%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL854-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:30:57 AM UTC 2026
% Result : Unsatisfiable 18.06s 3.27s
% Output : CNFRefutation 18.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 297
% Syntax : Number of formulae : 2374 (1565 unt; 0 typ; 0 def)
% Number of atoms : 11726 (4918 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 35241 (2741 ~;3288 |; 0 &;29212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 89 ( 86 usr; 16 con; 0-5 aty)
% Number of variables : 7284 ( 0 ^;7284 !; 0 ?;7284 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
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_Osko__Lambda__Xbeta__cases__2__1,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(tp_c_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_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_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $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 > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xabs__typeE__1__1,type,
c_Type_Osko__Type__Xabs__typeE__1__1: $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xabs__typeE__1__2,type,
c_Type_Osko__Type__Xabs__typeE__1__2: $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xlist__app__typeD__1__1,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xlist__app__typeE__1__1,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtype__induct__1__1,type,
c_Type_Osko__Type__Xtype__induct__1__1: $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__2__1,type,
c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__3__1,type,
c_Type_Osko__Type__Xtyping__elims__3__1: $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__3__2,type,
c_Type_Osko__Type__Xtyping__elims__3__2: $i > $i > $i > $i ).
thf(tp_c_Type_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_OAtom,type,
c_Type_Otype_OAtom: $i > $i ).
thf(tp_c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
thf(tp_c_Type_Otype_Otype__case,type,
c_Type_Otype_Otype__case: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otype_Otype__rec,type,
c_Type_Otype_Otype__rec: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otype_Otype__size,type,
c_Type_Otype_Otype__size: $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_c_Type_Otypings,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__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_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_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_Ta____,type,
v_Ta____: $i ).
thf(tp_v_U____,type,
v_U____: $i ).
thf(tp_v_ea____,type,
v_ea____: $i ).
thf(tp_v_s____,type,
v_s____: $i ).
thf(tp_v_ta____,type,
v_ta____: $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_Power_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(6,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(7,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(8,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(9,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(10,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(11,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(12,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(13,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(14,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(15,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(16,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(17,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(18,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(19,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(20,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(21,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(22,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(23,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(24,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(25,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(26,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(27,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(28,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(29,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
thf(30,axiom,
! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
thf(31,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_1) ).
thf(32,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).
thf(33,axiom,
! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(34,axiom,
c_Type_Otyping @ v_ea____ @ v_s____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_Ta____ ) @ v_U____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I1_J_0) ).
thf(35,axiom,
! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
thf(36,axiom,
! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).
thf(37,axiom,
c_Type_Otyping @ v_ea____ @ v_ta____ @ v_Ta____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I3_J_0) ).
thf(38,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(39,axiom,
! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(40,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I2_J_0) ).
thf(41,axiom,
! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OApp_0) ).
thf(42,axiom,
! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_0) ).
thf(43,axiom,
! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_1) ).
thf(44,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(45,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(46,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(47,axiom,
! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
thf(48,axiom,
! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
thf(49,axiom,
! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(50,axiom,
! [V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_U )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__type__IT_0) ).
thf(51,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(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_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( 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(59,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(60,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(61,axiom,
! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Type_Otype_OAtom @ V_nat ) @ tc_Type_Otype )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I3_J_0) ).
thf(62,axiom,
! [V_r: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).
thf(63,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(64,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(65,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(66,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(67,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(68,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(69,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(70,axiom,
! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(71,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 ) ) @ ( 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(72,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(73,axiom,
! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
thf(74,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(75,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(76,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(77,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(78,axiom,
! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(79,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 @ ( 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(80,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(81,axiom,
! [V_e: $i,V_i: $i,V_U: $i,T_a: $i,V_T: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a )
= ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a ) @ ( c_Suc @ V_i ) @ V_U @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).
thf(82,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(83,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
thf(84,axiom,
! [V_e: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__typeE_0) ).
thf(85,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(86,axiom,
! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( 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 ) )
| ~ ( 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(87,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(88,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(89,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ta____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
thf(90,axiom,
! [V_e: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).
thf(91,axiom,
! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
thf(92,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(93,axiom,
! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_2) ).
thf(94,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(95,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(96,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(97,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(98,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).
thf(99,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_0) ).
thf(100,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(101,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(102,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(103,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(104,axiom,
! [V_nat: $i] :
( ( c_Type_Otype_Otype__size @ ( c_Type_Otype_OAtom @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I1_J_0) ).
thf(105,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_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(106,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(107,axiom,
! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(108,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(109,axiom,
! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).
thf(110,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(111,axiom,
! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
thf(112,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(113,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(114,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(115,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(116,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(117,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(118,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(119,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(120,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(121,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(122,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(123,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(124,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(125,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(126,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(127,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(128,axiom,
! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(129,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 @ ( 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(130,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(131,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( 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(132,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(133,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(134,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(135,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(136,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(137,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(138,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(139,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( 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(140,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(141,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(142,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 ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( 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(143,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( 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(144,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(145,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(146,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(147,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(148,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(149,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(150,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(151,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(152,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(153,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(154,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(155,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(156,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(157,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(158,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(159,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 ) )
| ~ ( 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 )
| ~ ( 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(160,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(161,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(162,axiom,
! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(163,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(164,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 ) )
| ~ ( 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(165,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(166,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(167,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(168,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(169,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(170,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(171,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(172,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(173,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(174,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(175,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(176,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(177,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(178,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(179,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(180,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(181,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(182,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(183,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(184,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(185,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(186,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(187,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(188,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(189,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(190,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(191,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(192,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(193,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(194,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(195,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(196,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(197,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(198,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(199,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(200,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(201,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(202,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(203,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(204,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(205,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(206,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(207,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(208,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(209,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(210,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(211,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(212,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(213,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(214,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(215,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(216,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(217,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(218,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(219,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(220,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(221,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(222,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(223,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(224,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(225,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(226,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(227,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(228,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(229,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(230,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(231,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(232,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(233,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(234,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(235,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(236,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(237,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(238,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(239,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(240,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(241,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(242,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(243,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(244,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(245,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(246,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(247,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(248,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(249,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(250,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(251,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(252,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(253,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(254,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(255,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(256,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(257,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(258,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(259,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(260,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(261,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(262,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(263,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(264,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(265,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(266,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(267,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(268,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(269,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(270,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(271,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(272,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(273,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(274,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(275,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(276,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(277,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(278,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(279,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(280,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(281,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(282,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(283,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(284,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(285,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(286,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 ) )
| ~ ( 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 )
| ~ ( 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(287,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(288,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(289,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(290,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(291,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(292,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(293,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(294,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(295,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(296,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(297,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[296]) ).
thf(298,negated_conjecture,
~ ( c_Type_Otyping @ v_ea____ @ v_s____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_Ta____ ) @ v_U____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(299,plain,
$false = $false,
inference(unfold_def,[status(thm)],[297]) ).
thf(300,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(301,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(302,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(303,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(304,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(305,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(306,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(307,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(308,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(309,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(310,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(311,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(312,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(313,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(314,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(315,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(316,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(317,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(318,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(319,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(320,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(321,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(322,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(323,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(324,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(325,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(326,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)],[27]) ).
thf(327,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)],[28]) ).
thf(328,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(329,plain,
( ( ! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(330,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(331,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(332,plain,
( ( ! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(333,plain,
( ( c_Type_Otyping @ v_ea____ @ v_s____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_Ta____ ) @ v_U____ ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(334,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(335,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(336,plain,
( ( c_Type_Otyping @ v_ea____ @ v_ta____ @ v_Ta____ )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(337,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(338,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(339,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s____ ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(340,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(341,plain,
( ( ! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(342,plain,
( ( ! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(343,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)],[44]) ).
thf(344,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)],[45]) ).
thf(345,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(346,plain,
( ( ! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(347,plain,
( ( ! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(348,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(349,plain,
( ( ! [V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_U )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(350,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)],[51]) ).
thf(351,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(352,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(353,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(354,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(355,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(356,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(357,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( 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)],[58]) ).
thf(358,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(359,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(360,plain,
( ( ! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Type_Otype_OAtom @ V_nat ) @ tc_Type_Otype )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(361,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(362,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)],[63]) ).
thf(363,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)],[64]) ).
thf(364,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)],[65]) ).
thf(365,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)],[66]) ).
thf(366,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)],[67]) ).
thf(367,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)],[68]) ).
thf(368,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)],[69]) ).
thf(369,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(370,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 ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(371,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)],[72]) ).
thf(372,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(373,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)],[74]) ).
thf(374,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)],[75]) ).
thf(375,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)],[76]) ).
thf(376,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)],[77]) ).
thf(377,plain,
( ( ! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(378,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 @ ( 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)],[79]) ).
thf(379,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)],[80]) ).
thf(380,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,T_a: $i,V_T: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a )
= ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a ) @ ( c_Suc @ V_i ) @ V_U @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(381,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(382,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(383,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(384,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)],[85]) ).
thf(385,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( 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 ) )
| ~ ( 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)],[86]) ).
thf(386,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)],[87]) ).
thf(387,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)],[88]) ).
thf(388,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ta____ ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(389,plain,
( ( ! [V_e: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(390,plain,
( ( ! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(391,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(392,plain,
( ( ! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(393,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)],[94]) ).
thf(394,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)],[95]) ).
thf(395,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)],[96]) ).
thf(396,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)],[97]) ).
thf(397,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(398,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(399,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)],[100]) ).
thf(400,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)],[101]) ).
thf(401,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)],[102]) ).
thf(402,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)],[103]) ).
thf(403,plain,
( ( ! [V_nat: $i] :
( ( c_Type_Otype_Otype__size @ ( c_Type_Otype_OAtom @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(404,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_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)],[105]) ).
thf(405,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)],[106]) ).
thf(406,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(407,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)],[108]) ).
thf(408,plain,
( ( ! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(409,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)],[110]) ).
thf(410,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(411,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)],[112]) ).
thf(412,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)],[113]) ).
thf(413,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(414,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)],[115]) ).
thf(415,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(416,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)],[117]) ).
thf(417,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)],[118]) ).
thf(418,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)],[119]) ).
thf(419,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(420,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)],[121]) ).
thf(421,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)],[122]) ).
thf(422,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)],[123]) ).
thf(423,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)],[124]) ).
thf(424,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)],[125]) ).
thf(425,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)],[126]) ).
thf(426,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)],[127]) ).
thf(427,plain,
( ( ! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(428,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 @ ( 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)],[129]) ).
thf(429,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(430,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( 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)],[131]) ).
thf(431,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)],[132]) ).
thf(432,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)],[133]) ).
thf(433,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)],[134]) ).
thf(434,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(435,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(436,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(437,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(438,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( 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)],[139]) ).
thf(439,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)],[140]) ).
thf(440,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)],[141]) ).
thf(441,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 ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( 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)],[142]) ).
thf(442,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( 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)],[143]) ).
thf(443,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)],[144]) ).
thf(444,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)],[145]) ).
thf(445,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)],[146]) ).
thf(446,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)],[147]) ).
thf(447,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)],[148]) ).
thf(448,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)],[149]) ).
thf(449,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)],[150]) ).
thf(450,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(451,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(452,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)],[153]) ).
thf(453,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(454,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)],[155]) ).
thf(455,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(456,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(457,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)],[158]) ).
thf(458,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 ) )
| ~ ( 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 )
| ~ ( 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)],[159]) ).
thf(459,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(460,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(461,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(462,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)],[163]) ).
thf(463,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 ) )
| ~ ( 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)],[164]) ).
thf(464,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(465,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)],[166]) ).
thf(466,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)],[167]) ).
thf(467,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)],[168]) ).
thf(468,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)],[169]) ).
thf(469,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)],[170]) ).
thf(470,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(471,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)],[172]) ).
thf(472,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)],[173]) ).
thf(473,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)],[174]) ).
thf(474,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)],[175]) ).
thf(475,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)],[176]) ).
thf(476,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)],[177]) ).
thf(477,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(478,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(479,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(480,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(481,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(482,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(483,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(484,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(485,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)],[186]) ).
thf(486,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(487,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(488,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(489,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)],[190]) ).
thf(490,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(491,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(492,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(493,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(494,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(495,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(496,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(497,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(498,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(499,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(500,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)],[201]) ).
thf(501,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(502,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)],[203]) ).
thf(503,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)],[204]) ).
thf(504,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)],[205]) ).
thf(505,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)],[206]) ).
thf(506,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)],[207]) ).
thf(507,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)],[208]) ).
thf(508,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)],[209]) ).
thf(509,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)],[210]) ).
thf(510,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)],[211]) ).
thf(511,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)],[212]) ).
thf(512,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)],[213]) ).
thf(513,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)],[214]) ).
thf(514,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(515,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(516,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)],[217]) ).
thf(517,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)],[218]) ).
thf(518,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)],[219]) ).
thf(519,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)],[220]) ).
thf(520,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)],[221]) ).
thf(521,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)],[222]) ).
thf(522,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)],[223]) ).
thf(523,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)],[224]) ).
thf(524,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(525,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(526,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)],[227]) ).
thf(527,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)],[228]) ).
thf(528,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(529,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)],[230]) ).
thf(530,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)],[231]) ).
thf(531,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)],[232]) ).
thf(532,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)],[233]) ).
thf(533,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(534,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)],[235]) ).
thf(535,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)],[236]) ).
thf(536,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(537,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(538,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(539,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)],[240]) ).
thf(540,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)],[241]) ).
thf(541,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(542,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(543,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)],[244]) ).
thf(544,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)],[245]) ).
thf(545,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)],[246]) ).
thf(546,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)],[247]) ).
thf(547,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)],[248]) ).
thf(548,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)],[249]) ).
thf(549,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)],[250]) ).
thf(550,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)],[251]) ).
thf(551,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)],[252]) ).
thf(552,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)],[253]) ).
thf(553,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)],[254]) ).
thf(554,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)],[255]) ).
thf(555,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)],[256]) ).
thf(556,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)],[257]) ).
thf(557,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)],[258]) ).
thf(558,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)],[259]) ).
thf(559,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(560,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(561,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)],[262]) ).
thf(562,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)],[263]) ).
thf(563,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(564,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)],[265]) ).
thf(565,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)],[266]) ).
thf(566,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)],[267]) ).
thf(567,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)],[268]) ).
thf(568,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)],[269]) ).
thf(569,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)],[270]) ).
thf(570,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)],[271]) ).
thf(571,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)],[272]) ).
thf(572,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)],[273]) ).
thf(573,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)],[274]) ).
thf(574,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)],[275]) ).
thf(575,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)],[276]) ).
thf(576,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)],[277]) ).
thf(577,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)],[278]) ).
thf(578,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)],[279]) ).
thf(579,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)],[280]) ).
thf(580,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(581,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(582,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)],[283]) ).
thf(583,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)],[284]) ).
thf(584,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)],[285]) ).
thf(585,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 ) )
| ~ ( 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 )
| ~ ( 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)],[286]) ).
thf(586,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)],[287]) ).
thf(587,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)],[288]) ).
thf(588,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)],[289]) ).
thf(589,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)],[290]) ).
thf(590,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)],[291]) ).
thf(591,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)],[292]) ).
thf(592,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)],[293]) ).
thf(593,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)],[294]) ).
thf(594,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)],[295]) ).
thf(595,plain,
( ( ~ ( c_Type_Otyping @ v_ea____ @ v_s____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_Ta____ ) @ v_U____ ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(596,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[299]) ).
thf(597,plain,
( ( ~ ( c_Type_Otyping @ v_ea____ @ v_s____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_Ta____ ) @ v_U____ ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(598,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)],[594]) ).
thf(599,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)],[593]) ).
thf(600,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)],[592]) ).
thf(601,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)],[591]) ).
thf(602,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)],[590]) ).
thf(603,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)],[589]) ).
thf(604,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)],[588]) ).
thf(605,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)],[587]) ).
thf(606,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)],[586]) ).
thf(607,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 ) )
| ~ ( 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 )
| ~ ( 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)],[585]) ).
thf(608,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)],[584]) ).
thf(609,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)],[583]) ).
thf(610,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)],[582]) ).
thf(611,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(612,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(613,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)],[579]) ).
thf(614,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)],[578]) ).
thf(615,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)],[577]) ).
thf(616,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)],[576]) ).
thf(617,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)],[575]) ).
thf(618,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)],[574]) ).
thf(619,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)],[573]) ).
thf(620,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)],[572]) ).
thf(621,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)],[571]) ).
thf(622,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)],[570]) ).
thf(623,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)],[569]) ).
thf(624,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)],[568]) ).
thf(625,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)],[567]) ).
thf(626,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)],[566]) ).
thf(627,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)],[565]) ).
thf(628,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)],[564]) ).
thf(629,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(630,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)],[562]) ).
thf(631,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)],[561]) ).
thf(632,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(633,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(634,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)],[558]) ).
thf(635,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)],[557]) ).
thf(636,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)],[556]) ).
thf(637,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)],[555]) ).
thf(638,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)],[554]) ).
thf(639,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)],[553]) ).
thf(640,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)],[552]) ).
thf(641,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)],[551]) ).
thf(642,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)],[550]) ).
thf(643,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)],[549]) ).
thf(644,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)],[548]) ).
thf(645,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)],[547]) ).
thf(646,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)],[546]) ).
thf(647,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)],[545]) ).
thf(648,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)],[544]) ).
thf(649,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)],[543]) ).
thf(650,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(651,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(652,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)],[540]) ).
thf(653,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)],[539]) ).
thf(654,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(655,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(656,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(657,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)],[535]) ).
thf(658,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)],[534]) ).
thf(659,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(660,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)],[532]) ).
thf(661,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)],[531]) ).
thf(662,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)],[530]) ).
thf(663,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)],[529]) ).
thf(664,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(665,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)],[527]) ).
thf(666,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)],[526]) ).
thf(667,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(668,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(669,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)],[523]) ).
thf(670,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)],[522]) ).
thf(671,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)],[521]) ).
thf(672,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)],[520]) ).
thf(673,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)],[519]) ).
thf(674,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)],[518]) ).
thf(675,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)],[517]) ).
thf(676,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)],[516]) ).
thf(677,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(678,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(679,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)],[513]) ).
thf(680,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)],[512]) ).
thf(681,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)],[511]) ).
thf(682,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)],[510]) ).
thf(683,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)],[509]) ).
thf(684,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)],[508]) ).
thf(685,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)],[507]) ).
thf(686,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)],[506]) ).
thf(687,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)],[505]) ).
thf(688,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)],[504]) ).
thf(689,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)],[503]) ).
thf(690,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(691,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(692,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)],[500]) ).
thf(693,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(694,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(695,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(696,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(697,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(698,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(699,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(700,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(701,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(702,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(703,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)],[489]) ).
thf(704,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(705,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(706,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(707,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)],[485]) ).
thf(708,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(709,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(710,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(711,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(712,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(713,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(714,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(715,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(716,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)],[476]) ).
thf(717,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)],[475]) ).
thf(718,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)],[474]) ).
thf(719,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)],[473]) ).
thf(720,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)],[472]) ).
thf(721,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)],[471]) ).
thf(722,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(723,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)],[469]) ).
thf(724,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)],[468]) ).
thf(725,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)],[467]) ).
thf(726,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)],[466]) ).
thf(727,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)],[465]) ).
thf(728,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(729,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 ) )
| ~ ( 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)],[463]) ).
thf(730,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)],[462]) ).
thf(731,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(732,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(733,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(734,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 ) )
| ~ ( 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 )
| ~ ( 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)],[458]) ).
thf(735,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)],[457]) ).
thf(736,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(737,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(738,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)],[454]) ).
thf(739,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(740,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)],[452]) ).
thf(741,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(742,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(743,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)],[449]) ).
thf(744,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)],[448]) ).
thf(745,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)],[447]) ).
thf(746,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)],[446]) ).
thf(747,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)],[445]) ).
thf(748,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)],[444]) ).
thf(749,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(750,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( 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)],[442]) ).
thf(751,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 ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( 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)],[441]) ).
thf(752,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)],[440]) ).
thf(753,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)],[439]) ).
thf(754,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 ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(755,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(756,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(757,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(758,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(759,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)],[433]) ).
thf(760,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)],[432]) ).
thf(761,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)],[431]) ).
thf(762,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(763,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(764,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 @ ( 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)],[428]) ).
thf(765,plain,
( ( ! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(766,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)],[426]) ).
thf(767,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)],[425]) ).
thf(768,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)],[424]) ).
thf(769,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)],[423]) ).
thf(770,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)],[422]) ).
thf(771,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)],[421]) ).
thf(772,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)],[420]) ).
thf(773,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(774,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)],[418]) ).
thf(775,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)],[417]) ).
thf(776,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)],[416]) ).
thf(777,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(778,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)],[414]) ).
thf(779,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(780,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)],[412]) ).
thf(781,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)],[411]) ).
thf(782,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(783,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)],[409]) ).
thf(784,plain,
( ( ! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(785,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)],[407]) ).
thf(786,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(787,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)],[405]) ).
thf(788,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_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)],[404]) ).
thf(789,plain,
( ( ! [V_nat: $i] :
( ( c_Type_Otype_Otype__size @ ( c_Type_Otype_OAtom @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(790,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)],[402]) ).
thf(791,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)],[401]) ).
thf(792,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)],[400]) ).
thf(793,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)],[399]) ).
thf(794,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(795,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(796,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)],[396]) ).
thf(797,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)],[395]) ).
thf(798,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)],[394]) ).
thf(799,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)],[393]) ).
thf(800,plain,
( ( ! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(801,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(802,plain,
( ( ! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(803,plain,
( ( ! [V_e: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(804,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ta____ ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(805,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)],[387]) ).
thf(806,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)],[386]) ).
thf(807,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,V_ts: $i] :
( ( 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 ) )
| ~ ( 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)],[385]) ).
thf(808,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)],[384]) ).
thf(809,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(810,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(811,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(812,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,T_a: $i,V_T: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a )
= ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a ) @ ( c_Suc @ V_i ) @ V_U @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(813,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)],[379]) ).
thf(814,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 @ ( 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)],[378]) ).
thf(815,plain,
( ( ! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(816,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)],[376]) ).
thf(817,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)],[375]) ).
thf(818,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)],[374]) ).
thf(819,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)],[373]) ).
thf(820,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(821,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)],[371]) ).
thf(822,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 ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(823,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(824,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)],[368]) ).
thf(825,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)],[367]) ).
thf(826,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)],[366]) ).
thf(827,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)],[365]) ).
thf(828,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)],[364]) ).
thf(829,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)],[363]) ).
thf(830,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)],[362]) ).
thf(831,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(832,plain,
( ( ! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Type_Otype_OAtom @ V_nat ) @ tc_Type_Otype )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(833,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(834,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(835,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( 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)],[357]) ).
thf(836,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)],[356]) ).
thf(837,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)],[355]) ).
thf(838,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)],[354]) ).
thf(839,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)],[353]) ).
thf(840,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)],[352]) ).
thf(841,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)],[351]) ).
thf(842,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)],[350]) ).
thf(843,plain,
( ( ! [V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_U )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(844,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(845,plain,
( ( ! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(846,plain,
( ( ! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(847,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(848,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)],[344]) ).
thf(849,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)],[343]) ).
thf(850,plain,
( ( ! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(851,plain,
( ( ! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(852,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(853,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s____ ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(854,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(855,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(856,plain,
( ( c_Type_Otyping @ v_ea____ @ v_ta____ @ v_Ta____ )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(857,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(858,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(859,plain,
( ( c_Type_Otyping @ v_ea____ @ v_s____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_Ta____ ) @ v_U____ ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(860,plain,
( ( ! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(861,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(862,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(863,plain,
( ( ! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(864,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(865,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)],[327]) ).
thf(866,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)],[326]) ).
thf(867,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(868,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(869,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(870,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(871,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(872,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(873,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(874,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(875,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(876,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(877,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(878,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(879,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(880,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(881,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(882,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(883,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(884,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(885,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(886,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(887,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(888,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(889,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(890,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(891,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(892,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)],[300]) ).
thf(893,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[596]) ).
thf(894,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)],[771]) ).
thf(895,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)],[770]) ).
thf(896,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)],[679]) ).
thf(897,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)],[601]) ).
thf(898,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)],[836]) ).
thf(899,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)],[848]) ).
thf(900,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)],[674]) ).
thf(901,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)],[825]) ).
thf(902,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)],[819]) ).
thf(903,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)],[606]) ).
thf(904,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)],[676]) ).
thf(905,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[850]) ).
thf(906,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)],[602]) ).
thf(907,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)],[608]) ).
thf(908,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)],[818]) ).
thf(909,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[737]) ).
thf(910,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX2 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(911,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)],[745]) ).
thf(912,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX2 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(913,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(914,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[801]) ).
thf(915,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)],[675]) ).
thf(916,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_Suc @ SX2 ) @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX3 @ ( c_Suc @ SX2 ) @ SX0 ) )
| ( SX1 = SX3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX3 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(917,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)],[798]) ).
thf(918,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)],[626]) ).
thf(919,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)],[703]) ).
thf(920,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)],[785]) ).
thf(921,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[841]) ).
thf(922,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 )
!= ( c_Type_Otype_OAtom @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[845]) ).
thf(923,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)],[816]) ).
thf(924,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)],[837]) ).
thf(925,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)],[600]) ).
thf(926,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[813]) ).
thf(927,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)],[720]) ).
thf(928,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)],[628]) ).
thf(929,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)],[604]) ).
thf(930,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)],[603]) ).
thf(931,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[742]) ).
thf(932,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)],[680]) ).
thf(933,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)],[609]) ).
thf(934,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)],[719]) ).
thf(935,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[839]) ).
thf(936,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)],[828]) ).
thf(937,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)],[849]) ).
thf(938,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)],[840]) ).
thf(939,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(940,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[817]) ).
thf(941,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[748]) ).
thf(942,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[741]) ).
thf(943,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)],[838]) ).
thf(944,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[733]) ).
thf(945,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Type_Otype_OAtom @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[863]) ).
thf(946,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[749]) ).
thf(947,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[851]) ).
thf(948,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)],[752]) ).
thf(949,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)],[681]) ).
thf(950,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)],[827]) ).
thf(951,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)],[685]) ).
thf(952,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)],[824]) ).
thf(953,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Type_Otype_OAtom @ SX0 )
!= ( c_Type_Otype_OAtom @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[810]) ).
thf(954,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)],[689]) ).
thf(955,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)],[605]) ).
thf(956,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)],[829]) ).
thf(957,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(958,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)],[686]) ).
thf(959,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)],[627]) ).
thf(960,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)],[634]) ).
thf(961,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)],[776]) ).
thf(962,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)],[781]) ).
thf(963,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[756]) ).
thf(964,plain,
( ( c_Type_Otyping @ v_ea____ @ v_s____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_Ta____ ) @ v_U____ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(965,plain,
! [SV1: $i] :
( ( ! [SY777: $i,SY778: $i,SY779: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV1 @ SY777 ) @ SY778 ) @ SY779 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV1 @ SY777 @ SY777 ) @ SY777 ) @ SY779 ) @ SY778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(966,plain,
! [SV2: $i] :
( ( ! [SY780: $i,SY781: $i,SY782: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV2 @ SY780 @ SY780 ) @ SY780 ) @ SY781 ) @ SY782 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV2 @ SY780 ) @ SY782 ) @ SY781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(967,plain,
! [SV3: $i] :
( ( ! [SY783: $i,SY784: $i,SY785: $i,SY786: $i,SY787: $i,SY788: $i] :
( ( c_Type_Otypings @ SV3 @ SY783 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY784 @ SY785 @ SV3 @ SY783 ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY786 ) @ SY787 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY785 )
| ~ ( c_Type_Otypings @ SV3 @ SY787 @ SY788 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY786 ) @ SY787 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY783 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(968,plain,
! [SV4: $i] :
( ( ! [SY789: $i,SY790: $i,SY791: $i,SY792: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SY789 ) @ SY790 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SY791 ) @ SY792 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SY789 ) @ SY791 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SY790 ) @ SY792 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(969,plain,
! [SV5: $i] :
( ( ! [SY793: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV5 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY793 @ SV5 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(970,plain,
! [SV6: $i] :
( ( ! [SY794: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV6 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY794 @ SV6 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(971,plain,
! [SV7: $i] :
( ( ! [SY795: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) ) @ SY795 )
= SY795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(972,plain,
! [SV8: $i] :
( ( ! [SY796: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV8 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) ) @ SY796 )
= SY796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(973,plain,
! [SV9: $i] :
( ( SV9
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(974,plain,
! [SV10: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV10 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(975,plain,
! [SV11: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV11 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(976,plain,
! [SV12: $i] :
( ( ! [SY797: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV12 )
| ~ ( class_Int_Onumber__ring @ SV12 )
| ( SY797
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV12 ) @ SY797 ) @ ( c_HOL_Ozero__class_Ozero @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(977,plain,
! [SV13: $i] :
( ( ! [SY798: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV13 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV13 ) @ SY798 ) @ ( c_HOL_Ozero__class_Ozero @ SV13 ) )
= SY798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(978,plain,
! [SV14: $i] :
( ( ! [SY799: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV14 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) ) @ SY799 )
= SY799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(979,plain,
! [SV15: $i] :
( ( ! [SY800: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV15 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SY800 ) @ ( c_HOL_Ozero__class_Ozero @ SV15 ) )
= SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(980,plain,
! [SV16: $i] :
( ( ! [SY801: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV16 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SY801 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) )
= SY801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(981,plain,
! [SV17: $i] :
( ( ! [SY802: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV17 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) ) @ SY802 )
= SY802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(982,plain,
! [SV18: $i] :
( ( ! [SY803: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV18 ) ) @ SY803 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV18 ) @ ( c_Suc @ SY803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(983,plain,
! [SV19: $i] :
( ( ! [SY804: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV19 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SY804 ) @ SV19 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ ( c_HOL_Oone__class_Oone @ SV19 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY804 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(984,plain,
! [SV20: $i] :
( ( ! [SY805: $i,SY806: $i,SY807: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY805 @ SY806 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SY807 @ SY806 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SY805 @ SV20 )
| ~ ( c_lessequals @ SY805 @ SY807 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(985,plain,
! [SV21: $i] :
( ( ! [SY808: $i,SY809: $i,SY810: $i] :
( ( c_List_Ofoldr @ SV21 @ ( c_List_Olist_ONil @ SY808 ) @ SY809 @ SY808 @ SY810 )
= SY809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(986,plain,
! [SV22: $i] :
( ( ! [SY811: $i,SY812: $i,SY813: $i] :
( ( c_Type_Otypings @ SV22 @ SY811 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY812 @ SV22 @ SY813 @ SY811 ) )
| ~ ( c_Type_Otyping @ SV22 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY813 @ SY811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(987,plain,
! [SV23: $i] :
( ( ! [SY814: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV23 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV23 ) @ SY814 @ SV23 )
= ( c_HOL_Oone__class_Oone @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(988,plain,
! [SV24: $i] :
( ( ! [SY815: $i,SY816: $i,SY817: $i,SY818: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SY815 ) @ SY816 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV24 @ SY817 @ SY818 ) @ SY816 ) @ SY815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(989,plain,
! [SV25: $i] :
( ( ! [SY819: $i,SY820: $i,SY821: $i,SY822: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV25 @ SY819 @ SY820 ) @ SY821 ) @ SY822 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV25 @ SY822 ) @ SY821 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(990,plain,
! [SV26: $i] :
( ( ! [SY823: $i,SY824: $i,SY825: $i,SY826: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV26 @ SY823 ) @ SY824 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV26 @ SY825 @ SY826 ) @ SY824 ) @ SY823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(991,plain,
! [SV27: $i] :
( ( ! [SY827: $i,SY828: $i,SY829: $i,SY830: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV27 @ SY827 @ SY828 ) @ SY829 ) @ SY830 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV27 @ SY830 ) @ SY829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(992,plain,
! [SV28: $i] :
( ( ! [SY831: $i,SY832: $i,SY833: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV28 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SY831 ) @ SY832 ) ) @ SY833 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SY831 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SY832 ) @ SY833 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(993,plain,
! [SV29: $i] :
( ( ! [SY834: $i,SY835: $i,SY836: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV29 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SY834 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SY835 ) @ SY836 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SY835 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SY834 ) @ SY836 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(994,plain,
! [SV30: $i] :
( ( ! [SY837: $i,SY838: $i,SY839: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SY837 ) @ SY838 ) ) @ SY839 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SY837 ) @ SY839 ) ) @ SY838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(995,plain,
! [SV31: $i] :
( ( ! [SY840: $i,SY841: $i,SY842: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SY840 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SY841 ) @ SY842 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SY840 ) @ SY841 ) ) @ SY842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(996,plain,
! [SV32: $i] :
( ( ! [SY843: $i,SY844: $i,SY845: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV32 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SY843 ) @ SY844 ) ) @ SY845 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SY843 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SY844 ) @ SY845 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(997,plain,
! [SV33: $i] :
( ( ! [SY846: $i,SY847: $i,SY848: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV33 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SY846 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SY847 ) @ SY848 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SY847 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SY846 ) @ SY848 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(998,plain,
! [SV34: $i] :
( ( ! [SY849: $i,SY850: $i,SY851: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV34 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SY849 ) @ SY850 ) ) @ SY851 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SY849 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SY850 ) @ SY851 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(999,plain,
! [SV35: $i] :
( ( ! [SY852: $i,SY853: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV35 ) @ SY852 ) ) @ SY853 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY852 ) @ SY853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(1000,plain,
! [SV36: $i] :
( ( ! [SY854: $i,SY855: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV36 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY854 ) @ SY855 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY854 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV36 ) @ SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(1001,plain,
! [SV37: $i] :
( ( ! [SY856: $i,SY857: $i,SY858: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV37 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY856 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY857 ) @ SY858 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY857 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY856 ) @ SY858 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(1002,plain,
! [SV38: $i] :
( ( ! [SY859: $i,SY860: $i,SY861: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY859 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY860 ) @ SY861 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY859 ) @ SY860 ) ) @ SY861 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(1003,plain,
! [SV39: $i] :
( ( ! [SY862: $i,SY863: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SY862 ) @ SY863 ) @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SY863 @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SY862 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(1004,plain,
! [SV40: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV40 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(1005,plain,
! [SV41: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(1006,plain,
! [SV42: $i] :
( ( ! [SY864: $i,SY865: $i,SY866: $i,SY867: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SY864 ) @ SY865 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SY866 ) @ SY867 ) @ SV42 )
| ~ ( c_lessequals @ SY865 @ SY867 @ SV42 )
| ~ ( c_lessequals @ SY864 @ SY866 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(1007,plain,
! [SV43: $i] :
( ( ! [SY868: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV43 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SY868 ) @ SY868 ) @ SV43 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SY868 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(1008,plain,
! [SV44: $i] :
( ( ! [SY869: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV44 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ SY869 @ SV44 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SY869 ) @ SY869 ) @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(1009,plain,
! [SV45: $i] :
( ( ! [SY870: $i] : ( c_List_Olistsp @ SV45 @ ( c_List_Olist_ONil @ SY870 ) @ SY870 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(1010,plain,
! [SV46: $i] :
( ( ! [SY871: $i,SY872: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV46 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Power_Opower__class_Opower @ SY871 @ SY872 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ SY871 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(1011,plain,
! [SV47: $i] :
( ( ! [SY873: $i,SY874: $i,SY875: $i] :
( ( c_Wellfounded_Oaccp @ SV47 @ SY873 @ SY874 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SY874 ) @ SY873 ) @ SY875 ) )
| ~ ( c_Wellfounded_Oaccp @ SV47 @ SY875 @ SY874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(1012,plain,
! [SV48: $i] :
( ( ! [SY876: $i,SY877: $i,SY878: $i] :
( ( c_Wellfounded_Oaccp @ SV48 @ SY876 @ SY877 )
| ~ ( c_Wellfounded_Oaccp @ SV48 @ SY878 @ SY877 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SY877 ) @ SY876 ) @ SY878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(1013,plain,
! [SV49: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV49 @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(1014,plain,
! [SV50: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV50 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(1015,plain,
! [SV51: $i] :
( ( ! [SY879: $i,SY880: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV51 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ ( c_Power_Opower__class_Opower @ SY879 @ SY880 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SY879 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(1016,plain,
! [SV52: $i] :
( ( ! [SY881: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV52 ) @ ( c_Suc @ SY881 ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV52 ) @ SY881 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(1017,plain,
! [SV53: $i] :
( ( ! [SY882: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV53 ) ) @ SY882 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV53 ) @ SY882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(1018,plain,
! [SV54: $i] :
( ( ! [SY883: $i,SY884: $i,SY885: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
| ( c_lessequals @ SY883 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY884 ) @ SY885 ) @ SV54 )
| ~ ( c_lessequals @ SY883 @ SY885 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SY884 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(1019,plain,
! [SV55: $i] :
( ( ! [SY886: $i,SY887: $i,SY888: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
| ( c_lessequals @ SY886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SY887 ) @ SY888 ) @ SV55 )
| ~ ( c_lessequals @ SY886 @ SY887 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SY888 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(1020,plain,
! [SV56: $i] :
( ( ! [SY889: $i,SY890: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SY889 ) @ SY890 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SY890 ) @ SY889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(1021,plain,
! [SV57: $i] :
( ( ! [SY891: $i,SY892: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV57 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SY891 ) @ SY892 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SY892 ) @ SY891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(1022,plain,
! [SV58: $i] :
( ( ! [SY893: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SY893 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY893 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(1023,plain,
! [SV59: $i] :
( ( ! [SY894: $i,SY895: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY894 ) @ SY895 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY895 ) @ SY894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(1024,plain,
! [SV60: $i] :
( ( ! [SY896: $i,SY897: $i,SY898: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV60 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY896 ) @ SY897 ) @ SY898 @ SV60 @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY896 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY897 @ SY898 @ SV60 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(1025,plain,
! [SV61: $i] :
( ( ! [SY899: $i,SY900: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV61 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY899 @ SY900 @ SV61 @ SV61 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY900 @ SY899 @ SV61 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(1026,plain,
! [SV62: $i] :
( ( ! [SY901: $i,SY902: $i] :
~ ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Olist_ONil @ SY901 ) @ SY902 @ SY901 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(1027,plain,
! [SV63: $i] :
( ( ! [SY903: $i,SY904: $i] :
~ ( c_ListOrder_Ostep1 @ SV63 @ SY903 @ ( c_List_Olist_ONil @ SY904 ) @ SY904 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(1028,plain,
! [SV64: $i] :
( ( ! [SY905: $i,SY906: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV64 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SY905 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SY906 @ SV64 @ SV64 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SY905 @ SY906 @ SV64 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(1029,plain,
! [SV65: $i] :
( ( ! [SY907: $i,SY908: $i,SY909: $i] :
( ( c_List_Ofoldl @ SV65 @ SY907 @ ( c_List_Olist_ONil @ SY908 ) @ SY909 @ SY908 )
= SY907 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(1030,plain,
! [SV66: $i] :
( ( ( c_Predicate_Oconversep @ ( c_fequal @ SV66 ) @ SV66 @ SV66 )
= ( c_fequal @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(1031,plain,
! [SV67: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV67 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ ( c_HOL_Oone__class_Oone @ SV67 ) @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(1032,plain,
! [SV68: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV68 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(1033,plain,
! [SV69: $i] :
( ( ! [SY910: $i,SY911: $i] :
( ~ ( class_Orderings_Oorder @ SV69 )
| ( SY910 = SY911 )
| ~ ( c_lessequals @ SY911 @ SY910 @ SV69 )
| ~ ( c_lessequals @ SY910 @ SY911 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(1034,plain,
! [SV70: $i] :
( ( ! [SY912: $i,SY913: $i] :
( ~ ( class_Orderings_Oorder @ SV70 )
| ( SY912 = SY913 )
| ~ ( c_lessequals @ SY913 @ SY912 @ SV70 )
| ~ ( c_lessequals @ SY912 @ SY913 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(1035,plain,
! [SV71: $i] :
( ( ! [SY914: $i,SY915: $i] :
( ~ ( class_Orderings_Oorder @ SV71 )
| ( SY914 = SY915 )
| ~ ( c_lessequals @ SY914 @ SY915 @ SV71 )
| ~ ( c_lessequals @ SY915 @ SY914 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(1036,plain,
! [SV72: $i] :
( ( ! [SY916: $i,SY917: $i,SY918: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV72 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SY916 ) @ SY917 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SY918 ) @ SY917 ) @ SV72 )
| ~ ( c_lessequals @ SY916 @ SY918 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(1037,plain,
! [SV73: $i] :
( ( ! [SY919: $i,SY920: $i,SY921: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV73 )
| ( c_lessequals @ SY919 @ SY920 @ SV73 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY919 ) @ SY921 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY920 ) @ SY921 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(1038,plain,
! [SV74: $i] :
( ( ! [SY922: $i,SY923: $i,SY924: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV74 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SY922 ) @ SY923 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SY922 ) @ SY924 ) @ SV74 )
| ~ ( c_lessequals @ SY923 @ SY924 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(1039,plain,
! [SV75: $i] :
( ( ! [SY925: $i,SY926: $i,SY927: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV75 )
| ( c_lessequals @ SY925 @ SY926 @ SV75 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SY927 ) @ SY925 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SY927 ) @ SY926 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(1040,plain,
! [SV76: $i] :
( ( ! [SY928: $i,SY929: $i,SY930: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV76 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SY928 ) @ SY929 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SY930 ) @ SY929 ) @ SV76 )
| ~ ( c_lessequals @ SY928 @ SY930 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(1041,plain,
! [SV77: $i] :
( ( ! [SY931: $i,SY932: $i,SY933: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV77 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SY931 ) @ SY932 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SY931 ) @ SY933 ) @ SV77 )
| ~ ( c_lessequals @ SY932 @ SY933 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(1042,plain,
! [SV78: $i] :
( ( ! [SY934: $i] :
( ~ ( class_Power_Opower @ SV78 )
| ( ( c_Power_Opower__class_Opower @ SY934 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV78 )
= ( c_HOL_Oone__class_Oone @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(1043,plain,
! [SV79: $i] :
( ( ! [SY935: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV79 )
| ( ( c_Power_Opower__class_Opower @ SY935 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV79 )
= ( c_HOL_Oone__class_Oone @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(1044,plain,
! [SV80: $i] :
( ( ! [SY936: $i,SY937: $i,SY938: $i] :
( ( c_Type_Otypings @ SV80 @ SY936 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY937 @ SV80 @ SY938 @ SY936 ) )
| ~ ( c_Type_Otyping @ SV80 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY938 @ SY936 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(1045,plain,
! [SV81: $i] :
( ( ! [SY939: $i,SY940: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV81 @ SY939 @ SY940 ) @ SY940 @ SY939 )
= SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(1046,plain,
! [SV82: $i] :
( ( ! [SY941: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV82 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ SY941 ) @ SY941 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 )
| ~ ( c_lessequals @ SY941 @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(1047,plain,
! [SV83: $i] :
( ( ! [SY942: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV83 )
| ( c_lessequals @ SY942 @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ SY942 ) @ SY942 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(1048,plain,
! [SV84: $i] :
( ( ! [SY943: $i,SY944: $i,SY945: $i] :
( ~ ( class_Orderings_Oorder @ SV84 )
| ( c_lessequals @ SY943 @ SY944 @ SV84 )
| ~ ( c_lessequals @ SY943 @ SY945 @ SV84 )
| ~ ( c_lessequals @ SY945 @ SY944 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(1049,plain,
! [SV85: $i] :
( ( ! [SY946: $i,SY947: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SY946 ) @ SY947 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SY947 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SY946 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(1050,plain,
! [SV86: $i] :
( ( ! [SY948: $i,SY949: $i,SY950: $i] :
( ~ ( class_Orderings_Opreorder @ SV86 )
| ( c_lessequals @ SY948 @ SY949 @ SV86 )
| ~ ( c_lessequals @ SY950 @ SY949 @ SV86 )
| ~ ( c_lessequals @ SY948 @ SY950 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(1051,plain,
! [SV87: $i] :
( ( ! [SY951: $i] :
( ~ ( class_Orderings_Oorder @ SV87 )
| ( c_lessequals @ SY951 @ SY951 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(1052,plain,
! [SV88: $i] :
( ( ! [SY952: $i] :
( ~ ( class_Orderings_Opreorder @ SV88 )
| ( c_lessequals @ SY952 @ SY952 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(1053,plain,
! [SV89: $i] :
( ( ! [SY953: $i,SY954: $i,SY955: $i,SY956: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
| ( c_lessequals @ SY953 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SY954 ) @ SY955 ) @ SV89 )
| ~ ( c_lessequals @ SY956 @ SY955 @ SV89 )
| ~ ( c_lessequals @ SY953 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SY954 ) @ SY956 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(1054,plain,
! [SV90: $i] :
( ( ! [SY957: $i,SY958: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV90 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY957 ) @ SY958 ) @ SV90 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY957 @ SV90 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY958 @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(1055,plain,
! [SV91: $i] :
( ( ! [SY959: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV91 ) @ SY959 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV91 ) @ SY959 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(1056,plain,
! [SV92: $i] :
( ( ! [SY960: $i,SY961: $i,SY962: $i] :
( ( c_Wellfounded_Oaccp @ SV92 @ SY960 @ SY961 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY960 ) @ SY962 ) )
| ~ ( c_Wellfounded_Oaccp @ SV92 @ SY962 @ SY961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(1057,plain,
! [SV93: $i] :
( ( ! [SY963: $i,SY964: $i] :
( ~ ( class_Orderings_Olinorder @ SV93 )
| ( c_lessequals @ SY963 @ SY964 @ SV93 )
| ( c_lessequals @ SY964 @ SY963 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(1058,plain,
! [SV94: $i] :
( ( ! [SY965: $i,SY966: $i,SY967: $i] :
( ( c_Wellfounded_Oaccp @ SV94 @ SY965 @ SY966 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SY965 ) @ SY967 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SY967 @ SY966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(1059,plain,
! [SV95: $i] :
( ( ! [SY968: $i,SY969: $i,SY970: $i,SY971: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SY968 ) @ SY969 ) @ SY970 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SY971 ) @ SY970 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SY968 ) @ SY969 ) @ SY971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(1060,plain,
! [SV96: $i] :
( ( ! [SY972: $i,SY973: $i,SY974: $i,SY975: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SY972 ) @ SY973 ) @ SY974 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SY972 ) @ SY975 ) @ SY974 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SY973 ) @ SY975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(1061,plain,
! [SV97: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ SV97 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ SV97 ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(1062,plain,
! [SV98: $i] :
( ( ! [SY976: $i] :
( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV98 ) @ SY976 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ SV98 ) ) @ ( c_Lambda_OdB_OdB__size @ SY976 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(1063,plain,
! [SV99: $i] :
( ( ! [SY977: $i,SY978: $i,SY979: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV99 ) @ SY977 ) @ SY978 @ SY979 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV99 @ SY978 @ SY979 ) ) @ ( c_Lambda_Osubst @ SY977 @ SY978 @ SY979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(1064,plain,
! [SV100: $i] :
( ( ! [SY980: $i,SY981: $i,SY982: $i] :
( ( c_Type_Otypings @ SV100 @ SY980 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY981 @ SV100 @ SY982 @ SY980 ) )
| ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY982 ) @ SY980 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(1065,plain,
! [SV101: $i] :
( ( ! [SY983: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV101 ) @ SY983 ) @ 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 @ SV101 @ tc_Type_Otype ) ) @ ( c_Nat_Osize__class_Osize @ SY983 @ tc_Type_Otype ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(1066,plain,
! [SV102: $i] :
( ( ! [SY984: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV102 ) @ SY984 @ SV102 )
= SY984 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(1067,plain,
! [SV103: $i] :
( ( ! [SY985: $i,SY986: $i,SY987: $i,SY988: $i,SY989: $i,SY990: $i] :
( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY985 @ SV103 @ SY986 @ SY987 ) @ SY985 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY986 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY988 ) @ SY989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
| ~ ( c_Type_Otypings @ SY986 @ SY989 @ SY990 )
| ~ ( c_Type_Otyping @ SY986 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY988 ) @ SY989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY987 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(1068,plain,
! [SV104: $i] :
( ( ! [SY991: $i,SY992: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV104 @ SY991 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY992 @ SY991 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV104 ) @ SY992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1069,plain,
! [SV105: $i] :
( ( ! [SY993: $i] :
( ( c_Type_Otype_Otype__size @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV105 ) @ SY993 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Type_Otype_Otype__size @ SV105 ) ) @ ( c_Type_Otype_Otype__size @ SY993 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1070,plain,
! [SV106: $i] :
( ( ! [SY994: $i,SY995: $i,SY996: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV106 )
| ( c_lessequals @ SY994 @ SY995 @ SV106 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SY995 @ SV106 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY994 @ ( c_Suc @ SY996 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SY995 @ ( c_Suc @ SY996 ) @ SV106 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(1071,plain,
! [SV107: $i] :
( ( ! [SY997: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV107 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SY997 @ SV107 @ SV107 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SY997 @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(1072,plain,
! [SV108: $i] :
( ( ! [SY998: $i,SY999: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SY998 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SY999 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY998 @ SY999 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1073,plain,
! [SV109: $i] :
( ( ! [SY1000: $i,SY1001: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV109 @ SY1000 ) ) @ ( c_Lambda_Olift @ SY1001 @ SY1000 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SY1001 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1074,plain,
! [SV110: $i] :
( ( ! [SY1002: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV110 @ SY1002 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1075,plain,
! [SV111: $i] :
( ( ! [SY1003: $i,SY1004: $i,SY1005: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV111 @ SY1003 ) @ SY1004 ) @ SY1005 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV111 @ SY1004 ) @ SY1005 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(1076,plain,
! [SV112: $i] :
( ( ! [SY1006: $i,SY1007: $i,SY1008: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV112 @ SY1006 @ SY1007 ) ) @ ( c_Lambda_Osubst @ SV112 @ SY1008 @ SY1007 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1006 ) @ SY1008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1077,plain,
! [SV113: $i] :
( ( ! [SY1009: $i,SY1010: $i,SY1011: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV113 @ SY1009 @ SY1010 ) ) @ ( c_Lambda_Osubst @ SY1011 @ SY1009 @ SY1010 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV113 ) @ SY1011 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1078,plain,
! [SV114: $i] :
( ( ! [SY1012: $i,SY1013: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV114 ) @ SY1012 ) @ SY1013 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV114 @ SY1013 ) ) @ ( c_Lambda_Olift @ SY1012 @ SY1013 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1079,plain,
! [SV115: $i] :
( ( ! [SY1014: $i,SY1015: $i,SY1016: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV115 @ SY1014 @ SY1015 ) ) @ ( c_Lambda_Osubst @ SV115 @ SY1016 @ SY1015 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1014 ) @ SY1016 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1080,plain,
! [SV116: $i] :
( ( ! [SY1017: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV116 )
| ~ ( class_Power_Opower @ SV116 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Suc @ SY1017 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1081,plain,
! [SV117: $i] :
( ( ! [SY1018: $i,SY1019: $i,SY1020: $i] :
( ( c_Type_Otyping @ SV117 @ SY1018 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1019 @ SV117 @ SY1018 @ SY1020 ) @ SY1019 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV117 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1018 @ SY1020 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1082,plain,
! [SV118: $i] :
( ( ! [SY1021: $i,SY1022: $i,SY1023: $i,SY1024: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SY1021 ) @ SY1022 ) @ SY1023 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SY1021 ) @ SY1024 ) @ SY1023 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SY1021 ) @ SY1022 ) @ SY1024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1083,plain,
! [SV119: $i] :
( ( ! [SY1025: $i,SY1026: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SY1025 ) @ SY1026 ) @ SY1026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1084,plain,
! [SV120: $i] :
( ( ! [SY1027: $i,SY1028: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV120 @ SY1027 ) @ SY1028 ) @ SY1028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1085,plain,
! [SV121: $i] :
( ( ! [SY1029: $i,SY1030: $i,SY1031: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV121 @ SY1029 @ SY1030 ) ) @ ( c_Lambda_Osubst @ SY1031 @ SY1029 @ SY1030 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV121 ) @ SY1031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1086,plain,
! [SV122: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV122 )
| ~ ( class_Power_Opower @ SV122 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV122 )
= ( c_HOL_Oone__class_Oone @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(1087,plain,
! [SV123: $i] :
( ( ! [SY1032: $i,SY1033: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV123 @ SY1032 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1033 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1032 @ 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 @ SV123 ) ) @ SY1032 ) @ SY1033 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1088,plain,
! [SV124: $i] :
( ( ! [SY1034: $i,SY1035: $i,SY1036: $i,SY1037: $i] :
( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1034 @ SY1035 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1036 )
| ~ ( c_Type_Otypings @ SV124 @ SY1035 @ SY1037 )
| ~ ( c_Type_Otyping @ SV124 @ SY1034 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1037 @ SY1036 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1089,plain,
! [SV125: $i] :
( ( ( c_Lambda_OdB_OVar @ SV125 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV125 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1090,plain,
! [SV126: $i] :
( ( ! [SY1038: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV126 ) @ SY1038 ) @ 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 @ SV126 @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ SY1038 @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1091,plain,
! [SV127: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV127 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV127 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1092,plain,
! [SV128: $i] :
( ( ! [SY1039: $i,SY1040: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV128 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SY1039 @ SY1040 @ SV128 @ SV128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SY1039 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SY1040 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1093,plain,
! [SV129: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ SV129 ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV129 @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1094,plain,
! [SV130: $i] :
( ( ! [SY1041: $i,SY1042: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV130 @ SY1041 ) @ SY1042 @ SY1041 )
= SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1095,plain,
! [SV131: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV131 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1096,plain,
! [SV132: $i] :
( ( ! [SY1043: $i,SY1044: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV132 @ SY1043 ) ) @ ( c_Lambda_Olift @ SY1044 @ SY1043 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV132 ) @ SY1044 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1097,plain,
! [SV133: $i] :
( ( ! [SY1045: $i,SY1046: $i,SY1047: $i] :
( ( c_Type_Otyping @ SV133 @ SY1045 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1046 @ SV133 @ SY1045 @ SY1047 ) @ SY1046 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV133 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1045 @ SY1047 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1098,plain,
! [SV134: $i] :
( ( ! [SY1048: $i,SY1049: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV134 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1048 @ SV134 @ SY1049 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1048 ) @ SV134 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1049 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1099,plain,
! [SV135: $i] :
( ( ! [SY1050: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SY1050 ) @ SY1050 )
= ( c_Transitive__Closure_Ortranclp @ SV135 @ SY1050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1100,plain,
! [SV136: $i] :
( ( ! [SY1051: $i,SY1052: $i,SY1053: $i] :
( ( c_Type_Otype_Otype__case @ SV136 @ SY1051 @ ( c_Type_Otype_OAtom @ SY1052 ) @ SY1053 )
= ( hAPP @ SV136 @ SY1052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1101,plain,
! [SV137: $i] :
( ( ! [SY1054: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV137 ) ) @ ( c_Lambda_OdB_OAbs @ SY1054 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV137 ) @ SY1054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1102,plain,
! [SV138: $i] :
( ( ! [SY1055: $i] :
( ( SV138
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SY1055 @ SV138 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SY1055 ) ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1103,plain,
! [SV139: $i] :
( ( ! [SY1056: $i,SY1057: $i,SY1058: $i,SY1059: $i,SY1060: $i] :
( ~ ( c_Type_Otyping @ SV139 @ SY1056 @ SY1057 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SY1058 @ SY1057 @ tc_Type_Otype ) @ SY1059 @ SY1060 )
| ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SY1059 @ SY1056 @ SY1058 ) @ SY1060 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1104,plain,
! [SV140: $i] :
( ( ! [SY1061: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV140 ) @ ( c_Lambda_OdB_OVar @ SY1061 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1105,plain,
! [SV141: $i] :
( ( ! [SY1062: $i,SY1063: $i,SY1064: $i] :
( ( c_Type_Otyping @ SV141 @ SY1062 @ SY1063 )
| ~ ( c_Type_Otyping @ SV141 @ SY1064 @ SY1063 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1064 ) @ SY1062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1106,plain,
! [SV142: $i] :
( ( ( c_Type_Otype_Otype__size @ ( c_Type_Otype_OAtom @ SV142 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1107,plain,
! [SV143: $i] :
( ( ! [SY1065: $i,SY1066: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV143 ) @ SY1065 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1066 ) @ SY1065 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV143 ) @ SY1066 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1108,plain,
! [SV144: $i] :
( ( ! [SY1067: $i,SY1068: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SY1067 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SY1068 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1067 ) @ SY1068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1109,plain,
! [SV145: $i] :
( ( ! [SY1069: $i,SY1070: $i,SY1071: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV145 ) @ SY1069 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1070 ) @ SY1071 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1069 ) @ SY1071 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV145 ) @ SY1070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1110,plain,
! [SV146: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV146 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1111,plain,
! [SV147: $i] :
( ( ! [SY1072: $i,SY1073: $i,SY1074: $i] :
( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Type_Otype_Otype__case @ SY1072 @ SY1073 @ ( c_Type_Otype_OAtom @ SY1074 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SY1072 @ SY1074 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1112,plain,
! [SV148: $i] :
( ( ! [SY1075: $i,SY1076: $i,SY1077: $i] :
( ~ ( hBOOL @ ( hAPP @ SV148 @ ( c_Type_Otype_Otype__case @ SY1075 @ SY1076 @ ( c_Type_Otype_OAtom @ SY1077 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV148 @ ( hAPP @ SY1075 @ SY1077 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1113,plain,
! [SV149: $i] :
( ( ! [SY1078: $i,SY1079: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV149 ) @ SY1078 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1079 ) @ SY1078 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV149 ) @ SY1079 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1114,plain,
! [SV150: $i] :
( ( ! [SY1080: $i,SY1081: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SY1080 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SY1081 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1080 ) @ SY1081 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1115,plain,
! [SV151: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV151 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV151 )
= ( c_HOL_Ozero__class_Ozero @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1116,plain,
! [SV152: $i] :
( ( ! [SY1082: $i] :
( ( hBOOL @ ( hAPP @ SV152 @ SY1082 ) )
| ~ ( hBOOL @ ( hAPP @ SV152 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1117,plain,
! [SV153: $i] :
( ( ! [SY1083: $i,SY1084: $i,SY1085: $i] :
( ( c_Type_Otyping @ SV153 @ SY1083 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1084 @ SV153 @ SY1085 @ SY1083 ) )
| ~ ( c_Type_Otyping @ SV153 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1085 ) @ SY1083 ) @ SY1084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1118,plain,
! [SV154: $i] :
( ( ! [SY1086: $i,SY1087: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV154 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SY1086 @ SV154 @ SY1087 ) @ tc_Type_Otype ) @ SY1087 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SY1086 @ SV154 @ SY1087 ) )
| ~ ( c_Type_Otyping @ SV154 @ ( c_Lambda_OdB_OAbs @ SY1087 ) @ SY1086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1119,plain,
! [SV155: $i] :
( ( ! [SY1088: $i,SY1089: $i] :
( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1088 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1088 @ SY1089 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1088 ) @ SY1089 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1120,plain,
! [SV156: $i] :
( ( ! [SY1090: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV156 ) ) @ ( c_Lambda_OdB_OAbs @ SY1090 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV156 ) @ SY1090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1121,plain,
! [SV157: $i] :
( ( ! [SY1091: $i,SY1092: $i,SY1093: $i] :
( ( c_Type_Otyping @ SV157 @ ( c_Lambda_OdB_OVar @ SY1091 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1092 @ SV157 @ SY1091 @ SY1093 ) @ SY1092 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV157 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1091 ) @ SY1093 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1122,plain,
! [SV158: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ SV158 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1123,plain,
! [SV159: $i] :
( ( ! [SY1094: $i,SY1095: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV159 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV159 @ SY1094 ) @ tc_Type_Otype ) @ SY1094 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV159 @ SY1094 ) )
| ~ ( c_Type_Otyping @ SV159 @ ( c_Lambda_OdB_OAbs @ SY1094 ) @ SY1095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1124,plain,
! [SV160: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1125,plain,
! [SV161: $i] :
( ( ! [SY1096: $i,SY1097: $i,SY1098: $i,SY1099: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ SY1096 @ SY1097 @ SY1098 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1099 @ SY1098 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1099 @ SY1098 ) @ ( c_Suc @ SY1096 ) @ SY1097 @ SY1098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1126,plain,
! [SV162: $i] :
( ( ! [SY1100: $i,SY1101: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV162 ) ) @ SY1100 ) @ SY1101 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1100 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV162 @ SY1100 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1101 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1127,plain,
! [SV163: $i] :
( ( ! [SY1102: $i,SY1103: $i,SY1104: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV163 @ SY1102 @ SY1103 @ SY1104 ) @ SY1102 )
= SY1103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1128,plain,
! [SV164: $i] :
( ( ! [SY1105: $i,SY1106: $i,SY1107: $i] :
( ( c_Type_Otype_Otype__rec @ SV164 @ SY1105 @ ( c_Type_Otype_OAtom @ SY1106 ) @ SY1107 )
= ( hAPP @ SV164 @ SY1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1129,plain,
! [SV165: $i] :
( ( ! [SY1108: $i,SY1109: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV165 @ SY1108 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1109 @ SY1108 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV165 ) @ SY1109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1130,plain,
! [SV166: $i] :
( ( ! [SY1110: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV166 ) ) @ SY1110 ) ) @ ( c_Lambda_Osubst @ SV166 @ SY1110 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1131,plain,
! [SV167: $i] :
( ( ! [SY1111: $i,SY1112: $i,SY1113: $i,SY1114: $i] :
( ( SV167 = SY1111 )
| ~ ( c_Type_Otyping @ SY1112 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1113 ) @ SY1114 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1111 )
| ~ ( c_Type_Otyping @ SY1112 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1113 ) @ SY1114 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1132,plain,
! [SV168: $i] :
( ( ! [SY1115: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SY1115 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY1115 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1133,plain,
! [SV169: $i] :
( ( ! [SY1116: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV169 ) ) @ SY1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1134,plain,
! [SV170: $i] :
( ( ! [SY1117: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV170 ) @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV170 @ SY1117 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV170 ) ) @ SY1117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1135,plain,
! [SV171: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_Type_Otype_OAtom @ SV171 ) @ tc_Type_Otype )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1136,plain,
! [SV172: $i] :
( ( ! [SY1118: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV172 )
| ~ ( class_Power_Opower @ SV172 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SY1118 @ SV172 )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
| ( SY1118
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1137,plain,
! [SV173: $i] :
( ( ! [SY1119: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV173 )
| ~ ( class_Power_Opower @ SV173 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SY1119 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SY1119
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1138,plain,
! [SV174: $i] :
( ( ! [SY1120: $i,SY1121: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV174 @ ( c_Lambda_OdB_OVar @ SY1120 ) @ SY1121 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1139,plain,
! [SV175: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ SV175 ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1140,plain,
! [SV176: $i] :
( ( ! [SY1122: $i,SY1123: $i,SY1124: $i,SY1125: $i,SY1126: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SY1122 @ SY1123 ) ) )
| ~ ( c_Type_Otyping @ SY1124 @ SY1122 @ SY1125 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1122 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1124 @ SY1123 @ SY1125 @ tc_Type_Otype ) @ SV176 @ SY1126 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1141,plain,
! [SV177: $i] :
( ( ! [SY1127: $i,SY1128: $i,SY1129: $i,SY1130: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ SY1127 @ SY1128 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1129 @ SY1127 ) @ SY1130 )
| ~ ( c_Type_Otyping @ SV177 @ SY1129 @ SY1130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1142,plain,
! [SV178: $i] :
( ( ! [SY1131: $i,SY1132: $i] :
( ( SV178
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV178 @ SY1131 @ SY1132 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV178 @ SY1131 @ SY1132 ) ) )
| ~ ( c_Type_Otyping @ SY1131 @ ( c_Lambda_OdB_OAbs @ SY1132 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1143,plain,
! [SV179: $i] :
( ( ! [SY1133: $i,SY1134: $i,SY1135: $i] :
( ( c_Type_Otyping @ SV179 @ SY1133 @ SY1134 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1135 ) @ SY1133 ) )
| ~ ( c_Type_Otyping @ SV179 @ SY1135 @ SY1134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1144,plain,
! [SV180: $i] :
( ( ! [SY1136: $i,SY1137: $i,SY1138: $i,SY1139: $i] :
( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1136 ) @ SY1137 ) @ SY1138 )
| ~ ( c_Type_Otyping @ SV180 @ SY1137 @ SY1139 )
| ~ ( c_Type_Otyping @ SV180 @ SY1136 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1139 ) @ SY1138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1145,plain,
! [SV181: $i] :
( ( ! [SY1140: $i,SY1141: $i,SY1142: $i] :
( ( c_Type_Otyping @ SV181 @ ( c_Lambda_OdB_OAbs @ SY1140 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1141 ) @ SY1142 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV181 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1141 @ tc_Type_Otype ) @ SY1140 @ SY1142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1146,plain,
! [SV182: $i] :
( ( ! [SY1143: $i,SY1144: $i] :
( ( ( hAPP @ SV182 @ SY1143 )
= SY1144 )
| ~ ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SY1143 ) @ SY1144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1147,plain,
! [SV183: $i] :
( ( ! [SY1145: $i,SY1146: $i,SY1147: $i,SY1148: $i] :
( ( c_Type_Otype_Otype__rec @ SV183 @ SY1145 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1146 ) @ SY1147 ) @ SY1148 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SY1145 @ SY1146 ) @ SY1147 ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SY1145 @ SY1146 @ SY1148 ) ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SY1145 @ SY1147 @ SY1148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1148,plain,
! [SV184: $i] :
( ( ! [SY1149: $i,SY1150: $i,SY1151: $i,SY1152: $i] :
( ( c_Type_Otype_Otype__case @ SV184 @ SY1149 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1150 ) @ SY1151 ) @ SY1152 )
= ( hAPP @ ( hAPP @ SY1149 @ SY1150 ) @ SY1151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1149,plain,
! [SV185: $i] :
( ( ! [SY1153: $i] : ( c_Type_Otyping @ SV185 @ ( c_Lambda_OdB_OVar @ SY1153 ) @ ( hAPP @ SV185 @ SY1153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1150,plain,
! [SV186: $i] :
( ( ! [SY1154: $i,SY1155: $i,SY1156: $i,SY1157: $i] :
( ~ ( hBOOL @ ( hAPP @ SV186 @ ( c_Type_Otype_Otype__case @ SY1154 @ SY1155 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1156 ) @ SY1157 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV186 @ ( hAPP @ ( hAPP @ SY1155 @ SY1156 ) @ SY1157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1151,plain,
! [SV187: $i] :
( ( ! [SY1158: $i,SY1159: $i,SY1160: $i,SY1161: $i] :
( ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_Type_Otype_Otype__case @ SY1158 @ SY1159 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1160 ) @ SY1161 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV187 @ ( hAPP @ ( hAPP @ SY1159 @ SY1160 ) @ SY1161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1152,plain,
! [SV188: $i] :
( ( ! [SY1162: $i,SY1163: $i,SY1164: $i] :
( ( c_Type_Otyping @ SV188 @ SY1162 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1163 @ SV188 @ SY1162 @ SY1164 ) ) @ SY1163 ) )
| ~ ( c_Type_Otyping @ SV188 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1162 ) @ SY1164 ) @ SY1163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1153,plain,
! [SV189: $i] :
( ( ! [SY1165: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV189 @ SY1165 ) )
| ~ ( class_Orderings_Opreorder @ SY1165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1154,plain,
! [SV190: $i] :
( ( ! [SY1166: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV190 @ SY1166 ) )
| ~ ( class_Orderings_Oorder @ SY1166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1155,plain,
! [SV191: $i] :
( ( ! [SY1167: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV191 ) @ SY1167 ) @ SY1167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1156,plain,
! [SV192: $i] :
( ( ! [SY1168: $i,SY1169: $i] :
( ( SV192 = SY1168 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1169 ) @ SV192 ) @ SY1168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1157,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(1158,plain,
! [SV193: $i] :
( ( ! [SY1170: $i,SY1171: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV193 @ SY1170 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1171 @ SY1170 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV193 = SY1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1159,plain,
! [SV194: $i] :
( ( ! [SY1172: $i,SY1173: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV194 @ SY1172 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1173 ) )
| ( SY1172
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1160,plain,
! [SV195: $i] :
( ( ! [SY1174: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV195 ) @ SY1174 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV195
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1161,plain,
! [SV196: $i] :
( ( ! [SY1175: $i,SY1176: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV196 ) @ SY1175 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1176 ) @ SY1175 ) )
| ( SV196 = SY1176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1162,plain,
! [SV197: $i] :
( ( ! [SY1177: $i,SY1178: $i,SY1179: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV197 ) @ SY1177 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1178 ) @ SY1179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1177 = SY1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1163,plain,
! [SV198: $i] :
( ( ! [SY1180: $i,SY1181: $i,SY1182: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV198 ) @ SY1180 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1181 ) @ SY1182 ) )
| ( SV198 = SY1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1164,plain,
! [SV199: $i] :
( ( ! [SY1183: $i,SY1184: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV199 )
| ~ ( class_Int_Onumber__ring @ SV199 )
| ( SY1183
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SY1183 ) @ SY1184 ) )
| ( SY1184
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1165,plain,
! [SV200: $i] :
( ( ! [SY1185: $i,SY1186: $i,SY1187: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SY1185 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1186 ) @ SY1187 ) )
| ( SV200 = SY1186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1166,plain,
! [SV201: $i] :
( ( ! [SY1188: $i,SY1189: $i] :
( ( ( c_Lambda_OdB_OVar @ SV201 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1188 @ SY1189 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV201 )
= SY1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1167,plain,
! [SV202: $i] :
( ( ! [SY1190: $i,SY1191: $i,SY1192: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV202 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SY1190 ) @ SY1191 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SY1192 ) @ SY1191 ) )
| ( SY1190 = SY1192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1168,plain,
! [SV203: $i] :
( ( ! [SY1193: $i] :
( ( SV203
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV203 ) @ SY1193 ) )
| ( SY1193
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1169,plain,
! [SV204: $i] :
( ( ! [SY1194: $i,SY1195: $i,SY1196: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV204 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1194 ) @ SY1195 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SY1196 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SY1195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1170,plain,
! [SV205: $i] :
( ( ! [SY1197: $i,SY1198: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SY1197 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SY1198 ) )
| ( SY1197 = SY1198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1171,plain,
! [SV206: $i] :
( ( ! [SY1199: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV206 ) @ SY1199 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1199
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1199
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1172,plain,
! [SV207: $i] :
( ( ! [SY1200: $i,SY1201: $i] :
( ( c_Lambda_OdB_OVar @ SV207 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1200 ) @ SY1201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1173,plain,
! [SV208: $i] :
( ( ! [SY1202: $i,SY1203: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV208 )
| ( ( c_Power_Opower__class_Opower @ SY1202 @ SY1203 @ SV208 )
!= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
| ( SY1202
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1174,plain,
! [SV209: $i] :
( ( ! [SY1204: $i,SY1205: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SY1204 ) @ SY1205 )
!= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SY1205 @ SV209 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SY1204 @ SV209 )
| ( SY1204
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1175,plain,
! [SV210: $i] :
( ( ! [SY1206: $i,SY1207: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV210 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1206 @ SY1207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1207
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1176,plain,
! [SV211: $i] :
( ( ! [SY1208: $i,SY1209: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SY1208 ) @ SY1209 )
!= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SY1209 @ SV211 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SY1208 @ SV211 )
| ( SY1209
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1177,plain,
! [SV212: $i] :
( ( ! [SY1210: $i,SY1211: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV212 )
| ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SY1210 @ SY1211 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SY1210
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1178,plain,
! [SV213: $i] :
( ( ! [SY1212: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV213 )
| ~ ( class_Power_Opower @ SV213 )
| ( ( c_Power_Opower__class_Opower @ SY1212 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1179,plain,
! [SV214: $i] :
( ( ! [SY1213: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV214 ) @ SY1213 )
!= SV214 )
| ( SY1213
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1180,plain,
! [SV215: $i] :
( ( ! [SY1214: $i,SY1215: $i,SY1216: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV215 )
| ( ( c_Power_Opower__class_Opower @ SY1214 @ ( c_Suc @ SY1215 ) @ SV215 )
!= ( c_Power_Opower__class_Opower @ SY1216 @ ( c_Suc @ SY1215 ) @ SV215 ) )
| ( SY1214 = SY1216 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SY1216 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SY1214 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1181,plain,
! [SV216: $i] :
( ( ! [SY1217: $i,SY1218: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV216 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1217 @ SY1218 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV216 )
= SY1217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1182,plain,
! [SV217: $i] :
( ( ! [SY1219: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV217 ) @ SY1219 ) )
| ( SV217
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV217
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1183,plain,
! [SV218: $i] :
( ( ! [SY1220: $i,SY1221: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SY1220 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1221 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SY1220 )
= SY1221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1184,plain,
! [SV219: $i] :
( ( ! [SY1222: $i,SY1223: $i,SY1224: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV219 ) ) @ SY1222 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1223 ) @ SY1224 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1185,plain,
! [SV220: $i] :
( ( ! [SY1225: $i] :
( ( c_Lambda_OdB_OAbs @ SV220 )
!= ( c_Lambda_OdB_OVar @ SY1225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1186,plain,
! [SV221: $i] :
( ( ! [SY1226: $i,SY1227: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV221 ) @ SY1226 )
!= ( c_Type_Otype_OAtom @ SY1227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1187,plain,
! [SV222: $i] :
( ( ! [SY1228: $i,SY1229: $i,SY1230: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV222 ) @ SY1228 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1229 ) @ SY1230 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1188,plain,
! [SV223: $i] :
( ( ! [SY1231: $i,SY1232: $i,SY1233: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV223 ) @ SY1231 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1232 ) @ SY1233 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV223 = SY1232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1189,plain,
! [SV224: $i] :
( ( ! [SY1234: $i,SY1235: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SY1234 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SY1235 ) )
| ( SY1234 = SY1235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1190,plain,
! [SV225: $i] :
( ( ! [SY1236: $i] :
( ( c_Lambda_OdB_OVar @ SV225 )
!= ( c_Lambda_OdB_OAbs @ SY1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1191,plain,
! [SV226: $i] :
( ( ! [SY1237: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV226 ) @ SY1237 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1237
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1192,plain,
! [SV227: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV227 )
| ( ( c_HOL_Ozero__class_Ozero @ SV227 )
!= ( c_HOL_Oone__class_Oone @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1193,plain,
! [SV228: $i] :
( ( ! [SY1238: $i,SY1239: $i,SY1240: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV228 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SY1238 ) @ SY1239 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SY1238 ) @ SY1240 ) )
| ( SY1239 = SY1240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1194,plain,
! [SV229: $i] :
( ( ! [SY1241: $i,SY1242: $i,SY1243: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV229 )
| ~ ( class_Int_Onumber__ring @ SV229 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SY1241 ) @ SY1242 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SY1241 ) @ SY1243 ) )
| ( SY1242 = SY1243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1195,plain,
! [SV230: $i] :
( ( ( c_Suc @ SV230 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1196,plain,
! [SV231: $i] :
( ( ! [SY1244: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV231 ) @ SY1244 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1244
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1197,plain,
! [SV232: $i] :
( ( ! [SY1245: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV232 ) @ SY1245 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV232
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1198,plain,
! [SV233: $i] :
( ( ! [SY1246: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV233 ) @ SY1246 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1246
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV233
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1199,plain,
! [SV234: $i] :
( ( ! [SY1247: $i] :
( ( ( c_Lambda_OdB_OVar @ SV234 )
!= ( c_Lambda_OdB_OVar @ SY1247 ) )
| ( SV234 = SY1247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1200,plain,
! [SV235: $i] :
( ( ! [SY1248: $i,SY1249: $i,SY1250: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SY1248 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1249 ) @ SY1250 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV235 = SY1249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1201,plain,
! [SV236: $i] :
( ( ! [SY1251: $i,SY1252: $i,SY1253: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SY1251 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1252 ) @ SY1253 ) )
| ( SY1251 = SY1253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1202,plain,
! [SV237: $i] :
( ( ! [SY1254: $i,SY1255: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV237 ) @ SY1254 )
!= ( c_Lambda_OdB_OAbs @ SY1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1203,plain,
! [SV238: $i] :
( ( SV238
!= ( c_Suc @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1204,plain,
! [SV239: $i] :
( ( ! [SY1256: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV239 )
!= ( c_Lambda_OdB_OAbs @ SY1256 ) )
| ( SV239 = SY1256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1205,plain,
! [SV240: $i] :
( ( ! [SY1257: $i] :
( ( ( c_Suc @ SV240 )
!= ( c_Suc @ SY1257 ) )
| ( SV240 = SY1257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1206,plain,
! [SV241: $i] :
( ( ( c_Suc @ SV241 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1207,plain,
! [SV242: $i] :
( ( ! [SY1258: $i,SY1259: $i] :
( ( c_Lambda_OdB_OAbs @ SV242 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1258 ) @ SY1259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1208,plain,
! [SV243: $i] :
( ( ( c_Suc @ SV243 )
!= SV243 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1209,plain,
! [SV244: $i] :
( ( ! [SY1260: $i,SY1261: $i] :
( ( c_Type_Otype_OAtom @ SV244 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1260 ) @ SY1261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1210,plain,
! [SV245: $i] :
( ( ! [SY1262: $i] :
( ( ( c_Suc @ SV245 )
!= ( c_Suc @ SY1262 ) )
| ( SV245 = SY1262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1211,plain,
! [SV246: $i] :
( ( ! [SY1263: $i,SY1264: $i,SY1265: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV246 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1263 ) @ SY1264 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SY1265 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SY1263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1212,plain,
! [SV247: $i] :
( ( ! [SY1266: $i,SY1267: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV247 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY1266 @ SV247 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1267 @ SV247 ) )
| ( SY1266 = SY1267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1213,plain,
! [SV248: $i] :
( ( ! [SY1268: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV248 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV248 ) @ SY1268 ) @ SY1268 )
!= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
| ( SY1268
= ( c_HOL_Ozero__class_Ozero @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1214,plain,
! [SV249: $i] :
( ( ! [SY1269: $i,SY1270: $i,SY1271: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SY1269 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1270 ) @ SY1271 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1269 = SY1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1215,plain,
! [SV250: $i] :
( ( ! [SY1272: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV250 ) @ SY1272 ) )
| ( SY1272
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV250
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1216,plain,
! [SV251: $i] :
( ( ! [SY1273: $i,SY1274: $i,SY1275: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV251 ) @ SY1273 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1274 ) @ SY1275 ) )
| ( SY1273 = SY1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1217,plain,
! [SV252: $i] :
( ( ! [SY1276: $i] :
( ( ( c_Type_Otype_OAtom @ SV252 )
!= ( c_Type_Otype_OAtom @ SY1276 ) )
| ( SV252 = SY1276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1218,plain,
! [SV253: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV253 )
| ( ( c_HOL_Oone__class_Oone @ SV253 )
!= ( c_HOL_Ozero__class_Ozero @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1219,plain,
! [SV254: $i] :
( ( ! [SY1277: $i,SY1278: $i,SY1279: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV254 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SY1277 ) @ SY1278 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SY1277 ) @ SY1279 ) )
| ( SY1278 = SY1279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1220,plain,
! [SV255: $i] :
( ( ! [SY1280: $i,SY1281: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SY1280 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1281 ) )
| ( SV255
= ( c_Lambda_OdB_OAbs @ SY1281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1221,plain,
! [SV256: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1222,plain,
! [SV257: $i] :
( ( ! [SY1282: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV257 ) @ SY1282 ) )
| ( SV257
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1282
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1223,plain,
! [SV258: $i] :
( ( ! [SY1283: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV258 ) @ SY1283 ) )
| ( SY1283
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1283
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1224,plain,
! [SV259: $i] :
( ( ! [SY1284: $i,SY1285: $i,SY1286: $i,SY1287: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV259 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SY1284 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SY1285 ) @ SY1286 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SY1285 ) @ SY1287 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SY1284 ) @ SY1286 )
= SY1287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1225,plain,
! [SV260: $i] :
( ( ! [SY1288: $i,SY1289: $i] :
( ( ( c_Lambda_OdB_OVar @ SV260 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1288 @ SY1289 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1289
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1226,plain,
! [SV261: $i] :
( ( ! [SY1290: $i,SY1291: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV261 ) @ SY1290 )
!= ( c_Lambda_OdB_OVar @ SY1291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1227,plain,
! [SV262: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1228,plain,
! [SV263: $i,SV1: $i] :
( ( ! [SY1292: $i,SY1293: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV1 @ SV263 ) @ SY1292 ) @ SY1293 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV1 @ SV263 @ SV263 ) @ SV263 ) @ SY1293 ) @ SY1292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1229,plain,
! [SV264: $i,SV2: $i] :
( ( ! [SY1294: $i,SY1295: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV2 @ SV264 @ SV264 ) @ SV264 ) @ SY1294 ) @ SY1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV2 @ SV264 ) @ SY1295 ) @ SY1294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1230,plain,
! [SV265: $i,SV3: $i] :
( ( ! [SY1296: $i,SY1297: $i,SY1298: $i,SY1299: $i,SY1300: $i] :
( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1296 @ SY1297 @ SV3 @ SV265 ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1298 ) @ SY1299 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1297 )
| ~ ( c_Type_Otypings @ SV3 @ SY1299 @ SY1300 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1298 ) @ SY1299 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1231,plain,
! [SV266: $i,SV4: $i] :
( ( ! [SY1301: $i,SY1302: $i,SY1303: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SY1301 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SY1302 ) @ SY1303 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SY1302 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SY1301 ) @ SY1303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1232,plain,
! [SV267: $i,SV5: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV5 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV267 @ SV5 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1233,plain,
! [SV268: $i,SV6: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV6 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV268 @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1234,plain,
! [SV269: $i,SV7: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) ) @ SV269 )
= SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1235,plain,
! [SV270: $i,SV8: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV8 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) ) @ SV270 )
= SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1236,plain,
! [SV271: $i,SV12: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV12 )
| ~ ( class_Int_Onumber__ring @ SV12 )
| ( SV271
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV12 ) @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1237,plain,
! [SV272: $i,SV13: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV13 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV13 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV13 ) )
= SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1238,plain,
! [SV273: $i,SV14: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV14 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) ) @ SV273 )
= SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1239,plain,
! [SV274: $i,SV15: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV15 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ SV15 ) )
= SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1240,plain,
! [SV275: $i,SV16: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV16 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV275 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) )
= SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1241,plain,
! [SV276: $i,SV17: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV17 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) ) @ SV276 )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1242,plain,
! [SV277: $i,SV18: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV18 ) ) @ SV277 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV18 ) @ ( c_Suc @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1243,plain,
! [SV278: $i,SV19: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV19 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV278 ) @ SV19 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ ( c_HOL_Oone__class_Oone @ SV19 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV278 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1244,plain,
! [SV279: $i,SV20: $i] :
( ( ! [SY1304: $i,SY1305: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SY1304 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SY1305 @ SY1304 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 )
| ~ ( c_lessequals @ SV279 @ SY1305 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1245,plain,
! [SV280: $i,SV21: $i] :
( ( ! [SY1306: $i,SY1307: $i] :
( ( c_List_Ofoldr @ SV21 @ ( c_List_Olist_ONil @ SV280 ) @ SY1306 @ SV280 @ SY1307 )
= SY1306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1246,plain,
! [SV281: $i,SV22: $i] :
( ( ! [SY1308: $i,SY1309: $i] :
( ( c_Type_Otypings @ SV22 @ SV281 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1308 @ SV22 @ SY1309 @ SV281 ) )
| ~ ( c_Type_Otyping @ SV22 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1309 @ SV281 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1247,plain,
! [SV282: $i,SV23: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV23 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV23 ) @ SV282 @ SV23 )
= ( c_HOL_Oone__class_Oone @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1248,plain,
! [SV283: $i,SV24: $i] :
( ( ! [SY1310: $i,SY1311: $i,SY1312: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV283 ) @ SY1310 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV24 @ SY1311 @ SY1312 ) @ SY1310 ) @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1249,plain,
! [SV284: $i,SV25: $i] :
( ( ! [SY1313: $i,SY1314: $i,SY1315: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV25 @ SV284 @ SY1313 ) @ SY1314 ) @ SY1315 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV25 @ SY1315 ) @ SY1314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1250,plain,
! [SV285: $i,SV26: $i] :
( ( ! [SY1316: $i,SY1317: $i,SY1318: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV26 @ SV285 ) @ SY1316 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV26 @ SY1317 @ SY1318 ) @ SY1316 ) @ SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1251,plain,
! [SV286: $i,SV27: $i] :
( ( ! [SY1319: $i,SY1320: $i,SY1321: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV27 @ SV286 @ SY1319 ) @ SY1320 ) @ SY1321 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV27 @ SY1321 ) @ SY1320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1252,plain,
! [SV287: $i,SV28: $i] :
( ( ! [SY1322: $i,SY1323: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV28 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ SY1322 ) ) @ SY1323 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SY1322 ) @ SY1323 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1253,plain,
! [SV288: $i,SV29: $i] :
( ( ! [SY1324: $i,SY1325: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV29 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SY1324 ) @ SY1325 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SY1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ SY1325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1254,plain,
! [SV289: $i,SV30: $i] :
( ( ! [SY1326: $i,SY1327: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SY1326 ) ) @ SY1327 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SY1327 ) ) @ SY1326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1255,plain,
! [SV290: $i,SV31: $i] :
( ( ! [SY1328: $i,SY1329: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SY1328 ) @ SY1329 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ SY1328 ) ) @ SY1329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1256,plain,
! [SV291: $i,SV32: $i] :
( ( ! [SY1330: $i,SY1331: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV32 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ SY1330 ) ) @ SY1331 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SY1330 ) @ SY1331 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1257,plain,
! [SV292: $i,SV33: $i] :
( ( ! [SY1332: $i,SY1333: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV33 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SY1332 ) @ SY1333 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SY1332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ SY1333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1258,plain,
! [SV293: $i,SV34: $i] :
( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV34 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ SY1334 ) ) @ SY1335 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SY1334 ) @ SY1335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1259,plain,
! [SV294: $i,SV35: $i] :
( ( ! [SY1336: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV35 ) @ SV294 ) ) @ SY1336 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV294 ) @ SY1336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1260,plain,
! [SV295: $i,SV36: $i] :
( ( ! [SY1337: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV36 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV295 ) @ SY1337 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV295 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV36 ) @ SY1337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1261,plain,
! [SV296: $i,SV37: $i] :
( ( ! [SY1338: $i,SY1339: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV37 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY1338 ) @ SY1339 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY1338 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ SY1339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1262,plain,
! [SV297: $i,SV38: $i] :
( ( ! [SY1340: $i,SY1341: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SY1340 ) @ SY1341 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ SY1340 ) ) @ SY1341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1263,plain,
! [SV298: $i,SV39: $i] :
( ( ! [SY1342: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV298 ) @ SY1342 ) @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SY1342 @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV298 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1264,plain,
! [SV40: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV40 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1265,plain,
! [SV41: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV41 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1266,plain,
! [SV299: $i,SV42: $i] :
( ( ! [SY1343: $i,SY1344: $i,SY1345: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SY1343 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SY1344 ) @ SY1345 ) @ SV42 )
| ~ ( c_lessequals @ SY1343 @ SY1345 @ SV42 )
| ~ ( c_lessequals @ SV299 @ SY1344 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1267,plain,
! [SV300: $i,SV43: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV43 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV300 ) @ SV300 ) @ SV43 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV300 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1268,plain,
! [SV301: $i,SV44: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV44 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ SV301 @ SV44 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV301 ) @ SV301 ) @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1269,plain,
! [SV302: $i,SV45: $i] :
( ( c_List_Olistsp @ SV45 @ ( c_List_Olist_ONil @ SV302 ) @ SV302 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1270,plain,
! [SV303: $i,SV46: $i] :
( ( ! [SY1346: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV46 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Power_Opower__class_Opower @ SV303 @ SY1346 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ SV303 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1271,plain,
! [SV304: $i,SV47: $i] :
( ( ! [SY1347: $i,SY1348: $i] :
( ( c_Wellfounded_Oaccp @ SV47 @ SV304 @ SY1347 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SY1347 ) @ SV304 ) @ SY1348 ) )
| ~ ( c_Wellfounded_Oaccp @ SV47 @ SY1348 @ SY1347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1272,plain,
! [SV305: $i,SV48: $i] :
( ( ! [SY1349: $i,SY1350: $i] :
( ( c_Wellfounded_Oaccp @ SV48 @ SV305 @ SY1349 )
| ~ ( c_Wellfounded_Oaccp @ SV48 @ SY1350 @ SY1349 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SY1349 ) @ SV305 ) @ SY1350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1273,plain,
! [SV49: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV49 @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1274,plain,
! [SV50: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV50 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1275,plain,
! [SV306: $i,SV51: $i] :
( ( ! [SY1351: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV51 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ ( c_Power_Opower__class_Opower @ SV306 @ SY1351 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV306 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1276,plain,
! [SV307: $i,SV52: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV52 ) @ ( c_Suc @ SV307 ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV52 ) @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1277,plain,
! [SV308: $i,SV53: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV53 ) ) @ SV308 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV53 ) @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1278,plain,
! [SV309: $i,SV54: $i] :
( ( ! [SY1352: $i,SY1353: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
| ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY1352 ) @ SY1353 ) @ SV54 )
| ~ ( c_lessequals @ SV309 @ SY1353 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SY1352 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1279,plain,
! [SV310: $i,SV55: $i] :
( ( ! [SY1354: $i,SY1355: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
| ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SY1354 ) @ SY1355 ) @ SV55 )
| ~ ( c_lessequals @ SV310 @ SY1354 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SY1355 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1280,plain,
! [SV311: $i,SV56: $i] :
( ( ! [SY1356: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SY1356 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SY1356 ) @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1281,plain,
! [SV312: $i,SV57: $i] :
( ( ! [SY1357: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV57 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SY1357 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SY1357 ) @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1282,plain,
! [SV313: $i,SV58: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV58 ) @ SV313 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1283,plain,
! [SV314: $i,SV59: $i] :
( ( ! [SY1358: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SY1358 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1358 ) @ SV314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1284,plain,
! [SV315: $i,SV60: $i] :
( ( ! [SY1359: $i,SY1360: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV60 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SY1359 ) @ SY1360 @ SV60 @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1359 @ SY1360 @ SV60 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1285,plain,
! [SV316: $i,SV61: $i] :
( ( ! [SY1361: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV61 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 @ SY1361 @ SV61 @ SV61 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1361 @ SV316 @ SV61 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1286,plain,
! [SV317: $i,SV62: $i] :
( ( ! [SY1362: $i] :
~ ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Olist_ONil @ SV317 ) @ SY1362 @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1287,plain,
! [SV318: $i,SV63: $i] :
( ( ! [SY1363: $i] :
~ ( c_ListOrder_Ostep1 @ SV63 @ SV318 @ ( c_List_Olist_ONil @ SY1363 ) @ SY1363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1288,plain,
! [SV319: $i,SV64: $i] :
( ( ! [SY1364: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV64 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV319 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SY1364 @ SV64 @ SV64 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV319 @ SY1364 @ SV64 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1289,plain,
! [SV320: $i,SV65: $i] :
( ( ! [SY1365: $i,SY1366: $i] :
( ( c_List_Ofoldl @ SV65 @ SV320 @ ( c_List_Olist_ONil @ SY1365 ) @ SY1366 @ SY1365 )
= SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1290,plain,
! [SV67: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV67 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ ( c_HOL_Oone__class_Oone @ SV67 ) @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1291,plain,
! [SV68: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV68 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1292,plain,
! [SV321: $i,SV69: $i] :
( ( ! [SY1367: $i] :
( ~ ( class_Orderings_Oorder @ SV69 )
| ( SV321 = SY1367 )
| ~ ( c_lessequals @ SY1367 @ SV321 @ SV69 )
| ~ ( c_lessequals @ SV321 @ SY1367 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1293,plain,
! [SV322: $i,SV70: $i] :
( ( ! [SY1368: $i] :
( ~ ( class_Orderings_Oorder @ SV70 )
| ( SV322 = SY1368 )
| ~ ( c_lessequals @ SY1368 @ SV322 @ SV70 )
| ~ ( c_lessequals @ SV322 @ SY1368 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1294,plain,
! [SV323: $i,SV71: $i] :
( ( ! [SY1369: $i] :
( ~ ( class_Orderings_Oorder @ SV71 )
| ( SV323 = SY1369 )
| ~ ( c_lessequals @ SV323 @ SY1369 @ SV71 )
| ~ ( c_lessequals @ SY1369 @ SV323 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1295,plain,
! [SV324: $i,SV72: $i] :
( ( ! [SY1370: $i,SY1371: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV72 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SY1370 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SY1371 ) @ SY1370 ) @ SV72 )
| ~ ( c_lessequals @ SV324 @ SY1371 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1296,plain,
! [SV325: $i,SV73: $i] :
( ( ! [SY1372: $i,SY1373: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV73 )
| ( c_lessequals @ SV325 @ SY1372 @ SV73 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SY1373 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY1372 ) @ SY1373 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1297,plain,
! [SV326: $i,SV74: $i] :
( ( ! [SY1374: $i,SY1375: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV74 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SY1374 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SY1375 ) @ SV74 )
| ~ ( c_lessequals @ SY1374 @ SY1375 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1298,plain,
! [SV327: $i,SV75: $i] :
( ( ! [SY1376: $i,SY1377: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV75 )
| ( c_lessequals @ SV327 @ SY1376 @ SV75 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SY1377 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SY1377 ) @ SY1376 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1299,plain,
! [SV328: $i,SV76: $i] :
( ( ! [SY1378: $i,SY1379: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV76 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV328 ) @ SY1378 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SY1379 ) @ SY1378 ) @ SV76 )
| ~ ( c_lessequals @ SV328 @ SY1379 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1300,plain,
! [SV329: $i,SV77: $i] :
( ( ! [SY1380: $i,SY1381: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV77 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SY1380 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SY1381 ) @ SV77 )
| ~ ( c_lessequals @ SY1380 @ SY1381 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1301,plain,
! [SV330: $i,SV78: $i] :
( ( ~ ( class_Power_Opower @ SV78 )
| ( ( c_Power_Opower__class_Opower @ SV330 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV78 )
= ( c_HOL_Oone__class_Oone @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1302,plain,
! [SV331: $i,SV79: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV79 )
| ( ( c_Power_Opower__class_Opower @ SV331 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV79 )
= ( c_HOL_Oone__class_Oone @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1303,plain,
! [SV332: $i,SV80: $i] :
( ( ! [SY1382: $i,SY1383: $i] :
( ( c_Type_Otypings @ SV80 @ SV332 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1382 @ SV80 @ SY1383 @ SV332 ) )
| ~ ( c_Type_Otyping @ SV80 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1383 @ SV332 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1304,plain,
! [SV333: $i,SV81: $i] :
( ( ! [SY1384: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV81 @ SV333 @ SY1384 ) @ SY1384 @ SV333 )
= SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1305,plain,
! [SV334: $i,SV82: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV82 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ SV334 ) @ SV334 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 )
| ~ ( c_lessequals @ SV334 @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1306,plain,
! [SV335: $i,SV83: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV83 )
| ( c_lessequals @ SV335 @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ SV335 ) @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1307,plain,
! [SV336: $i,SV84: $i] :
( ( ! [SY1385: $i,SY1386: $i] :
( ~ ( class_Orderings_Oorder @ SV84 )
| ( c_lessequals @ SV336 @ SY1385 @ SV84 )
| ~ ( c_lessequals @ SV336 @ SY1386 @ SV84 )
| ~ ( c_lessequals @ SY1386 @ SY1385 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1308,plain,
! [SV337: $i,SV85: $i] :
( ( ! [SY1387: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV337 ) @ SY1387 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SY1387 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV337 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1309,plain,
! [SV338: $i,SV86: $i] :
( ( ! [SY1388: $i,SY1389: $i] :
( ~ ( class_Orderings_Opreorder @ SV86 )
| ( c_lessequals @ SV338 @ SY1388 @ SV86 )
| ~ ( c_lessequals @ SY1389 @ SY1388 @ SV86 )
| ~ ( c_lessequals @ SV338 @ SY1389 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1310,plain,
! [SV339: $i,SV87: $i] :
( ( ~ ( class_Orderings_Oorder @ SV87 )
| ( c_lessequals @ SV339 @ SV339 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1311,plain,
! [SV340: $i,SV88: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV88 )
| ( c_lessequals @ SV340 @ SV340 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1312,plain,
! [SV341: $i,SV89: $i] :
( ( ! [SY1390: $i,SY1391: $i,SY1392: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
| ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SY1390 ) @ SY1391 ) @ SV89 )
| ~ ( c_lessequals @ SY1392 @ SY1391 @ SV89 )
| ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SY1390 ) @ SY1392 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1313,plain,
! [SV342: $i,SV90: $i] :
( ( ! [SY1393: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV90 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SY1393 ) @ SV90 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV342 @ SV90 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1393 @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1314,plain,
! [SV343: $i,SV91: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV91 ) @ SV343 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV91 ) @ SV343 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1315,plain,
! [SV344: $i,SV92: $i] :
( ( ! [SY1394: $i,SY1395: $i] :
( ( c_Wellfounded_Oaccp @ SV92 @ SV344 @ SY1394 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV344 ) @ SY1395 ) )
| ~ ( c_Wellfounded_Oaccp @ SV92 @ SY1395 @ SY1394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1316,plain,
! [SV345: $i,SV93: $i] :
( ( ! [SY1396: $i] :
( ~ ( class_Orderings_Olinorder @ SV93 )
| ( c_lessequals @ SV345 @ SY1396 @ SV93 )
| ( c_lessequals @ SY1396 @ SV345 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1317,plain,
! [SV346: $i,SV94: $i] :
( ( ! [SY1397: $i,SY1398: $i] :
( ( c_Wellfounded_Oaccp @ SV94 @ SV346 @ SY1397 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV346 ) @ SY1398 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SY1398 @ SY1397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1318,plain,
! [SV347: $i,SV95: $i] :
( ( ! [SY1399: $i,SY1400: $i,SY1401: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SY1399 ) @ SY1400 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SY1401 ) @ SY1400 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SY1399 ) @ SY1401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1319,plain,
! [SV348: $i,SV96: $i] :
( ( ! [SY1402: $i,SY1403: $i,SY1404: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SY1402 ) @ SY1403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SY1404 ) @ SY1403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SY1402 ) @ SY1404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1320,plain,
! [SV349: $i,SV98: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV98 ) @ SV349 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ SV98 ) ) @ ( c_Lambda_OdB_OdB__size @ SV349 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1321,plain,
! [SV350: $i,SV99: $i] :
( ( ! [SY1405: $i,SY1406: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV99 ) @ SV350 ) @ SY1405 @ SY1406 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV99 @ SY1405 @ SY1406 ) ) @ ( c_Lambda_Osubst @ SV350 @ SY1405 @ SY1406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1322,plain,
! [SV351: $i,SV100: $i] :
( ( ! [SY1407: $i,SY1408: $i] :
( ( c_Type_Otypings @ SV100 @ SV351 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1407 @ SV100 @ SY1408 @ SV351 ) )
| ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1408 ) @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1323,plain,
! [SV352: $i,SV101: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV101 ) @ SV352 ) @ 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 @ SV101 @ tc_Type_Otype ) ) @ ( c_Nat_Osize__class_Osize @ SV352 @ tc_Type_Otype ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1324,plain,
! [SV353: $i,SV102: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV102 ) @ SV353 @ SV102 )
= SV353 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1325,plain,
! [SV354: $i,SV103: $i] :
( ( ! [SY1409: $i,SY1410: $i,SY1411: $i,SY1412: $i,SY1413: $i] :
( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SY1409 @ SY1410 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY1409 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1411 ) @ SY1412 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
| ~ ( c_Type_Otypings @ SY1409 @ SY1412 @ SY1413 )
| ~ ( c_Type_Otyping @ SY1409 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1411 ) @ SY1412 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1410 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1326,plain,
! [SV355: $i,SV104: $i] :
( ( ! [SY1414: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV104 @ SV355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1414 @ SV355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV104 ) @ SY1414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1327,plain,
! [SV356: $i,SV105: $i] :
( ( ( c_Type_Otype_Otype__size @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV105 ) @ SV356 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Type_Otype_Otype__size @ SV105 ) ) @ ( c_Type_Otype_Otype__size @ SV356 ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1328,plain,
! [SV357: $i,SV106: $i] :
( ( ! [SY1415: $i,SY1416: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV106 )
| ( c_lessequals @ SV357 @ SY1415 @ SV106 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SY1415 @ SV106 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SY1416 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SY1415 @ ( c_Suc @ SY1416 ) @ SV106 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1329,plain,
! [SV358: $i,SV107: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV107 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV358 @ SV107 @ SV107 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV358 @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1330,plain,
! [SV359: $i,SV108: $i] :
( ( ! [SY1417: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SV359 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SY1417 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV359 @ SY1417 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1331,plain,
! [SV360: $i,SV109: $i] :
( ( ! [SY1418: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV109 @ SV360 ) ) @ ( c_Lambda_Olift @ SY1418 @ SV360 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SY1418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1332,plain,
! [SV361: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV110 @ SV361 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1333,plain,
! [SV362: $i,SV111: $i] :
( ( ! [SY1419: $i,SY1420: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV111 @ SV362 ) @ SY1419 ) @ SY1420 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV111 @ SY1419 ) @ SY1420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1334,plain,
! [SV363: $i,SV112: $i] :
( ( ! [SY1421: $i,SY1422: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV112 @ SV363 @ SY1421 ) ) @ ( c_Lambda_Osubst @ SV112 @ SY1422 @ SY1421 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV363 ) @ SY1422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1335,plain,
! [SV364: $i,SV113: $i] :
( ( ! [SY1423: $i,SY1424: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV113 @ SV364 @ SY1423 ) ) @ ( c_Lambda_Osubst @ SY1424 @ SV364 @ SY1423 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV113 ) @ SY1424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1336,plain,
! [SV365: $i,SV114: $i] :
( ( ! [SY1425: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV114 ) @ SV365 ) @ SY1425 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV114 @ SY1425 ) ) @ ( c_Lambda_Olift @ SV365 @ SY1425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1337,plain,
! [SV366: $i,SV115: $i] :
( ( ! [SY1426: $i,SY1427: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV115 @ SV366 @ SY1426 ) ) @ ( c_Lambda_Osubst @ SV115 @ SY1427 @ SY1426 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV366 ) @ SY1427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1338,plain,
! [SV367: $i,SV116: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV116 )
| ~ ( class_Power_Opower @ SV116 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Suc @ SV367 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1339,plain,
! [SV368: $i,SV117: $i] :
( ( ! [SY1428: $i,SY1429: $i] :
( ( c_Type_Otyping @ SV117 @ SV368 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1428 @ SV117 @ SV368 @ SY1429 ) @ SY1428 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV117 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV368 @ SY1429 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1340,plain,
! [SV369: $i,SV118: $i] :
( ( ! [SY1430: $i,SY1431: $i,SY1432: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SY1430 ) @ SY1431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SY1432 ) @ SY1431 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SY1430 ) @ SY1432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1341,plain,
! [SV370: $i,SV119: $i] :
( ( ! [SY1433: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SV370 ) @ SY1433 ) @ SY1433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1342,plain,
! [SV371: $i,SV120: $i] :
( ( ! [SY1434: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV120 @ SV371 ) @ SY1434 ) @ SY1434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1343,plain,
! [SV372: $i,SV121: $i] :
( ( ! [SY1435: $i,SY1436: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV121 @ SV372 @ SY1435 ) ) @ ( c_Lambda_Osubst @ SY1436 @ SV372 @ SY1435 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV121 ) @ SY1436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1344,plain,
! [SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV122 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV122 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV122 )
= ( c_HOL_Oone__class_Oone @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1345,plain,
! [SV373: $i,SV123: $i] :
( ( ! [SY1437: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV123 @ SV373 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1437 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV373 @ 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 @ SV123 ) ) @ SV373 ) @ SY1437 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1346,plain,
! [SV374: $i,SV124: $i] :
( ( ! [SY1438: $i,SY1439: $i,SY1440: $i] :
( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV374 @ SY1438 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1439 )
| ~ ( c_Type_Otypings @ SV124 @ SY1438 @ SY1440 )
| ~ ( c_Type_Otyping @ SV124 @ SV374 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1440 @ SY1439 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1347,plain,
! [SV375: $i,SV126: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV126 ) @ SV375 ) @ 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 @ SV126 @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ SV375 @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1348,plain,
! [SV376: $i,SV128: $i] :
( ( ! [SY1441: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV128 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV376 @ SY1441 @ SV128 @ SV128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV376 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SY1441 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1349,plain,
! [SV377: $i,SV130: $i] :
( ( ! [SY1442: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV130 @ SV377 ) @ SY1442 @ SV377 )
= SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1350,plain,
! [SV378: $i,SV132: $i] :
( ( ! [SY1443: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV132 @ SV378 ) ) @ ( c_Lambda_Olift @ SY1443 @ SV378 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV132 ) @ SY1443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1351,plain,
! [SV379: $i,SV133: $i] :
( ( ! [SY1444: $i,SY1445: $i] :
( ( c_Type_Otyping @ SV133 @ SV379 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1444 @ SV133 @ SV379 @ SY1445 ) @ SY1444 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV133 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV379 @ SY1445 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1352,plain,
! [SV380: $i,SV134: $i] :
( ( ! [SY1446: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV134 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV380 @ SV134 @ SY1446 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV380 ) @ SV134 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1353,plain,
! [SV381: $i,SV135: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV381 ) @ SV381 )
= ( c_Transitive__Closure_Ortranclp @ SV135 @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1354,plain,
! [SV382: $i,SV136: $i] :
( ( ! [SY1447: $i,SY1448: $i] :
( ( c_Type_Otype_Otype__case @ SV136 @ SV382 @ ( c_Type_Otype_OAtom @ SY1447 ) @ SY1448 )
= ( hAPP @ SV136 @ SY1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1355,plain,
! [SV383: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV137 ) ) @ ( c_Lambda_OdB_OAbs @ SV383 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV137 ) @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1356,plain,
! [SV384: $i,SV138: $i] :
( ( ( SV138
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV384 @ SV138 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV384 ) ) @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1357,plain,
! [SV385: $i,SV139: $i] :
( ( ! [SY1449: $i,SY1450: $i,SY1451: $i,SY1452: $i] :
( ~ ( c_Type_Otyping @ SV139 @ SV385 @ SY1449 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SY1450 @ SY1449 @ tc_Type_Otype ) @ SY1451 @ SY1452 )
| ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SY1451 @ SV385 @ SY1450 ) @ SY1452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1358,plain,
! [SV386: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV140 ) @ ( c_Lambda_OdB_OVar @ SV386 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1359,plain,
! [SV387: $i,SV141: $i] :
( ( ! [SY1453: $i,SY1454: $i] :
( ( c_Type_Otyping @ SV141 @ SV387 @ SY1453 )
| ~ ( c_Type_Otyping @ SV141 @ SY1454 @ SY1453 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1454 ) @ SV387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1360,plain,
! [SV388: $i,SV143: $i] :
( ( ! [SY1455: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV143 ) @ SV388 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1455 ) @ SV388 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV143 ) @ SY1455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1361,plain,
! [SV389: $i,SV144: $i] :
( ( ! [SY1456: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SV389 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SY1456 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV389 ) @ SY1456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1362,plain,
! [SV390: $i,SV145: $i] :
( ( ! [SY1457: $i,SY1458: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV145 ) @ SV390 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1457 ) @ SY1458 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV390 ) @ SY1458 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV145 ) @ SY1457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1363,plain,
! [SV146: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV146 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1364,plain,
! [SV391: $i,SV147: $i] :
( ( ! [SY1459: $i,SY1460: $i] :
( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Type_Otype_Otype__case @ SV391 @ SY1459 @ ( c_Type_Otype_OAtom @ SY1460 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV391 @ SY1460 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1365,plain,
! [SV392: $i,SV148: $i] :
( ( ! [SY1461: $i,SY1462: $i] :
( ~ ( hBOOL @ ( hAPP @ SV148 @ ( c_Type_Otype_Otype__case @ SV392 @ SY1461 @ ( c_Type_Otype_OAtom @ SY1462 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV148 @ ( hAPP @ SV392 @ SY1462 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1366,plain,
! [SV393: $i,SV149: $i] :
( ( ! [SY1463: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV149 ) @ SV393 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1463 ) @ SV393 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV149 ) @ SY1463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1367,plain,
! [SV394: $i,SV150: $i] :
( ( ! [SY1464: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SV394 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SY1464 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV394 ) @ SY1464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1368,plain,
! [SV151: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV151 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV151 )
= ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1369,plain,
! [SV395: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP @ SV152 @ SV395 ) )
| ~ ( hBOOL @ ( hAPP @ SV152 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1370,plain,
! [SV396: $i,SV153: $i] :
( ( ! [SY1465: $i,SY1466: $i] :
( ( c_Type_Otyping @ SV153 @ SV396 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1465 @ SV153 @ SY1466 @ SV396 ) )
| ~ ( c_Type_Otyping @ SV153 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1466 ) @ SV396 ) @ SY1465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1371,plain,
! [SV397: $i,SV154: $i] :
( ( ! [SY1467: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV154 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV397 @ SV154 @ SY1467 ) @ tc_Type_Otype ) @ SY1467 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV397 @ SV154 @ SY1467 ) )
| ~ ( c_Type_Otyping @ SV154 @ ( c_Lambda_OdB_OAbs @ SY1467 ) @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1372,plain,
! [SV398: $i,SV155: $i] :
( ( ! [SY1468: $i] :
( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV398 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV398 @ SY1468 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV398 ) @ SY1468 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1373,plain,
! [SV399: $i,SV156: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV156 ) ) @ ( c_Lambda_OdB_OAbs @ SV399 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV156 ) @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1374,plain,
! [SV400: $i,SV157: $i] :
( ( ! [SY1469: $i,SY1470: $i] :
( ( c_Type_Otyping @ SV157 @ ( c_Lambda_OdB_OVar @ SV400 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1469 @ SV157 @ SV400 @ SY1470 ) @ SY1469 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV157 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV400 ) @ SY1470 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1375,plain,
! [SV401: $i,SV159: $i] :
( ( ! [SY1471: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV159 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV159 @ SV401 ) @ tc_Type_Otype ) @ SV401 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV159 @ SV401 ) )
| ~ ( c_Type_Otyping @ SV159 @ ( c_Lambda_OdB_OAbs @ SV401 ) @ SY1471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1376,plain,
! [SV402: $i,SV161: $i] :
( ( ! [SY1472: $i,SY1473: $i,SY1474: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ SV402 @ SY1472 @ SY1473 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1474 @ SY1473 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1474 @ SY1473 ) @ ( c_Suc @ SV402 ) @ SY1472 @ SY1473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1377,plain,
! [SV403: $i,SV162: $i] :
( ( ! [SY1475: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV162 ) ) @ SV403 ) @ SY1475 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV162 @ SV403 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1475 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1378,plain,
! [SV404: $i,SV163: $i] :
( ( ! [SY1476: $i,SY1477: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV163 @ SV404 @ SY1476 @ SY1477 ) @ SV404 )
= SY1476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1379,plain,
! [SV405: $i,SV164: $i] :
( ( ! [SY1478: $i,SY1479: $i] :
( ( c_Type_Otype_Otype__rec @ SV164 @ SV405 @ ( c_Type_Otype_OAtom @ SY1478 ) @ SY1479 )
= ( hAPP @ SV164 @ SY1478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1380,plain,
! [SV406: $i,SV165: $i] :
( ( ! [SY1480: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV165 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1480 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV165 ) @ SY1480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1381,plain,
! [SV407: $i,SV166: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV166 ) ) @ SV407 ) ) @ ( c_Lambda_Osubst @ SV166 @ SV407 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1382,plain,
! [SV408: $i,SV167: $i] :
( ( ! [SY1481: $i,SY1482: $i,SY1483: $i] :
( ( SV167 = SV408 )
| ~ ( c_Type_Otyping @ SY1481 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1482 ) @ SY1483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV408 )
| ~ ( c_Type_Otyping @ SY1481 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1482 ) @ SY1483 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1383,plain,
! [SV409: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SV409 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV409 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1384,plain,
! [SV410: $i,SV169: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV169 ) ) @ SV410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1385,plain,
! [SV411: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV170 ) @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV170 @ SV411 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV170 ) ) @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1386,plain,
! [SV412: $i,SV172: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV172 )
| ~ ( class_Power_Opower @ SV172 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV412 @ SV172 )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
| ( SV412
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1387,plain,
! [SV413: $i,SV173: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV173 )
| ~ ( class_Power_Opower @ SV173 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1388,plain,
! [SV414: $i,SV174: $i] :
( ( ! [SY1484: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV174 @ ( c_Lambda_OdB_OVar @ SV414 ) @ SY1484 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1389,plain,
! [SV415: $i,SV176: $i] :
( ( ! [SY1485: $i,SY1486: $i,SY1487: $i,SY1488: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SY1485 ) ) )
| ~ ( c_Type_Otyping @ SY1486 @ SV415 @ SY1487 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1486 @ SY1485 @ SY1487 @ tc_Type_Otype ) @ SV176 @ SY1488 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1390,plain,
! [SV416: $i,SV177: $i] :
( ( ! [SY1489: $i,SY1490: $i,SY1491: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ SV416 @ SY1489 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1490 @ SV416 ) @ SY1491 )
| ~ ( c_Type_Otyping @ SV177 @ SY1490 @ SY1491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1391,plain,
! [SV417: $i,SV178: $i] :
( ( ! [SY1492: $i] :
( ( SV178
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV178 @ SV417 @ SY1492 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV178 @ SV417 @ SY1492 ) ) )
| ~ ( c_Type_Otyping @ SV417 @ ( c_Lambda_OdB_OAbs @ SY1492 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1392,plain,
! [SV418: $i,SV179: $i] :
( ( ! [SY1493: $i,SY1494: $i] :
( ( c_Type_Otyping @ SV179 @ SV418 @ SY1493 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1494 ) @ SV418 ) )
| ~ ( c_Type_Otyping @ SV179 @ SY1494 @ SY1493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1393,plain,
! [SV419: $i,SV180: $i] :
( ( ! [SY1495: $i,SY1496: $i,SY1497: $i] :
( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV419 ) @ SY1495 ) @ SY1496 )
| ~ ( c_Type_Otyping @ SV180 @ SY1495 @ SY1497 )
| ~ ( c_Type_Otyping @ SV180 @ SV419 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1497 ) @ SY1496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1394,plain,
! [SV420: $i,SV181: $i] :
( ( ! [SY1498: $i,SY1499: $i] :
( ( c_Type_Otyping @ SV181 @ ( c_Lambda_OdB_OAbs @ SV420 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1498 ) @ SY1499 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV181 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1498 @ tc_Type_Otype ) @ SV420 @ SY1499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1395,plain,
! [SV421: $i,SV182: $i] :
( ( ! [SY1500: $i] :
( ( ( hAPP @ SV182 @ SV421 )
= SY1500 )
| ~ ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SV421 ) @ SY1500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1396,plain,
! [SV422: $i,SV183: $i] :
( ( ! [SY1501: $i,SY1502: $i,SY1503: $i] :
( ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1501 ) @ SY1502 ) @ SY1503 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV422 @ SY1501 ) @ SY1502 ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ SY1501 @ SY1503 ) ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ SY1502 @ SY1503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1397,plain,
! [SV423: $i,SV184: $i] :
( ( ! [SY1504: $i,SY1505: $i,SY1506: $i] :
( ( c_Type_Otype_Otype__case @ SV184 @ SV423 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1504 ) @ SY1505 ) @ SY1506 )
= ( hAPP @ ( hAPP @ SV423 @ SY1504 ) @ SY1505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1398,plain,
! [SV424: $i,SV185: $i] :
( ( c_Type_Otyping @ SV185 @ ( c_Lambda_OdB_OVar @ SV424 ) @ ( hAPP @ SV185 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1399,plain,
! [SV425: $i,SV186: $i] :
( ( ! [SY1507: $i,SY1508: $i,SY1509: $i] :
( ~ ( hBOOL @ ( hAPP @ SV186 @ ( c_Type_Otype_Otype__case @ SV425 @ SY1507 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1508 ) @ SY1509 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV186 @ ( hAPP @ ( hAPP @ SY1507 @ SY1508 ) @ SY1509 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1400,plain,
! [SV426: $i,SV187: $i] :
( ( ! [SY1510: $i,SY1511: $i,SY1512: $i] :
( ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_Type_Otype_Otype__case @ SV426 @ SY1510 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1511 ) @ SY1512 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV187 @ ( hAPP @ ( hAPP @ SY1510 @ SY1511 ) @ SY1512 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1401,plain,
! [SV427: $i,SV188: $i] :
( ( ! [SY1513: $i,SY1514: $i] :
( ( c_Type_Otyping @ SV188 @ SV427 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1513 @ SV188 @ SV427 @ SY1514 ) ) @ SY1513 ) )
| ~ ( c_Type_Otyping @ SV188 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV427 ) @ SY1514 ) @ SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1402,plain,
! [SV428: $i,SV189: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV189 @ SV428 ) )
| ~ ( class_Orderings_Opreorder @ SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1403,plain,
! [SV429: $i,SV190: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV190 @ SV429 ) )
| ~ ( class_Orderings_Oorder @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1404,plain,
! [SV430: $i,SV191: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV191 ) @ SV430 ) @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1405,plain,
! [SV431: $i,SV192: $i] :
( ( ! [SY1515: $i] :
( ( SV192 = SV431 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1515 ) @ SV192 ) @ SV431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1406,plain,
! [SV432: $i,SV193: $i] :
( ( ! [SY1516: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV193 @ SV432 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1516 @ SV432 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV193 = SY1516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1407,plain,
! [SV433: $i,SV194: $i] :
( ( ! [SY1517: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV194 @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1517 ) )
| ( SV433
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1408,plain,
! [SV434: $i,SV195: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV195 ) @ SV434 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV195
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1409,plain,
! [SV435: $i,SV196: $i] :
( ( ! [SY1518: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV196 ) @ SV435 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1518 ) @ SV435 ) )
| ( SV196 = SY1518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1410,plain,
! [SV436: $i,SV197: $i] :
( ( ! [SY1519: $i,SY1520: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV197 ) @ SV436 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1519 ) @ SY1520 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV436 = SY1520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1411,plain,
! [SV437: $i,SV198: $i] :
( ( ! [SY1521: $i,SY1522: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV198 ) @ SV437 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1521 ) @ SY1522 ) )
| ( SV198 = SY1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1412,plain,
! [SV438: $i,SV199: $i] :
( ( ! [SY1523: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV199 )
| ~ ( class_Int_Onumber__ring @ SV199 )
| ( SV438
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV438 ) @ SY1523 ) )
| ( SY1523
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1413,plain,
! [SV439: $i,SV200: $i] :
( ( ! [SY1524: $i,SY1525: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SV439 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1524 ) @ SY1525 ) )
| ( SV200 = SY1524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1414,plain,
! [SV440: $i,SV201: $i] :
( ( ! [SY1526: $i] :
( ( ( c_Lambda_OdB_OVar @ SV201 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV440 @ SY1526 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV201 )
= SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1415,plain,
! [SV441: $i,SV202: $i] :
( ( ! [SY1527: $i,SY1528: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV202 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV441 ) @ SY1527 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SY1528 ) @ SY1527 ) )
| ( SV441 = SY1528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1416,plain,
! [SV442: $i,SV203: $i] :
( ( ( SV203
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV203 ) @ SV442 ) )
| ( SV442
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1417,plain,
! [SV443: $i,SV204: $i] :
( ( ! [SY1529: $i,SY1530: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV204 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV443 ) @ SY1529 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SY1530 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SY1529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1418,plain,
! [SV444: $i,SV205: $i] :
( ( ! [SY1531: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV444 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SY1531 ) )
| ( SV444 = SY1531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1419,plain,
! [SV445: $i,SV206: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV206 ) @ SV445 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV445
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV445
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1420,plain,
! [SV446: $i,SV207: $i] :
( ( ! [SY1532: $i] :
( ( c_Lambda_OdB_OVar @ SV207 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV446 ) @ SY1532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1421,plain,
! [SV447: $i,SV208: $i] :
( ( ! [SY1533: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV208 )
| ( ( c_Power_Opower__class_Opower @ SV447 @ SY1533 @ SV208 )
!= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
| ( SV447
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1422,plain,
! [SV448: $i,SV209: $i] :
( ( ! [SY1534: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SY1534 )
!= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SY1534 @ SV209 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
| ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1423,plain,
! [SV449: $i,SV210: $i] :
( ( ! [SY1535: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV210 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV449 @ SY1535 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1535
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1424,plain,
! [SV450: $i,SV211: $i] :
( ( ! [SY1536: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SY1536 )
!= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SY1536 @ SV211 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
| ( SY1536
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1425,plain,
! [SV451: $i,SV212: $i] :
( ( ! [SY1537: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV212 )
| ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SV451 @ SY1537 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1426,plain,
! [SV452: $i,SV213: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV213 )
| ~ ( class_Power_Opower @ SV213 )
| ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1427,plain,
! [SV453: $i,SV214: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV214 ) @ SV453 )
!= SV214 )
| ( SV453
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1428,plain,
! [SV454: $i,SV215: $i] :
( ( ! [SY1538: $i,SY1539: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV215 )
| ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SY1538 ) @ SV215 )
!= ( c_Power_Opower__class_Opower @ SY1539 @ ( c_Suc @ SY1538 ) @ SV215 ) )
| ( SV454 = SY1539 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SY1539 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1429,plain,
! [SV455: $i,SV216: $i] :
( ( ! [SY1540: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV216 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV455 @ SY1540 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV216 )
= SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1430,plain,
! [SV456: $i,SV217: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV217 ) @ SV456 ) )
| ( SV217
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV217
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1431,plain,
! [SV457: $i,SV218: $i] :
( ( ! [SY1541: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV457 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1541 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV457 )
= SY1541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1432,plain,
! [SV458: $i,SV219: $i] :
( ( ! [SY1542: $i,SY1543: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV219 ) ) @ SV458 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1542 ) @ SY1543 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1433,plain,
! [SV459: $i,SV220: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV220 )
!= ( c_Lambda_OdB_OVar @ SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1434,plain,
! [SV460: $i,SV221: $i] :
( ( ! [SY1544: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV221 ) @ SV460 )
!= ( c_Type_Otype_OAtom @ SY1544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1435,plain,
! [SV461: $i,SV222: $i] :
( ( ! [SY1545: $i,SY1546: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV222 ) @ SV461 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1545 ) @ SY1546 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1436,plain,
! [SV462: $i,SV223: $i] :
( ( ! [SY1547: $i,SY1548: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV223 ) @ SV462 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1547 ) @ SY1548 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV223 = SY1547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1437,plain,
! [SV463: $i,SV224: $i] :
( ( ! [SY1549: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SV463 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SY1549 ) )
| ( SV463 = SY1549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1438,plain,
! [SV464: $i,SV225: $i] :
( ( ( c_Lambda_OdB_OVar @ SV225 )
!= ( c_Lambda_OdB_OAbs @ SV464 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1439,plain,
! [SV465: $i,SV226: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV226 ) @ SV465 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1440,plain,
! [SV227: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV227 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV227 )
!= ( c_HOL_Oone__class_Oone @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1441,plain,
! [SV466: $i,SV228: $i] :
( ( ! [SY1550: $i,SY1551: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV228 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SY1550 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SY1551 ) )
| ( SY1550 = SY1551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1442,plain,
! [SV467: $i,SV229: $i] :
( ( ! [SY1552: $i,SY1553: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV229 )
| ~ ( class_Int_Onumber__ring @ SV229 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SY1552 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SY1553 ) )
| ( SY1552 = SY1553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1443,plain,
! [SV230: $i] :
( ( ( c_Suc @ SV230 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1444,plain,
! [SV468: $i,SV231: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV231 ) @ SV468 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV468
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1445,plain,
! [SV469: $i,SV232: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV232 ) @ SV469 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV232
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1446,plain,
! [SV470: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV233 ) @ SV470 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV470
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV233
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1447,plain,
! [SV471: $i,SV234: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV234 )
!= ( c_Lambda_OdB_OVar @ SV471 ) )
| ( SV234 = SV471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1448,plain,
! [SV472: $i,SV235: $i] :
( ( ! [SY1554: $i,SY1555: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1554 ) @ SY1555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV235 = SY1554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1449,plain,
! [SV473: $i,SV236: $i] :
( ( ! [SY1556: $i,SY1557: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV473 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1556 ) @ SY1557 ) )
| ( SV473 = SY1557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1450,plain,
! [SV474: $i,SV237: $i] :
( ( ! [SY1558: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV237 ) @ SV474 )
!= ( c_Lambda_OdB_OAbs @ SY1558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1451,plain,
! [SV238: $i] :
( ( SV238
= ( c_Suc @ SV238 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1452,plain,
! [SV475: $i,SV239: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV239 )
!= ( c_Lambda_OdB_OAbs @ SV475 ) )
| ( SV239 = SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1453,plain,
! [SV476: $i,SV240: $i] :
( ( ( ( c_Suc @ SV240 )
!= ( c_Suc @ SV476 ) )
| ( SV240 = SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1454,plain,
! [SV241: $i] :
( ( ( c_Suc @ SV241 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1455,plain,
! [SV477: $i,SV242: $i] :
( ( ! [SY1559: $i] :
( ( c_Lambda_OdB_OAbs @ SV242 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV477 ) @ SY1559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1456,plain,
! [SV243: $i] :
( ( ( c_Suc @ SV243 )
= SV243 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1457,plain,
! [SV478: $i,SV244: $i] :
( ( ! [SY1560: $i] :
( ( c_Type_Otype_OAtom @ SV244 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV478 ) @ SY1560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1458,plain,
! [SV479: $i,SV245: $i] :
( ( ( ( c_Suc @ SV245 )
!= ( c_Suc @ SV479 ) )
| ( SV245 = SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1459,plain,
! [SV480: $i,SV246: $i] :
( ( ! [SY1561: $i,SY1562: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV246 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV480 ) @ SY1561 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SY1562 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SV480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1460,plain,
! [SV481: $i,SV247: $i] :
( ( ! [SY1563: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV247 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV481 @ SV247 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1563 @ SV247 ) )
| ( SV481 = SY1563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1461,plain,
! [SV482: $i,SV248: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV248 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV248 ) @ SV482 ) @ SV482 )
!= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1462,plain,
! [SV483: $i,SV249: $i] :
( ( ! [SY1564: $i,SY1565: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1564 ) @ SY1565 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV483 = SY1565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1463,plain,
! [SV484: $i,SV250: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV250 ) @ SV484 ) )
| ( SV484
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV250
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1464,plain,
! [SV485: $i,SV251: $i] :
( ( ! [SY1566: $i,SY1567: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV251 ) @ SV485 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1566 ) @ SY1567 ) )
| ( SV485 = SY1567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1465,plain,
! [SV486: $i,SV252: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV252 )
!= ( c_Type_Otype_OAtom @ SV486 ) )
| ( SV252 = SV486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1466,plain,
! [SV253: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV253 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV253 )
!= ( c_HOL_Ozero__class_Ozero @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1467,plain,
! [SV487: $i,SV254: $i] :
( ( ! [SY1568: $i,SY1569: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV254 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SY1568 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SY1569 ) )
| ( SY1568 = SY1569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1468,plain,
! [SV488: $i,SV255: $i] :
( ( ! [SY1570: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SV488 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1570 ) )
| ( SV255
= ( c_Lambda_OdB_OAbs @ SY1570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1469,plain,
! [SV256: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV256 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1470,plain,
! [SV489: $i,SV257: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV257 ) @ SV489 ) )
| ( SV257
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV489
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1471,plain,
! [SV490: $i,SV258: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV258 ) @ SV490 ) )
| ( SV490
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV490
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1472,plain,
! [SV491: $i,SV259: $i] :
( ( ! [SY1571: $i,SY1572: $i,SY1573: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV259 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SY1571 ) @ SY1572 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SY1571 ) @ SY1573 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ SY1572 )
= SY1573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1473,plain,
! [SV492: $i,SV260: $i] :
( ( ! [SY1574: $i] :
( ( ( c_Lambda_OdB_OVar @ SV260 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV492 @ SY1574 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1574
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1474,plain,
! [SV493: $i,SV261: $i] :
( ( ! [SY1575: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV261 ) @ SV493 )
!= ( c_Lambda_OdB_OVar @ SY1575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1475,plain,
! [SV262: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV262 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1476,plain,
! [SV494: $i,SV263: $i,SV1: $i] :
( ( ! [SY1576: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV1 @ SV263 ) @ SV494 ) @ SY1576 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV1 @ SV263 @ SV263 ) @ SV263 ) @ SY1576 ) @ SV494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1477,plain,
! [SV495: $i,SV264: $i,SV2: $i] :
( ( ! [SY1577: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV2 @ SV264 @ SV264 ) @ SV264 ) @ SV495 ) @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV2 @ SV264 ) @ SY1577 ) @ SV495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1478,plain,
! [SV496: $i,SV265: $i,SV3: $i] :
( ( ! [SY1578: $i,SY1579: $i,SY1580: $i,SY1581: $i] :
( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SY1578 @ SV3 @ SV265 ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1579 ) @ SY1580 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1578 )
| ~ ( c_Type_Otypings @ SV3 @ SY1580 @ SY1581 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1579 ) @ SY1580 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1479,plain,
! [SV497: $i,SV266: $i,SV4: $i] :
( ( ! [SY1582: $i,SY1583: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SY1582 ) @ SY1583 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SY1582 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV497 ) @ SY1583 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1480,plain,
! [SV267: $i,SV5: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV5 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV267 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1481,plain,
! [SV268: $i,SV6: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV6 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV268 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1482,plain,
! [SV269: $i,SV7: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) ) @ SV269 )
= SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1483,plain,
! [SV270: $i,SV8: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV8 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) ) @ SV270 )
= SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1484,plain,
! [SV271: $i,SV12: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV12 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV12 )
| ( SV271
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV12 ) @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1485,plain,
! [SV272: $i,SV13: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV13 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV13 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV13 ) )
= SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1486,plain,
! [SV273: $i,SV14: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV14 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) ) @ SV273 )
= SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1487,plain,
! [SV274: $i,SV15: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV15 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ SV15 ) )
= SV274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1488,plain,
! [SV275: $i,SV16: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV16 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV275 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) )
= SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1489,plain,
! [SV276: $i,SV17: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV17 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) ) @ SV276 )
= SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1490,plain,
! [SV278: $i,SV19: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV19 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV278 ) @ SV19 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ ( c_HOL_Oone__class_Oone @ SV19 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV278 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1491,plain,
! [SV498: $i,SV279: $i,SV20: $i] :
( ( ! [SY1584: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SV498 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SY1584 @ SV498 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 )
| ~ ( c_lessequals @ SV279 @ SY1584 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1492,plain,
! [SV499: $i,SV280: $i,SV21: $i] :
( ( ! [SY1585: $i] :
( ( c_List_Ofoldr @ SV21 @ ( c_List_Olist_ONil @ SV280 ) @ SV499 @ SV280 @ SY1585 )
= SV499 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1493,plain,
! [SV500: $i,SV281: $i,SV22: $i] :
( ( ! [SY1586: $i] :
( ( c_Type_Otypings @ SV22 @ SV281 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV500 @ SV22 @ SY1586 @ SV281 ) )
| ~ ( c_Type_Otyping @ SV22 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1586 @ SV281 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1494,plain,
! [SV282: $i,SV23: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV23 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV23 ) @ SV282 @ SV23 )
= ( c_HOL_Oone__class_Oone @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1495,plain,
! [SV501: $i,SV283: $i,SV24: $i] :
( ( ! [SY1587: $i,SY1588: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV283 ) @ SV501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV24 @ SY1587 @ SY1588 ) @ SV501 ) @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1496,plain,
! [SV502: $i,SV284: $i,SV25: $i] :
( ( ! [SY1589: $i,SY1590: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV25 @ SV284 @ SV502 ) @ SY1589 ) @ SY1590 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV25 @ SY1590 ) @ SY1589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1497,plain,
! [SV503: $i,SV285: $i,SV26: $i] :
( ( ! [SY1591: $i,SY1592: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV26 @ SV285 ) @ SV503 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV26 @ SY1591 @ SY1592 ) @ SV503 ) @ SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1498,plain,
! [SV504: $i,SV286: $i,SV27: $i] :
( ( ! [SY1593: $i,SY1594: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV27 @ SV286 @ SV504 ) @ SY1593 ) @ SY1594 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV27 @ SY1594 ) @ SY1593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1499,plain,
! [SV505: $i,SV287: $i,SV28: $i] :
( ( ! [SY1595: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV28 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ SV505 ) ) @ SY1595 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV505 ) @ SY1595 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1500,plain,
! [SV506: $i,SV288: $i,SV29: $i] :
( ( ! [SY1596: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV29 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV506 ) @ SY1596 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV506 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ SY1596 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1501,plain,
! [SV507: $i,SV289: $i,SV30: $i] :
( ( ! [SY1597: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SV507 ) ) @ SY1597 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SY1597 ) ) @ SV507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1502,plain,
! [SV508: $i,SV290: $i,SV31: $i] :
( ( ! [SY1598: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV508 ) @ SY1598 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ SV508 ) ) @ SY1598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1503,plain,
! [SV509: $i,SV291: $i,SV32: $i] :
( ( ! [SY1599: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV32 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ SV509 ) ) @ SY1599 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV509 ) @ SY1599 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1504,plain,
! [SV510: $i,SV292: $i,SV33: $i] :
( ( ! [SY1600: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV33 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV510 ) @ SY1600 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV510 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ SY1600 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1505,plain,
! [SV511: $i,SV293: $i,SV34: $i] :
( ( ! [SY1601: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV34 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ SV511 ) ) @ SY1601 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV511 ) @ SY1601 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1506,plain,
! [SV512: $i,SV294: $i,SV35: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV35 ) @ SV294 ) ) @ SV512 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV294 ) @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1507,plain,
! [SV513: $i,SV295: $i,SV36: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV36 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV295 ) @ SV513 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV295 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV36 ) @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1508,plain,
! [SV514: $i,SV296: $i,SV37: $i] :
( ( ! [SY1602: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV37 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV514 ) @ SY1602 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV514 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ SY1602 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1509,plain,
! [SV515: $i,SV297: $i,SV38: $i] :
( ( ! [SY1603: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV515 ) @ SY1603 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ SV515 ) ) @ SY1603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1510,plain,
! [SV516: $i,SV298: $i,SV39: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV298 ) @ SV516 ) @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV516 @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV298 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1511,plain,
! [SV40: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV40 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1512,plain,
! [SV41: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV41 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1513,plain,
! [SV517: $i,SV299: $i,SV42: $i] :
( ( ! [SY1604: $i,SY1605: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SY1604 ) @ SY1605 ) @ SV42 )
| ~ ( c_lessequals @ SV517 @ SY1605 @ SV42 )
| ~ ( c_lessequals @ SV299 @ SY1604 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1514,plain,
! [SV300: $i,SV43: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV43 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV300 ) @ SV300 ) @ SV43 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV300 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1515,plain,
! [SV301: $i,SV44: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV44 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ SV301 @ SV44 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV301 ) @ SV301 ) @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1516,plain,
! [SV518: $i,SV303: $i,SV46: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV46 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Power_Opower__class_Opower @ SV303 @ SV518 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ SV303 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1517,plain,
! [SV519: $i,SV304: $i,SV47: $i] :
( ( ! [SY1606: $i] :
( ( c_Wellfounded_Oaccp @ SV47 @ SV304 @ SV519 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SV519 ) @ SV304 ) @ SY1606 ) )
| ~ ( c_Wellfounded_Oaccp @ SV47 @ SY1606 @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1518,plain,
! [SV520: $i,SV305: $i,SV48: $i] :
( ( ! [SY1607: $i] :
( ( c_Wellfounded_Oaccp @ SV48 @ SV305 @ SV520 )
| ~ ( c_Wellfounded_Oaccp @ SV48 @ SY1607 @ SV520 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV520 ) @ SV305 ) @ SY1607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1519,plain,
! [SV49: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV49 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV49 @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1520,plain,
! [SV50: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV50 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1521,plain,
! [SV521: $i,SV306: $i,SV51: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV51 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ ( c_Power_Opower__class_Opower @ SV306 @ SV521 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV306 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1522,plain,
! [SV522: $i,SV309: $i,SV54: $i] :
( ( ! [SY1608: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
| ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SY1608 ) @ SV54 )
| ~ ( c_lessequals @ SV309 @ SY1608 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1523,plain,
! [SV523: $i,SV310: $i,SV55: $i] :
( ( ! [SY1609: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
| ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SY1609 ) @ SV55 )
| ~ ( c_lessequals @ SV310 @ SV523 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SY1609 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1524,plain,
! [SV524: $i,SV311: $i,SV56: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SV524 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV524 ) @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1525,plain,
! [SV525: $i,SV312: $i,SV57: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV57 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SV525 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV525 ) @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1526,plain,
! [SV526: $i,SV314: $i,SV59: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SV526 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV526 ) @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1527,plain,
! [SV527: $i,SV315: $i,SV60: $i] :
( ( ! [SY1610: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV60 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SV527 ) @ SY1610 @ SV60 @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV527 @ SY1610 @ SV60 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1528,plain,
! [SV528: $i,SV316: $i,SV61: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV61 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 @ SV528 @ SV61 @ SV61 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV528 @ SV316 @ SV61 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1529,plain,
! [SV529: $i,SV317: $i,SV62: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Olist_ONil @ SV317 ) @ SV529 @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1530,plain,
! [SV530: $i,SV318: $i,SV63: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV63 @ SV318 @ ( c_List_Olist_ONil @ SV530 ) @ SV530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1531,plain,
! [SV531: $i,SV319: $i,SV64: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV64 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV319 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV531 @ SV64 @ SV64 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV319 @ SV531 @ SV64 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1532,plain,
! [SV532: $i,SV320: $i,SV65: $i] :
( ( ! [SY1611: $i] :
( ( c_List_Ofoldl @ SV65 @ SV320 @ ( c_List_Olist_ONil @ SV532 ) @ SY1611 @ SV532 )
= SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1533,plain,
! [SV67: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV67 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ ( c_HOL_Oone__class_Oone @ SV67 ) @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1534,plain,
! [SV68: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV68 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1535,plain,
! [SV533: $i,SV321: $i,SV69: $i] :
( ( ~ ( class_Orderings_Oorder @ SV69 )
| ( SV321 = SV533 )
| ~ ( c_lessequals @ SV533 @ SV321 @ SV69 )
| ~ ( c_lessequals @ SV321 @ SV533 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1536,plain,
! [SV534: $i,SV322: $i,SV70: $i] :
( ( ~ ( class_Orderings_Oorder @ SV70 )
| ( SV322 = SV534 )
| ~ ( c_lessequals @ SV534 @ SV322 @ SV70 )
| ~ ( c_lessequals @ SV322 @ SV534 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1537,plain,
! [SV535: $i,SV323: $i,SV71: $i] :
( ( ~ ( class_Orderings_Oorder @ SV71 )
| ( SV323 = SV535 )
| ~ ( c_lessequals @ SV323 @ SV535 @ SV71 )
| ~ ( c_lessequals @ SV535 @ SV323 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1538,plain,
! [SV536: $i,SV324: $i,SV72: $i] :
( ( ! [SY1612: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV72 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV536 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SY1612 ) @ SV536 ) @ SV72 )
| ~ ( c_lessequals @ SV324 @ SY1612 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1539,plain,
! [SV537: $i,SV325: $i,SV73: $i] :
( ( ! [SY1613: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV73 )
| ( c_lessequals @ SV325 @ SV537 @ SV73 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SY1613 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV537 ) @ SY1613 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1540,plain,
! [SV538: $i,SV326: $i,SV74: $i] :
( ( ! [SY1614: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV74 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SY1614 ) @ SV74 )
| ~ ( c_lessequals @ SV538 @ SY1614 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1541,plain,
! [SV539: $i,SV327: $i,SV75: $i] :
( ( ! [SY1615: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV75 )
| ( c_lessequals @ SV327 @ SV539 @ SV75 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SY1615 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SY1615 ) @ SV539 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1542,plain,
! [SV540: $i,SV328: $i,SV76: $i] :
( ( ! [SY1616: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV76 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV328 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SY1616 ) @ SV540 ) @ SV76 )
| ~ ( c_lessequals @ SV328 @ SY1616 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1543,plain,
! [SV541: $i,SV329: $i,SV77: $i] :
( ( ! [SY1617: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV77 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV541 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SY1617 ) @ SV77 )
| ~ ( c_lessequals @ SV541 @ SY1617 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1544,plain,
! [SV330: $i,SV78: $i] :
( ( ( ~ ( class_Power_Opower @ SV78 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV330 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV78 )
= ( c_HOL_Oone__class_Oone @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1545,plain,
! [SV331: $i,SV79: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV79 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV331 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV79 )
= ( c_HOL_Oone__class_Oone @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1546,plain,
! [SV542: $i,SV332: $i,SV80: $i] :
( ( ! [SY1618: $i] :
( ( c_Type_Otypings @ SV80 @ SV332 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV542 @ SV80 @ SY1618 @ SV332 ) )
| ~ ( c_Type_Otyping @ SV80 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1618 @ SV332 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1547,plain,
! [SV543: $i,SV333: $i,SV81: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV81 @ SV333 @ SV543 ) @ SV543 @ SV333 )
= SV81 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1548,plain,
! [SV334: $i,SV82: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV82 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ SV334 ) @ SV334 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 )
| ~ ( c_lessequals @ SV334 @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1549,plain,
! [SV335: $i,SV83: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV83 ) )
= $true )
| ( ( ( c_lessequals @ SV335 @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ SV335 ) @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1550,plain,
! [SV544: $i,SV336: $i,SV84: $i] :
( ( ! [SY1619: $i] :
( ~ ( class_Orderings_Oorder @ SV84 )
| ( c_lessequals @ SV336 @ SV544 @ SV84 )
| ~ ( c_lessequals @ SV336 @ SY1619 @ SV84 )
| ~ ( c_lessequals @ SY1619 @ SV544 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1551,plain,
! [SV545: $i,SV337: $i,SV85: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV337 ) @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV545 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV337 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1552,plain,
! [SV546: $i,SV338: $i,SV86: $i] :
( ( ! [SY1620: $i] :
( ~ ( class_Orderings_Opreorder @ SV86 )
| ( c_lessequals @ SV338 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SY1620 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SV338 @ SY1620 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1553,plain,
! [SV339: $i,SV87: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV87 ) )
= $true )
| ( ( c_lessequals @ SV339 @ SV339 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1554,plain,
! [SV340: $i,SV88: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV88 ) )
= $true )
| ( ( c_lessequals @ SV340 @ SV340 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1555,plain,
! [SV547: $i,SV341: $i,SV89: $i] :
( ( ! [SY1621: $i,SY1622: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
| ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SY1621 ) @ SV89 )
| ~ ( c_lessequals @ SY1622 @ SY1621 @ SV89 )
| ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SY1622 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1556,plain,
! [SV548: $i,SV342: $i,SV90: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV90 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV548 ) @ SV90 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV342 @ SV90 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV548 @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1557,plain,
! [SV549: $i,SV344: $i,SV92: $i] :
( ( ! [SY1623: $i] :
( ( c_Wellfounded_Oaccp @ SV92 @ SV344 @ SV549 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV344 ) @ SY1623 ) )
| ~ ( c_Wellfounded_Oaccp @ SV92 @ SY1623 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1558,plain,
! [SV550: $i,SV345: $i,SV93: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV93 )
| ( c_lessequals @ SV345 @ SV550 @ SV93 )
| ( c_lessequals @ SV550 @ SV345 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1559,plain,
! [SV551: $i,SV346: $i,SV94: $i] :
( ( ! [SY1624: $i] :
( ( c_Wellfounded_Oaccp @ SV94 @ SV346 @ SV551 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV346 ) @ SY1624 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SY1624 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1560,plain,
! [SV552: $i,SV347: $i,SV95: $i] :
( ( ! [SY1625: $i,SY1626: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SY1625 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SY1626 ) @ SY1625 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SY1626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1561,plain,
! [SV553: $i,SV348: $i,SV96: $i] :
( ( ! [SY1627: $i,SY1628: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV553 ) @ SY1627 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SY1628 ) @ SY1627 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV553 ) @ SY1628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1562,plain,
! [SV554: $i,SV350: $i,SV99: $i] :
( ( ! [SY1629: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV99 ) @ SV350 ) @ SV554 @ SY1629 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV99 @ SV554 @ SY1629 ) ) @ ( c_Lambda_Osubst @ SV350 @ SV554 @ SY1629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1563,plain,
! [SV555: $i,SV351: $i,SV100: $i] :
( ( ! [SY1630: $i] :
( ( c_Type_Otypings @ SV100 @ SV351 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV555 @ SV100 @ SY1630 @ SV351 ) )
| ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1630 ) @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1564,plain,
! [SV556: $i,SV354: $i,SV103: $i] :
( ( ! [SY1631: $i,SY1632: $i,SY1633: $i,SY1634: $i] :
( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SY1631 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1632 ) @ SY1633 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
| ~ ( c_Type_Otypings @ SV556 @ SY1633 @ SY1634 )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1632 ) @ SY1633 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1631 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1565,plain,
! [SV557: $i,SV355: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV104 @ SV355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV557 @ SV355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV104 ) @ SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1566,plain,
! [SV558: $i,SV357: $i,SV106: $i] :
( ( ! [SY1635: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV106 )
| ( c_lessequals @ SV357 @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SY1635 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SV558 @ ( c_Suc @ SY1635 ) @ SV106 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1567,plain,
! [SV358: $i,SV107: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV107 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV358 @ SV107 @ SV107 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV358 @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1568,plain,
! [SV559: $i,SV359: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SV359 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SV559 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV359 @ SV559 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1569,plain,
! [SV560: $i,SV360: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV109 @ SV360 ) ) @ ( c_Lambda_Olift @ SV560 @ SV360 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1570,plain,
! [SV361: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV110 @ SV361 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1571,plain,
! [SV561: $i,SV362: $i,SV111: $i] :
( ( ! [SY1636: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV111 @ SV362 ) @ SV561 ) @ SY1636 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV111 @ SV561 ) @ SY1636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1572,plain,
! [SV562: $i,SV363: $i,SV112: $i] :
( ( ! [SY1637: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV112 @ SV363 @ SV562 ) ) @ ( c_Lambda_Osubst @ SV112 @ SY1637 @ SV562 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV363 ) @ SY1637 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1573,plain,
! [SV563: $i,SV364: $i,SV113: $i] :
( ( ! [SY1638: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV113 @ SV364 @ SV563 ) ) @ ( c_Lambda_Osubst @ SY1638 @ SV364 @ SV563 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV113 ) @ SY1638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1574,plain,
! [SV564: $i,SV365: $i,SV114: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV114 ) @ SV365 ) @ SV564 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV114 @ SV564 ) ) @ ( c_Lambda_Olift @ SV365 @ SV564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1575,plain,
! [SV565: $i,SV366: $i,SV115: $i] :
( ( ! [SY1639: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV115 @ SV366 @ SV565 ) ) @ ( c_Lambda_Osubst @ SV115 @ SY1639 @ SV565 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV366 ) @ SY1639 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1576,plain,
! [SV367: $i,SV116: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV116 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV116 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Suc @ SV367 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1577,plain,
! [SV566: $i,SV368: $i,SV117: $i] :
( ( ! [SY1640: $i] :
( ( c_Type_Otyping @ SV117 @ SV368 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV566 @ SV117 @ SV368 @ SY1640 ) @ SV566 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV117 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV368 @ SY1640 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1578,plain,
! [SV567: $i,SV369: $i,SV118: $i] :
( ( ! [SY1641: $i,SY1642: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SY1641 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SY1642 ) @ SY1641 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SY1642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1579,plain,
! [SV568: $i,SV370: $i,SV119: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SV370 ) @ SV568 ) @ SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1580,plain,
! [SV569: $i,SV371: $i,SV120: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV120 @ SV371 ) @ SV569 ) @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1581,plain,
! [SV570: $i,SV372: $i,SV121: $i] :
( ( ! [SY1643: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV121 @ SV372 @ SV570 ) ) @ ( c_Lambda_Osubst @ SY1643 @ SV372 @ SV570 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV121 ) @ SY1643 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1582,plain,
! [SV122: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV122 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV122 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV122 )
= ( c_HOL_Oone__class_Oone @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1583,plain,
! [SV571: $i,SV373: $i,SV123: $i] :
( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV123 @ SV373 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV373 @ 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 @ SV123 ) ) @ SV373 ) @ SV571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1584,plain,
! [SV572: $i,SV374: $i,SV124: $i] :
( ( ! [SY1644: $i,SY1645: $i] :
( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV374 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1644 )
| ~ ( c_Type_Otypings @ SV124 @ SV572 @ SY1645 )
| ~ ( c_Type_Otyping @ SV124 @ SV374 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1645 @ SY1644 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1585,plain,
! [SV573: $i,SV376: $i,SV128: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV128 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV376 @ SV573 @ SV128 @ SV128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV376 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV573 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1586,plain,
! [SV574: $i,SV377: $i,SV130: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV130 @ SV377 ) @ SV574 @ SV377 )
= SV130 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1587,plain,
! [SV575: $i,SV378: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV132 @ SV378 ) ) @ ( c_Lambda_Olift @ SV575 @ SV378 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV132 ) @ SV575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1588,plain,
! [SV576: $i,SV379: $i,SV133: $i] :
( ( ! [SY1646: $i] :
( ( c_Type_Otyping @ SV133 @ SV379 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV576 @ SV133 @ SV379 @ SY1646 ) @ SV576 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV133 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV379 @ SY1646 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1589,plain,
! [SV577: $i,SV380: $i,SV134: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV134 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV380 @ SV134 @ SV577 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV380 ) @ SV134 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1590,plain,
! [SV578: $i,SV382: $i,SV136: $i] :
( ( ! [SY1647: $i] :
( ( c_Type_Otype_Otype__case @ SV136 @ SV382 @ ( c_Type_Otype_OAtom @ SV578 ) @ SY1647 )
= ( hAPP @ SV136 @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1591,plain,
! [SV383: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV137 ) ) @ ( c_Lambda_OdB_OAbs @ SV383 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV137 ) @ SV383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1592,plain,
! [SV384: $i,SV138: $i] :
( ( ( SV138
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV384 @ SV138 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV384 ) ) @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1593,plain,
! [SV579: $i,SV385: $i,SV139: $i] :
( ( ! [SY1648: $i,SY1649: $i,SY1650: $i] :
( ~ ( c_Type_Otyping @ SV139 @ SV385 @ SV579 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SY1648 @ SV579 @ tc_Type_Otype ) @ SY1649 @ SY1650 )
| ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SY1649 @ SV385 @ SY1648 ) @ SY1650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1594,plain,
! [SV386: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV140 ) @ ( c_Lambda_OdB_OVar @ SV386 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1595,plain,
! [SV580: $i,SV387: $i,SV141: $i] :
( ( ! [SY1651: $i] :
( ( c_Type_Otyping @ SV141 @ SV387 @ SV580 )
| ~ ( c_Type_Otyping @ SV141 @ SY1651 @ SV580 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1651 ) @ SV387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1596,plain,
! [SV581: $i,SV388: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV143 ) @ SV388 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV581 ) @ SV388 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV143 ) @ SV581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1597,plain,
! [SV582: $i,SV389: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SV389 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SV582 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV389 ) @ SV582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1598,plain,
! [SV583: $i,SV390: $i,SV145: $i] :
( ( ! [SY1652: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV145 ) @ SV390 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV583 ) @ SY1652 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV390 ) @ SY1652 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV145 ) @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1599,plain,
! [SV146: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV146 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1600,plain,
! [SV584: $i,SV391: $i,SV147: $i] :
( ( ! [SY1653: $i] :
( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Type_Otype_Otype__case @ SV391 @ SV584 @ ( c_Type_Otype_OAtom @ SY1653 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV391 @ SY1653 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1601,plain,
! [SV585: $i,SV392: $i,SV148: $i] :
( ( ! [SY1654: $i] :
( ~ ( hBOOL @ ( hAPP @ SV148 @ ( c_Type_Otype_Otype__case @ SV392 @ SV585 @ ( c_Type_Otype_OAtom @ SY1654 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV148 @ ( hAPP @ SV392 @ SY1654 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1602,plain,
! [SV586: $i,SV393: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV149 ) @ SV393 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV586 ) @ SV393 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV149 ) @ SV586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1603,plain,
! [SV587: $i,SV394: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SV394 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SV587 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV394 ) @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1604,plain,
! [SV151: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV151 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV151 )
= ( c_HOL_Ozero__class_Ozero @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1605,plain,
! [SV395: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP @ SV152 @ SV395 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV152 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV152 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1606,plain,
! [SV588: $i,SV396: $i,SV153: $i] :
( ( ! [SY1655: $i] :
( ( c_Type_Otyping @ SV153 @ SV396 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV588 @ SV153 @ SY1655 @ SV396 ) )
| ~ ( c_Type_Otyping @ SV153 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1655 ) @ SV396 ) @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1607,plain,
! [SV589: $i,SV397: $i,SV154: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV154 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV397 @ SV154 @ SV589 ) @ tc_Type_Otype ) @ SV589 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV397 @ SV154 @ SV589 ) )
| ~ ( c_Type_Otyping @ SV154 @ ( c_Lambda_OdB_OAbs @ SV589 ) @ SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1608,plain,
! [SV590: $i,SV398: $i,SV155: $i] :
( ( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV398 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV398 @ SV590 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV398 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1609,plain,
! [SV399: $i,SV156: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV156 ) ) @ ( c_Lambda_OdB_OAbs @ SV399 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV156 ) @ SV399 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1610,plain,
! [SV591: $i,SV400: $i,SV157: $i] :
( ( ! [SY1656: $i] :
( ( c_Type_Otyping @ SV157 @ ( c_Lambda_OdB_OVar @ SV400 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV591 @ SV157 @ SV400 @ SY1656 ) @ SV591 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV157 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV400 ) @ SY1656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1611,plain,
! [SV592: $i,SV401: $i,SV159: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV159 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV159 @ SV401 ) @ tc_Type_Otype ) @ SV401 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV159 @ SV401 ) )
| ~ ( c_Type_Otyping @ SV159 @ ( c_Lambda_OdB_OAbs @ SV401 ) @ SV592 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1612,plain,
! [SV593: $i,SV402: $i,SV161: $i] :
( ( ! [SY1657: $i,SY1658: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ SV402 @ SV593 @ SY1657 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1658 @ SY1657 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1658 @ SY1657 ) @ ( c_Suc @ SV402 ) @ SV593 @ SY1657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1613,plain,
! [SV594: $i,SV403: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV162 ) ) @ SV403 ) @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV162 @ SV403 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1614,plain,
! [SV595: $i,SV404: $i,SV163: $i] :
( ( ! [SY1659: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV163 @ SV404 @ SV595 @ SY1659 ) @ SV404 )
= SV595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1615,plain,
! [SV596: $i,SV405: $i,SV164: $i] :
( ( ! [SY1660: $i] :
( ( c_Type_Otype_Otype__rec @ SV164 @ SV405 @ ( c_Type_Otype_OAtom @ SV596 ) @ SY1660 )
= ( hAPP @ SV164 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1616,plain,
! [SV597: $i,SV406: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV165 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV597 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV165 ) @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1617,plain,
! [SV598: $i,SV408: $i,SV167: $i] :
( ( ! [SY1661: $i,SY1662: $i] :
( ( SV167 = SV408 )
| ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1661 ) @ SY1662 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV408 )
| ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1661 ) @ SY1662 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1618,plain,
! [SV409: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SV409 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV409 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1619,plain,
! [SV410: $i,SV169: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV169 ) ) @ SV410 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1620,plain,
! [SV411: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV170 ) @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV170 @ SV411 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV170 ) ) @ SV411 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1621,plain,
! [SV412: $i,SV172: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV172 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV172 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV412 @ SV172 )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
| ( SV412
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1622,plain,
! [SV413: $i,SV173: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV173 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV173 )
| ~ ( class_Power_Opower @ SV173 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1623,plain,
! [SV599: $i,SV414: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV174 @ ( c_Lambda_OdB_OVar @ SV414 ) @ SV599 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1624,plain,
! [SV600: $i,SV415: $i,SV176: $i] :
( ( ! [SY1663: $i,SY1664: $i,SY1665: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
| ~ ( c_Type_Otyping @ SY1663 @ SV415 @ SY1664 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1663 @ SV600 @ SY1664 @ tc_Type_Otype ) @ SV176 @ SY1665 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1625,plain,
! [SV601: $i,SV416: $i,SV177: $i] :
( ( ! [SY1666: $i,SY1667: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ SV416 @ SV601 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1666 @ SV416 ) @ SY1667 )
| ~ ( c_Type_Otyping @ SV177 @ SY1666 @ SY1667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1626,plain,
! [SV602: $i,SV417: $i,SV178: $i] :
( ( ( SV178
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV178 @ SV417 @ SV602 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV178 @ SV417 @ SV602 ) ) )
| ~ ( c_Type_Otyping @ SV417 @ ( c_Lambda_OdB_OAbs @ SV602 ) @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1627,plain,
! [SV603: $i,SV418: $i,SV179: $i] :
( ( ! [SY1668: $i] :
( ( c_Type_Otyping @ SV179 @ SV418 @ SV603 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1668 ) @ SV418 ) )
| ~ ( c_Type_Otyping @ SV179 @ SY1668 @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1628,plain,
! [SV604: $i,SV419: $i,SV180: $i] :
( ( ! [SY1669: $i,SY1670: $i] :
( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV419 ) @ SV604 ) @ SY1669 )
| ~ ( c_Type_Otyping @ SV180 @ SV604 @ SY1670 )
| ~ ( c_Type_Otyping @ SV180 @ SV419 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1670 ) @ SY1669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1629,plain,
! [SV605: $i,SV420: $i,SV181: $i] :
( ( ! [SY1671: $i] :
( ( c_Type_Otyping @ SV181 @ ( c_Lambda_OdB_OAbs @ SV420 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV605 ) @ SY1671 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV181 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV605 @ tc_Type_Otype ) @ SV420 @ SY1671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1630,plain,
! [SV606: $i,SV421: $i,SV182: $i] :
( ( ( ( hAPP @ SV182 @ SV421 )
= SV606 )
| ~ ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SV421 ) @ SV606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1631,plain,
! [SV607: $i,SV422: $i,SV183: $i] :
( ( ! [SY1672: $i,SY1673: $i] :
( ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV607 ) @ SY1672 ) @ SY1673 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV422 @ SV607 ) @ SY1672 ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ SV607 @ SY1673 ) ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ SY1672 @ SY1673 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1632,plain,
! [SV608: $i,SV423: $i,SV184: $i] :
( ( ! [SY1674: $i,SY1675: $i] :
( ( c_Type_Otype_Otype__case @ SV184 @ SV423 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV608 ) @ SY1674 ) @ SY1675 )
= ( hAPP @ ( hAPP @ SV423 @ SV608 ) @ SY1674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1633,plain,
! [SV609: $i,SV425: $i,SV186: $i] :
( ( ! [SY1676: $i,SY1677: $i] :
( ~ ( hBOOL @ ( hAPP @ SV186 @ ( c_Type_Otype_Otype__case @ SV425 @ SV609 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1676 ) @ SY1677 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV186 @ ( hAPP @ ( hAPP @ SV609 @ SY1676 ) @ SY1677 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1634,plain,
! [SV610: $i,SV426: $i,SV187: $i] :
( ( ! [SY1678: $i,SY1679: $i] :
( ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_Type_Otype_Otype__case @ SV426 @ SV610 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1678 ) @ SY1679 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV187 @ ( hAPP @ ( hAPP @ SV610 @ SY1678 ) @ SY1679 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1635,plain,
! [SV611: $i,SV427: $i,SV188: $i] :
( ( ! [SY1680: $i] :
( ( c_Type_Otyping @ SV188 @ SV427 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV611 @ SV188 @ SV427 @ SY1680 ) ) @ SV611 ) )
| ~ ( c_Type_Otyping @ SV188 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV427 ) @ SY1680 ) @ SV611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1636,plain,
! [SV428: $i,SV189: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV189 @ SV428 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1637,plain,
! [SV429: $i,SV190: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV190 @ SV429 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1638,plain,
! [SV612: $i,SV431: $i,SV192: $i] :
( ( ( SV192 = SV431 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV612 ) @ SV192 ) @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1639,plain,
! [SV613: $i,SV432: $i,SV193: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV193 @ SV432 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV613 @ SV432 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV193 = SV613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1640,plain,
! [SV614: $i,SV433: $i,SV194: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV194 @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV614 ) )
| ( SV433
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1641,plain,
! [SV434: $i,SV195: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV195 ) @ SV434 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV195
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1642,plain,
! [SV615: $i,SV435: $i,SV196: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV196 ) @ SV435 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV615 ) @ SV435 ) )
| ( SV196 = SV615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1643,plain,
! [SV616: $i,SV436: $i,SV197: $i] :
( ( ! [SY1681: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV197 ) @ SV436 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV616 ) @ SY1681 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV436 = SY1681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1644,plain,
! [SV617: $i,SV437: $i,SV198: $i] :
( ( ! [SY1682: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV198 ) @ SV437 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV617 ) @ SY1682 ) )
| ( SV198 = SV617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1645,plain,
! [SV618: $i,SV438: $i,SV199: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV199 )
| ~ ( class_Int_Onumber__ring @ SV199 )
| ( SV438
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV438 ) @ SV618 ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1646,plain,
! [SV619: $i,SV439: $i,SV200: $i] :
( ( ! [SY1683: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SV439 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV619 ) @ SY1683 ) )
| ( SV200 = SV619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1647,plain,
! [SV620: $i,SV440: $i,SV201: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV201 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV440 @ SV620 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV201 )
= SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1648,plain,
! [SV621: $i,SV441: $i,SV202: $i] :
( ( ! [SY1684: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV202 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV441 ) @ SV621 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SY1684 ) @ SV621 ) )
| ( SV441 = SY1684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1649,plain,
! [SV442: $i,SV203: $i] :
( ( ( SV203
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV203 ) @ SV442 ) )
= $true )
| ( ( SV442
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1650,plain,
! [SV622: $i,SV443: $i,SV204: $i] :
( ( ! [SY1685: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV204 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV443 ) @ SV622 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SY1685 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SV622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1651,plain,
! [SV623: $i,SV444: $i,SV205: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV444 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV623 ) )
| ( SV444 = SV623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1652,plain,
! [SV445: $i,SV206: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV206 ) @ SV445 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV445
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV445
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1653,plain,
! [SV624: $i,SV446: $i,SV207: $i] :
( ( ( c_Lambda_OdB_OVar @ SV207 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV446 ) @ SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1654,plain,
! [SV625: $i,SV447: $i,SV208: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV208 )
| ( ( c_Power_Opower__class_Opower @ SV447 @ SV625 @ SV208 )
!= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
| ( SV447
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1655,plain,
! [SV626: $i,SV448: $i,SV209: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
!= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
| ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1656,plain,
! [SV627: $i,SV449: $i,SV210: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV210 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV449 @ SV627 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV627
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1657,plain,
! [SV628: $i,SV450: $i,SV211: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
!= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
| ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1658,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV212 )
| ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1659,plain,
! [SV452: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV213 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV213 )
| ~ ( class_Power_Opower @ SV213 )
| ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1660,plain,
! [SV453: $i,SV214: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV214 ) @ SV453 )
!= SV214 )
= $true )
| ( ( SV453
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1661,plain,
! [SV630: $i,SV454: $i,SV215: $i] :
( ( ! [SY1686: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV215 )
| ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
!= ( c_Power_Opower__class_Opower @ SY1686 @ ( c_Suc @ SV630 ) @ SV215 ) )
| ( SV454 = SY1686 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SY1686 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1662,plain,
! [SV631: $i,SV455: $i,SV216: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV216 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV455 @ SV631 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV216 )
= SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1663,plain,
! [SV456: $i,SV217: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV217 ) @ SV456 ) )
= $true )
| ( ( ( SV217
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV217
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1664,plain,
! [SV632: $i,SV457: $i,SV218: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV457 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV632 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV457 )
= SV632 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1665,plain,
! [SV633: $i,SV458: $i,SV219: $i] :
( ( ! [SY1687: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV219 ) ) @ SV458 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV633 ) @ SY1687 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1666,plain,
! [SV459: $i,SV220: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV220 )
= ( c_Lambda_OdB_OVar @ SV459 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1667,plain,
! [SV634: $i,SV460: $i,SV221: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV221 ) @ SV460 )
!= ( c_Type_Otype_OAtom @ SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1668,plain,
! [SV635: $i,SV461: $i,SV222: $i] :
( ( ! [SY1688: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV222 ) @ SV461 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV635 ) @ SY1688 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1669,plain,
! [SV636: $i,SV462: $i,SV223: $i] :
( ( ! [SY1689: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV223 ) @ SV462 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ SY1689 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV223 = SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1670,plain,
! [SV637: $i,SV463: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SV463 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SV637 ) )
| ( SV463 = SV637 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1671,plain,
! [SV464: $i,SV225: $i] :
( ( ( c_Lambda_OdB_OVar @ SV225 )
= ( c_Lambda_OdB_OAbs @ SV464 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1672,plain,
! [SV465: $i,SV226: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV226 ) @ SV465 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1673,plain,
! [SV227: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV227 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV227 )
!= ( c_HOL_Oone__class_Oone @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1674,plain,
! [SV638: $i,SV466: $i,SV228: $i] :
( ( ! [SY1690: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV228 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SY1690 ) )
| ( SV638 = SY1690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1675,plain,
! [SV639: $i,SV467: $i,SV229: $i] :
( ( ! [SY1691: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV229 )
| ~ ( class_Int_Onumber__ring @ SV229 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV639 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SY1691 ) )
| ( SV639 = SY1691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1676,plain,
! [SV468: $i,SV231: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV231 ) @ SV468 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV468
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1677,plain,
! [SV469: $i,SV232: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV232 ) @ SV469 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV232
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1678,plain,
! [SV470: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV233 ) @ SV470 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV470
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV233
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1679,plain,
! [SV471: $i,SV234: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV234 )
!= ( c_Lambda_OdB_OVar @ SV471 ) )
= $true )
| ( ( SV234 = SV471 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1680,plain,
! [SV640: $i,SV472: $i,SV235: $i] :
( ( ! [SY1692: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV640 ) @ SY1692 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV235 = SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1681,plain,
! [SV641: $i,SV473: $i,SV236: $i] :
( ( ! [SY1693: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV473 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV641 ) @ SY1693 ) )
| ( SV473 = SY1693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1682,plain,
! [SV642: $i,SV474: $i,SV237: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV237 ) @ SV474 )
!= ( c_Lambda_OdB_OAbs @ SV642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1683,plain,
! [SV475: $i,SV239: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV239 )
!= ( c_Lambda_OdB_OAbs @ SV475 ) )
= $true )
| ( ( SV239 = SV475 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1452]) ).
thf(1684,plain,
! [SV476: $i,SV240: $i] :
( ( ( ( c_Suc @ SV240 )
!= ( c_Suc @ SV476 ) )
= $true )
| ( ( SV240 = SV476 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1685,plain,
! [SV643: $i,SV477: $i,SV242: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV242 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV477 ) @ SV643 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1686,plain,
! [SV644: $i,SV478: $i,SV244: $i] :
( ( ( c_Type_Otype_OAtom @ SV244 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV478 ) @ SV644 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1687,plain,
! [SV479: $i,SV245: $i] :
( ( ( ( c_Suc @ SV245 )
!= ( c_Suc @ SV479 ) )
= $true )
| ( ( SV245 = SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1688,plain,
! [SV645: $i,SV480: $i,SV246: $i] :
( ( ! [SY1694: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV246 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV480 ) @ SV645 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SY1694 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SV480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1689,plain,
! [SV646: $i,SV481: $i,SV247: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV247 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV481 @ SV247 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV646 @ SV247 ) )
| ( SV481 = SV646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1690,plain,
! [SV482: $i,SV248: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV248 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV248 ) @ SV482 ) @ SV482 )
!= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1691,plain,
! [SV647: $i,SV483: $i,SV249: $i] :
( ( ! [SY1695: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV647 ) @ SY1695 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV483 = SY1695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1692,plain,
! [SV484: $i,SV250: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV250 ) @ SV484 ) )
= $true )
| ( ( ( SV484
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV250
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1693,plain,
! [SV648: $i,SV485: $i,SV251: $i] :
( ( ! [SY1696: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV251 ) @ SV485 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV648 ) @ SY1696 ) )
| ( SV485 = SY1696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1694,plain,
! [SV486: $i,SV252: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV252 )
!= ( c_Type_Otype_OAtom @ SV486 ) )
= $true )
| ( ( SV252 = SV486 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1695,plain,
! [SV253: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV253 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV253 )
!= ( c_HOL_Ozero__class_Ozero @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1696,plain,
! [SV649: $i,SV487: $i,SV254: $i] :
( ( ! [SY1697: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV254 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV649 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SY1697 ) )
| ( SV649 = SY1697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1697,plain,
! [SV650: $i,SV488: $i,SV255: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SV488 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV650 ) )
| ( SV255
= ( c_Lambda_OdB_OAbs @ SV650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1698,plain,
! [SV489: $i,SV257: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV257 ) @ SV489 ) )
= $true )
| ( ( ( SV257
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV489
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1699,plain,
! [SV490: $i,SV258: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV258 ) @ SV490 ) )
= $true )
| ( ( ( SV490
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV490
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1700,plain,
! [SV651: $i,SV491: $i,SV259: $i] :
( ( ! [SY1698: $i,SY1699: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV259 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SY1698 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SY1699 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ SY1698 )
= SY1699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1701,plain,
! [SV652: $i,SV492: $i,SV260: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV260 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV492 @ SV652 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV652
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1702,plain,
! [SV653: $i,SV493: $i,SV261: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV261 ) @ SV493 )
!= ( c_Lambda_OdB_OVar @ SV653 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1703,plain,
! [SV654: $i,SV494: $i,SV263: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV1 @ SV263 ) @ SV494 ) @ SV654 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV1 @ SV263 @ SV263 ) @ SV263 ) @ SV654 ) @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1704,plain,
! [SV655: $i,SV495: $i,SV264: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV2 @ SV264 @ SV264 ) @ SV264 ) @ SV495 ) @ SV655 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV2 @ SV264 ) @ SV655 ) @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1705,plain,
! [SV656: $i,SV496: $i,SV265: $i,SV3: $i] :
( ( ! [SY1700: $i,SY1701: $i,SY1702: $i] :
( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1700 ) @ SY1701 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
| ~ ( c_Type_Otypings @ SV3 @ SY1701 @ SY1702 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1700 ) @ SY1701 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1706,plain,
! [SV657: $i,SV497: $i,SV266: $i,SV4: $i] :
( ( ! [SY1703: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV657 ) @ SY1703 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV657 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV497 ) @ SY1703 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1707,plain,
! [SV267: $i,SV5: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV5 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV267 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1708,plain,
! [SV268: $i,SV6: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV6 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV268 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1709,plain,
! [SV269: $i,SV7: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) ) @ SV269 )
= SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1710,plain,
! [SV270: $i,SV8: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV8 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) ) @ SV270 )
= SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1711,plain,
! [SV271: $i,SV12: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV12 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV12 )
| ( SV271
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV12 ) @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1712,plain,
! [SV272: $i,SV13: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV13 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV13 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV13 ) )
= SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1713,plain,
! [SV273: $i,SV14: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV14 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) ) @ SV273 )
= SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1714,plain,
! [SV274: $i,SV15: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV15 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV274 ) @ ( c_HOL_Ozero__class_Ozero @ SV15 ) )
= SV274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1715,plain,
! [SV275: $i,SV16: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV16 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV275 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) )
= SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1716,plain,
! [SV276: $i,SV17: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV17 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) ) @ SV276 )
= SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1717,plain,
! [SV278: $i,SV19: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV19 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV278 ) @ SV19 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ ( c_HOL_Oone__class_Oone @ SV19 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV278 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1718,plain,
! [SV658: $i,SV498: $i,SV279: $i,SV20: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SV498 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV658 @ SV498 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 )
| ~ ( c_lessequals @ SV279 @ SV658 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1719,plain,
! [SV659: $i,SV499: $i,SV280: $i,SV21: $i] :
( ( ( c_List_Ofoldr @ SV21 @ ( c_List_Olist_ONil @ SV280 ) @ SV499 @ SV280 @ SV659 )
= SV499 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1720,plain,
! [SV660: $i,SV500: $i,SV281: $i,SV22: $i] :
( ( ( c_Type_Otypings @ SV22 @ SV281 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV500 @ SV22 @ SV660 @ SV281 ) )
| ~ ( c_Type_Otyping @ SV22 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV660 @ SV281 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1721,plain,
! [SV282: $i,SV23: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV23 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV23 ) @ SV282 @ SV23 )
= ( c_HOL_Oone__class_Oone @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1722,plain,
! [SV661: $i,SV501: $i,SV283: $i,SV24: $i] :
( ( ! [SY1704: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV283 ) @ SV501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV24 @ SV661 @ SY1704 ) @ SV501 ) @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1723,plain,
! [SV662: $i,SV502: $i,SV284: $i,SV25: $i] :
( ( ! [SY1705: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV25 @ SV284 @ SV502 ) @ SV662 ) @ SY1705 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV25 @ SY1705 ) @ SV662 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1724,plain,
! [SV663: $i,SV503: $i,SV285: $i,SV26: $i] :
( ( ! [SY1706: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV26 @ SV285 ) @ SV503 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV26 @ SV663 @ SY1706 ) @ SV503 ) @ SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1725,plain,
! [SV664: $i,SV504: $i,SV286: $i,SV27: $i] :
( ( ! [SY1707: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV27 @ SV286 @ SV504 ) @ SV664 ) @ SY1707 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV27 @ SY1707 ) @ SV664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1726,plain,
! [SV665: $i,SV505: $i,SV287: $i,SV28: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV28 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ SV505 ) ) @ SV665 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV505 ) @ SV665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1727,plain,
! [SV666: $i,SV506: $i,SV288: $i,SV29: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV29 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV506 ) @ SV666 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV506 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ SV666 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1728,plain,
! [SV667: $i,SV507: $i,SV289: $i,SV30: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SV507 ) ) @ SV667 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SV667 ) ) @ SV507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1729,plain,
! [SV668: $i,SV508: $i,SV290: $i,SV31: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV508 ) @ SV668 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ SV508 ) ) @ SV668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1730,plain,
! [SV669: $i,SV509: $i,SV291: $i,SV32: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV32 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ SV509 ) ) @ SV669 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV509 ) @ SV669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1731,plain,
! [SV670: $i,SV510: $i,SV292: $i,SV33: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV33 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV510 ) @ SV670 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV510 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ SV670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1732,plain,
! [SV671: $i,SV511: $i,SV293: $i,SV34: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV34 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ SV511 ) ) @ SV671 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV511 ) @ SV671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1733,plain,
! [SV672: $i,SV514: $i,SV296: $i,SV37: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV37 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV514 ) @ SV672 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV514 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ SV672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1734,plain,
! [SV673: $i,SV515: $i,SV297: $i,SV38: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV515 ) @ SV673 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ SV515 ) ) @ SV673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1735,plain,
! [SV516: $i,SV298: $i,SV39: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV298 ) @ SV516 ) @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV516 @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV298 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1736,plain,
! [SV40: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1737,plain,
! [SV674: $i,SV517: $i,SV299: $i,SV42: $i] :
( ( ! [SY1708: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV674 ) @ SY1708 ) @ SV42 )
| ~ ( c_lessequals @ SV517 @ SY1708 @ SV42 )
| ~ ( c_lessequals @ SV299 @ SV674 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1738,plain,
! [SV300: $i,SV43: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV43 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV300 ) @ SV300 ) @ SV43 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV300 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1739,plain,
! [SV301: $i,SV44: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV44 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ SV301 @ SV44 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV301 ) @ SV301 ) @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1740,plain,
! [SV518: $i,SV303: $i,SV46: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV46 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Power_Opower__class_Opower @ SV303 @ SV518 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ SV303 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1741,plain,
! [SV675: $i,SV519: $i,SV304: $i,SV47: $i] :
( ( ( c_Wellfounded_Oaccp @ SV47 @ SV304 @ SV519 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SV519 ) @ SV304 ) @ SV675 ) )
| ~ ( c_Wellfounded_Oaccp @ SV47 @ SV675 @ SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1742,plain,
! [SV676: $i,SV520: $i,SV305: $i,SV48: $i] :
( ( ( c_Wellfounded_Oaccp @ SV48 @ SV305 @ SV520 )
| ~ ( c_Wellfounded_Oaccp @ SV48 @ SV676 @ SV520 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV520 ) @ SV305 ) @ SV676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1743,plain,
! [SV521: $i,SV306: $i,SV51: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV51 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ ( c_Power_Opower__class_Opower @ SV306 @ SV521 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV306 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1744,plain,
! [SV677: $i,SV522: $i,SV309: $i,SV54: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
| ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
| ~ ( c_lessequals @ SV309 @ SV677 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1745,plain,
! [SV678: $i,SV523: $i,SV310: $i,SV55: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
| ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
| ~ ( c_lessequals @ SV310 @ SV523 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1746,plain,
! [SV524: $i,SV311: $i,SV56: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SV524 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV524 ) @ SV311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1747,plain,
! [SV525: $i,SV312: $i,SV57: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV57 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SV525 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV525 ) @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1748,plain,
! [SV526: $i,SV314: $i,SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SV526 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV526 ) @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1749,plain,
! [SV679: $i,SV527: $i,SV315: $i,SV60: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV60 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SV527 ) @ SV679 @ SV60 @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV527 @ SV679 @ SV60 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1750,plain,
! [SV528: $i,SV316: $i,SV61: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV61 ) )
= $true )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 @ SV528 @ SV61 @ SV61 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV528 @ SV316 @ SV61 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1751,plain,
! [SV529: $i,SV317: $i,SV62: $i] :
( ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Olist_ONil @ SV317 ) @ SV529 @ SV317 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1752,plain,
! [SV530: $i,SV318: $i,SV63: $i] :
( ( c_ListOrder_Ostep1 @ SV63 @ SV318 @ ( c_List_Olist_ONil @ SV530 ) @ SV530 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1753,plain,
! [SV531: $i,SV319: $i,SV64: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV64 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV319 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV531 @ SV64 @ SV64 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV319 @ SV531 @ SV64 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1754,plain,
! [SV680: $i,SV532: $i,SV320: $i,SV65: $i] :
( ( ( c_List_Ofoldl @ SV65 @ SV320 @ ( c_List_Olist_ONil @ SV532 ) @ SV680 @ SV532 )
= SV320 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1755,plain,
! [SV68: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1756,plain,
! [SV533: $i,SV321: $i,SV69: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV69 ) )
= $true )
| ( ( ( SV321 = SV533 )
| ~ ( c_lessequals @ SV533 @ SV321 @ SV69 )
| ~ ( c_lessequals @ SV321 @ SV533 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1757,plain,
! [SV534: $i,SV322: $i,SV70: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV70 ) )
= $true )
| ( ( ( SV322 = SV534 )
| ~ ( c_lessequals @ SV534 @ SV322 @ SV70 )
| ~ ( c_lessequals @ SV322 @ SV534 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1758,plain,
! [SV535: $i,SV323: $i,SV71: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV71 ) )
= $true )
| ( ( ( SV323 = SV535 )
| ~ ( c_lessequals @ SV323 @ SV535 @ SV71 )
| ~ ( c_lessequals @ SV535 @ SV323 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1759,plain,
! [SV681: $i,SV536: $i,SV324: $i,SV72: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV72 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV536 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV681 ) @ SV536 ) @ SV72 )
| ~ ( c_lessequals @ SV324 @ SV681 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1760,plain,
! [SV682: $i,SV537: $i,SV325: $i,SV73: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV73 )
| ( c_lessequals @ SV325 @ SV537 @ SV73 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV537 ) @ SV682 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1761,plain,
! [SV683: $i,SV538: $i,SV326: $i,SV74: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV74 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV683 ) @ SV74 )
| ~ ( c_lessequals @ SV538 @ SV683 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1762,plain,
! [SV684: $i,SV539: $i,SV327: $i,SV75: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV75 )
| ( c_lessequals @ SV327 @ SV539 @ SV75 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV539 ) @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1763,plain,
! [SV685: $i,SV540: $i,SV328: $i,SV76: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV76 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV328 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV685 ) @ SV540 ) @ SV76 )
| ~ ( c_lessequals @ SV328 @ SV685 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1764,plain,
! [SV686: $i,SV541: $i,SV329: $i,SV77: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV77 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV541 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV686 ) @ SV77 )
| ~ ( c_lessequals @ SV541 @ SV686 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1765,plain,
! [SV330: $i,SV78: $i] :
( ( ( class_Power_Opower @ SV78 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV330 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV78 )
= ( c_HOL_Oone__class_Oone @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1766,plain,
! [SV331: $i,SV79: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV79 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV331 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV79 )
= ( c_HOL_Oone__class_Oone @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1767,plain,
! [SV687: $i,SV542: $i,SV332: $i,SV80: $i] :
( ( ( c_Type_Otypings @ SV80 @ SV332 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV542 @ SV80 @ SV687 @ SV332 ) )
| ~ ( c_Type_Otyping @ SV80 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV687 @ SV332 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1768,plain,
! [SV334: $i,SV82: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV82 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ SV334 ) @ SV334 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 )
| ~ ( c_lessequals @ SV334 @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1769,plain,
! [SV335: $i,SV83: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV83 )
= $false )
| ( ( ( c_lessequals @ SV335 @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ SV335 ) @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1770,plain,
! [SV688: $i,SV544: $i,SV336: $i,SV84: $i] :
( ( ~ ( class_Orderings_Oorder @ SV84 )
| ( c_lessequals @ SV336 @ SV544 @ SV84 )
| ~ ( c_lessequals @ SV336 @ SV688 @ SV84 )
| ~ ( c_lessequals @ SV688 @ SV544 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1771,plain,
! [SV545: $i,SV337: $i,SV85: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV337 ) @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV545 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV337 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1772,plain,
! [SV689: $i,SV546: $i,SV338: $i,SV86: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV86 )
| ( c_lessequals @ SV338 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SV689 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SV338 @ SV689 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1773,plain,
! [SV339: $i,SV87: $i] :
( ( ( class_Orderings_Oorder @ SV87 )
= $false )
| ( ( c_lessequals @ SV339 @ SV339 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1774,plain,
! [SV340: $i,SV88: $i] :
( ( ( class_Orderings_Opreorder @ SV88 )
= $false )
| ( ( c_lessequals @ SV340 @ SV340 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1775,plain,
! [SV690: $i,SV547: $i,SV341: $i,SV89: $i] :
( ( ! [SY1709: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
| ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV690 ) @ SV89 )
| ~ ( c_lessequals @ SY1709 @ SV690 @ SV89 )
| ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SY1709 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1776,plain,
! [SV548: $i,SV342: $i,SV90: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV90 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV548 ) @ SV90 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV342 @ SV90 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV548 @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1777,plain,
! [SV691: $i,SV549: $i,SV344: $i,SV92: $i] :
( ( ( c_Wellfounded_Oaccp @ SV92 @ SV344 @ SV549 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV344 ) @ SV691 ) )
| ~ ( c_Wellfounded_Oaccp @ SV92 @ SV691 @ SV549 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1778,plain,
! [SV550: $i,SV345: $i,SV93: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV93 ) )
= $true )
| ( ( ( c_lessequals @ SV345 @ SV550 @ SV93 )
| ( c_lessequals @ SV550 @ SV345 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1779,plain,
! [SV692: $i,SV551: $i,SV346: $i,SV94: $i] :
( ( ( c_Wellfounded_Oaccp @ SV94 @ SV346 @ SV551 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV346 ) @ SV692 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SV692 @ SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1780,plain,
! [SV693: $i,SV552: $i,SV347: $i,SV95: $i] :
( ( ! [SY1710: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV693 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SY1710 ) @ SV693 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SY1710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1781,plain,
! [SV694: $i,SV553: $i,SV348: $i,SV96: $i] :
( ( ! [SY1711: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV553 ) @ SV694 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SY1711 ) @ SV694 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV553 ) @ SY1711 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1782,plain,
! [SV695: $i,SV554: $i,SV350: $i,SV99: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV99 ) @ SV350 ) @ SV554 @ SV695 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV99 @ SV554 @ SV695 ) ) @ ( c_Lambda_Osubst @ SV350 @ SV554 @ SV695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1783,plain,
! [SV696: $i,SV555: $i,SV351: $i,SV100: $i] :
( ( ( c_Type_Otypings @ SV100 @ SV351 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV555 @ SV100 @ SV696 @ SV351 ) )
| ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV696 ) @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1784,plain,
! [SV697: $i,SV556: $i,SV354: $i,SV103: $i] :
( ( ! [SY1712: $i,SY1713: $i,SY1714: $i] :
( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1712 ) @ SY1713 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
| ~ ( c_Type_Otypings @ SV556 @ SY1713 @ SY1714 )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1712 ) @ SY1713 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1785,plain,
! [SV557: $i,SV355: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV104 @ SV355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV557 @ SV355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV104 ) @ SV557 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1786,plain,
! [SV698: $i,SV558: $i,SV357: $i,SV106: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV106 )
| ( c_lessequals @ SV357 @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SV698 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SV558 @ ( c_Suc @ SV698 ) @ SV106 ) @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1787,plain,
! [SV358: $i,SV107: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV107 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV358 @ SV107 @ SV107 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ SV358 @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1788,plain,
! [SV559: $i,SV359: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SV359 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SV559 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV359 @ SV559 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1789,plain,
! [SV560: $i,SV360: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV109 @ SV360 ) ) @ ( c_Lambda_Olift @ SV560 @ SV360 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SV560 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1790,plain,
! [SV361: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV110 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV110 @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1791,plain,
! [SV699: $i,SV561: $i,SV362: $i,SV111: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV111 @ SV362 ) @ SV561 ) @ SV699 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV111 @ SV561 ) @ SV699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1792,plain,
! [SV700: $i,SV562: $i,SV363: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV112 @ SV363 @ SV562 ) ) @ ( c_Lambda_Osubst @ SV112 @ SV700 @ SV562 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV363 ) @ SV700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1793,plain,
! [SV701: $i,SV563: $i,SV364: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV113 @ SV364 @ SV563 ) ) @ ( c_Lambda_Osubst @ SV701 @ SV364 @ SV563 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV113 ) @ SV701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1794,plain,
! [SV702: $i,SV565: $i,SV366: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV115 @ SV366 @ SV565 ) ) @ ( c_Lambda_Osubst @ SV115 @ SV702 @ SV565 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV366 ) @ SV702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1795,plain,
! [SV367: $i,SV116: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV116 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV116 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Suc @ SV367 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1796,plain,
! [SV703: $i,SV566: $i,SV368: $i,SV117: $i] :
( ( ( c_Type_Otyping @ SV117 @ SV368 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV566 @ SV117 @ SV368 @ SV703 ) @ SV566 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV117 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV368 @ SV703 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1797,plain,
! [SV704: $i,SV567: $i,SV369: $i,SV118: $i] :
( ( ! [SY1715: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV704 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SY1715 ) @ SV704 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SY1715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1798,plain,
! [SV705: $i,SV570: $i,SV372: $i,SV121: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV121 @ SV372 @ SV570 ) ) @ ( c_Lambda_Osubst @ SV705 @ SV372 @ SV570 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV121 ) @ SV705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1799,plain,
! [SV122: $i] :
( ( ( ~ ( class_Power_Opower @ SV122 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV122 )
= ( c_HOL_Oone__class_Oone @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1800,plain,
! [SV571: $i,SV373: $i,SV123: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV123 @ SV373 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV571 @ 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 ) @ SV373 @ 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 @ SV123 ) ) @ SV373 ) @ SV571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1801,plain,
! [SV706: $i,SV572: $i,SV374: $i,SV124: $i] :
( ( ! [SY1716: $i] :
( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV374 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV706 )
| ~ ( c_Type_Otypings @ SV124 @ SV572 @ SY1716 )
| ~ ( c_Type_Otyping @ SV124 @ SV374 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1716 @ SV706 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1802,plain,
! [SV573: $i,SV376: $i,SV128: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV128 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV376 @ SV573 @ SV128 @ SV128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV376 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV573 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 @ SV128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1803,plain,
! [SV575: $i,SV378: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV132 @ SV378 ) ) @ ( c_Lambda_Olift @ SV575 @ SV378 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV132 ) @ SV575 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1804,plain,
! [SV707: $i,SV576: $i,SV379: $i,SV133: $i] :
( ( ( c_Type_Otyping @ SV133 @ SV379 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV576 @ SV133 @ SV379 @ SV707 ) @ SV576 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV133 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV379 @ SV707 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1805,plain,
! [SV577: $i,SV380: $i,SV134: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV134 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV380 @ SV134 @ SV577 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV380 ) @ SV134 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV577 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1806,plain,
! [SV708: $i,SV578: $i,SV382: $i,SV136: $i] :
( ( ( c_Type_Otype_Otype__case @ SV136 @ SV382 @ ( c_Type_Otype_OAtom @ SV578 ) @ SV708 )
= ( hAPP @ SV136 @ SV578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1807,plain,
! [SV383: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV137 ) @ SV383 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV137 ) ) @ ( c_Lambda_OdB_OAbs @ SV383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1808,plain,
! [SV138: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV384 ) ) @ SV138 ) )
= $false )
| ( ( SV138
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV384 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1809,plain,
! [SV709: $i,SV579: $i,SV385: $i,SV139: $i] :
( ( ! [SY1717: $i,SY1718: $i] :
( ~ ( c_Type_Otyping @ SV139 @ SV385 @ SV579 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SV709 @ SV579 @ tc_Type_Otype ) @ SY1717 @ SY1718 )
| ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SY1717 @ SV385 @ SV709 ) @ SY1718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1810,plain,
! [SV386: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV140 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV140 ) @ ( c_Lambda_OdB_OVar @ SV386 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1811,plain,
! [SV710: $i,SV580: $i,SV387: $i,SV141: $i] :
( ( ( c_Type_Otyping @ SV141 @ SV387 @ SV580 )
| ~ ( c_Type_Otyping @ SV141 @ SV710 @ SV580 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV710 ) @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1812,plain,
! [SV581: $i,SV388: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV143 ) @ SV388 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV581 ) @ SV388 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV143 ) @ SV581 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1813,plain,
! [SV582: $i,SV389: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SV389 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SV582 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV389 ) @ SV582 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1814,plain,
! [SV711: $i,SV583: $i,SV390: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV145 ) @ SV390 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV583 ) @ SV711 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV390 ) @ SV711 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV145 ) @ SV583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1815,plain,
! [SV712: $i,SV584: $i,SV391: $i,SV147: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Type_Otype_Otype__case @ SV391 @ SV584 @ ( c_Type_Otype_OAtom @ SV712 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV391 @ SV712 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1816,plain,
! [SV713: $i,SV585: $i,SV392: $i,SV148: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV148 @ ( c_Type_Otype_Otype__case @ SV392 @ SV585 @ ( c_Type_Otype_OAtom @ SV713 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV148 @ ( hAPP @ SV392 @ SV713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1817,plain,
! [SV586: $i,SV393: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV149 ) @ SV393 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV586 ) @ SV393 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV149 ) @ SV586 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1818,plain,
! [SV587: $i,SV394: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SV394 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SV587 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV394 ) @ SV587 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1603]) ).
thf(1819,plain,
! [SV395: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP @ SV152 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV152 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV152 @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1820,plain,
! [SV714: $i,SV588: $i,SV396: $i,SV153: $i] :
( ( ( c_Type_Otyping @ SV153 @ SV396 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV588 @ SV153 @ SV714 @ SV396 ) )
| ~ ( c_Type_Otyping @ SV153 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV714 ) @ SV396 ) @ SV588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1821,plain,
! [SV589: $i,SV397: $i,SV154: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV154 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV397 @ SV154 @ SV589 ) @ tc_Type_Otype ) @ SV589 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV397 @ SV154 @ SV589 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV154 @ ( c_Lambda_OdB_OAbs @ SV589 ) @ SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1607]) ).
thf(1822,plain,
! [SV590: $i,SV398: $i,SV155: $i] :
( ( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV398 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV398 @ SV590 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV398 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1608]) ).
thf(1823,plain,
! [SV399: $i,SV156: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV156 ) @ SV399 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV156 ) ) @ ( c_Lambda_OdB_OAbs @ SV399 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1824,plain,
! [SV715: $i,SV591: $i,SV400: $i,SV157: $i] :
( ( ( c_Type_Otyping @ SV157 @ ( c_Lambda_OdB_OVar @ SV400 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV591 @ SV157 @ SV400 @ SV715 ) @ SV591 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV157 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV400 ) @ SV715 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1825,plain,
! [SV592: $i,SV401: $i,SV159: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV159 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV159 @ SV401 ) @ tc_Type_Otype ) @ SV401 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV159 @ SV401 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV159 @ ( c_Lambda_OdB_OAbs @ SV401 ) @ SV592 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1611]) ).
thf(1826,plain,
! [SV716: $i,SV593: $i,SV402: $i,SV161: $i] :
( ( ! [SY1719: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ SV402 @ SV593 @ SV716 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1719 @ SV716 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1719 @ SV716 ) @ ( c_Suc @ SV402 ) @ SV593 @ SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1827,plain,
! [SV594: $i,SV403: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV162 ) ) @ SV403 ) @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV162 @ SV403 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1828,plain,
! [SV717: $i,SV595: $i,SV404: $i,SV163: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV163 @ SV404 @ SV595 @ SV717 ) @ SV404 )
= SV595 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1829,plain,
! [SV718: $i,SV596: $i,SV405: $i,SV164: $i] :
( ( ( c_Type_Otype_Otype__rec @ SV164 @ SV405 @ ( c_Type_Otype_OAtom @ SV596 ) @ SV718 )
= ( hAPP @ SV164 @ SV596 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1830,plain,
! [SV597: $i,SV406: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV165 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV597 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV165 ) @ SV597 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1831,plain,
! [SV719: $i,SV598: $i,SV408: $i,SV167: $i] :
( ( ! [SY1720: $i] :
( ( SV167 = SV408 )
| ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SY1720 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV408 )
| ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SY1720 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1832,plain,
! [SV168: $i,SV409: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV409 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SV409 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1833,plain,
! [SV411: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV170 ) ) @ SV411 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV170 ) @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV170 @ SV411 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1834,plain,
! [SV412: $i,SV172: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV172 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV172 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV412 @ SV172 )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
| ( SV412
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1835,plain,
! [SV413: $i,SV173: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV173 )
| ~ ( class_Power_Opower @ SV173 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1836,plain,
! [SV599: $i,SV414: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV174 @ ( c_Lambda_OdB_OVar @ SV414 ) @ SV599 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1837,plain,
! [SV720: $i,SV600: $i,SV415: $i,SV176: $i] :
( ( ! [SY1721: $i,SY1722: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
| ~ ( c_Type_Otyping @ SV720 @ SV415 @ SY1721 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SY1721 @ tc_Type_Otype ) @ SV176 @ SY1722 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1838,plain,
! [SV721: $i,SV601: $i,SV416: $i,SV177: $i] :
( ( ! [SY1723: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ SV416 @ SV601 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV721 @ SV416 ) @ SY1723 )
| ~ ( c_Type_Otyping @ SV177 @ SV721 @ SY1723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1839,plain,
! [SV602: $i,SV417: $i,SV178: $i] :
( ( ( SV178
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV178 @ SV417 @ SV602 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV178 @ SV417 @ SV602 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV417 @ ( c_Lambda_OdB_OAbs @ SV602 ) @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1840,plain,
! [SV722: $i,SV603: $i,SV418: $i,SV179: $i] :
( ( ( c_Type_Otyping @ SV179 @ SV418 @ SV603 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV722 ) @ SV418 ) )
| ~ ( c_Type_Otyping @ SV179 @ SV722 @ SV603 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1841,plain,
! [SV723: $i,SV604: $i,SV419: $i,SV180: $i] :
( ( ! [SY1724: $i] :
( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV419 ) @ SV604 ) @ SV723 )
| ~ ( c_Type_Otyping @ SV180 @ SV604 @ SY1724 )
| ~ ( c_Type_Otyping @ SV180 @ SV419 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1724 ) @ SV723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1842,plain,
! [SV724: $i,SV605: $i,SV420: $i,SV181: $i] :
( ( ( c_Type_Otyping @ SV181 @ ( c_Lambda_OdB_OAbs @ SV420 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV605 ) @ SV724 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV181 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV605 @ tc_Type_Otype ) @ SV420 @ SV724 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1843,plain,
! [SV606: $i,SV421: $i,SV182: $i] :
( ( ( ( hAPP @ SV182 @ SV421 )
= SV606 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SV421 ) @ SV606 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1844,plain,
! [SV725: $i,SV607: $i,SV422: $i,SV183: $i] :
( ( ! [SY1725: $i] :
( ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV607 ) @ SV725 ) @ SY1725 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV422 @ SV607 ) @ SV725 ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ SV607 @ SY1725 ) ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ SV725 @ SY1725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1845,plain,
! [SV726: $i,SV608: $i,SV423: $i,SV184: $i] :
( ( ! [SY1726: $i] :
( ( c_Type_Otype_Otype__case @ SV184 @ SV423 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV608 ) @ SV726 ) @ SY1726 )
= ( hAPP @ ( hAPP @ SV423 @ SV608 ) @ SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1846,plain,
! [SV727: $i,SV609: $i,SV425: $i,SV186: $i] :
( ( ! [SY1727: $i] :
( ~ ( hBOOL @ ( hAPP @ SV186 @ ( c_Type_Otype_Otype__case @ SV425 @ SV609 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV727 ) @ SY1727 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV186 @ ( hAPP @ ( hAPP @ SV609 @ SV727 ) @ SY1727 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1847,plain,
! [SV728: $i,SV610: $i,SV426: $i,SV187: $i] :
( ( ! [SY1728: $i] :
( ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_Type_Otype_Otype__case @ SV426 @ SV610 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV728 ) @ SY1728 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV187 @ ( hAPP @ ( hAPP @ SV610 @ SV728 ) @ SY1728 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1848,plain,
! [SV729: $i,SV611: $i,SV427: $i,SV188: $i] :
( ( ( c_Type_Otyping @ SV188 @ SV427 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV611 @ SV188 @ SV427 @ SV729 ) ) @ SV611 ) )
| ~ ( c_Type_Otyping @ SV188 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV427 ) @ SV729 ) @ SV611 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1849,plain,
! [SV189: $i,SV428: $i] :
( ( ( class_Orderings_Opreorder @ SV428 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV189 @ SV428 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1850,plain,
! [SV190: $i,SV429: $i] :
( ( ( class_Orderings_Oorder @ SV429 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV190 @ SV429 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1851,plain,
! [SV612: $i,SV431: $i,SV192: $i] :
( ( ( SV192 = SV431 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV612 ) @ SV192 ) @ SV431 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1638]) ).
thf(1852,plain,
! [SV613: $i,SV432: $i,SV193: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV193 @ SV432 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV613 @ SV432 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV193 = SV613 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1853,plain,
! [SV614: $i,SV433: $i,SV194: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV194 @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV614 ) )
= $true )
| ( ( SV433
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1854,plain,
! [SV434: $i,SV195: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV195 ) @ SV434 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV195
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1855,plain,
! [SV615: $i,SV435: $i,SV196: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV196 ) @ SV435 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV615 ) @ SV435 ) )
= $true )
| ( ( SV196 = SV615 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1856,plain,
! [SV730: $i,SV616: $i,SV436: $i,SV197: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV197 ) @ SV436 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV616 ) @ SV730 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV436 = SV730 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1857,plain,
! [SV731: $i,SV617: $i,SV437: $i,SV198: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV198 ) @ SV437 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV617 ) @ SV731 ) )
| ( SV198 = SV617 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1858,plain,
! [SV618: $i,SV438: $i,SV199: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV199 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV199 )
| ( SV438
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV438 ) @ SV618 ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1859,plain,
! [SV732: $i,SV619: $i,SV439: $i,SV200: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SV439 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV619 ) @ SV732 ) )
| ( SV200 = SV619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1860,plain,
! [SV620: $i,SV440: $i,SV201: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV201 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV440 @ SV620 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV201 )
= SV440 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1861,plain,
! [SV733: $i,SV621: $i,SV441: $i,SV202: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV202 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV441 ) @ SV621 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV733 ) @ SV621 ) )
| ( SV441 = SV733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1862,plain,
! [SV442: $i,SV203: $i] :
( ( ( SV203
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV203 ) @ SV442 ) )
= $false )
| ( ( SV442
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1863,plain,
! [SV734: $i,SV622: $i,SV443: $i,SV204: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV204 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV443 ) @ SV622 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SV734 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SV622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1864,plain,
! [SV623: $i,SV444: $i,SV205: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV444 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV623 ) )
= $true )
| ( ( SV444 = SV623 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1865,plain,
! [SV445: $i,SV206: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV206 ) @ SV445 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV445
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV445
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1866,plain,
! [SV624: $i,SV446: $i,SV207: $i] :
( ( ( c_Lambda_OdB_OVar @ SV207 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV446 ) @ SV624 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1867,plain,
! [SV625: $i,SV447: $i,SV208: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV208 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV447 @ SV625 @ SV208 )
!= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
| ( SV447
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1868,plain,
! [SV626: $i,SV448: $i,SV209: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
!= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
| ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1869,plain,
! [SV627: $i,SV449: $i,SV210: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV210 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV449 @ SV627 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV627
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1870,plain,
! [SV628: $i,SV450: $i,SV211: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
!= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
| ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1871,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV212 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV212 )
| ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1872,plain,
! [SV452: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV213 )
| ~ ( class_Power_Opower @ SV213 )
| ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1873,plain,
! [SV453: $i,SV214: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV214 ) @ SV453 )
= SV214 )
= $false )
| ( ( SV453
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1874,plain,
! [SV735: $i,SV630: $i,SV454: $i,SV215: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV215 )
| ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
!= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
| ( SV454 = SV735 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1875,plain,
! [SV631: $i,SV455: $i,SV216: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV216 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV455 @ SV631 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV216 )
= SV455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1876,plain,
! [SV456: $i,SV217: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV217 ) @ SV456 ) )
= $false )
| ( ( ( SV217
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV217
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1877,plain,
! [SV632: $i,SV457: $i,SV218: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV457 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV632 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV457 )
= SV632 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(1878,plain,
! [SV736: $i,SV633: $i,SV458: $i,SV219: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV219 ) ) @ SV458 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV633 ) @ SV736 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1879,plain,
! [SV634: $i,SV460: $i,SV221: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV221 ) @ SV460 )
= ( c_Type_Otype_OAtom @ SV634 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1880,plain,
! [SV737: $i,SV635: $i,SV461: $i,SV222: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV222 ) @ SV461 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV635 ) @ SV737 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1881,plain,
! [SV738: $i,SV636: $i,SV462: $i,SV223: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV223 ) @ SV462 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ SV738 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV223 = SV636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1882,plain,
! [SV637: $i,SV463: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SV463 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SV637 ) )
= $true )
| ( ( SV463 = SV637 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1883,plain,
! [SV465: $i,SV226: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV226 ) @ SV465 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1884,plain,
! [SV227: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV227 )
= ( c_HOL_Oone__class_Oone @ SV227 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1885,plain,
! [SV739: $i,SV638: $i,SV466: $i,SV228: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV228 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV739 ) )
| ( SV638 = SV739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1886,plain,
! [SV740: $i,SV639: $i,SV467: $i,SV229: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV229 )
| ~ ( class_Int_Onumber__ring @ SV229 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV639 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV740 ) )
| ( SV639 = SV740 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1887,plain,
! [SV468: $i,SV231: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV231 ) @ SV468 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV468
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1888,plain,
! [SV469: $i,SV232: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV232 ) @ SV469 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV232
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1889,plain,
! [SV470: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV233 ) @ SV470 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV470
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV233
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1890,plain,
! [SV471: $i,SV234: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV234 )
= ( c_Lambda_OdB_OVar @ SV471 ) )
= $false )
| ( ( SV234 = SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1891,plain,
! [SV741: $i,SV640: $i,SV472: $i,SV235: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV640 ) @ SV741 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV235 = SV640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1892,plain,
! [SV742: $i,SV641: $i,SV473: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV473 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV641 ) @ SV742 ) )
| ( SV473 = SV742 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1893,plain,
! [SV642: $i,SV474: $i,SV237: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV237 ) @ SV474 )
= ( c_Lambda_OdB_OAbs @ SV642 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1894,plain,
! [SV475: $i,SV239: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV239 )
= ( c_Lambda_OdB_OAbs @ SV475 ) )
= $false )
| ( ( SV239 = SV475 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1895,plain,
! [SV476: $i,SV240: $i] :
( ( ( ( c_Suc @ SV240 )
= ( c_Suc @ SV476 ) )
= $false )
| ( ( SV240 = SV476 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1896,plain,
! [SV643: $i,SV477: $i,SV242: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV242 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV477 ) @ SV643 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1897,plain,
! [SV644: $i,SV478: $i,SV244: $i] :
( ( ( c_Type_Otype_OAtom @ SV244 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV478 ) @ SV644 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1898,plain,
! [SV479: $i,SV245: $i] :
( ( ( ( c_Suc @ SV245 )
= ( c_Suc @ SV479 ) )
= $false )
| ( ( SV245 = SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1899,plain,
! [SV743: $i,SV645: $i,SV480: $i,SV246: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV246 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV480 ) @ SV645 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SV743 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SV480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(1900,plain,
! [SV646: $i,SV481: $i,SV247: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV247 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV481 @ SV247 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV646 @ SV247 ) )
| ( SV481 = SV646 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(1901,plain,
! [SV482: $i,SV248: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV248 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV248 ) @ SV482 ) @ SV482 )
!= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
| ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV248 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1902,plain,
! [SV744: $i,SV647: $i,SV483: $i,SV249: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV647 ) @ SV744 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV483 = SV744 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1903,plain,
! [SV484: $i,SV250: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV250 ) @ SV484 ) )
= $false )
| ( ( ( SV484
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV250
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1904,plain,
! [SV745: $i,SV648: $i,SV485: $i,SV251: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV251 ) @ SV485 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV648 ) @ SV745 ) )
| ( SV485 = SV745 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1905,plain,
! [SV486: $i,SV252: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV252 )
= ( c_Type_Otype_OAtom @ SV486 ) )
= $false )
| ( ( SV252 = SV486 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1906,plain,
! [SV253: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV253 )
= ( c_HOL_Ozero__class_Ozero @ SV253 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1907,plain,
! [SV746: $i,SV649: $i,SV487: $i,SV254: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV254 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV649 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV746 ) )
| ( SV649 = SV746 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(1908,plain,
! [SV650: $i,SV488: $i,SV255: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SV488 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV650 ) )
= $true )
| ( ( SV255
= ( c_Lambda_OdB_OAbs @ SV650 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1909,plain,
! [SV489: $i,SV257: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV257 ) @ SV489 ) )
= $false )
| ( ( ( SV257
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV489
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1910,plain,
! [SV490: $i,SV258: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV258 ) @ SV490 ) )
= $false )
| ( ( ( SV490
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV490
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1911,plain,
! [SV747: $i,SV651: $i,SV491: $i,SV259: $i] :
( ( ! [SY1729: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV259 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV747 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SY1729 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ SV747 )
= SY1729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(1912,plain,
! [SV652: $i,SV492: $i,SV260: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV260 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV492 @ SV652 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV652
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1913,plain,
! [SV653: $i,SV493: $i,SV261: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV261 ) @ SV493 )
= ( c_Lambda_OdB_OVar @ SV653 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1914,plain,
! [SV654: $i,SV494: $i,SV263: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV1 @ SV263 ) @ SV494 ) @ SV654 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV1 @ SV263 @ SV263 ) @ SV263 ) @ SV654 ) @ SV494 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1915,plain,
! [SV655: $i,SV495: $i,SV264: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV2 @ SV264 @ SV264 ) @ SV264 ) @ SV495 ) @ SV655 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV2 @ SV264 ) @ SV655 ) @ SV495 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1916,plain,
! [SV748: $i,SV656: $i,SV496: $i,SV265: $i,SV3: $i] :
( ( ! [SY1730: $i,SY1731: $i] :
( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SY1730 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
| ~ ( c_Type_Otypings @ SV3 @ SY1730 @ SY1731 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SY1730 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1917,plain,
! [SV749: $i,SV657: $i,SV497: $i,SV266: $i,SV4: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV657 ) @ SV749 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV657 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV497 ) @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(1918,plain,
! [SV271: $i,SV12: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV12 ) )
= $true )
| ( ( SV271
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV12 ) @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV12 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1919,plain,
! [SV658: $i,SV498: $i,SV279: $i,SV20: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SV498 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV658 @ SV498 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 )
| ~ ( c_lessequals @ SV279 @ SV658 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1920,plain,
! [SV660: $i,SV500: $i,SV281: $i,SV22: $i] :
( ( ( c_Type_Otypings @ SV22 @ SV281 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV500 @ SV22 @ SV660 @ SV281 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV22 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV660 @ SV281 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1921,plain,
! [SV750: $i,SV661: $i,SV501: $i,SV283: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV283 ) @ SV501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV24 @ SV661 @ SV750 ) @ SV501 ) @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(1922,plain,
! [SV751: $i,SV662: $i,SV502: $i,SV284: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV25 @ SV284 @ SV502 ) @ SV662 ) @ SV751 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV25 @ SV751 ) @ SV662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(1923,plain,
! [SV752: $i,SV663: $i,SV503: $i,SV285: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV26 @ SV285 ) @ SV503 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV26 @ SV663 @ SV752 ) @ SV503 ) @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(1924,plain,
! [SV753: $i,SV664: $i,SV504: $i,SV286: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV27 @ SV286 @ SV504 ) @ SV664 ) @ SV753 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV27 @ SV753 ) @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(1925,plain,
! [SV665: $i,SV505: $i,SV287: $i,SV28: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV28 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ SV505 ) ) @ SV665 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV505 ) @ SV665 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1926,plain,
! [SV666: $i,SV506: $i,SV288: $i,SV29: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV29 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV506 ) @ SV666 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV506 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ SV666 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1927,plain,
! [SV667: $i,SV507: $i,SV289: $i,SV30: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV30 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SV507 ) ) @ SV667 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SV667 ) ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(1928,plain,
! [SV668: $i,SV508: $i,SV290: $i,SV31: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV31 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV508 ) @ SV668 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ SV508 ) ) @ SV668 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(1929,plain,
! [SV669: $i,SV509: $i,SV291: $i,SV32: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV32 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ SV509 ) ) @ SV669 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV509 ) @ SV669 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(1930,plain,
! [SV670: $i,SV510: $i,SV292: $i,SV33: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV33 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV510 ) @ SV670 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV510 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ SV670 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1931,plain,
! [SV671: $i,SV511: $i,SV293: $i,SV34: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV34 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ SV511 ) ) @ SV671 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV511 ) @ SV671 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1932,plain,
! [SV672: $i,SV514: $i,SV296: $i,SV37: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV37 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV514 ) @ SV672 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV514 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ SV672 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1933,plain,
! [SV673: $i,SV515: $i,SV297: $i,SV38: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV38 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV515 ) @ SV673 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ SV515 ) ) @ SV673 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1934,plain,
! [SV516: $i,SV298: $i,SV39: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV298 ) @ SV516 ) @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV516 @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV298 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1935,plain,
! [SV40: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1936,plain,
! [SV754: $i,SV674: $i,SV517: $i,SV299: $i,SV42: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV674 ) @ SV754 ) @ SV42 )
| ~ ( c_lessequals @ SV517 @ SV754 @ SV42 )
| ~ ( c_lessequals @ SV299 @ SV674 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(1937,plain,
! [SV300: $i,SV43: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV300 ) @ SV300 ) @ SV43 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV300 @ SV43 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1938,plain,
! [SV301: $i,SV44: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ SV301 @ SV44 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV301 ) @ SV301 ) @ SV44 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1939,plain,
! [SV518: $i,SV303: $i,SV46: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV46 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Power_Opower__class_Opower @ SV303 @ SV518 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ SV303 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1940,plain,
! [SV675: $i,SV519: $i,SV304: $i,SV47: $i] :
( ( ( c_Wellfounded_Oaccp @ SV47 @ SV304 @ SV519 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SV519 ) @ SV304 ) @ SV675 ) )
| ~ ( c_Wellfounded_Oaccp @ SV47 @ SV675 @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1941,plain,
! [SV676: $i,SV520: $i,SV305: $i,SV48: $i] :
( ( ( c_Wellfounded_Oaccp @ SV48 @ SV305 @ SV520 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV48 @ SV676 @ SV520 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV520 ) @ SV305 ) @ SV676 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(1942,plain,
! [SV521: $i,SV306: $i,SV51: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV51 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ ( c_Power_Opower__class_Opower @ SV306 @ SV521 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV306 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1943,plain,
! [SV677: $i,SV522: $i,SV309: $i,SV54: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
| ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
| ~ ( c_lessequals @ SV309 @ SV677 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(1944,plain,
! [SV678: $i,SV523: $i,SV310: $i,SV55: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
| ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
| ~ ( c_lessequals @ SV310 @ SV523 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(1945,plain,
! [SV524: $i,SV311: $i,SV56: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SV524 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV524 ) @ SV311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1946,plain,
! [SV525: $i,SV312: $i,SV57: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV57 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SV525 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV525 ) @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1947,plain,
! [SV526: $i,SV314: $i,SV59: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV59 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SV526 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV526 ) @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1948,plain,
! [SV679: $i,SV527: $i,SV315: $i,SV60: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV60 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SV527 ) @ SV679 @ SV60 @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV527 @ SV679 @ SV60 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(1949,plain,
! [SV528: $i,SV316: $i,SV61: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV61 )
= $false )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 @ SV528 @ SV61 @ SV61 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV528 @ SV316 @ SV61 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1950,plain,
! [SV531: $i,SV319: $i,SV64: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV64 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV319 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV531 @ SV64 @ SV64 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV319 @ SV531 @ SV64 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1951,plain,
! [SV533: $i,SV321: $i,SV69: $i] :
( ( ( class_Orderings_Oorder @ SV69 )
= $false )
| ( ( ( SV321 = SV533 )
| ~ ( c_lessequals @ SV533 @ SV321 @ SV69 )
| ~ ( c_lessequals @ SV321 @ SV533 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1952,plain,
! [SV534: $i,SV322: $i,SV70: $i] :
( ( ( class_Orderings_Oorder @ SV70 )
= $false )
| ( ( ( SV322 = SV534 )
| ~ ( c_lessequals @ SV534 @ SV322 @ SV70 )
| ~ ( c_lessequals @ SV322 @ SV534 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1953,plain,
! [SV535: $i,SV323: $i,SV71: $i] :
( ( ( class_Orderings_Oorder @ SV71 )
= $false )
| ( ( ( SV323 = SV535 )
| ~ ( c_lessequals @ SV323 @ SV535 @ SV71 )
| ~ ( c_lessequals @ SV535 @ SV323 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1954,plain,
! [SV681: $i,SV536: $i,SV324: $i,SV72: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV72 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV536 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV681 ) @ SV536 ) @ SV72 )
| ~ ( c_lessequals @ SV324 @ SV681 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1955,plain,
! [SV682: $i,SV537: $i,SV325: $i,SV73: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV73 ) )
= $true )
| ( ( ( c_lessequals @ SV325 @ SV537 @ SV73 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV537 ) @ SV682 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1956,plain,
! [SV683: $i,SV538: $i,SV326: $i,SV74: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV74 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV683 ) @ SV74 )
| ~ ( c_lessequals @ SV538 @ SV683 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(1957,plain,
! [SV684: $i,SV539: $i,SV327: $i,SV75: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV75 ) )
= $true )
| ( ( ( c_lessequals @ SV327 @ SV539 @ SV75 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV539 ) @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(1958,plain,
! [SV685: $i,SV540: $i,SV328: $i,SV76: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV76 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV328 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV685 ) @ SV540 ) @ SV76 )
| ~ ( c_lessequals @ SV328 @ SV685 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(1959,plain,
! [SV686: $i,SV541: $i,SV329: $i,SV77: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV77 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV541 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV686 ) @ SV77 )
| ~ ( c_lessequals @ SV541 @ SV686 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(1960,plain,
! [SV687: $i,SV542: $i,SV332: $i,SV80: $i] :
( ( ( c_Type_Otypings @ SV80 @ SV332 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV542 @ SV80 @ SV687 @ SV332 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV80 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV687 @ SV332 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(1961,plain,
! [SV334: $i,SV82: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ SV334 ) @ SV334 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 )
= $true )
| ( ( ~ ( c_lessequals @ SV334 @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1962,plain,
! [SV83: $i,SV335: $i] :
( ( ( c_lessequals @ SV335 @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ SV335 ) @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1963,plain,
! [SV688: $i,SV544: $i,SV336: $i,SV84: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV84 ) )
= $true )
| ( ( ( c_lessequals @ SV336 @ SV544 @ SV84 )
| ~ ( c_lessequals @ SV336 @ SV688 @ SV84 )
| ~ ( c_lessequals @ SV688 @ SV544 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1964,plain,
! [SV545: $i,SV337: $i,SV85: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV337 ) @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV545 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV337 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1965,plain,
! [SV689: $i,SV546: $i,SV338: $i,SV86: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV86 ) )
= $true )
| ( ( ( c_lessequals @ SV338 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SV689 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SV338 @ SV689 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1966,plain,
! [SV755: $i,SV690: $i,SV547: $i,SV341: $i,SV89: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
| ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV690 ) @ SV89 )
| ~ ( c_lessequals @ SV755 @ SV690 @ SV89 )
| ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV755 ) @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(1967,plain,
! [SV548: $i,SV342: $i,SV90: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV90 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV548 ) @ SV90 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV90 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV342 @ SV90 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV548 @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1968,plain,
! [SV691: $i,SV549: $i,SV344: $i,SV92: $i] :
( ( ( c_Wellfounded_Oaccp @ SV92 @ SV344 @ SV549 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV344 ) @ SV691 ) )
| ~ ( c_Wellfounded_Oaccp @ SV92 @ SV691 @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1969,plain,
! [SV550: $i,SV345: $i,SV93: $i] :
( ( ( class_Orderings_Olinorder @ SV93 )
= $false )
| ( ( ( c_lessequals @ SV345 @ SV550 @ SV93 )
| ( c_lessequals @ SV550 @ SV345 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1970,plain,
! [SV692: $i,SV551: $i,SV346: $i,SV94: $i] :
( ( ( c_Wellfounded_Oaccp @ SV94 @ SV346 @ SV551 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV346 ) @ SV692 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SV692 @ SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1971,plain,
! [SV756: $i,SV693: $i,SV552: $i,SV347: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV693 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV756 ) @ SV693 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(1972,plain,
! [SV757: $i,SV694: $i,SV553: $i,SV348: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV553 ) @ SV694 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV757 ) @ SV694 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV553 ) @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(1973,plain,
! [SV696: $i,SV555: $i,SV351: $i,SV100: $i] :
( ( ( c_Type_Otypings @ SV100 @ SV351 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV555 @ SV100 @ SV696 @ SV351 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV696 ) @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV555 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(1974,plain,
! [SV758: $i,SV697: $i,SV556: $i,SV354: $i,SV103: $i] :
( ( ! [SY1732: $i,SY1733: $i] :
( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SY1732 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
| ~ ( c_Type_Otypings @ SV556 @ SY1732 @ SY1733 )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SY1732 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(1975,plain,
! [SV355: $i,SV557: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV104 ) @ SV557 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV104 @ SV355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV557 @ SV355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1976,plain,
! [SV698: $i,SV558: $i,SV357: $i,SV106: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV106 ) )
= $true )
| ( ( ( c_lessequals @ SV357 @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SV698 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SV558 @ ( c_Suc @ SV698 ) @ SV106 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(1977,plain,
! [SV108: $i,SV559: $i,SV359: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV359 @ SV559 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SV359 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV108 @ SV559 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1978,plain,
! [SV360: $i,SV560: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV109 ) @ SV560 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV109 @ SV360 ) ) @ ( c_Lambda_Olift @ SV560 @ SV360 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1979,plain,
! [SV699: $i,SV561: $i,SV362: $i,SV111: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV111 @ SV362 ) @ SV561 ) @ SV699 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV111 @ SV561 ) @ SV699 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1980,plain,
! [SV700: $i,SV562: $i,SV363: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV112 @ SV363 @ SV562 ) ) @ ( c_Lambda_Osubst @ SV112 @ SV700 @ SV562 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV363 ) @ SV700 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(1981,plain,
! [SV701: $i,SV563: $i,SV364: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV113 @ SV364 @ SV563 ) ) @ ( c_Lambda_Osubst @ SV701 @ SV364 @ SV563 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV113 ) @ SV701 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1982,plain,
! [SV702: $i,SV565: $i,SV366: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV115 @ SV366 @ SV565 ) ) @ ( c_Lambda_Osubst @ SV115 @ SV702 @ SV565 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV366 ) @ SV702 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1983,plain,
! [SV367: $i,SV116: $i] :
( ( ( ~ ( class_Power_Opower @ SV116 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Suc @ SV367 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(1984,plain,
! [SV703: $i,SV566: $i,SV368: $i,SV117: $i] :
( ( ( c_Type_Otyping @ SV117 @ SV368 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV566 @ SV117 @ SV368 @ SV703 ) @ SV566 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV117 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV368 @ SV703 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1985,plain,
! [SV759: $i,SV704: $i,SV567: $i,SV369: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV704 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV759 ) @ SV704 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(1986,plain,
! [SV705: $i,SV570: $i,SV372: $i,SV121: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV121 @ SV372 @ SV570 ) ) @ ( c_Lambda_Osubst @ SV705 @ SV372 @ SV570 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV121 ) @ SV705 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1987,plain,
! [SV122: $i] :
( ( ( class_Power_Opower @ SV122 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV122 )
= ( c_HOL_Oone__class_Oone @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1988,plain,
! [SV571: $i,SV373: $i,SV123: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV123 @ SV373 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV571 @ 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 ) @ SV373 @ 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 @ SV123 ) ) @ SV373 ) @ SV571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1989,plain,
! [SV760: $i,SV706: $i,SV572: $i,SV374: $i,SV124: $i] :
( ( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV374 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV706 )
| ~ ( c_Type_Otypings @ SV124 @ SV572 @ SV760 )
| ~ ( c_Type_Otyping @ SV124 @ SV374 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV760 @ SV706 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(1990,plain,
! [SV573: $i,SV376: $i,SV128: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV128 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV376 @ SV573 @ SV128 @ SV128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV376 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV128 ) @ SV573 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 @ SV128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1991,plain,
! [SV378: $i,SV575: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV132 ) @ SV575 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV132 @ SV378 ) ) @ ( c_Lambda_Olift @ SV575 @ SV378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1992,plain,
! [SV707: $i,SV576: $i,SV379: $i,SV133: $i] :
( ( ( c_Type_Otyping @ SV133 @ SV379 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV576 @ SV133 @ SV379 @ SV707 ) @ SV576 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV133 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV379 @ SV707 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV576 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1993,plain,
! [SV577: $i,SV134: $i,SV380: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV380 ) @ SV134 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV577 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV134 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV380 @ SV134 @ SV577 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1994,plain,
! [SV761: $i,SV709: $i,SV579: $i,SV385: $i,SV139: $i] :
( ( ! [SY1734: $i] :
( ~ ( c_Type_Otyping @ SV139 @ SV385 @ SV579 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SV709 @ SV579 @ tc_Type_Otype ) @ SV761 @ SY1734 )
| ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SV761 @ SV385 @ SV709 ) @ SY1734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(1995,plain,
! [SV710: $i,SV580: $i,SV387: $i,SV141: $i] :
( ( ( c_Type_Otyping @ SV141 @ SV387 @ SV580 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV141 @ SV710 @ SV580 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV710 ) @ SV387 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(1996,plain,
! [SV388: $i,SV581: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV143 ) @ SV581 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV143 ) @ SV388 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV581 ) @ SV388 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1997,plain,
! [SV144: $i,SV582: $i,SV389: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV389 ) @ SV582 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SV389 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV144 ) @ SV582 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1998,plain,
! [SV711: $i,SV583: $i,SV390: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV145 ) @ SV390 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV583 ) @ SV711 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV390 ) @ SV711 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV145 ) @ SV583 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(1999,plain,
! [SV712: $i,SV584: $i,SV391: $i,SV147: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV147 @ ( c_Type_Otype_Otype__case @ SV391 @ SV584 @ ( c_Type_Otype_OAtom @ SV712 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV391 @ SV712 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(2000,plain,
! [SV713: $i,SV585: $i,SV392: $i,SV148: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV148 @ ( c_Type_Otype_Otype__case @ SV392 @ SV585 @ ( c_Type_Otype_OAtom @ SV713 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV148 @ ( hAPP @ SV392 @ SV713 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(2001,plain,
! [SV393: $i,SV586: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV149 ) @ SV586 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV149 ) @ SV393 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV586 ) @ SV393 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(2002,plain,
! [SV150: $i,SV587: $i,SV394: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV394 ) @ SV587 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SV394 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV150 ) @ SV587 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(2003,plain,
! [SV714: $i,SV588: $i,SV396: $i,SV153: $i] :
( ( ( c_Type_Otyping @ SV153 @ SV396 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV588 @ SV153 @ SV714 @ SV396 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV153 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV714 ) @ SV396 ) @ SV588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2004,plain,
! [SV397: $i,SV589: $i,SV154: $i] :
( ( ( c_Type_Otyping @ SV154 @ ( c_Lambda_OdB_OAbs @ SV589 ) @ SV397 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV154 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV397 @ SV154 @ SV589 ) @ tc_Type_Otype ) @ SV589 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV397 @ SV154 @ SV589 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(2005,plain,
! [SV155: $i,SV590: $i,SV398: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV398 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV155 ) )
= $false )
| ( ( SV155
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV398 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV398 @ SV590 @ SV155 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(2006,plain,
! [SV715: $i,SV591: $i,SV400: $i,SV157: $i] :
( ( ( c_Type_Otyping @ SV157 @ ( c_Lambda_OdB_OVar @ SV400 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV591 @ SV157 @ SV400 @ SV715 ) @ SV591 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV157 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV400 ) @ SV715 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(2007,plain,
! [SV592: $i,SV401: $i,SV159: $i] :
( ( ( c_Type_Otyping @ SV159 @ ( c_Lambda_OdB_OAbs @ SV401 ) @ SV592 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV159 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV159 @ SV401 ) @ tc_Type_Otype ) @ SV401 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV159 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(2008,plain,
! [SV762: $i,SV716: $i,SV593: $i,SV402: $i,SV161: $i] :
( ( ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ SV402 @ SV593 @ SV716 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV762 @ SV716 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV161 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV762 @ SV716 ) @ ( c_Suc @ SV402 ) @ SV593 @ SV716 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2009,plain,
! [SV594: $i,SV162: $i,SV403: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV162 @ SV403 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV594 @ 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 @ SV162 ) ) @ SV403 ) @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2010,plain,
! [SV406: $i,SV597: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV165 ) @ SV597 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV165 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV597 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(2011,plain,
! [SV763: $i,SV719: $i,SV598: $i,SV408: $i,SV167: $i] :
( ( ( SV167 = SV408 )
| ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV408 )
| ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2012,plain,
! [SV412: $i,SV172: $i] :
( ( ( ~ ( class_Power_Opower @ SV172 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV412 @ SV172 )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
| ( SV412
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2013,plain,
! [SV413: $i,SV173: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV173 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV173 )
| ~ ( class_Power_Opower @ SV173 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2014,plain,
! [SV599: $i,SV414: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV174 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV174 @ ( c_Lambda_OdB_OVar @ SV414 ) @ SV599 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(2015,plain,
! [SV764: $i,SV720: $i,SV600: $i,SV415: $i,SV176: $i] :
( ( ! [SY1735: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
| ~ ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SY1735 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2016,plain,
! [SV765: $i,SV721: $i,SV601: $i,SV416: $i,SV177: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ SV416 @ SV601 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV721 @ SV416 ) @ SV765 )
| ~ ( c_Type_Otyping @ SV177 @ SV721 @ SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2017,plain,
! [SV178: $i,SV602: $i,SV417: $i] :
( ( ( c_Type_Otyping @ SV417 @ ( c_Lambda_OdB_OAbs @ SV602 ) @ SV178 )
= $false )
| ( ( SV178
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV178 @ SV417 @ SV602 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV178 @ SV417 @ SV602 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(2018,plain,
! [SV722: $i,SV603: $i,SV418: $i,SV179: $i] :
( ( ( c_Type_Otyping @ SV179 @ SV418 @ SV603 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV722 ) @ SV418 ) )
| ~ ( c_Type_Otyping @ SV179 @ SV722 @ SV603 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(2019,plain,
! [SV766: $i,SV723: $i,SV604: $i,SV419: $i,SV180: $i] :
( ( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV419 ) @ SV604 ) @ SV723 )
| ~ ( c_Type_Otyping @ SV180 @ SV604 @ SV766 )
| ~ ( c_Type_Otyping @ SV180 @ SV419 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2020,plain,
! [SV724: $i,SV605: $i,SV420: $i,SV181: $i] :
( ( ( c_Type_Otyping @ SV181 @ ( c_Lambda_OdB_OAbs @ SV420 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV605 ) @ SV724 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV181 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV605 @ tc_Type_Otype ) @ SV420 @ SV724 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(2021,plain,
! [SV606: $i,SV421: $i,SV182: $i] :
( ( ( c_Type_Otyping @ SV182 @ ( c_Lambda_OdB_OVar @ SV421 ) @ SV606 )
= $false )
| ( ( ( hAPP @ SV182 @ SV421 )
= SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(2022,plain,
! [SV767: $i,SV725: $i,SV607: $i,SV422: $i,SV183: $i] :
( ( ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV607 ) @ SV725 ) @ SV767 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV422 @ SV607 ) @ SV725 ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ SV607 @ SV767 ) ) @ ( c_Type_Otype_Otype__rec @ SV183 @ SV422 @ SV725 @ SV767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2023,plain,
! [SV768: $i,SV726: $i,SV608: $i,SV423: $i,SV184: $i] :
( ( ( c_Type_Otype_Otype__case @ SV184 @ SV423 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV608 ) @ SV726 ) @ SV768 )
= ( hAPP @ ( hAPP @ SV423 @ SV608 ) @ SV726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2024,plain,
! [SV769: $i,SV727: $i,SV609: $i,SV425: $i,SV186: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV186 @ ( c_Type_Otype_Otype__case @ SV425 @ SV609 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV727 ) @ SV769 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV186 @ ( hAPP @ ( hAPP @ SV609 @ SV727 ) @ SV769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2025,plain,
! [SV770: $i,SV728: $i,SV610: $i,SV426: $i,SV187: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_Type_Otype_Otype__case @ SV426 @ SV610 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV728 ) @ SV770 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV187 @ ( hAPP @ ( hAPP @ SV610 @ SV728 ) @ SV770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2026,plain,
! [SV729: $i,SV611: $i,SV427: $i,SV188: $i] :
( ( ( c_Type_Otyping @ SV188 @ SV427 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV611 @ SV188 @ SV427 @ SV729 ) ) @ SV611 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV188 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV427 ) @ SV729 ) @ SV611 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2027,plain,
! [SV431: $i,SV192: $i,SV612: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV612 ) @ SV192 ) @ SV431 ) )
= $false )
| ( ( SV192 = SV431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(2028,plain,
! [SV613: $i,SV432: $i,SV193: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV193 @ SV432 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV613 @ SV432 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV193 = SV613 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2029,plain,
! [SV614: $i,SV433: $i,SV194: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV194 @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV614 ) )
= $false )
| ( ( SV433
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(2030,plain,
! [SV615: $i,SV435: $i,SV196: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV196 ) @ SV435 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV615 ) @ SV435 ) )
= $false )
| ( ( SV196 = SV615 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(2031,plain,
! [SV730: $i,SV616: $i,SV436: $i,SV197: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV197 ) @ SV436 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV616 ) @ SV730 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV436 = SV730 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(2032,plain,
! [SV731: $i,SV617: $i,SV437: $i,SV198: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV198 ) @ SV437 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV617 ) @ SV731 ) )
= $true )
| ( ( SV198 = SV617 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(2033,plain,
! [SV618: $i,SV438: $i,SV199: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV199 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV199 )
| ( SV438
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV438 ) @ SV618 ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2034,plain,
! [SV732: $i,SV619: $i,SV439: $i,SV200: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SV439 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV619 ) @ SV732 ) )
= $true )
| ( ( SV200 = SV619 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(2035,plain,
! [SV620: $i,SV440: $i,SV201: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV201 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV440 @ SV620 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV201 )
= SV440 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2036,plain,
! [SV733: $i,SV621: $i,SV441: $i,SV202: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV202 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV441 ) @ SV621 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV733 ) @ SV621 ) )
| ( SV441 = SV733 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2037,plain,
! [SV734: $i,SV622: $i,SV443: $i,SV204: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV204 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV443 ) @ SV622 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV204 @ SV734 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SV622 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(2038,plain,
! [SV623: $i,SV444: $i,SV205: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV444 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV205 ) @ SV623 ) )
= $false )
| ( ( SV444 = SV623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2039,plain,
! [SV206: $i,SV445: $i] :
( ( ( SV445
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV445
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV206 ) @ SV445 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(2040,plain,
! [SV625: $i,SV447: $i,SV208: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV208 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV447 @ SV625 @ SV208 )
!= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
| ( SV447
= ( c_HOL_Ozero__class_Ozero @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2041,plain,
! [SV626: $i,SV448: $i,SV209: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
!= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
| ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(2042,plain,
! [SV627: $i,SV449: $i,SV210: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV210 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV449 @ SV627 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV627
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(2043,plain,
! [SV628: $i,SV450: $i,SV211: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
!= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
| ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2044,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV212 )
| ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(2045,plain,
! [SV452: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV213 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV213 )
| ~ ( class_Power_Opower @ SV213 )
| ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2046,plain,
! [SV735: $i,SV630: $i,SV454: $i,SV215: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV215 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
!= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
| ( SV454 = SV735 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2047,plain,
! [SV631: $i,SV455: $i,SV216: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV216 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV455 @ SV631 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV216 )
= SV455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(2048,plain,
! [SV456: $i,SV217: $i] :
( ( ( SV217
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV217
= ( 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 ) @ SV217 ) @ SV456 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2049,plain,
! [SV632: $i,SV457: $i,SV218: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV457 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV632 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV457 )
= SV632 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(2050,plain,
! [SV736: $i,SV633: $i,SV458: $i,SV219: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV219 ) ) @ SV458 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV633 ) @ SV736 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2051,plain,
! [SV737: $i,SV635: $i,SV461: $i,SV222: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV222 ) @ SV461 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV635 ) @ SV737 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2052,plain,
! [SV738: $i,SV636: $i,SV462: $i,SV223: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV223 ) @ SV462 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ SV738 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV223 = SV636 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2053,plain,
! [SV637: $i,SV463: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SV463 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV224 ) @ SV637 ) )
= $false )
| ( ( SV463 = SV637 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(2054,plain,
! [SV465: $i,SV226: $i] :
( ( ( SV226
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV226 ) @ SV465 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2055,plain,
! [SV739: $i,SV638: $i,SV466: $i,SV228: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV228 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV739 ) )
| ( SV638 = SV739 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2056,plain,
! [SV740: $i,SV639: $i,SV467: $i,SV229: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV229 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV229 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV639 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV740 ) )
| ( SV639 = SV740 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(2057,plain,
! [SV469: $i,SV232: $i] :
( ( ( SV232
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV232
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV232 ) @ SV469 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2058,plain,
! [SV233: $i,SV470: $i] :
( ( ( SV470
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV233
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV233 ) @ SV470 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2059,plain,
! [SV741: $i,SV640: $i,SV472: $i,SV235: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV640 ) @ SV741 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV235 = SV640 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2060,plain,
! [SV742: $i,SV641: $i,SV473: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV473 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV641 ) @ SV742 ) )
= $true )
| ( ( SV473 = SV742 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2061,plain,
! [SV743: $i,SV645: $i,SV480: $i,SV246: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV246 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV480 ) @ SV645 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV246 @ SV743 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SV480 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2062,plain,
! [SV646: $i,SV481: $i,SV247: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV247 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV481 @ SV247 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV646 @ SV247 ) )
| ( SV481 = SV646 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(2063,plain,
! [SV482: $i,SV248: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV248 ) @ SV482 ) @ SV482 )
!= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
= $true )
| ( ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2064,plain,
! [SV744: $i,SV647: $i,SV483: $i,SV249: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV647 ) @ SV744 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV483 = SV744 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2065,plain,
! [SV250: $i,SV484: $i] :
( ( ( SV484
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV250
= ( 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 ) @ SV250 ) @ SV484 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2066,plain,
! [SV745: $i,SV648: $i,SV485: $i,SV251: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV251 ) @ SV485 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV648 ) @ SV745 ) )
= $true )
| ( ( SV485 = SV745 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2067,plain,
! [SV746: $i,SV649: $i,SV487: $i,SV254: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV254 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV649 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV746 ) )
| ( SV649 = SV746 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2068,plain,
! [SV650: $i,SV488: $i,SV255: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV255 @ SV488 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV650 ) )
= $false )
| ( ( SV255
= ( c_Lambda_OdB_OAbs @ SV650 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2069,plain,
! [SV489: $i,SV257: $i] :
( ( ( SV257
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV489
= ( 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 ) @ SV257 ) @ SV489 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(2070,plain,
! [SV258: $i,SV490: $i] :
( ( ( SV490
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV490
= ( 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 ) @ SV258 ) @ SV490 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2071,plain,
! [SV771: $i,SV747: $i,SV651: $i,SV491: $i,SV259: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV259 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV747 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV771 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ SV747 )
= SV771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2072,plain,
! [SV652: $i,SV492: $i,SV260: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV260 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV492 @ SV652 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV652
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2073,plain,
! [SV494: $i,SV654: $i,SV263: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV1 @ SV263 @ SV263 ) @ SV263 ) @ SV654 ) @ SV494 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV1 @ SV263 ) @ SV494 ) @ SV654 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2074,plain,
! [SV495: $i,SV655: $i,SV264: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV2 @ SV264 ) @ SV655 ) @ SV495 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV2 @ SV264 @ SV264 ) @ SV264 ) @ SV495 ) @ SV655 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(2075,plain,
! [SV772: $i,SV748: $i,SV656: $i,SV496: $i,SV265: $i,SV3: $i] :
( ( ! [SY1736: $i] :
( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
| ~ ( c_Type_Otypings @ SV3 @ SV772 @ SY1736 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2076,plain,
! [SV749: $i,SV657: $i,SV497: $i,SV266: $i,SV4: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV657 ) @ SV749 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV657 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV497 ) @ SV749 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2077,plain,
! [SV271: $i,SV12: $i] :
( ( ( class_Int_Onumber__ring @ SV12 )
= $false )
| ( ( SV271
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV12 ) @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV12 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(2078,plain,
! [SV658: $i,SV498: $i,SV279: $i,SV20: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SV498 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV658 @ SV498 @ SV20 ) @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 )
| ~ ( c_lessequals @ SV279 @ SV658 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2079,plain,
! [SV500: $i,SV281: $i,SV660: $i,SV22: $i] :
( ( ( c_Type_Otyping @ SV22 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV660 @ SV281 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV500 )
= $false )
| ( ( c_Type_Otypings @ SV22 @ SV281 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV500 @ SV22 @ SV660 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2080,plain,
! [SV750: $i,SV661: $i,SV501: $i,SV283: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV283 ) @ SV501 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV24 @ SV661 @ SV750 ) @ SV501 ) @ SV283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1921]) ).
thf(2081,plain,
! [SV751: $i,SV662: $i,SV502: $i,SV284: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV25 @ SV284 @ SV502 ) @ SV662 ) @ SV751 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV25 @ SV751 ) @ SV662 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2082,plain,
! [SV752: $i,SV663: $i,SV503: $i,SV285: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV26 @ SV285 ) @ SV503 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV26 @ SV663 @ SV752 ) @ SV503 ) @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2083,plain,
! [SV753: $i,SV664: $i,SV504: $i,SV286: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV27 @ SV286 @ SV504 ) @ SV664 ) @ SV753 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV27 @ SV753 ) @ SV664 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2084,plain,
! [SV665: $i,SV505: $i,SV287: $i,SV28: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV28 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ SV505 ) ) @ SV665 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV28 ) @ SV505 ) @ SV665 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2085,plain,
! [SV666: $i,SV506: $i,SV288: $i,SV29: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV29 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV506 ) @ SV666 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV506 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV29 ) @ SV288 ) @ SV666 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2086,plain,
! [SV667: $i,SV507: $i,SV289: $i,SV30: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV30 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SV507 ) ) @ SV667 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV289 ) @ SV667 ) ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(2087,plain,
! [SV668: $i,SV508: $i,SV290: $i,SV31: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV31 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV508 ) @ SV668 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV290 ) @ SV508 ) ) @ SV668 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2088,plain,
! [SV669: $i,SV509: $i,SV291: $i,SV32: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV32 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ SV509 ) ) @ SV669 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV291 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ SV509 ) @ SV669 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2089,plain,
! [SV670: $i,SV510: $i,SV292: $i,SV33: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV33 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV510 ) @ SV670 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV510 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV292 ) @ SV670 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2090,plain,
! [SV671: $i,SV511: $i,SV293: $i,SV34: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV34 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ SV511 ) ) @ SV671 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV511 ) @ SV671 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2091,plain,
! [SV672: $i,SV514: $i,SV296: $i,SV37: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV37 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV514 ) @ SV672 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV514 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV296 ) @ SV672 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2092,plain,
! [SV673: $i,SV515: $i,SV297: $i,SV38: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV38 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV515 ) @ SV673 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ SV297 ) @ SV515 ) ) @ SV673 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2093,plain,
! [SV516: $i,SV298: $i,SV39: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV298 ) @ SV516 ) @ SV39 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV516 @ SV39 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV298 @ SV39 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2094,plain,
! [SV40: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2095,plain,
! [SV754: $i,SV674: $i,SV517: $i,SV299: $i,SV42: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV674 ) @ SV754 ) @ SV42 )
| ~ ( c_lessequals @ SV517 @ SV754 @ SV42 )
| ~ ( c_lessequals @ SV299 @ SV674 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2096,plain,
! [SV300: $i,SV43: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV300 @ SV43 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV300 ) @ SV300 ) @ SV43 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2097,plain,
! [SV301: $i,SV44: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV44 ) @ SV301 ) @ SV301 ) @ SV44 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV44 ) @ SV301 @ SV44 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2098,plain,
! [SV518: $i,SV303: $i,SV46: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Power_Opower__class_Opower @ SV303 @ SV518 @ SV46 ) @ SV46 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ SV303 @ SV46 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2099,plain,
! [SV675: $i,SV304: $i,SV519: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SV519 ) @ SV304 ) @ SV675 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV47 @ SV675 @ SV519 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV47 @ SV304 @ SV519 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1940]) ).
thf(2100,plain,
! [SV305: $i,SV520: $i,SV676: $i,SV48: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV48 @ SV676 @ SV520 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV520 ) @ SV305 ) @ SV676 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV48 @ SV305 @ SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2101,plain,
! [SV521: $i,SV306: $i,SV51: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ ( c_Power_Opower__class_Opower @ SV306 @ SV521 @ SV51 ) @ SV51 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV306 @ SV51 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(2102,plain,
! [SV677: $i,SV522: $i,SV309: $i,SV54: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
| ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
| ~ ( c_lessequals @ SV309 @ SV677 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2103,plain,
! [SV678: $i,SV523: $i,SV310: $i,SV55: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
| ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
| ~ ( c_lessequals @ SV310 @ SV523 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2104,plain,
! [SV679: $i,SV527: $i,SV315: $i,SV60: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV60 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SV527 ) @ SV679 @ SV60 @ SV60 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV527 @ SV679 @ SV60 @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2105,plain,
! [SV69: $i,SV533: $i,SV321: $i] :
( ( ( SV321 = SV533 )
= $true )
| ( ( ~ ( c_lessequals @ SV533 @ SV321 @ SV69 )
| ~ ( c_lessequals @ SV321 @ SV533 @ SV69 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2106,plain,
! [SV70: $i,SV534: $i,SV322: $i] :
( ( ( SV322 = SV534 )
= $true )
| ( ( ~ ( c_lessequals @ SV534 @ SV322 @ SV70 )
| ~ ( c_lessequals @ SV322 @ SV534 @ SV70 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1952]) ).
thf(2107,plain,
! [SV71: $i,SV535: $i,SV323: $i] :
( ( ( SV323 = SV535 )
= $true )
| ( ( ~ ( c_lessequals @ SV323 @ SV535 @ SV71 )
| ~ ( c_lessequals @ SV535 @ SV323 @ SV71 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2108,plain,
! [SV681: $i,SV536: $i,SV324: $i,SV72: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV72 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV536 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV681 ) @ SV536 ) @ SV72 )
| ~ ( c_lessequals @ SV324 @ SV681 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2109,plain,
! [SV682: $i,SV537: $i,SV325: $i,SV73: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV73 )
= $false )
| ( ( ( c_lessequals @ SV325 @ SV537 @ SV73 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV537 ) @ SV682 ) @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2110,plain,
! [SV683: $i,SV538: $i,SV326: $i,SV74: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV74 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV683 ) @ SV74 )
| ~ ( c_lessequals @ SV538 @ SV683 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2111,plain,
! [SV684: $i,SV539: $i,SV327: $i,SV75: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV75 )
= $false )
| ( ( ( c_lessequals @ SV327 @ SV539 @ SV75 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV539 ) @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2112,plain,
! [SV685: $i,SV540: $i,SV328: $i,SV76: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV76 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV328 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV685 ) @ SV540 ) @ SV76 )
| ~ ( c_lessequals @ SV328 @ SV685 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2113,plain,
! [SV686: $i,SV541: $i,SV329: $i,SV77: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV77 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV541 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV686 ) @ SV77 )
| ~ ( c_lessequals @ SV541 @ SV686 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2114,plain,
! [SV542: $i,SV332: $i,SV687: $i,SV80: $i] :
( ( ( c_Type_Otyping @ SV80 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV687 @ SV332 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV542 )
= $false )
| ( ( c_Type_Otypings @ SV80 @ SV332 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV542 @ SV80 @ SV687 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2115,plain,
! [SV82: $i,SV334: $i] :
( ( ( c_lessequals @ SV334 @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV82 ) @ SV334 ) @ SV334 ) @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ SV82 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2116,plain,
! [SV335: $i,SV83: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV83 ) @ SV335 ) @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 )
= $false )
| ( ( c_lessequals @ SV335 @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ SV83 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2117,plain,
! [SV688: $i,SV544: $i,SV336: $i,SV84: $i] :
( ( ( class_Orderings_Oorder @ SV84 )
= $false )
| ( ( ( c_lessequals @ SV336 @ SV544 @ SV84 )
| ~ ( c_lessequals @ SV336 @ SV688 @ SV84 )
| ~ ( c_lessequals @ SV688 @ SV544 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2118,plain,
! [SV545: $i,SV337: $i,SV85: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV337 ) @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ( c_lessequals @ SV545 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV337 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2119,plain,
! [SV689: $i,SV546: $i,SV338: $i,SV86: $i] :
( ( ( class_Orderings_Opreorder @ SV86 )
= $false )
| ( ( ( c_lessequals @ SV338 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SV689 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SV338 @ SV689 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2120,plain,
! [SV755: $i,SV690: $i,SV547: $i,SV341: $i,SV89: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV89 ) )
= $true )
| ( ( ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV690 ) @ SV89 )
| ~ ( c_lessequals @ SV755 @ SV690 @ SV89 )
| ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV755 ) @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2121,plain,
! [SV549: $i,SV691: $i,SV344: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV344 ) @ SV691 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV92 @ SV691 @ SV549 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV92 @ SV344 @ SV549 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2122,plain,
! [SV93: $i,SV550: $i,SV345: $i] :
( ( ( c_lessequals @ SV345 @ SV550 @ SV93 )
= $true )
| ( ( c_lessequals @ SV550 @ SV345 @ SV93 )
= $true )
| ( ( class_Orderings_Olinorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2123,plain,
! [SV551: $i,SV692: $i,SV346: $i,SV94: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV346 ) @ SV692 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV94 @ SV692 @ SV551 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV94 @ SV346 @ SV551 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(2124,plain,
! [SV756: $i,SV693: $i,SV552: $i,SV347: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV693 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV756 ) @ SV693 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV756 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2125,plain,
! [SV757: $i,SV694: $i,SV553: $i,SV348: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV553 ) @ SV694 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV757 ) @ SV694 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV553 ) @ SV757 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2126,plain,
! [SV555: $i,SV351: $i,SV696: $i,SV100: $i] :
( ( ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV696 ) @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV555 )
= $false )
| ( ( c_Type_Otypings @ SV100 @ SV351 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV555 @ SV100 @ SV696 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2127,plain,
! [SV773: $i,SV758: $i,SV697: $i,SV556: $i,SV354: $i,SV103: $i] :
( ( ! [SY1737: $i] :
( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
| ~ ( c_Type_Otypings @ SV556 @ SV773 @ SY1737 )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2128,plain,
! [SV698: $i,SV558: $i,SV357: $i,SV106: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV106 )
= $false )
| ( ( ( c_lessequals @ SV357 @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SV698 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SV558 @ ( c_Suc @ SV698 ) @ SV106 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2129,plain,
! [SV362: $i,SV699: $i,SV561: $i,SV111: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV111 @ SV561 ) @ SV699 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV111 @ SV362 ) @ SV561 ) @ SV699 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2130,plain,
! [SV562: $i,SV112: $i,SV700: $i,SV363: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV363 ) @ SV700 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV112 @ SV363 @ SV562 ) ) @ ( c_Lambda_Osubst @ SV112 @ SV700 @ SV562 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2131,plain,
! [SV563: $i,SV364: $i,SV701: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV113 ) @ SV701 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV113 @ SV364 @ SV563 ) ) @ ( c_Lambda_Osubst @ SV701 @ SV364 @ SV563 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2132,plain,
! [SV565: $i,SV115: $i,SV702: $i,SV366: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV366 ) @ SV702 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV115 @ SV366 @ SV565 ) ) @ ( c_Lambda_Osubst @ SV115 @ SV702 @ SV565 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2133,plain,
! [SV367: $i,SV116: $i] :
( ( ( class_Power_Opower @ SV116 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Suc @ SV367 ) @ SV116 )
= ( c_HOL_Ozero__class_Ozero @ SV116 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2134,plain,
! [SV566: $i,SV703: $i,SV368: $i,SV117: $i] :
( ( ( c_Type_Otyping @ SV117 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV368 @ SV703 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV566 )
= $false )
| ( ( c_Type_Otyping @ SV117 @ SV368 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV566 @ SV117 @ SV368 @ SV703 ) @ SV566 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2135,plain,
! [SV759: $i,SV704: $i,SV567: $i,SV369: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV704 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV759 ) @ SV704 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV759 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2136,plain,
! [SV570: $i,SV372: $i,SV705: $i,SV121: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV121 ) @ SV705 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV121 @ SV372 @ SV570 ) ) @ ( c_Lambda_Osubst @ SV705 @ SV372 @ SV570 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2137,plain,
! [SV571: $i,SV123: $i,SV373: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV373 @ 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 @ SV123 ) ) @ SV373 ) @ SV571 @ 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 @ ( c_Lambda_Osubst @ SV123 @ SV373 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2138,plain,
! [SV760: $i,SV706: $i,SV572: $i,SV374: $i,SV124: $i] :
( ( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV374 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV706 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV124 @ SV572 @ SV760 )
| ~ ( c_Type_Otyping @ SV124 @ SV374 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV760 @ SV706 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2139,plain,
! [SV576: $i,SV707: $i,SV379: $i,SV133: $i] :
( ( ( c_Type_Otyping @ SV133 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV379 @ SV707 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV576 )
= $false )
| ( ( c_Type_Otyping @ SV133 @ SV379 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV576 @ SV133 @ SV379 @ SV707 ) @ SV576 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2140,plain,
! [SV774: $i,SV761: $i,SV709: $i,SV579: $i,SV385: $i,SV139: $i] :
( ( ~ ( c_Type_Otyping @ SV139 @ SV385 @ SV579 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SV709 @ SV579 @ tc_Type_Otype ) @ SV761 @ SV774 )
| ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SV761 @ SV385 @ SV709 ) @ SV774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2141,plain,
! [SV387: $i,SV580: $i,SV710: $i,SV141: $i] :
( ( ( ~ ( c_Type_Otyping @ SV141 @ SV710 @ SV580 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV710 ) @ SV387 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV141 @ SV387 @ SV580 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2142,plain,
! [SV583: $i,SV145: $i,SV711: $i,SV390: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV390 ) @ SV711 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV145 ) @ SV583 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV145 ) @ SV390 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV583 ) @ SV711 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2143,plain,
! [SV712: $i,SV584: $i,SV391: $i,SV147: $i] :
( ( ( hBOOL @ ( hAPP @ SV147 @ ( c_Type_Otype_Otype__case @ SV391 @ SV584 @ ( c_Type_Otype_OAtom @ SV712 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV147 @ ( hAPP @ SV391 @ SV712 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2144,plain,
! [SV713: $i,SV585: $i,SV392: $i,SV148: $i] :
( ( ( hBOOL @ ( hAPP @ SV148 @ ( c_Type_Otype_Otype__case @ SV392 @ SV585 @ ( c_Type_Otype_OAtom @ SV713 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV148 @ ( hAPP @ SV392 @ SV713 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2145,plain,
! [SV588: $i,SV396: $i,SV714: $i,SV153: $i] :
( ( ( c_Type_Otyping @ SV153 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV714 ) @ SV396 ) @ SV588 )
= $false )
| ( ( c_Type_Otyping @ SV153 @ SV396 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV588 @ SV153 @ SV714 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2146,plain,
! [SV591: $i,SV715: $i,SV400: $i,SV157: $i] :
( ( ( c_Type_Otyping @ SV157 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV400 ) @ SV715 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV591 )
= $false )
| ( ( c_Type_Otyping @ SV157 @ ( c_Lambda_OdB_OVar @ SV400 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV591 @ SV157 @ SV400 @ SV715 ) @ SV591 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2147,plain,
! [SV594: $i,SV162: $i,SV403: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV162 @ SV403 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV594 @ 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 @ SV162 ) ) @ SV403 ) @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2148,plain,
! [SV763: $i,SV719: $i,SV598: $i,SV408: $i,SV167: $i] :
( ( ( SV167 = SV408 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV408 )
| ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2149,plain,
! [SV412: $i,SV172: $i] :
( ( ( class_Power_Opower @ SV172 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV412 @ SV172 )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
| ( SV412
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2150,plain,
! [SV413: $i,SV173: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV173 )
| ~ ( class_Power_Opower @ SV173 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2151,plain,
! [SV775: $i,SV764: $i,SV720: $i,SV600: $i,SV415: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
| ~ ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2152,plain,
! [SV765: $i,SV721: $i,SV601: $i,SV416: $i,SV177: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ SV416 @ SV601 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV721 @ SV416 ) @ SV765 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV177 @ SV721 @ SV765 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2153,plain,
! [SV603: $i,SV179: $i,SV418: $i,SV722: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV722 ) @ SV418 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV179 @ SV722 @ SV603 ) )
= $true )
| ( ( c_Type_Otyping @ SV179 @ SV418 @ SV603 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2154,plain,
! [SV766: $i,SV723: $i,SV604: $i,SV419: $i,SV180: $i] :
( ( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV419 ) @ SV604 ) @ SV723 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV180 @ SV604 @ SV766 )
| ~ ( c_Type_Otyping @ SV180 @ SV419 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV723 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2155,plain,
! [SV724: $i,SV420: $i,SV605: $i,SV181: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV181 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV605 @ tc_Type_Otype ) @ SV420 @ SV724 )
= $false )
| ( ( c_Type_Otyping @ SV181 @ ( c_Lambda_OdB_OAbs @ SV420 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV605 ) @ SV724 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2156,plain,
! [SV769: $i,SV727: $i,SV609: $i,SV425: $i,SV186: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV186 @ ( c_Type_Otype_Otype__case @ SV425 @ SV609 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV727 ) @ SV769 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ ( hAPP @ ( hAPP @ SV609 @ SV727 ) @ SV769 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2157,plain,
! [SV770: $i,SV728: $i,SV610: $i,SV426: $i,SV187: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_Type_Otype_Otype__case @ SV426 @ SV610 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV728 ) @ SV770 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV187 @ ( hAPP @ ( hAPP @ SV610 @ SV728 ) @ SV770 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2158,plain,
! [SV611: $i,SV729: $i,SV427: $i,SV188: $i] :
( ( ( c_Type_Otyping @ SV188 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV427 ) @ SV729 ) @ SV611 )
= $false )
| ( ( c_Type_Otyping @ SV188 @ SV427 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV611 @ SV188 @ SV427 @ SV729 ) ) @ SV611 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2159,plain,
! [SV730: $i,SV616: $i,SV436: $i,SV197: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV197 ) @ SV436 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV616 ) @ SV730 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV436 = SV730 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2160,plain,
! [SV731: $i,SV617: $i,SV437: $i,SV198: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV198 ) @ SV437 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV617 ) @ SV731 ) )
= $false )
| ( ( SV198 = SV617 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2161,plain,
! [SV618: $i,SV438: $i,SV199: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV199 ) )
= $true )
| ( ( ( SV438
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV438 ) @ SV618 ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2162,plain,
! [SV732: $i,SV619: $i,SV439: $i,SV200: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV200 ) @ SV439 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV619 ) @ SV732 ) )
= $false )
| ( ( SV200 = SV619 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2163,plain,
! [SV733: $i,SV621: $i,SV441: $i,SV202: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV202 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV441 ) @ SV621 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV733 ) @ SV621 ) )
| ( SV441 = SV733 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2164,plain,
! [SV734: $i,SV622: $i,SV443: $i,SV204: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV204 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV443 ) @ SV622 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV204 @ SV734 ) )
| ( hBOOL @ ( hAPP @ SV204 @ SV622 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2165,plain,
! [SV208: $i,SV625: $i,SV447: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV447 @ SV625 @ SV208 )
!= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
= $true )
| ( ( SV447
= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2166,plain,
! [SV626: $i,SV448: $i,SV209: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
!= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
| ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2167,plain,
! [SV628: $i,SV450: $i,SV211: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
!= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
| ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2168,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV212 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV212 )
| ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2169,plain,
! [SV452: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV213 )
| ~ ( class_Power_Opower @ SV213 )
| ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2170,plain,
! [SV735: $i,SV630: $i,SV454: $i,SV215: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV215 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
!= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
| ( SV454 = SV735 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2171,plain,
! [SV738: $i,SV636: $i,SV462: $i,SV223: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV223 ) @ SV462 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV636 ) @ SV738 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV223 = SV636 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2172,plain,
! [SV739: $i,SV638: $i,SV466: $i,SV228: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV228 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV739 ) )
| ( SV638 = SV739 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2173,plain,
! [SV740: $i,SV639: $i,SV467: $i,SV229: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV229 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV229 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV639 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV740 ) )
| ( SV639 = SV740 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2174,plain,
! [SV741: $i,SV640: $i,SV472: $i,SV235: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV640 ) @ SV741 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV235 = SV640 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2175,plain,
! [SV742: $i,SV641: $i,SV473: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV473 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV641 ) @ SV742 ) )
= $false )
| ( ( SV473 = SV742 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2176,plain,
! [SV743: $i,SV645: $i,SV480: $i,SV246: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV246 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV480 ) @ SV645 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV246 @ SV743 ) )
| ( hBOOL @ ( hAPP @ SV246 @ SV480 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2177,plain,
! [SV646: $i,SV247: $i,SV481: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV481 @ SV247 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV646 @ SV247 ) )
= $true )
| ( ( SV481 = SV646 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2178,plain,
! [SV482: $i,SV248: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV248 ) @ SV482 ) @ SV482 )
= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
= $false )
| ( ( SV482
= ( c_HOL_Ozero__class_Ozero @ SV248 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2179,plain,
! [SV744: $i,SV647: $i,SV483: $i,SV249: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SV483 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV647 ) @ SV744 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV483 = SV744 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2180,plain,
! [SV745: $i,SV648: $i,SV485: $i,SV251: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV251 ) @ SV485 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV648 ) @ SV745 ) )
= $false )
| ( ( SV485 = SV745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2181,plain,
! [SV746: $i,SV649: $i,SV487: $i,SV254: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV254 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV649 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV746 ) )
| ( SV649 = SV746 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2182,plain,
! [SV771: $i,SV747: $i,SV651: $i,SV491: $i,SV259: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV259 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV747 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV771 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ SV747 )
= SV771 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2183,plain,
! [SV776: $i,SV772: $i,SV748: $i,SV656: $i,SV496: $i,SV265: $i,SV3: $i] :
( ( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
| ~ ( c_Type_Otypings @ SV3 @ SV772 @ SV776 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2184,plain,
! [SV749: $i,SV657: $i,SV497: $i,SV266: $i,SV4: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV497 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV657 ) @ SV749 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV266 ) @ SV657 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV4 ) @ SV497 ) @ SV749 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2185,plain,
! [SV658: $i,SV20: $i,SV498: $i,SV279: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SV498 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV658 @ SV498 @ SV20 ) @ SV20 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 )
| ~ ( c_lessequals @ SV279 @ SV658 @ SV20 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2186,plain,
! [SV283: $i,SV501: $i,SV750: $i,SV661: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV24 @ SV661 @ SV750 ) @ SV501 ) @ SV283 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV283 ) @ SV501 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2187,plain,
! [SV502: $i,SV284: $i,SV662: $i,SV751: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV25 @ SV751 ) @ SV662 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV25 @ SV284 @ SV502 ) @ SV662 ) @ SV751 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2188,plain,
! [SV285: $i,SV503: $i,SV752: $i,SV663: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV26 @ SV663 @ SV752 ) @ SV503 ) @ SV285 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV26 @ SV285 ) @ SV503 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2189,plain,
! [SV504: $i,SV286: $i,SV664: $i,SV753: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV27 @ SV753 ) @ SV664 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV27 @ SV286 @ SV504 ) @ SV664 ) @ SV753 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2190,plain,
! [SV298: $i,SV516: $i,SV39: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV516 @ SV39 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV298 @ SV39 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV298 ) @ SV516 ) @ SV39 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2191,plain,
! [SV40: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2192,plain,
! [SV754: $i,SV674: $i,SV517: $i,SV299: $i,SV42: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV674 ) @ SV754 ) @ SV42 )
| ~ ( c_lessequals @ SV517 @ SV754 @ SV42 )
| ~ ( c_lessequals @ SV299 @ SV674 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2193,plain,
! [SV518: $i,SV303: $i,SV46: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ SV303 @ SV46 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Power_Opower__class_Opower @ SV303 @ SV518 @ SV46 ) @ SV46 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2194,plain,
! [SV675: $i,SV304: $i,SV519: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SV519 ) @ SV304 ) @ SV675 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV47 @ SV675 @ SV519 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV47 @ SV304 @ SV519 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2195,plain,
! [SV305: $i,SV520: $i,SV676: $i,SV48: $i] :
( ( ( c_Wellfounded_Oaccp @ SV48 @ SV676 @ SV520 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV520 ) @ SV305 ) @ SV676 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV48 @ SV305 @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2196,plain,
! [SV521: $i,SV306: $i,SV51: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ SV306 @ SV51 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV51 ) @ ( c_Power_Opower__class_Opower @ SV306 @ SV521 @ SV51 ) @ SV51 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2197,plain,
! [SV677: $i,SV522: $i,SV309: $i,SV54: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV54 ) )
= $true )
| ( ( ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
| ~ ( c_lessequals @ SV309 @ SV677 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2198,plain,
! [SV678: $i,SV523: $i,SV310: $i,SV55: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV55 ) )
= $true )
| ( ( ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
| ~ ( c_lessequals @ SV310 @ SV523 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2199,plain,
! [SV69: $i,SV321: $i,SV533: $i] :
( ( ( ~ ( c_lessequals @ SV533 @ SV321 @ SV69 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV321 @ SV533 @ SV69 ) )
= $true )
| ( ( SV321 = SV533 )
= $true )
| ( ( class_Orderings_Oorder @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2200,plain,
! [SV70: $i,SV322: $i,SV534: $i] :
( ( ( ~ ( c_lessequals @ SV534 @ SV322 @ SV70 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV322 @ SV534 @ SV70 ) )
= $true )
| ( ( SV322 = SV534 )
= $true )
| ( ( class_Orderings_Oorder @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2201,plain,
! [SV71: $i,SV535: $i,SV323: $i] :
( ( ( ~ ( c_lessequals @ SV323 @ SV535 @ SV71 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV535 @ SV323 @ SV71 ) )
= $true )
| ( ( SV323 = SV535 )
= $true )
| ( ( class_Orderings_Oorder @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2107]) ).
thf(2202,plain,
! [SV681: $i,SV536: $i,SV324: $i,SV72: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV536 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV681 ) @ SV536 ) @ SV72 )
= $true )
| ( ( ~ ( c_lessequals @ SV324 @ SV681 @ SV72 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2203,plain,
! [SV682: $i,SV73: $i,SV537: $i,SV325: $i] :
( ( ( c_lessequals @ SV325 @ SV537 @ SV73 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV537 ) @ SV682 ) @ SV73 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2204,plain,
! [SV683: $i,SV538: $i,SV326: $i,SV74: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV683 ) @ SV74 )
= $true )
| ( ( ~ ( c_lessequals @ SV538 @ SV683 @ SV74 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2205,plain,
! [SV684: $i,SV75: $i,SV539: $i,SV327: $i] :
( ( ( c_lessequals @ SV327 @ SV539 @ SV75 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV539 ) @ SV75 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2206,plain,
! [SV685: $i,SV540: $i,SV328: $i,SV76: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV328 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV685 ) @ SV540 ) @ SV76 )
= $true )
| ( ( ~ ( c_lessequals @ SV328 @ SV685 @ SV76 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2207,plain,
! [SV686: $i,SV541: $i,SV329: $i,SV77: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV541 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV686 ) @ SV77 )
= $true )
| ( ( ~ ( c_lessequals @ SV541 @ SV686 @ SV77 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2208,plain,
! [SV688: $i,SV84: $i,SV544: $i,SV336: $i] :
( ( ( c_lessequals @ SV336 @ SV544 @ SV84 )
= $true )
| ( ( ~ ( c_lessequals @ SV336 @ SV688 @ SV84 )
| ~ ( c_lessequals @ SV688 @ SV544 @ SV84 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2209,plain,
! [SV337: $i,SV85: $i,SV545: $i] :
( ( ( ~ ( c_lessequals @ SV545 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV337 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV337 ) @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2210,plain,
! [SV689: $i,SV86: $i,SV546: $i,SV338: $i] :
( ( ( c_lessequals @ SV338 @ SV546 @ SV86 )
= $true )
| ( ( ~ ( c_lessequals @ SV689 @ SV546 @ SV86 )
| ~ ( c_lessequals @ SV338 @ SV689 @ SV86 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2119]) ).
thf(2211,plain,
! [SV755: $i,SV690: $i,SV547: $i,SV341: $i,SV89: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
= $false )
| ( ( ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV690 ) @ SV89 )
| ~ ( c_lessequals @ SV755 @ SV690 @ SV89 )
| ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV755 ) @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2212,plain,
! [SV549: $i,SV691: $i,SV344: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV344 ) @ SV691 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV92 @ SV691 @ SV549 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV92 @ SV344 @ SV549 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2213,plain,
! [SV551: $i,SV692: $i,SV346: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV346 ) @ SV692 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV94 @ SV692 @ SV551 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV94 @ SV346 @ SV551 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2214,plain,
! [SV552: $i,SV347: $i,SV693: $i,SV756: $i,SV95: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV756 ) @ SV693 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV756 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV693 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2215,plain,
! [SV553: $i,SV694: $i,SV757: $i,SV348: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV757 ) @ SV694 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV553 ) @ SV757 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV553 ) @ SV694 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2216,plain,
! [SV777: $i,SV773: $i,SV758: $i,SV697: $i,SV556: $i,SV354: $i,SV103: $i] :
( ( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
| ~ ( c_Type_Otypings @ SV556 @ SV773 @ SV777 )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2217,plain,
! [SV698: $i,SV106: $i,SV558: $i,SV357: $i] :
( ( ( c_lessequals @ SV357 @ SV558 @ SV106 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV558 @ SV106 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SV698 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SV558 @ ( c_Suc @ SV698 ) @ SV106 ) @ SV106 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2218,plain,
! [SV567: $i,SV704: $i,SV759: $i,SV369: $i,SV118: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV759 ) @ SV704 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV759 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV704 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2219,plain,
! [SV571: $i,SV123: $i,SV373: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV373 @ 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 @ SV123 ) ) @ SV373 ) @ SV571 @ 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 @ ( c_Lambda_Osubst @ SV123 @ SV373 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2220,plain,
! [SV706: $i,SV374: $i,SV760: $i,SV572: $i,SV124: $i] :
( ( ( ~ ( c_Type_Otypings @ SV124 @ SV572 @ SV760 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV124 @ SV374 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV760 @ SV706 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV374 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV706 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2221,plain,
! [SV774: $i,SV761: $i,SV709: $i,SV579: $i,SV385: $i,SV139: $i] :
( ( ( ~ ( c_Type_Otyping @ SV139 @ SV385 @ SV579 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SV709 @ SV579 @ tc_Type_Otype ) @ SV761 @ SV774 )
| ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SV761 @ SV385 @ SV709 ) @ SV774 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2222,plain,
! [SV387: $i,SV580: $i,SV710: $i,SV141: $i] :
( ( ( c_Type_Otyping @ SV141 @ SV710 @ SV580 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV710 ) @ SV387 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV141 @ SV387 @ SV580 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2223,plain,
! [SV583: $i,SV145: $i,SV711: $i,SV390: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV390 ) @ SV711 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV145 ) @ SV583 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV145 ) @ SV390 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV583 ) @ SV711 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2224,plain,
! [SV594: $i,SV403: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV162 @ SV403 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV162 ) ) @ SV403 ) @ SV594 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2225,plain,
! [SV167: $i,SV408: $i,SV763: $i,SV719: $i,SV598: $i] :
( ( ( ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV408 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 ) )
= $true )
| ( ( SV167 = SV408 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2226,plain,
! [SV412: $i,SV172: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV412 @ SV172 )
= ( c_HOL_Ozero__class_Ozero @ SV172 ) )
= $true )
| ( ( SV412
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV172 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2227,plain,
! [SV413: $i,SV173: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV173 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV173 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2228,plain,
! [SV775: $i,SV764: $i,SV720: $i,SV600: $i,SV415: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2229,plain,
! [SV601: $i,SV416: $i,SV765: $i,SV721: $i,SV177: $i] :
( ( ( c_Type_Otyping @ SV177 @ SV721 @ SV765 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ SV416 @ SV601 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV721 @ SV416 ) @ SV765 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2230,plain,
! [SV603: $i,SV179: $i,SV418: $i,SV722: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV722 ) @ SV418 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV179 @ SV722 @ SV603 ) )
= $true )
| ( ( c_Type_Otyping @ SV179 @ SV418 @ SV603 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2231,plain,
! [SV723: $i,SV419: $i,SV766: $i,SV604: $i,SV180: $i] :
( ( ( ~ ( c_Type_Otyping @ SV180 @ SV604 @ SV766 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV180 @ SV419 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV723 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV419 ) @ SV604 ) @ SV723 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2232,plain,
! [SV769: $i,SV727: $i,SV609: $i,SV425: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ SV186 @ ( c_Type_Otype_Otype__case @ SV425 @ SV609 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV727 ) @ SV769 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV186 @ ( hAPP @ ( hAPP @ SV609 @ SV727 ) @ SV769 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2233,plain,
! [SV770: $i,SV728: $i,SV610: $i,SV426: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ SV187 @ ( c_Type_Otype_Otype__case @ SV426 @ SV610 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV728 ) @ SV770 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV187 @ ( hAPP @ ( hAPP @ SV610 @ SV728 ) @ SV770 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2234,plain,
! [SV618: $i,SV438: $i,SV199: $i] :
( ( ( class_Int_Onumber__ring @ SV199 )
= $false )
| ( ( ( SV438
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV438 ) @ SV618 ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ SV199 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2235,plain,
! [SV733: $i,SV621: $i,SV441: $i,SV202: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV441 ) @ SV621 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV733 ) @ SV621 ) )
= $true )
| ( ( SV441 = SV733 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2236,plain,
! [SV443: $i,SV622: $i,SV734: $i,SV204: $i] :
( ( ( hBOOL @ ( hAPP @ SV204 @ SV734 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV204 @ SV622 ) )
= $true )
| ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV204 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV443 ) @ SV622 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2237,plain,
! [SV208: $i,SV625: $i,SV447: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV447 @ SV625 @ SV208 )
= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
= $false )
| ( ( SV447
= ( c_HOL_Ozero__class_Ozero @ SV208 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2238,plain,
! [SV626: $i,SV448: $i,SV209: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
| ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2239,plain,
! [SV628: $i,SV450: $i,SV211: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
| ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2240,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV212 )
| ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2241,plain,
! [SV452: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV213 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV213 )
| ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2242,plain,
! [SV735: $i,SV215: $i,SV630: $i,SV454: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
!= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
= $true )
| ( ( ( SV454 = SV735 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2243,plain,
! [SV739: $i,SV638: $i,SV466: $i,SV228: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV638 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV739 ) )
= $true )
| ( ( SV638 = SV739 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2172]) ).
thf(2244,plain,
! [SV740: $i,SV639: $i,SV467: $i,SV229: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV229 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV639 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV740 ) )
| ( SV639 = SV740 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2245,plain,
! [SV645: $i,SV480: $i,SV743: $i,SV246: $i] :
( ( ( hBOOL @ ( hAPP @ SV246 @ SV743 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV246 @ SV480 ) )
= $true )
| ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV246 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV480 ) @ SV645 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2246,plain,
! [SV646: $i,SV247: $i,SV481: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV481 @ SV247 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV646 @ SV247 ) )
= $false )
| ( ( SV481 = SV646 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2247,plain,
! [SV746: $i,SV649: $i,SV487: $i,SV254: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV649 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV746 ) )
= $true )
| ( ( SV649 = SV746 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2248,plain,
! [SV771: $i,SV747: $i,SV651: $i,SV491: $i,SV259: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV259 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV747 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV771 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ SV747 )
= SV771 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2249,plain,
! [SV776: $i,SV772: $i,SV748: $i,SV656: $i,SV496: $i,SV265: $i,SV3: $i] :
( ( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
| ~ ( c_Type_Otypings @ SV3 @ SV772 @ SV776 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2250,plain,
! [SV498: $i,SV658: $i,SV279: $i,SV20: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV279 @ SV658 @ SV20 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SV498 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV658 @ SV498 @ SV20 ) @ SV20 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2251,plain,
! [SV298: $i,SV516: $i,SV39: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV516 @ SV39 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV298 @ SV39 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV298 ) @ SV516 ) @ SV39 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2252,plain,
! [SV754: $i,SV674: $i,SV517: $i,SV299: $i,SV42: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV674 ) @ SV754 ) @ SV42 )
= $true )
| ( ( ~ ( c_lessequals @ SV517 @ SV754 @ SV42 )
| ~ ( c_lessequals @ SV299 @ SV674 @ SV42 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2192]) ).
thf(2253,plain,
! [SV304: $i,SV519: $i,SV675: $i,SV47: $i] :
( ( ( c_Wellfounded_Oaccp @ SV47 @ SV675 @ SV519 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SV519 ) @ SV304 ) @ SV675 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV47 @ SV304 @ SV519 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2254,plain,
! [SV676: $i,SV305: $i,SV520: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV520 ) @ SV305 ) @ SV676 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV48 @ SV676 @ SV520 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV48 @ SV305 @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2255,plain,
! [SV677: $i,SV522: $i,SV309: $i,SV54: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
= $false )
| ( ( ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
| ~ ( c_lessequals @ SV309 @ SV677 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2256,plain,
! [SV678: $i,SV523: $i,SV310: $i,SV55: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
= $false )
| ( ( ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
| ~ ( c_lessequals @ SV310 @ SV523 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2257,plain,
! [SV69: $i,SV321: $i,SV533: $i] :
( ( ( c_lessequals @ SV533 @ SV321 @ SV69 )
= $false )
| ( ( ~ ( c_lessequals @ SV321 @ SV533 @ SV69 ) )
= $true )
| ( ( SV321 = SV533 )
= $true )
| ( ( class_Orderings_Oorder @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2258,plain,
! [SV70: $i,SV322: $i,SV534: $i] :
( ( ( c_lessequals @ SV534 @ SV322 @ SV70 )
= $false )
| ( ( ~ ( c_lessequals @ SV322 @ SV534 @ SV70 ) )
= $true )
| ( ( SV322 = SV534 )
= $true )
| ( ( class_Orderings_Oorder @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2259,plain,
! [SV71: $i,SV535: $i,SV323: $i] :
( ( ( c_lessequals @ SV323 @ SV535 @ SV71 )
= $false )
| ( ( ~ ( c_lessequals @ SV535 @ SV323 @ SV71 ) )
= $true )
| ( ( SV323 = SV535 )
= $true )
| ( ( class_Orderings_Oorder @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2260,plain,
! [SV536: $i,SV72: $i,SV681: $i,SV324: $i] :
( ( ( c_lessequals @ SV324 @ SV681 @ SV72 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV536 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV681 ) @ SV536 ) @ SV72 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2261,plain,
! [SV537: $i,SV682: $i,SV325: $i,SV73: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV682 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV537 ) @ SV682 ) @ SV73 )
= $false )
| ( ( c_lessequals @ SV325 @ SV537 @ SV73 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2262,plain,
! [SV326: $i,SV74: $i,SV683: $i,SV538: $i] :
( ( ( c_lessequals @ SV538 @ SV683 @ SV74 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 ) @ SV683 ) @ SV74 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2263,plain,
! [SV539: $i,SV327: $i,SV684: $i,SV75: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV75 ) @ SV684 ) @ SV539 ) @ SV75 )
= $false )
| ( ( c_lessequals @ SV327 @ SV539 @ SV75 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2264,plain,
! [SV540: $i,SV76: $i,SV685: $i,SV328: $i] :
( ( ( c_lessequals @ SV328 @ SV685 @ SV76 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV328 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV76 ) @ SV685 ) @ SV540 ) @ SV76 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2265,plain,
! [SV329: $i,SV77: $i,SV686: $i,SV541: $i] :
( ( ( c_lessequals @ SV541 @ SV686 @ SV77 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV541 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV686 ) @ SV77 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2266,plain,
! [SV544: $i,SV84: $i,SV688: $i,SV336: $i] :
( ( ( ~ ( c_lessequals @ SV336 @ SV688 @ SV84 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV688 @ SV544 @ SV84 ) )
= $true )
| ( ( c_lessequals @ SV336 @ SV544 @ SV84 )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2267,plain,
! [SV337: $i,SV85: $i,SV545: $i] :
( ( ( c_lessequals @ SV545 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
= $false )
| ( ( ~ ( c_lessequals @ SV337 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV337 ) @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2268,plain,
! [SV338: $i,SV86: $i,SV546: $i,SV689: $i] :
( ( ( ~ ( c_lessequals @ SV689 @ SV546 @ SV86 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV338 @ SV689 @ SV86 ) )
= $true )
| ( ( c_lessequals @ SV338 @ SV546 @ SV86 )
= $true )
| ( ( class_Orderings_Opreorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2269,plain,
! [SV755: $i,SV690: $i,SV547: $i,SV89: $i,SV341: $i] :
( ( ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV690 ) @ SV89 )
= $true )
| ( ( ~ ( c_lessequals @ SV755 @ SV690 @ SV89 )
| ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV755 ) @ SV89 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2270,plain,
! [SV344: $i,SV549: $i,SV691: $i,SV92: $i] :
( ( ( c_Wellfounded_Oaccp @ SV92 @ SV691 @ SV549 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV344 ) @ SV691 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV92 @ SV344 @ SV549 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2271,plain,
! [SV346: $i,SV551: $i,SV692: $i,SV94: $i] :
( ( ( c_Wellfounded_Oaccp @ SV94 @ SV692 @ SV551 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV346 ) @ SV692 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV94 @ SV346 @ SV551 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2272,plain,
! [SV552: $i,SV347: $i,SV693: $i,SV756: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV756 ) @ SV693 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV756 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV693 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2273,plain,
! [SV553: $i,SV694: $i,SV757: $i,SV348: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV757 ) @ SV694 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV553 ) @ SV757 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV553 ) @ SV694 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2274,plain,
! [SV777: $i,SV773: $i,SV758: $i,SV697: $i,SV556: $i,SV354: $i,SV103: $i] :
( ( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
| ~ ( c_Type_Otypings @ SV556 @ SV773 @ SV777 )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2275,plain,
! [SV698: $i,SV357: $i,SV558: $i,SV106: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV558 @ SV106 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SV698 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SV558 @ ( c_Suc @ SV698 ) @ SV106 ) @ SV106 ) )
= $true )
| ( ( c_lessequals @ SV357 @ SV558 @ SV106 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2217]) ).
thf(2276,plain,
! [SV567: $i,SV704: $i,SV759: $i,SV369: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV759 ) @ SV704 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV759 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV704 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2277,plain,
! [SV706: $i,SV374: $i,SV760: $i,SV572: $i,SV124: $i] :
( ( ( c_Type_Otypings @ SV124 @ SV572 @ SV760 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV124 @ SV374 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV760 @ SV706 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV374 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV706 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2278,plain,
! [SV774: $i,SV761: $i,SV709: $i,SV579: $i,SV385: $i,SV139: $i] :
( ( ( c_Type_Otyping @ SV139 @ SV385 @ SV579 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SV709 @ SV579 @ tc_Type_Otype ) @ SV761 @ SV774 )
| ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SV761 @ SV385 @ SV709 ) @ SV774 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2279,plain,
! [SV580: $i,SV141: $i,SV387: $i,SV710: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV710 ) @ SV387 ) )
= $false )
| ( ( c_Type_Otyping @ SV141 @ SV710 @ SV580 )
= $false )
| ( ( c_Type_Otyping @ SV141 @ SV387 @ SV580 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2280,plain,
! [SV711: $i,SV390: $i,SV583: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV145 ) @ SV583 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV390 ) @ SV711 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV145 ) @ SV390 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV583 ) @ SV711 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2281,plain,
! [SV167: $i,SV408: $i,SV763: $i,SV719: $i,SV598: $i] :
( ( ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV408 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 ) )
= $true )
| ( ( SV167 = SV408 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2282,plain,
! [SV413: $i,SV173: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV173 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV173 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2283,plain,
! [SV775: $i,SV176: $i,SV600: $i,SV764: $i,SV415: $i,SV720: $i] :
( ( ( ~ ( c_Type_Otyping @ SV720 @ SV415 @ SV764 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2284,plain,
! [SV418: $i,SV603: $i,SV722: $i,SV179: $i] :
( ( ( c_Type_Otyping @ SV179 @ SV722 @ SV603 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV722 ) @ SV418 ) )
= $false )
| ( ( c_Type_Otyping @ SV179 @ SV418 @ SV603 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2285,plain,
! [SV723: $i,SV419: $i,SV766: $i,SV604: $i,SV180: $i] :
( ( ( c_Type_Otyping @ SV180 @ SV604 @ SV766 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV180 @ SV419 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV723 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV419 ) @ SV604 ) @ SV723 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2286,plain,
! [SV618: $i,SV199: $i,SV438: $i] :
( ( ( SV438
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV438 ) @ SV618 ) )
= $true )
| ( ( SV618
= ( c_HOL_Ozero__class_Ozero @ SV199 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV199 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2287,plain,
! [SV733: $i,SV621: $i,SV441: $i,SV202: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV441 ) @ SV621 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV202 ) @ SV733 ) @ SV621 ) )
= $false )
| ( ( SV441 = SV733 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2288,plain,
! [SV448: $i,SV626: $i,SV209: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
| ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2289,plain,
! [SV450: $i,SV628: $i,SV211: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
| ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2290,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV212 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2291,plain,
! [SV452: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV213 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV213 )
| ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2292,plain,
! [SV735: $i,SV215: $i,SV630: $i,SV454: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
= $false )
| ( ( ( SV454 = SV735 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2293,plain,
! [SV739: $i,SV638: $i,SV466: $i,SV228: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV638 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV228 ) @ SV466 ) @ SV739 ) )
= $false )
| ( ( SV638 = SV739 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2294,plain,
! [SV740: $i,SV639: $i,SV467: $i,SV229: $i] :
( ( ( class_Int_Onumber__ring @ SV229 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV639 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV740 ) )
| ( SV639 = SV740 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2295,plain,
! [SV746: $i,SV649: $i,SV487: $i,SV254: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV649 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV254 ) @ SV487 ) @ SV746 ) )
= $false )
| ( ( SV649 = SV746 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2296,plain,
! [SV771: $i,SV747: $i,SV651: $i,SV491: $i,SV259: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV747 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV771 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ SV747 )
= SV771 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2297,plain,
! [SV496: $i,SV265: $i,SV776: $i,SV656: $i,SV772: $i,SV748: $i,SV3: $i] :
( ( ( ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV3 @ SV772 @ SV776 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) )
= $true )
| ( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2298,plain,
! [SV498: $i,SV658: $i,SV279: $i,SV20: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 )
= $false )
| ( ( ~ ( c_lessequals @ SV279 @ SV658 @ SV20 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SV498 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV658 @ SV498 @ SV20 ) @ SV20 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2299,plain,
! [SV516: $i,SV298: $i,SV39: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV298 @ SV39 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV516 @ SV39 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ SV298 ) @ SV516 ) @ SV39 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2300,plain,
! [SV674: $i,SV299: $i,SV42: $i,SV754: $i,SV517: $i] :
( ( ( ~ ( c_lessequals @ SV517 @ SV754 @ SV42 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV299 @ SV674 @ SV42 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV674 ) @ SV754 ) @ SV42 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2301,plain,
! [SV677: $i,SV522: $i,SV54: $i,SV309: $i] :
( ( ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
= $true )
| ( ( ~ ( c_lessequals @ SV309 @ SV677 @ SV54 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2302,plain,
! [SV678: $i,SV523: $i,SV55: $i,SV310: $i] :
( ( ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
= $true )
| ( ( ~ ( c_lessequals @ SV310 @ SV523 @ SV55 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2303,plain,
! [SV69: $i,SV533: $i,SV321: $i] :
( ( ( c_lessequals @ SV321 @ SV533 @ SV69 )
= $false )
| ( ( c_lessequals @ SV533 @ SV321 @ SV69 )
= $false )
| ( ( SV321 = SV533 )
= $true )
| ( ( class_Orderings_Oorder @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2304,plain,
! [SV70: $i,SV534: $i,SV322: $i] :
( ( ( c_lessequals @ SV322 @ SV534 @ SV70 )
= $false )
| ( ( c_lessequals @ SV534 @ SV322 @ SV70 )
= $false )
| ( ( SV322 = SV534 )
= $true )
| ( ( class_Orderings_Oorder @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2305,plain,
! [SV71: $i,SV323: $i,SV535: $i] :
( ( ( c_lessequals @ SV535 @ SV323 @ SV71 )
= $false )
| ( ( c_lessequals @ SV323 @ SV535 @ SV71 )
= $false )
| ( ( SV323 = SV535 )
= $true )
| ( ( class_Orderings_Oorder @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2306,plain,
! [SV544: $i,SV84: $i,SV688: $i,SV336: $i] :
( ( ( c_lessequals @ SV336 @ SV688 @ SV84 )
= $false )
| ( ( ~ ( c_lessequals @ SV688 @ SV544 @ SV84 ) )
= $true )
| ( ( c_lessequals @ SV336 @ SV544 @ SV84 )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2307,plain,
! [SV545: $i,SV85: $i,SV337: $i] :
( ( ( c_lessequals @ SV337 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
= $false )
| ( ( c_lessequals @ SV545 @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV85 ) @ SV337 ) @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ SV85 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2308,plain,
! [SV338: $i,SV86: $i,SV546: $i,SV689: $i] :
( ( ( c_lessequals @ SV689 @ SV546 @ SV86 )
= $false )
| ( ( ~ ( c_lessequals @ SV338 @ SV689 @ SV86 ) )
= $true )
| ( ( c_lessequals @ SV338 @ SV546 @ SV86 )
= $true )
| ( ( class_Orderings_Opreorder @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2309,plain,
! [SV547: $i,SV341: $i,SV89: $i,SV690: $i,SV755: $i] :
( ( ( ~ ( c_lessequals @ SV755 @ SV690 @ SV89 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV755 ) @ SV89 ) )
= $true )
| ( ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV690 ) @ SV89 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2310,plain,
! [SV693: $i,SV756: $i,SV552: $i,SV347: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV756 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV756 ) @ SV693 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV95 @ SV347 ) @ SV552 ) @ SV693 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2311,plain,
! [SV694: $i,SV348: $i,SV757: $i,SV553: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV553 ) @ SV757 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV757 ) @ SV694 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV96 @ SV348 ) @ SV553 ) @ SV694 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2312,plain,
! [SV354: $i,SV697: $i,SV777: $i,SV103: $i,SV773: $i,SV758: $i,SV556: $i] :
( ( ( ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV556 @ SV773 @ SV777 )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) )
= $true )
| ( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2313,plain,
! [SV698: $i,SV357: $i,SV558: $i,SV106: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV558 @ SV106 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SV698 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SV558 @ ( c_Suc @ SV698 ) @ SV106 ) @ SV106 ) )
= $true )
| ( ( c_lessequals @ SV357 @ SV558 @ SV106 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2314,plain,
! [SV704: $i,SV759: $i,SV567: $i,SV369: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV759 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV759 ) @ SV704 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV369 ) @ SV567 ) @ SV704 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2315,plain,
! [SV572: $i,SV706: $i,SV760: $i,SV374: $i,SV124: $i] :
( ( ( c_Type_Otyping @ SV124 @ SV374 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV760 @ SV706 @ tc_Type_Otype @ tc_Type_Otype ) )
= $false )
| ( ( c_Type_Otypings @ SV124 @ SV572 @ SV760 )
= $false )
| ( ( c_Type_Otyping @ SV124 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV374 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV706 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2316,plain,
! [SV385: $i,SV774: $i,SV761: $i,SV579: $i,SV709: $i,SV139: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SV709 @ SV579 @ tc_Type_Otype ) @ SV761 @ SV774 ) )
= $true )
| ( ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SV761 @ SV385 @ SV709 ) @ SV774 )
= $true )
| ( ( c_Type_Otyping @ SV139 @ SV385 @ SV579 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2317,plain,
! [SV408: $i,SV167: $i,SV763: $i,SV719: $i,SV598: $i] :
( ( ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV167 )
= $false )
| ( ( c_Type_Otyping @ SV598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV719 ) @ SV763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV408 )
= $false )
| ( ( SV167 = SV408 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2318,plain,
! [SV413: $i,SV173: $i] :
( ( ( ~ ( class_Power_Opower @ SV173 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2319,plain,
! [SV775: $i,SV176: $i,SV600: $i,SV764: $i,SV415: $i,SV720: $i] :
( ( ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2320,plain,
! [SV604: $i,SV723: $i,SV766: $i,SV419: $i,SV180: $i] :
( ( ( c_Type_Otyping @ SV180 @ SV419 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV723 ) )
= $false )
| ( ( c_Type_Otyping @ SV180 @ SV604 @ SV766 )
= $false )
| ( ( c_Type_Otyping @ SV180 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV419 ) @ SV604 ) @ SV723 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2321,plain,
! [SV618: $i,SV199: $i,SV438: $i] :
( ( ( SV438
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV438 ) @ SV618 ) )
= $false )
| ( ( SV618
= ( c_HOL_Ozero__class_Ozero @ SV199 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV199 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2322,plain,
! [SV448: $i,SV626: $i,SV209: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
| ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2323,plain,
! [SV450: $i,SV628: $i,SV211: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
| ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2324,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV212 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV212 )
| ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2325,plain,
! [SV452: $i,SV213: $i] :
( ( ( ~ ( class_Power_Opower @ SV213 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2326,plain,
! [SV630: $i,SV215: $i,SV735: $i,SV454: $i] :
( ( ( SV454 = SV735 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2292]) ).
thf(2327,plain,
! [SV740: $i,SV639: $i,SV467: $i,SV229: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV639 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV740 ) )
= $true )
| ( ( SV639 = SV740 )
= $true )
| ( ( class_Int_Onumber__ring @ SV229 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2328,plain,
! [SV771: $i,SV747: $i,SV651: $i,SV491: $i,SV259: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV747 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV651 ) @ SV771 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV259 ) @ SV491 ) @ SV747 )
= SV771 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2329,plain,
! [SV496: $i,SV265: $i,SV776: $i,SV656: $i,SV772: $i,SV748: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV3 @ SV772 @ SV776 )
| ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) )
= $true )
| ( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2330,plain,
! [SV498: $i,SV20: $i,SV658: $i,SV279: $i] :
( ( ( c_lessequals @ SV279 @ SV658 @ SV20 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV279 @ SV20 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV279 @ SV498 @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV658 @ SV498 @ SV20 ) @ SV20 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2331,plain,
! [SV674: $i,SV299: $i,SV42: $i,SV754: $i,SV517: $i] :
( ( ( c_lessequals @ SV517 @ SV754 @ SV42 )
= $false )
| ( ( ~ ( c_lessequals @ SV299 @ SV674 @ SV42 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV674 ) @ SV754 ) @ SV42 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2332,plain,
! [SV522: $i,SV54: $i,SV677: $i,SV309: $i] :
( ( ( ~ ( c_lessequals @ SV309 @ SV677 @ SV54 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) )
= $true )
| ( ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2333,plain,
! [SV678: $i,SV55: $i,SV523: $i,SV310: $i] :
( ( ( ~ ( c_lessequals @ SV310 @ SV523 @ SV55 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 ) )
= $true )
| ( ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2334,plain,
! [SV336: $i,SV84: $i,SV544: $i,SV688: $i] :
( ( ( c_lessequals @ SV688 @ SV544 @ SV84 )
= $false )
| ( ( c_lessequals @ SV336 @ SV688 @ SV84 )
= $false )
| ( ( c_lessequals @ SV336 @ SV544 @ SV84 )
= $true )
| ( ( class_Orderings_Oorder @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2335,plain,
! [SV546: $i,SV86: $i,SV689: $i,SV338: $i] :
( ( ( c_lessequals @ SV338 @ SV689 @ SV86 )
= $false )
| ( ( c_lessequals @ SV689 @ SV546 @ SV86 )
= $false )
| ( ( c_lessequals @ SV338 @ SV546 @ SV86 )
= $true )
| ( ( class_Orderings_Opreorder @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2336,plain,
! [SV547: $i,SV341: $i,SV89: $i,SV690: $i,SV755: $i] :
( ( ( c_lessequals @ SV755 @ SV690 @ SV89 )
= $false )
| ( ( ~ ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV755 ) @ SV89 ) )
= $true )
| ( ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV690 ) @ SV89 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2337,plain,
! [SV354: $i,SV697: $i,SV777: $i,SV103: $i,SV773: $i,SV758: $i,SV556: $i] :
( ( ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV556 @ SV773 @ SV777 )
| ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) )
= $true )
| ( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2338,plain,
! [SV558: $i,SV106: $i,SV698: $i,SV357: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV357 @ ( c_Suc @ SV698 ) @ SV106 ) @ ( c_Power_Opower__class_Opower @ SV558 @ ( c_Suc @ SV698 ) @ SV106 ) @ SV106 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV558 @ SV106 )
= $false )
| ( ( c_lessequals @ SV357 @ SV558 @ SV106 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2339,plain,
! [SV385: $i,SV774: $i,SV761: $i,SV579: $i,SV709: $i,SV139: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV139 @ SV709 @ SV579 @ tc_Type_Otype ) @ SV761 @ SV774 )
= $false )
| ( ( c_Type_Otyping @ SV139 @ ( c_Lambda_Osubst @ SV761 @ SV385 @ SV709 ) @ SV774 )
= $true )
| ( ( c_Type_Otyping @ SV139 @ SV385 @ SV579 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2340,plain,
! [SV413: $i,SV173: $i] :
( ( ( class_Power_Opower @ SV173 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
| ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2341,plain,
! [SV775: $i,SV176: $i,SV764: $i,SV600: $i,SV720: $i,SV415: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2342,plain,
! [SV626: $i,SV448: $i,SV209: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 ) )
= $true )
| ( ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2343,plain,
! [SV628: $i,SV450: $i,SV211: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 ) )
= $true )
| ( ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2344,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ( ~ ( class_Power_Opower @ SV212 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2345,plain,
! [SV452: $i,SV213: $i] :
( ( ( class_Power_Opower @ SV213 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
!= ( c_HOL_Ozero__class_Ozero @ SV213 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2346,plain,
! [SV630: $i,SV454: $i,SV735: $i,SV215: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) )
= $true )
| ( ( SV454 = SV735 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2347,plain,
! [SV740: $i,SV639: $i,SV467: $i,SV229: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV639 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV229 ) @ SV467 ) @ SV740 ) )
= $false )
| ( ( SV639 = SV740 )
= $true )
| ( ( class_Int_Onumber__ring @ SV229 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2348,plain,
! [SV656: $i,SV496: $i,SV265: $i,SV748: $i,SV776: $i,SV772: $i,SV3: $i] :
( ( ( ~ ( c_Type_Otypings @ SV3 @ SV772 @ SV776 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) )
= $true )
| ( ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
= $false )
| ( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2349,plain,
! [SV754: $i,SV517: $i,SV42: $i,SV674: $i,SV299: $i] :
( ( ( c_lessequals @ SV299 @ SV674 @ SV42 )
= $false )
| ( ( c_lessequals @ SV517 @ SV754 @ SV42 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV299 ) @ SV517 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV42 ) @ SV674 ) @ SV754 ) @ SV42 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2350,plain,
! [SV522: $i,SV54: $i,SV677: $i,SV309: $i] :
( ( ( c_lessequals @ SV309 @ SV677 @ SV54 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 ) )
= $true )
| ( ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2351,plain,
! [SV678: $i,SV55: $i,SV523: $i,SV310: $i] :
( ( ( c_lessequals @ SV310 @ SV523 @ SV55 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 ) )
= $true )
| ( ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2352,plain,
! [SV690: $i,SV755: $i,SV547: $i,SV89: $i,SV341: $i] :
( ( ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV755 ) @ SV89 )
= $false )
| ( ( c_lessequals @ SV755 @ SV690 @ SV89 )
= $false )
| ( ( c_lessequals @ SV341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV547 ) @ SV690 ) @ SV89 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2353,plain,
! [SV103: $i,SV354: $i,SV697: $i,SV758: $i,SV777: $i,SV773: $i,SV556: $i] :
( ( ( ~ ( c_Type_Otypings @ SV556 @ SV773 @ SV777 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) )
= $true )
| ( ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
= $false )
| ( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2354,plain,
! [SV413: $i,SV173: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV413 @ SV173 )
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
= $true )
| ( ( SV413
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV173 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2355,plain,
! [SV775: $i,SV176: $i,SV764: $i,SV600: $i,SV720: $i,SV415: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2356,plain,
! [SV626: $i,SV448: $i,SV209: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV448 @ SV209 )
= $false )
| ( ( SV448
= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV209 ) @ SV626 @ SV209 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV209 ) @ SV448 ) @ SV626 )
= ( c_HOL_Ozero__class_Ozero @ SV209 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2357,plain,
! [SV628: $i,SV450: $i,SV211: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV450 @ SV211 )
= $false )
| ( ( SV628
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV628 @ SV211 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV211 ) @ SV450 ) @ SV628 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2358,plain,
! [SV629: $i,SV451: $i,SV212: $i] :
( ( ( class_Power_Opower @ SV212 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
| ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2359,plain,
! [SV213: $i,SV452: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV452 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV213 )
= ( c_HOL_Ozero__class_Ozero @ SV213 ) )
= $false )
| ( ( class_Power_Opower @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2360,plain,
! [SV630: $i,SV454: $i,SV735: $i,SV215: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 ) )
= $true )
| ( ( SV454 = SV735 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2361,plain,
! [SV656: $i,SV496: $i,SV265: $i,SV748: $i,SV776: $i,SV772: $i,SV3: $i] :
( ( ( c_Type_Otypings @ SV3 @ SV772 @ SV776 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 ) )
= $true )
| ( ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
= $false )
| ( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2362,plain,
! [SV677: $i,SV309: $i,SV522: $i,SV54: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV522 @ SV54 )
= $false )
| ( ( c_lessequals @ SV309 @ SV677 @ SV54 )
= $false )
| ( ( c_lessequals @ SV309 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV522 ) @ SV677 ) @ SV54 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV54 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2363,plain,
! [SV523: $i,SV310: $i,SV678: $i,SV55: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV678 @ SV55 )
= $false )
| ( ( c_lessequals @ SV310 @ SV523 @ SV55 )
= $false )
| ( ( c_lessequals @ SV310 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV523 ) @ SV678 ) @ SV55 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV55 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2364,plain,
! [SV103: $i,SV354: $i,SV697: $i,SV758: $i,SV777: $i,SV773: $i,SV556: $i] :
( ( ( c_Type_Otypings @ SV556 @ SV773 @ SV777 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 ) )
= $true )
| ( ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
= $false )
| ( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2365,plain,
! [SV415: $i,SV775: $i,SV176: $i,SV764: $i,SV600: $i,SV720: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
= $false )
| ( ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2366,plain,
! [SV212: $i,SV629: $i,SV451: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
!= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
= $true )
| ( ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
= $true )
| ( ( class_Power_Opower @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2367,plain,
! [SV630: $i,SV735: $i,SV454: $i,SV215: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV454 @ SV215 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV735 @ SV215 )
= $false )
| ( ( SV454 = SV735 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV454 @ ( c_Suc @ SV630 ) @ SV215 )
= ( c_Power_Opower__class_Opower @ SV735 @ ( c_Suc @ SV630 ) @ SV215 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2368,plain,
! [SV656: $i,SV776: $i,SV496: $i,SV265: $i,SV772: $i,SV748: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV265 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV496 )
= $false )
| ( ( c_Type_Otypings @ SV3 @ SV772 @ SV776 )
= $false )
| ( ( c_Type_Otyping @ SV3 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV748 ) @ SV772 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV656 )
= $false )
| ( ( c_Type_Otypings @ SV3 @ SV265 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV496 @ SV656 @ SV3 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2369,plain,
! [SV103: $i,SV777: $i,SV354: $i,SV697: $i,SV773: $i,SV758: $i,SV556: $i] :
( ( ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV354 )
= $false )
| ( ( c_Type_Otypings @ SV556 @ SV773 @ SV777 )
= $false )
| ( ( c_Type_Otyping @ SV556 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV758 ) @ SV773 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV103 )
= $false )
| ( ( SV103
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV354 @ SV103 @ SV556 @ SV697 ) @ SV354 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2370,plain,
! [SV415: $i,SV775: $i,SV176: $i,SV764: $i,SV600: $i,SV720: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
= $false )
| ( ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2371,plain,
! [SV212: $i,SV629: $i,SV451: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV451 @ SV629 @ SV212 )
= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
= $false )
| ( ( SV451
= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
= $true )
| ( ( class_Power_Opower @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV212 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2372,plain,
! [SV415: $i,SV775: $i,SV764: $i,SV600: $i,SV720: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV176 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV720 @ SV600 @ SV764 @ tc_Type_Otype ) @ SV176 @ SV775 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
= $false )
| ( ( c_Type_Otyping @ SV720 @ SV415 @ SV764 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV176 @ SV415 @ SV600 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2373,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[630,2372,2371,2369,2368,2367,2363,2362,2359,2357,2356,2354,2352,2349,2347,2339,2338,2335,2334,2330,2328,2321,2320,2317,2315,2314,2311,2310,2307,2305,2304,2303,2299,2295,2293,2287,2284,2280,2279,2271,2270,2265,2264,2263,2262,2261,2260,2254,2253,2246,2245,2237,2236,2233,2232,2229,2226,2224,2219,2196,2193,2191,2189,2188,2187,2186,2184,2180,2179,2178,2175,2174,2171,2162,2160,2159,2158,2155,2146,2145,2144,2143,2139,2136,2134,2133,2132,2131,2130,2129,2126,2122,2116,2115,2114,2104,2097,2096,2092,2091,2090,2089,2088,2087,2086,2085,2084,2079,2077,2074,2073,2072,2070,2069,2068,2065,2058,2057,2054,2053,2051,2050,2049,2048,2047,2042,2039,2038,2035,2030,2029,2028,2027,2023,2022,2021,2017,2014,2010,2008,2007,2005,2004,2002,2001,1997,1996,1993,1991,1990,1987,1978,1977,1975,1967,1950,1949,1947,1946,1945,1913,1906,1905,1898,1897,1896,1895,1894,1893,1890,1887,1884,1879,1873,1866,1862,1854,1850,1849,1833,1832,1829,1828,1823,1819,1810,1808,1807,1806,1790,1787,1782,1774,1773,1766,1765,1755,1754,1752,1751,1721,1719,1717,1716,1715,1714,1713,1712,1710,1709,1708,1707,1671,1666,1619,1604,1599,1586,1580,1579,1574,1547,1533,1520,1519,1512,1507,1506,1475,1469,1456,1454,1451,1443,1404,1398,1381,1353,1347,1327,1324,1323,1320,1314,1282,1277,1276,1269,1242,1157,1139,1135,1124,1122,1106,1095,1093,1091,1089,1061,1030,975,974,973,964,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,859,856,853,804,716,692,657,652]) ).
thf(2374,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL854-1 : 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 : n001.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 12:41:54 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.06/3.27 ..
% 18.06/3.27
% 18.06/3.27 No.of.Axioms: 296
% 18.06/3.27
% 18.06/3.27 Length.of.Defs: 0
% 18.06/3.27
% 18.06/3.27 Contains.Choice.Funs: false
% 18.06/3.27 .................................................................................
% 18.06/3.27
% 18.06/3.27 ********************************
% 18.06/3.27 * All subproblems solved! *
% 18.06/3.27 ********************************
% 18.06/3.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:296,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2373,loop_count:0,foatp_calls:1,translation:fof_full)
% 18.06/3.27
% 18.06/3.27 %**** Beginning of derivation protocol ****
% 18.06/3.27 % SZS output start CNFRefutation
% See solution above
% 18.06/3.29
% 18.06/3.29 %**** End of derivation protocol ****
% 18.06/3.29 %**** no. of clauses in derivation: 2374 ****
% 18.06/3.29 %**** clause counter: 2373 ****
% 18.06/3.29
% 18.06/3.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:296,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2373,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------