foatp_calls:1,translation:fof_full)
% 198.12/33.26
% 198.12/33.26 %**** Beginning of derivation protocol ****
% 198.12/33.26 % SZS output start CNFRefutation
% See solution above
% 198.12/33.29
% 198.12/33.29 %**** End of derivation protocol ****
% 198.12/33.29 %**** no. of clauses in derivation: 3014 ****
% 198.12/33.29 %**** clause counter: 3013 ****
% 198.12/33.29
% 198.12/33.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:393,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:278,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3013,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------