%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL799-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 10:30:40 AM UTC 2026
% Result : Unsatisfiable 37.82s 6.57s
% Output : CNFRefutation 37.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 295
% Syntax : Number of formulae : 2391 (1638 unt; 0 typ; 0 def)
% Number of atoms : 11240 (4620 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 35360 (2499 ~;3023 |; 0 &;29838 @)
% ( 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 : 79 ( 76 usr; 25 con; 0-5 aty)
% Number of variables : 8245 ( 0 ^;8245 !; 0 ?;8245 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
thf(tp_c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
thf(tp_c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tp_c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
thf(tp_c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(tp_c_Lambda_Olift,type,
c_Lambda_Olift: $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_Oappend,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ofoldr,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_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_Predicate_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $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__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__Xtypes__snocE__1__2,type,
c_Type_Osko__Type__Xtypes__snocE__1__2: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__2__1,type,
c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xvar__app__typesE__1__1,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xvar__app__types__1__1,type,
c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
thf(tp_c_Type_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_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_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_Type_Otype,type,
tc_Type_Otype: $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_T_H_H____,type,
v_T_H_H____: $i ).
thf(tp_v_T_H____,type,
v_T_H____: $i ).
thf(tp_v_T_Ha______,type,
v_T_Ha______: $i ).
thf(tp_v_T____,type,
v_T____: $i ).
thf(tp_v_Ts____,type,
v_Ts____: $i ).
thf(tp_v_a____,type,
v_a____: $i ).
thf(tp_v_as____,type,
v_as____: $i ).
thf(tp_v_e____,type,
v_e____: $i ).
thf(tp_v_ea______,type,
v_ea______: $i ).
thf(tp_v_i____,type,
v_i____: $i ).
thf(tp_v_ia______,type,
v_ia______: $i ).
thf(tp_v_n____,type,
v_n____: $i ).
thf(tp_v_rs____,type,
v_rs____: $i ).
thf(tp_v_u____,type,
v_u____: $i ).
thf(tp_v_ua______,type,
v_ua______: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(4,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(6,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(8,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(9,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(10,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(11,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(12,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(13,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(14,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(15,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(16,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(17,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(18,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(19,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(20,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(21,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(22,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(23,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(24,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(27,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(28,axiom,
! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(30,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(31,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
thf(32,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argT_0) ).
thf(33,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_H_0) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(37,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(39,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(40,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(41,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(42,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(43,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(45,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_0) ).
thf(47,axiom,
! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(48,axiom,
! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
thf(49,axiom,
! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(50,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(51,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(52,axiom,
! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(56,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(57,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(59,axiom,
! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(60,axiom,
! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(61,axiom,
! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(62,axiom,
! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(63,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(67,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_ea______ @ v_ia______ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_Ha______,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(69,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_varT_0) ).
thf(70,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_headT_0) ).
thf(71,axiom,
c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argsT_0) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(73,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
thf(75,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nT_0) ).
thf(76,axiom,
! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
thf(79,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(80,axiom,
( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_0) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(86,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_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/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(87,axiom,
! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(90,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
thf(92,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(95,axiom,
! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(98,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/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(99,axiom,
( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_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/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_1) ).
thf(102,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(104,axiom,
! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(105,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(108,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(109,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(111,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(112,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(115,axiom,
c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(119,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(122,axiom,
! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(123,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(125,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(126,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(127,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(128,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(129,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(131,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(132,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(133,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(134,axiom,
! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(135,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(136,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(137,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(138,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(139,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(140,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(141,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(142,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(143,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(144,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(146,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(147,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(148,axiom,
! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(150,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
thf(152,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(153,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(154,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(157,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(158,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(159,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(162,axiom,
! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(164,axiom,
! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__last_0) ).
thf(165,axiom,
! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(166,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(167,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(168,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(169,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(170,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(171,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(172,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(173,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(174,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(176,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(177,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(179,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(180,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(181,axiom,
! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(182,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(183,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(184,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(185,axiom,
! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(186,axiom,
! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( 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_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_5) ).
thf(187,axiom,
! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(188,axiom,
! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(189,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(190,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(191,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(192,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(195,axiom,
! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(196,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(197,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(198,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(199,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(200,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(201,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(202,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(203,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/sandbox2/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(204,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/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(207,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(208,axiom,
! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(209,axiom,
! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(210,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(211,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(212,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(213,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(214,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(215,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(216,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(217,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(218,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(219,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(220,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(225,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(226,axiom,
! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(227,axiom,
! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(229,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/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(230,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(231,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(232,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(233,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(234,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(235,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(236,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(237,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(238,axiom,
! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(239,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(240,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(241,axiom,
! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(242,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(243,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(244,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(245,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(246,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(247,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(248,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(249,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(250,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(251,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(252,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(253,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(254,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(255,axiom,
! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(256,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(257,axiom,
! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(258,axiom,
! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(259,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(260,axiom,
! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(261,axiom,
! [V_e: $i,V_t: $i,V_Ts: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ V_Ts @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otypings @ V_e @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_Ts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_types__snocE_2) ).
thf(262,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(263,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(264,axiom,
! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(265,axiom,
! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(266,axiom,
! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(267,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(268,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(269,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(270,axiom,
! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(271,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(272,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(273,axiom,
! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(274,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(275,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(276,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(277,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(278,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(279,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(280,axiom,
! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(281,axiom,
! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(282,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(283,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(284,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(285,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(286,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(287,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(288,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(289,axiom,
! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(290,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(291,axiom,
! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(292,axiom,
! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(293,axiom,
! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(294,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(295,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[294]) ).
thf(296,negated_conjecture,
~ ( c_Type_Otyping @ v_e____ @ ( c_Lambda_Osubst @ v_a____ @ v_u____ @ v_i____ ) @ v_T_H_H____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(297,plain,
$false = $false,
inference(unfold_def,[status(thm)],[295]) ).
thf(298,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(299,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(300,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(301,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(302,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(303,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(304,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(305,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(306,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(307,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(308,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(309,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(310,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(311,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(312,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(313,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(314,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(315,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(316,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(317,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(318,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)],[21]) ).
thf(319,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)],[22]) ).
thf(320,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____ )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(321,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(322,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)],[25]) ).
thf(323,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)],[26]) ).
thf(324,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(325,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)],[28]) ).
thf(326,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)],[29]) ).
thf(327,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)],[30]) ).
thf(328,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(329,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____ )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(330,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(331,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)],[34]) ).
thf(332,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)],[35]) ).
thf(333,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)],[36]) ).
thf(334,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(335,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)],[38]) ).
thf(336,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(337,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)],[40]) ).
thf(338,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)],[41]) ).
thf(339,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)],[42]) ).
thf(340,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(341,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)],[44]) ).
thf(342,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(343,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)],[46]) ).
thf(344,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)],[47]) ).
thf(345,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)],[48]) ).
thf(346,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)],[49]) ).
thf(347,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)],[50]) ).
thf(348,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)],[51]) ).
thf(349,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)],[52]) ).
thf(350,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)],[53]) ).
thf(351,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)],[54]) ).
thf(352,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)],[55]) ).
thf(353,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)],[56]) ).
thf(354,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)],[57]) ).
thf(355,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)],[58]) ).
thf(356,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(357,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(358,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)],[61]) ).
thf(359,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)],[62]) ).
thf(360,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(361,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)],[64]) ).
thf(362,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)],[65]) ).
thf(363,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)],[66]) ).
thf(364,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_ea______ @ v_ia______ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_Ha______ )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(365,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)],[68]) ).
thf(366,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(367,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(368,plain,
( ( c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____ )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(369,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)],[72]) ).
thf(370,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(371,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)],[74]) ).
thf(372,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(373,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)],[76]) ).
thf(374,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)],[77]) ).
thf(375,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)],[78]) ).
thf(376,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(377,plain,
( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(378,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)],[81]) ).
thf(379,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)],[82]) ).
thf(380,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)],[83]) ).
thf(381,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)],[84]) ).
thf(382,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)],[85]) ).
thf(383,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)],[86]) ).
thf(384,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(385,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)],[88]) ).
thf(386,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)],[89]) ).
thf(387,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)],[90]) ).
thf(388,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)],[91]) ).
thf(389,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)],[92]) ).
thf(390,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)],[93]) ).
thf(391,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)],[94]) ).
thf(392,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)],[95]) ).
thf(393,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)],[96]) ).
thf(394,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)],[97]) ).
thf(395,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)],[98]) ).
thf(396,plain,
( ( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(397,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(398,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)],[101]) ).
thf(399,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)],[102]) ).
thf(400,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)],[103]) ).
thf(401,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)],[104]) ).
thf(402,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(403,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)],[106]) ).
thf(404,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)],[107]) ).
thf(405,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(406,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(407,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)],[110]) ).
thf(408,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(409,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(410,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)],[113]) ).
thf(411,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)],[114]) ).
thf(412,plain,
( ( c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(413,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)],[116]) ).
thf(414,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)],[117]) ).
thf(415,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)],[118]) ).
thf(416,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)],[119]) ).
thf(417,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)],[120]) ).
thf(418,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)],[121]) ).
thf(419,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)],[122]) ).
thf(420,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)],[123]) ).
thf(421,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)],[124]) ).
thf(422,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(423,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(424,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(425,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(426,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(427,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)],[130]) ).
thf(428,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(429,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(430,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(431,plain,
( ( ! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(432,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(433,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(434,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(435,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(436,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)],[139]) ).
thf(437,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)],[140]) ).
thf(438,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)],[141]) ).
thf(439,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)],[142]) ).
thf(440,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(441,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(442,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)],[145]) ).
thf(443,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(444,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(445,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(446,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)],[149]) ).
thf(447,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)],[150]) ).
thf(448,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)],[151]) ).
thf(449,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(450,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)],[153]) ).
thf(451,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(452,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)],[155]) ).
thf(453,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)],[156]) ).
thf(454,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(455,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(456,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(457,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)],[160]) ).
thf(458,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)],[161]) ).
thf(459,plain,
( ( ! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(460,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)],[163]) ).
thf(461,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(462,plain,
( ( ! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(463,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(464,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(465,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(466,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(467,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(468,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(469,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(470,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(471,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(472,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)],[175]) ).
thf(473,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(474,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(475,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)],[178]) ).
thf(476,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(477,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(478,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(479,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(480,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(481,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(482,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)],[185]) ).
thf(483,plain,
( ( ! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( 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_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(484,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)],[187]) ).
thf(485,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)],[188]) ).
thf(486,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(487,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(488,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(489,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(490,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)],[193]) ).
thf(491,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)],[194]) ).
thf(492,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)],[195]) ).
thf(493,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)],[196]) ).
thf(494,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)],[197]) ).
thf(495,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)],[198]) ).
thf(496,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)],[199]) ).
thf(497,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)],[200]) ).
thf(498,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)],[201]) ).
thf(499,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)],[202]) ).
thf(500,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)],[203]) ).
thf(501,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)],[204]) ).
thf(502,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)],[205]) ).
thf(503,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)],[206]) ).
thf(504,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)],[207]) ).
thf(505,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(506,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(507,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(508,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)],[211]) ).
thf(509,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)],[212]) ).
thf(510,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)],[213]) ).
thf(511,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)],[214]) ).
thf(512,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)],[215]) ).
thf(513,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)],[216]) ).
thf(514,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)],[217]) ).
thf(515,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)],[218]) ).
thf(516,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)],[219]) ).
thf(517,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)],[220]) ).
thf(518,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)],[221]) ).
thf(519,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)],[222]) ).
thf(520,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)],[223]) ).
thf(521,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)],[224]) ).
thf(522,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)],[225]) ).
thf(523,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)],[226]) ).
thf(524,plain,
( ( ! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(525,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)],[228]) ).
thf(526,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)],[229]) ).
thf(527,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)],[230]) ).
thf(528,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(529,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)],[232]) ).
thf(530,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)],[233]) ).
thf(531,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)],[234]) ).
thf(532,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)],[235]) ).
thf(533,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(534,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(535,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(536,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)],[239]) ).
thf(537,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(538,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(539,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(540,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)],[243]) ).
thf(541,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)],[244]) ).
thf(542,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)],[245]) ).
thf(543,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)],[246]) ).
thf(544,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)],[247]) ).
thf(545,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(546,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(547,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(548,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(549,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(550,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(551,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(552,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(553,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(554,plain,
( ( ! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(555,plain,
( ( ! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(556,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(557,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(558,plain,
( ( ! [V_e: $i,V_t: $i,V_Ts: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ V_Ts @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otypings @ V_e @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_Ts ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(559,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(560,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(561,plain,
( ( ! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(562,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(563,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(564,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(565,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(566,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(567,plain,
( ( ! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(568,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(569,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(570,plain,
( ( ! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(571,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(572,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(573,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(574,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(575,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(576,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(577,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(578,plain,
( ( ! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(579,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(580,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(581,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(582,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(583,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(584,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(585,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(586,plain,
( ( ! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(587,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(588,plain,
( ( ! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(589,plain,
( ( ! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(590,plain,
( ( ! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(591,plain,
( ( ~ ( c_Type_Otyping @ v_e____ @ ( c_Lambda_Osubst @ v_a____ @ v_u____ @ v_i____ ) @ v_T_H_H____ ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(592,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[297]) ).
thf(593,plain,
( ( ~ ( c_Type_Otyping @ v_e____ @ ( c_Lambda_Osubst @ v_a____ @ v_u____ @ v_i____ ) @ v_T_H_H____ ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(594,plain,
( ( ! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(595,plain,
( ( ! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(596,plain,
( ( ! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(597,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(598,plain,
( ( ! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(599,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(600,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(601,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(602,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(603,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(604,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(605,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(606,plain,
( ( ! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(607,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(608,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(609,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(610,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(611,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(612,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(613,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(614,plain,
( ( ! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(615,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(616,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(617,plain,
( ( ! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(618,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(619,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(620,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(621,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(622,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(623,plain,
( ( ! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(624,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(625,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(626,plain,
( ( ! [V_e: $i,V_t: $i,V_Ts: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ V_Ts @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otypings @ V_e @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_Ts ) ) )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(627,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(628,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(629,plain,
( ( ! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(630,plain,
( ( ! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(631,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(632,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(633,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(634,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(635,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(636,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(637,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)],[547]) ).
thf(638,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)],[546]) ).
thf(639,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)],[545]) ).
thf(640,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)],[544]) ).
thf(641,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)],[543]) ).
thf(642,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)],[542]) ).
thf(643,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)],[541]) ).
thf(644,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)],[540]) ).
thf(645,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(646,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(647,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(648,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)],[536]) ).
thf(649,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(650,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(651,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(652,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)],[532]) ).
thf(653,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)],[531]) ).
thf(654,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)],[530]) ).
thf(655,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)],[529]) ).
thf(656,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(657,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)],[527]) ).
thf(658,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)],[526]) ).
thf(659,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)],[525]) ).
thf(660,plain,
( ( ! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(661,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)],[523]) ).
thf(662,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)],[522]) ).
thf(663,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)],[521]) ).
thf(664,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)],[520]) ).
thf(665,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)],[519]) ).
thf(666,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)],[518]) ).
thf(667,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)],[517]) ).
thf(668,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)],[516]) ).
thf(669,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)],[515]) ).
thf(670,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)],[514]) ).
thf(671,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)],[513]) ).
thf(672,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)],[512]) ).
thf(673,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)],[511]) ).
thf(674,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)],[510]) ).
thf(675,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)],[509]) ).
thf(676,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)],[508]) ).
thf(677,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(678,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(679,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(680,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)],[504]) ).
thf(681,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)],[503]) ).
thf(682,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)],[502]) ).
thf(683,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)],[501]) ).
thf(684,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)],[500]) ).
thf(685,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)],[499]) ).
thf(686,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)],[498]) ).
thf(687,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)],[497]) ).
thf(688,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)],[496]) ).
thf(689,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)],[495]) ).
thf(690,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)],[494]) ).
thf(691,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)],[493]) ).
thf(692,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)],[492]) ).
thf(693,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)],[491]) ).
thf(694,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)],[490]) ).
thf(695,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(696,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(697,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(698,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(699,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)],[485]) ).
thf(700,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)],[484]) ).
thf(701,plain,
( ( ! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( 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_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(702,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(703,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(704,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(705,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(706,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(707,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(708,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(709,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)],[475]) ).
thf(710,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(711,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(712,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)],[472]) ).
thf(713,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(714,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(715,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(716,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(717,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(718,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(719,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(720,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(721,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(722,plain,
( ( ! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(723,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(724,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)],[460]) ).
thf(725,plain,
( ( ! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(726,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)],[458]) ).
thf(727,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)],[457]) ).
thf(728,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(729,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(730,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(731,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)],[453]) ).
thf(732,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)],[452]) ).
thf(733,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(734,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)],[450]) ).
thf(735,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(736,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)],[448]) ).
thf(737,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)],[447]) ).
thf(738,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)],[446]) ).
thf(739,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(740,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(741,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(742,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)],[442]) ).
thf(743,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(744,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(745,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)],[439]) ).
thf(746,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)],[438]) ).
thf(747,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)],[437]) ).
thf(748,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)],[436]) ).
thf(749,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(750,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(751,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(752,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(753,plain,
( ( ! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(754,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(755,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(756,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(757,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)],[427]) ).
thf(758,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(759,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(760,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(761,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(762,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(763,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)],[421]) ).
thf(764,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)],[420]) ).
thf(765,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)],[419]) ).
thf(766,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)],[418]) ).
thf(767,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)],[417]) ).
thf(768,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)],[416]) ).
thf(769,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)],[415]) ).
thf(770,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)],[414]) ).
thf(771,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)],[413]) ).
thf(772,plain,
( ( c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(773,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)],[411]) ).
thf(774,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)],[410]) ).
thf(775,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(776,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(777,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)],[407]) ).
thf(778,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(779,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(780,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)],[404]) ).
thf(781,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)],[403]) ).
thf(782,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)],[402]) ).
thf(783,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)],[401]) ).
thf(784,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)],[400]) ).
thf(785,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)],[399]) ).
thf(786,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)],[398]) ).
thf(787,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)],[397]) ).
thf(788,plain,
( ( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(789,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)],[395]) ).
thf(790,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)],[394]) ).
thf(791,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)],[393]) ).
thf(792,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)],[392]) ).
thf(793,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)],[391]) ).
thf(794,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)],[390]) ).
thf(795,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)],[389]) ).
thf(796,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)],[388]) ).
thf(797,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)],[387]) ).
thf(798,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)],[386]) ).
thf(799,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)],[385]) ).
thf(800,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(801,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)],[383]) ).
thf(802,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)],[382]) ).
thf(803,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)],[381]) ).
thf(804,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)],[380]) ).
thf(805,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)],[379]) ).
thf(806,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)],[378]) ).
thf(807,plain,
( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(808,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(809,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)],[375]) ).
thf(810,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)],[374]) ).
thf(811,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)],[373]) ).
thf(812,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____ )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(813,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)],[371]) ).
thf(814,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(815,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)],[369]) ).
thf(816,plain,
( ( c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____ )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(817,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(818,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(819,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)],[365]) ).
thf(820,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_ea______ @ v_ia______ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_Ha______ )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(821,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)],[363]) ).
thf(822,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)],[362]) ).
thf(823,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)],[361]) ).
thf(824,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(825,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)],[359]) ).
thf(826,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)],[358]) ).
thf(827,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(828,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(829,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)],[355]) ).
thf(830,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)],[354]) ).
thf(831,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)],[353]) ).
thf(832,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)],[352]) ).
thf(833,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)],[351]) ).
thf(834,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)],[350]) ).
thf(835,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)],[349]) ).
thf(836,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)],[348]) ).
thf(837,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)],[347]) ).
thf(838,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)],[346]) ).
thf(839,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)],[345]) ).
thf(840,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)],[344]) ).
thf(841,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)],[343]) ).
thf(842,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(843,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)],[341]) ).
thf(844,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)],[340]) ).
thf(845,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)],[339]) ).
thf(846,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)],[338]) ).
thf(847,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)],[337]) ).
thf(848,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)],[336]) ).
thf(849,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)],[335]) ).
thf(850,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(851,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)],[333]) ).
thf(852,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)],[332]) ).
thf(853,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)],[331]) ).
thf(854,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(855,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____ )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(856,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(857,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)],[327]) ).
thf(858,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)],[326]) ).
thf(859,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)],[325]) ).
thf(860,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(861,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)],[323]) ).
thf(862,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)],[322]) ).
thf(863,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(864,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____ )
= $true ),
inference(copy,[status(thm)],[320]) ).
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)],[319]) ).
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)],[318]) ).
thf(867,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(868,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(869,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(870,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(871,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(872,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(873,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(874,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(875,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(876,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(877,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(878,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(879,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(880,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(881,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(882,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(883,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(884,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(885,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(886,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)],[298]) ).
thf(887,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[592]) ).
thf(888,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(889,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)],[652]) ).
thf(890,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)],[709]) ).
thf(891,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oappend @ SX1 @ SX2 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(892,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)],[836]) ).
thf(893,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[734]) ).
thf(894,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)],[847]) ).
thf(895,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(896,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[848]) ).
thf(897,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)],[763]) ).
thf(898,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Oappend @ SX1 @ SX0 @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(899,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(900,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)],[831]) ).
thf(901,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(902,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)],[737]) ).
thf(903,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)],[795]) ).
thf(904,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)],[782]) ).
thf(905,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 )
!= ( c_List_Oappend @ SX3 @ ( c_List_Olist_OCons @ SX4 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(906,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)],[830]) ).
thf(907,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)],[785]) ).
thf(908,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)],[845]) ).
thf(909,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)],[837]) ).
thf(910,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 )
!= ( c_List_Oappend @ SX3 @ ( c_List_Olist_OCons @ SX4 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(911,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)],[792]) ).
thf(912,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(913,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(914,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(915,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Oappend @ SX0 @ SX1 @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(916,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= SX1 )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(917,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(918,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)],[735]) ).
thf(919,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[719]) ).
thf(920,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)],[747]) ).
thf(921,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)],[844]) ).
thf(922,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SX2 @ SX3 @ SX4 ) ) )
| ~ ( c_Type_Otyping @ SX5 @ SX3 @ SX1 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX3 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SX5 @ SX4 @ SX1 @ tc_Type_Otype ) @ SX2 @ SX6 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[828]) ).
thf(923,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)],[653]) ).
thf(924,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)],[655]) ).
thf(925,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 ) @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 ) @ ( c_List_Oappend @ SX2 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(926,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)],[748]) ).
thf(927,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Olist_OCons @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(928,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)],[690]) ).
thf(929,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)],[784]) ).
thf(930,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)],[662]) ).
thf(931,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)],[765]) ).
thf(932,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SX2 @ SX3 @ SX4 ) ) )
| ~ ( c_Type_Otyping @ SX5 @ SX3 @ SX0 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX3 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SX5 @ SX4 @ SX0 @ tc_Type_Otype ) @ SX2 @ SX6 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[827]) ).
thf(933,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oappend @ SX1 @ SX2 @ SX0 ) )
| ( SX2
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(934,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)],[689]) ).
thf(935,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= SX0 )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(936,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)],[846]) ).
thf(937,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)],[790]) ).
thf(938,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(939,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(940,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX0 @ SX3 @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(941,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)],[691]) ).
thf(942,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)],[746]) ).
thf(943,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)],[654]) ).
thf(944,plain,
( ( c_Type_Otyping @ v_e____ @ ( c_Lambda_Osubst @ v_a____ @ v_u____ @ v_i____ ) @ v_T_H_H____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(945,plain,
! [SV1: $i] :
( ( ! [SY865: $i,SY866: $i,SY867: $i] :
( ( c_List_Oappend @ SV1 @ ( c_List_Oappend @ SY865 @ SY866 @ SY867 ) @ SY867 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV1 @ SY865 @ SY867 ) @ SY866 @ SY867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(946,plain,
! [SV2: $i] :
( ( ! [SY868: $i,SY869: $i,SY870: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV2 @ SY868 @ SY869 ) @ SY870 @ SY869 )
= ( c_List_Oappend @ SV2 @ ( c_List_Oappend @ SY868 @ SY870 @ SY869 ) @ SY869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(947,plain,
! [SV3: $i] :
( ( ! [SY871: $i,SY872: $i,SY873: $i] :
( ( c_List_Oappend @ SV3 @ ( c_List_Oappend @ SY871 @ SY872 @ SY873 ) @ SY873 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV3 @ SY871 @ SY873 ) @ SY872 @ SY873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(948,plain,
! [SV4: $i] :
( ( ! [SY874: $i,SY875: $i,SY876: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV4 @ SY874 @ SY875 ) @ SY876 @ SY875 )
= ( c_List_Oappend @ SV4 @ ( c_List_Oappend @ SY874 @ SY876 @ SY875 ) @ SY875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(949,plain,
! [SV5: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV5 ) @ ( c_List_Olist_ONil @ SV5 ) @ SV5 )
= ( c_List_Olist_ONil @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(950,plain,
! [SV6: $i] :
( ( ! [SY877: $i,SY878: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV6 ) @ ( c_List_Olist_OCons @ SY877 @ SY878 @ SV6 ) @ SV6 )
= ( c_List_Olist_OCons @ SY877 @ SY878 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(951,plain,
! [SV7: $i] :
( ( ! [SY879: $i,SY880: $i,SY881: $i] :
( ( c_List_Olistsp @ SV7 @ ( c_List_Oappend @ SY879 @ SY880 @ SY881 ) @ SY881 )
| ~ ( c_List_Olistsp @ SV7 @ SY880 @ SY881 )
| ~ ( c_List_Olistsp @ SV7 @ SY879 @ SY881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(952,plain,
! [SV8: $i] :
( ( ! [SY882: $i,SY883: $i,SY884: $i,SY885: $i,SY886: $i] :
( ( SV8 = SY882 )
| ( SY883 = SY884 )
| ~ ( c_ListOrder_Ostep1 @ SY885 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SY883 @ ( c_List_Olist_ONil @ SY886 ) @ SY886 ) @ SY886 ) @ ( c_List_Oappend @ SY882 @ ( c_List_Olist_OCons @ SY884 @ ( c_List_Olist_ONil @ SY886 ) @ SY886 ) @ SY886 ) @ SY886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(953,plain,
! [SV9: $i] :
( ( ! [SY887: $i,SY888: $i,SY889: $i,SY890: $i,SY891: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SY887 ) @ SY888 ) )
| ( SY887 = SY888 )
| ~ ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SY889 @ ( c_List_Olist_OCons @ SY887 @ ( c_List_Olist_ONil @ SY890 ) @ SY890 ) @ SY890 ) @ ( c_List_Oappend @ SY891 @ ( c_List_Olist_OCons @ SY888 @ ( c_List_Olist_ONil @ SY890 ) @ SY890 ) @ SY890 ) @ SY890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(954,plain,
! [SV10: $i] :
( ( ! [SY892: $i,SY893: $i,SY894: $i,SY895: $i,SY896: $i] :
( ( c_List_Ofoldr @ SV10 @ ( c_List_Oappend @ SY892 @ SY893 @ SY894 ) @ SY895 @ SY894 @ SY896 )
= ( c_List_Ofoldr @ SV10 @ SY892 @ ( c_List_Ofoldr @ SV10 @ SY893 @ SY895 @ SY894 @ SY896 ) @ SY894 @ SY896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(955,plain,
! [SV11: $i] :
( ( ! [SY897: $i] :
( SV11
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY897 ) @ SV11 @ SY897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(956,plain,
! [SV12: $i] :
( ( ! [SY898: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV12 ) @ SY898 @ SV12 )
= SY898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(957,plain,
! [SV13: $i] :
( ( ! [SY899: $i] :
( SV13
= ( c_List_Oappend @ SV13 @ ( c_List_Olist_ONil @ SY899 ) @ SY899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(958,plain,
! [SV14: $i] :
( ( ! [SY900: $i] :
( SV14
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY900 ) @ SV14 @ SY900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(959,plain,
! [SV15: $i] :
( ( ! [SY901: $i] :
( ( c_List_Oappend @ SV15 @ ( c_List_Olist_ONil @ SY901 ) @ SY901 )
= SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(960,plain,
! [SV16: $i] :
( ( ! [SY902: $i,SY903: $i,SY904: $i] :
( ( c_List_Olistsp @ SV16 @ SY902 @ SY903 )
| ~ ( c_List_Olistsp @ SV16 @ ( c_List_Oappend @ SY904 @ SY902 @ SY903 ) @ SY903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(961,plain,
! [SV17: $i] :
( ( ! [SY905: $i,SY906: $i,SY907: $i] :
( ( c_List_Olistsp @ SV17 @ SY905 @ SY906 )
| ~ ( c_List_Olistsp @ SV17 @ ( c_List_Oappend @ SY905 @ SY907 @ SY906 ) @ SY906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(962,plain,
! [SV18: $i] :
( ( ! [SY908: $i,SY909: $i,SY910: $i,SY911: $i] :
( ( c_ListOrder_Ostep1 @ SV18 @ ( c_List_Oappend @ SY908 @ SY909 @ SY910 ) @ ( c_List_Oappend @ SY908 @ SY911 @ SY910 ) @ SY910 )
| ~ ( c_ListOrder_Ostep1 @ SV18 @ SY909 @ SY911 @ SY910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(963,plain,
! [SV19: $i] :
( ( ! [SY912: $i,SY913: $i,SY914: $i,SY915: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV19 @ SY912 @ SY913 @ SY914 )
| ( c_ListOrder_Ostep1 @ SV19 @ ( c_List_Oappend @ SY912 @ SY915 @ SY914 ) @ ( c_List_Oappend @ SY913 @ SY915 @ SY914 ) @ SY914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(964,plain,
! [SV20: $i] :
( ( ! [SY916: $i,SY917: $i,SY918: $i,SY919: $i,SY920: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SY916 ) @ SY917 ) )
| ( c_ListOrder_Ostep1 @ SV20 @ SY918 @ SY919 @ SY920 )
| ~ ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SY918 @ ( c_List_Olist_OCons @ SY916 @ ( c_List_Olist_ONil @ SY920 ) @ SY920 ) @ SY920 ) @ ( c_List_Oappend @ SY919 @ ( c_List_Olist_OCons @ SY917 @ ( c_List_Olist_ONil @ SY920 ) @ SY920 ) @ SY920 ) @ SY920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(965,plain,
! [SV21: $i] :
( ( ! [SY921: $i,SY922: $i,SY923: $i] :
( ( c_Type_Otyping @ SV21 @ SY921 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SY922 @ SV21 @ SY921 @ SY923 ) )
| ~ ( c_Type_Otypings @ SV21 @ ( c_List_Oappend @ SY923 @ ( c_List_Olist_OCons @ SY921 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(966,plain,
! [SV22: $i] :
( ( ! [SY924: $i,SY925: $i,SY926: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV22 @ SY924 @ SY925 ) @ SY926 @ SY925 )
= ( c_List_Olist_OCons @ SV22 @ ( c_List_Oappend @ SY924 @ SY926 @ SY925 ) @ SY925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(967,plain,
! [SV23: $i] :
( ( ! [SY927: $i,SY928: $i,SY929: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV23 @ SY927 @ SY928 ) @ SY929 @ SY928 )
= ( c_List_Olist_OCons @ SV23 @ ( c_List_Oappend @ SY927 @ SY929 @ SY928 ) @ SY928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(968,plain,
! [SV24: $i] :
( ( ! [SY930: $i,SY931: $i,SY932: $i] :
( ( c_List_Olist_OCons @ SV24 @ ( c_List_Oappend @ SY930 @ SY931 @ SY932 ) @ SY932 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV24 @ SY930 @ SY932 ) @ SY931 @ SY932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(969,plain,
! [SV25: $i] :
( ( ! [SY933: $i,SY934: $i,SY935: $i] :
( ( c_List_Olist_OCons @ SV25 @ ( c_List_Oappend @ SY933 @ SY934 @ SY935 ) @ SY935 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV25 @ SY933 @ SY935 ) @ SY934 @ SY935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(970,plain,
! [SV26: $i] :
( ( ! [SY936: $i,SY937: $i] :
( ( c_List_Olist_OCons @ SV26 @ SY936 @ SY937 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY937 ) @ ( c_List_Olist_OCons @ SV26 @ SY936 @ SY937 ) @ SY937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(971,plain,
! [SV27: $i] :
( ( ! [SY938: $i,SY939: $i,SY940: $i,SY941: $i,SY942: $i] :
( ( SV27 = SY938 )
| ( c_ListOrder_Ostep1 @ SY939 @ SV27 @ SY938 @ SY940 )
| ~ ( c_ListOrder_Ostep1 @ SY939 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SY941 @ ( c_List_Olist_ONil @ SY940 ) @ SY940 ) @ SY940 ) @ ( c_List_Oappend @ SY938 @ ( c_List_Olist_OCons @ SY942 @ ( c_List_Olist_ONil @ SY940 ) @ SY940 ) @ SY940 ) @ SY940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(972,plain,
! [SV28: $i] :
( ( ( c_List_Olist_ONil @ SV28 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV28 ) @ ( c_List_Olist_ONil @ SV28 ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(973,plain,
! [SV29: $i] :
( ( ! [SY943: $i,SY944: $i,SY945: $i,SY946: $i,SY947: $i] :
( ( c_List_Ofoldl @ SV29 @ SY943 @ ( c_List_Oappend @ SY944 @ SY945 @ SY946 ) @ SY947 @ SY946 )
= ( c_List_Ofoldl @ SV29 @ ( c_List_Ofoldl @ SV29 @ SY943 @ SY944 @ SY947 @ SY946 ) @ SY945 @ SY947 @ SY946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(974,plain,
! [SV30: $i] :
( ( ! [SY948: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SY948 ) @ SY948 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SY948 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(975,plain,
! [SV31: $i] :
( ( ! [SY949: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV31 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SY949 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SY949 ) @ SY949 ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(976,plain,
! [SV32: $i] :
( ( ! [SY950: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV32 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( c_HOL_Ozero__class_Ozero @ SV32 ) ) @ SY950 )
= SY950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(977,plain,
! [SV33: $i] :
( ( ! [SY951: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV33 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SY951 ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= SY951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(978,plain,
! [SV34: $i] :
( ( ! [SY952: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV34 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SY952 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) )
= SY952 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(979,plain,
! [SV35: $i] :
( ( ! [SY953: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV35 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) ) @ SY953 )
= SY953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(980,plain,
! [SV36: $i] :
( ( ! [SY954: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV36 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV36 ) @ SY954 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) )
= SY954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(981,plain,
! [SV37: $i] :
( ( ! [SY955: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV37 )
| ~ ( class_Int_Onumber__ring @ SV37 )
| ( SY955
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY955 ) @ ( c_HOL_Ozero__class_Ozero @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(982,plain,
! [SV38: $i] :
( ( ! [SY956: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) ) @ SY956 )
= SY956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(983,plain,
! [SV39: $i] :
( ( ! [SY957: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV39 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( c_HOL_Ozero__class_Ozero @ SV39 ) ) @ SY957 )
= SY957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(984,plain,
! [SV40: $i] :
( ( ! [SY958: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV40 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY958 @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(985,plain,
! [SV41: $i] :
( ( ! [SY959: $i,SY960: $i,SY961: $i,SY962: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY959 ) @ SY960 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY961 ) @ SY962 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY959 ) @ SY961 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY960 ) @ SY962 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(986,plain,
! [SV42: $i] :
( ( ! [SY963: $i,SY964: $i,SY965: $i,SY966: $i,SY967: $i] :
( ( SV42 = SY963 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY964 @ SY963 ) @ SV42 ) )
| ~ ( c_ListOrder_Ostep1 @ SY964 @ ( c_List_Olist_OCons @ SY963 @ SY965 @ SY966 ) @ ( c_List_Olist_OCons @ SV42 @ SY967 @ SY966 ) @ SY966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(987,plain,
! [SV43: $i] :
( ( ! [SY968: $i,SY969: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SY968 ) @ SY969 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SY969 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SY968 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(988,plain,
! [SV44: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV44 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV44 )
= ( c_HOL_Ozero__class_Ozero @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(989,plain,
! [SV45: $i] :
( ( ! [SY970: $i,SY971: $i,SY972: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV45 @ SY970 @ SY970 ) @ SY970 ) @ SY971 ) @ SY972 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SY970 ) @ SY972 ) @ SY971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(990,plain,
! [SV46: $i] :
( ( ! [SY973: $i,SY974: $i,SY975: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SY973 ) @ SY974 ) @ SY975 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV46 @ SY973 @ SY973 ) @ SY973 ) @ SY975 ) @ SY974 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(991,plain,
! [SV47: $i] :
( ( ! [SY976: $i,SY977: $i,SY978: $i,SY979: $i,SY980: $i] :
( ( c_List_Ofoldl @ SV47 @ SY976 @ ( c_List_Olist_OCons @ SY977 @ SY978 @ SY979 ) @ SY980 @ SY979 )
= ( c_List_Ofoldl @ SV47 @ ( hAPP @ ( hAPP @ SV47 @ SY976 ) @ SY977 ) @ SY978 @ SY980 @ SY979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(992,plain,
! [SV48: $i] :
( ( ! [SY981: $i,SY982: $i,SY983: $i] :
( ( c_List_Ofoldr @ SV48 @ ( c_List_Olist_ONil @ SY981 ) @ SY982 @ SY981 @ SY983 )
= SY982 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(993,plain,
! [SV49: $i] :
( ( ! [SY984: $i,SY985: $i,SY986: $i,SY987: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV49 @ SY984 ) @ SY985 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV49 @ SY986 @ SY987 ) @ SY985 ) @ SY984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(994,plain,
! [SV50: $i] :
( ( ! [SY988: $i,SY989: $i,SY990: $i,SY991: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV50 @ SY988 @ SY989 ) @ SY990 ) @ SY991 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY991 ) @ SY990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(995,plain,
! [SV51: $i] :
( ( ! [SY992: $i,SY993: $i,SY994: $i,SY995: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SY992 ) @ SY993 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV51 @ SY994 @ SY995 ) @ SY993 ) @ SY992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(996,plain,
! [SV52: $i] :
( ( ! [SY996: $i,SY997: $i,SY998: $i,SY999: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV52 @ SY996 @ SY997 ) @ SY998 ) @ SY999 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SY999 ) @ SY998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(997,plain,
! [SV53: $i] :
( ( ! [SY1000: $i,SY1001: $i,SY1002: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV53 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SY1000 ) @ SY1001 ) ) @ SY1002 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SY1000 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SY1001 ) @ SY1002 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(998,plain,
! [SV54: $i] :
( ( ! [SY1003: $i,SY1004: $i,SY1005: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV54 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY1003 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY1004 ) @ SY1005 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY1004 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY1003 ) @ SY1005 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(999,plain,
! [SV55: $i] :
( ( ! [SY1006: $i,SY1007: $i,SY1008: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SY1006 ) @ SY1007 ) ) @ SY1008 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SY1006 ) @ SY1008 ) ) @ SY1007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(1000,plain,
! [SV56: $i] :
( ( ! [SY1009: $i,SY1010: $i,SY1011: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SY1009 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SY1010 ) @ SY1011 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SY1009 ) @ SY1010 ) ) @ SY1011 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(1001,plain,
! [SV57: $i] :
( ( ! [SY1012: $i,SY1013: $i,SY1014: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV57 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SY1012 ) @ SY1013 ) ) @ SY1014 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SY1012 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SY1013 ) @ SY1014 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(1002,plain,
! [SV58: $i] :
( ( ! [SY1015: $i,SY1016: $i,SY1017: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV58 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SY1015 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SY1016 ) @ SY1017 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SY1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SY1015 ) @ SY1017 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(1003,plain,
! [SV59: $i] :
( ( ! [SY1018: $i,SY1019: $i,SY1020: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1018 ) @ SY1019 ) ) @ SY1020 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1019 ) @ SY1020 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(1004,plain,
! [SV60: $i] :
( ( ! [SY1021: $i,SY1022: $i,SY1023: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV60 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1021 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1022 ) @ SY1023 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1022 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1021 ) @ SY1023 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(1005,plain,
! [SV61: $i] :
( ( ! [SY1024: $i,SY1025: $i,SY1026: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV61 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1024 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1025 ) @ SY1026 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1024 ) @ SY1025 ) ) @ SY1026 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(1006,plain,
! [SV62: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV62 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) )
= ( c_HOL_Ozero__class_Ozero @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(1007,plain,
! [SV63: $i] :
( ( ! [SY1027: $i,SY1028: $i,SY1029: $i,SY1030: $i,SY1031: $i] :
( ( SV63 = SY1027 )
| ( SY1028 = SY1029 )
| ~ ( c_ListOrder_Ostep1 @ SY1030 @ ( c_List_Olist_OCons @ SY1027 @ SY1029 @ SY1031 ) @ ( c_List_Olist_OCons @ SV63 @ SY1028 @ SY1031 ) @ SY1031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(1008,plain,
! [SV64: $i] :
( ( ! [SY1032: $i,SY1033: $i,SY1034: $i,SY1035: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV64 @ SY1032 ) @ SY1033 ) )
| ( c_ListOrder_Ostep1 @ SV64 @ ( c_List_Olist_OCons @ SY1032 @ SY1034 @ SY1035 ) @ ( c_List_Olist_OCons @ SY1033 @ SY1034 @ SY1035 ) @ SY1035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(1009,plain,
! [SV65: $i] :
( ( ! [SY1036: $i] : ( c_List_Olistsp @ SV65 @ ( c_List_Olist_ONil @ SY1036 ) @ SY1036 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(1010,plain,
! [SV66: $i] :
( ( ! [SY1037: $i,SY1038: $i,SY1039: $i] :
( ( c_Wellfounded_Oaccp @ SV66 @ SY1037 @ SY1038 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SY1038 ) @ SY1037 ) @ SY1039 ) )
| ~ ( c_Wellfounded_Oaccp @ SV66 @ SY1039 @ SY1038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(1011,plain,
! [SV67: $i] :
( ( ! [SY1040: $i,SY1041: $i,SY1042: $i] :
( ( c_Wellfounded_Oaccp @ SV67 @ SY1040 @ SY1041 )
| ~ ( c_Wellfounded_Oaccp @ SV67 @ SY1042 @ SY1041 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SY1041 ) @ SY1040 ) @ SY1042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(1012,plain,
! [SV68: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV68 @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(1013,plain,
! [SV69: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV69 ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV69 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(1014,plain,
! [SV70: $i] :
( ( ! [SY1043: $i,SY1044: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SY1043 ) @ SY1044 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SY1044 ) @ SY1043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(1015,plain,
! [SV71: $i] :
( ( ! [SY1045: $i,SY1046: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV71 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SY1045 ) @ SY1046 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SY1046 ) @ SY1045 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(1016,plain,
! [SV72: $i] :
( ( ! [SY1047: $i,SY1048: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SY1047 ) @ SY1048 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SY1048 ) @ SY1047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(1017,plain,
! [SV73: $i] :
( ( ! [SY1049: $i,SY1050: $i,SY1051: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV73 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY1049 ) @ SY1050 ) @ SY1051 @ SV73 @ SV73 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY1049 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY1050 @ SY1051 @ SV73 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(1018,plain,
! [SV74: $i] :
( ( ! [SY1052: $i,SY1053: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV74 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SY1052 @ SY1053 @ SV74 @ SV74 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SY1053 @ SY1052 @ SV74 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(1019,plain,
! [SV75: $i] :
( ( ! [SY1054: $i,SY1055: $i] :
~ ( c_ListOrder_Ostep1 @ SV75 @ ( c_List_Olist_ONil @ SY1054 ) @ SY1055 @ SY1054 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(1020,plain,
! [SV76: $i] :
( ( ! [SY1056: $i,SY1057: $i] :
~ ( c_ListOrder_Ostep1 @ SV76 @ SY1056 @ ( c_List_Olist_ONil @ SY1057 ) @ SY1057 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(1021,plain,
! [SV77: $i] :
( ( ! [SY1058: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV77 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SY1058 ) @ SY1058 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SY1058 @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(1022,plain,
! [SV78: $i] :
( ( ! [SY1059: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV78 )
| ( c_HOL_Oord__class_Oless @ SY1059 @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ SY1059 ) @ SY1059 ) @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(1023,plain,
! [SV79: $i] :
( ( ! [SY1060: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV79 )
| ( c_HOL_Oord__class_Oless @ SY1060 @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV79 ) @ SY1060 ) @ SY1060 ) @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(1024,plain,
! [SV80: $i] :
( ( ! [SY1061: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV80 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SY1061 ) @ SY1061 ) @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ SY1061 @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(1025,plain,
! [SV81: $i] :
( ( ! [SY1062: $i,SY1063: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SY1062 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ ( c_HOL_Ozero__class_Ozero @ SV81 ) @ SY1063 @ SV81 @ SV81 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SY1062 @ SY1063 @ SV81 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(1026,plain,
! [SV82: $i] :
( ( ! [SY1064: $i,SY1065: $i,SY1066: $i] :
( ( c_List_Ofoldl @ SV82 @ SY1064 @ ( c_List_Olist_ONil @ SY1065 ) @ SY1066 @ SY1065 )
= SY1064 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(1027,plain,
! [SV83: $i] :
( ( ( c_Predicate_Oconversep @ ( c_fequal @ SV83 ) @ SV83 @ SV83 )
= ( c_fequal @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(1028,plain,
! [SV84: $i] :
( ( ! [SY1067: $i,SY1068: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SY1067 ) @ SY1068 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SY1068 @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SY1067 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(1029,plain,
! [SV85: $i] :
( ( ! [SY1069: $i,SY1070: $i,SY1071: $i,SY1072: $i,SY1073: $i] :
( ( c_ListOrder_Ostep1 @ SV85 @ SY1069 @ SY1070 @ SY1071 )
| ( SY1070 = SY1069 )
| ~ ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SY1072 @ SY1069 @ SY1071 ) @ ( c_List_Olist_OCons @ SY1073 @ SY1070 @ SY1071 ) @ SY1071 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(1030,plain,
! [SV86: $i] :
( ( ! [SY1074: $i,SY1075: $i,SY1076: $i,SY1077: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SY1074 ) @ SY1075 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SY1076 ) @ SY1077 ) @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SY1075 @ SY1077 @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SY1074 @ SY1076 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(1031,plain,
! [SV87: $i] :
( ( ! [SY1078: $i,SY1079: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV87 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1078 @ SV87 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1079 @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SY1078 @ SY1079 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(1032,plain,
! [SV88: $i] :
( ( ! [SY1080: $i,SY1081: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV88 )
| ( c_HOL_Oord__class_Oless @ SY1080 @ SY1081 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1080 @ SV88 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1081 @ SV88 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(1033,plain,
! [SV89: $i] :
( ( ! [SY1082: $i,SY1083: $i,SY1084: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV89 )
| ( c_HOL_Oord__class_Oless @ SY1082 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SY1083 ) @ SY1084 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY1082 @ SY1084 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SY1083 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(1034,plain,
! [SV90: $i] :
( ( ! [SY1085: $i,SY1086: $i,SY1087: $i,SY1088: $i,SY1089: $i] :
( ( c_List_Ofoldr @ SV90 @ ( c_List_Olist_OCons @ SY1085 @ SY1086 @ SY1087 ) @ SY1088 @ SY1087 @ SY1089 )
= ( hAPP @ ( hAPP @ SV90 @ SY1085 ) @ ( c_List_Ofoldr @ SV90 @ SY1086 @ SY1088 @ SY1087 @ SY1089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(1035,plain,
! [SV91: $i] :
( ( ! [SY1090: $i,SY1091: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV91 @ SY1090 @ SY1091 ) @ SY1091 @ SY1090 )
= SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(1036,plain,
! [SV92: $i] :
( ( ! [SY1092: $i,SY1093: $i,SY1094: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV92 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SY1092 ) @ SY1093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SY1094 ) @ SY1093 ) @ SV92 )
| ~ ( c_HOL_Oord__class_Oless @ SY1092 @ SY1094 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(1037,plain,
! [SV93: $i] :
( ( ! [SY1095: $i,SY1096: $i,SY1097: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY1095 ) @ SY1096 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY1097 ) @ SY1096 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SY1095 @ SY1097 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(1038,plain,
! [SV94: $i] :
( ( ! [SY1098: $i,SY1099: $i,SY1100: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
| ( c_HOL_Oord__class_Oless @ SY1098 @ SY1099 @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SY1098 ) @ SY1100 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SY1099 ) @ SY1100 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(1039,plain,
! [SV95: $i] :
( ( ! [SY1101: $i,SY1102: $i,SY1103: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY1101 ) @ SY1102 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY1101 ) @ SY1103 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SY1102 @ SY1103 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(1040,plain,
! [SV96: $i] :
( ( ! [SY1104: $i,SY1105: $i,SY1106: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SY1104 ) @ SY1105 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SY1104 ) @ SY1106 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SY1105 @ SY1106 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(1041,plain,
! [SV97: $i] :
( ( ! [SY1107: $i,SY1108: $i,SY1109: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
| ( c_HOL_Oord__class_Oless @ SY1107 @ SY1108 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1109 ) @ SY1107 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1109 ) @ SY1108 ) @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(1042,plain,
! [SV98: $i] :
( ( ! [SY1110: $i,SY1111: $i,SY1112: $i,SY1113: $i,SY1114: $i] :
( ( c_ListOrder_Ostep1 @ SV98 @ SY1110 @ SY1111 @ SY1112 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SY1113 ) @ SY1114 ) )
| ~ ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SY1113 @ SY1110 @ SY1112 ) @ ( c_List_Olist_OCons @ SY1114 @ SY1111 @ SY1112 ) @ SY1112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(1043,plain,
! [SV99: $i] :
( ( ! [SY1115: $i,SY1116: $i,SY1117: $i,SY1118: $i] :
( ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_OCons @ SY1115 @ SY1116 @ SY1117 ) @ ( c_List_Olist_OCons @ SY1115 @ SY1118 @ SY1117 ) @ SY1117 )
| ~ ( c_ListOrder_Ostep1 @ SV99 @ SY1116 @ SY1118 @ SY1117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(1044,plain,
! [SV100: $i] :
( ( ! [SY1119: $i,SY1120: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV100 @ SY1119 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1120 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV100 @ ( c_List_Oappend @ SY1119 @ ( c_List_Olist_OCons @ SY1120 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(1045,plain,
! [SV101: $i] :
( ( ! [SY1121: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV101 ) @ SY1121 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV101 ) @ SY1121 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(1046,plain,
! [SV102: $i] :
( ( ! [SY1122: $i,SY1123: $i] :
( ( ( c_List_Oappend @ SV102 @ ( c_List_Olist_OCons @ SY1122 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1123 @ SV102 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1122 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1123 @ ( c_List_Oappend @ SV102 @ ( c_List_Olist_OCons @ SY1122 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(1047,plain,
! [SV103: $i] :
( ( ! [SY1124: $i,SY1125: $i,SY1126: $i] :
( ( c_Wellfounded_Oaccp @ SV103 @ SY1124 @ SY1125 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ SY1124 ) @ SY1126 ) )
| ~ ( c_Wellfounded_Oaccp @ SV103 @ SY1126 @ SY1125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(1048,plain,
! [SV104: $i] :
( ( ! [SY1127: $i,SY1128: $i,SY1129: $i] :
( ( c_Wellfounded_Oaccp @ SV104 @ SY1127 @ SY1128 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SY1127 ) @ SY1129 ) )
| ~ ( c_Wellfounded_Oaccp @ SV104 @ SY1129 @ SY1128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(1049,plain,
! [SV105: $i] :
( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( class_Orderings_Opreorder @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SY1130 @ SY1131 @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SY1131 @ SY1130 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(1050,plain,
! [SV106: $i] :
( ( ! [SY1132: $i,SY1133: $i] :
( ~ ( class_Orderings_Opreorder @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SY1132 @ SY1133 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SY1133 @ SY1132 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(1051,plain,
! [SV107: $i] :
( ( ! [SY1134: $i,SY1135: $i] :
( ~ ( class_Orderings_Olinorder @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SY1134 @ SY1135 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SY1135 @ SY1134 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(1052,plain,
! [SV108: $i] :
( ( ! [SY1136: $i,SY1137: $i,SY1138: $i,SY1139: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SY1136 ) @ SY1137 ) @ SY1138 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SY1139 ) @ SY1138 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SY1136 ) @ SY1137 ) @ SY1139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(1053,plain,
! [SV109: $i] :
( ( ! [SY1140: $i,SY1141: $i,SY1142: $i,SY1143: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SY1140 ) @ SY1141 ) @ SY1142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SY1140 ) @ SY1143 ) @ SY1142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SY1141 ) @ SY1143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(1054,plain,
! [SV110: $i] :
( ( ! [SY1144: $i,SY1145: $i] :
( ~ ( class_Orderings_Oorder @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SY1144 @ SY1145 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SY1145 @ SY1144 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(1055,plain,
! [SV111: $i] :
( ( ! [SY1146: $i,SY1147: $i,SY1148: $i] :
( ( c_Type_Otypings @ SV111 @ SY1146 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1147 @ SV111 @ SY1148 @ SY1146 ) )
| ~ ( c_Type_Otyping @ SV111 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1148 ) @ SY1146 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1056,plain,
! [SV112: $i] :
( ( ! [SY1149: $i,SY1150: $i,SY1151: $i] :
( ( c_Type_Otypings @ SV112 @ SY1149 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1150 @ SV112 @ SY1151 @ SY1149 ) )
| ~ ( c_Type_Otyping @ SV112 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1151 @ SY1149 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1057,plain,
! [SV113: $i] :
( ( ! [SY1152: $i,SY1153: $i,SY1154: $i,SY1155: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV113 @ SY1152 @ SY1153 @ SY1154 ) @ SY1155 )
= ( hAPP @ SV113 @ SY1155 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1155 @ SY1152 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(1058,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(1059,plain,
! [SV114: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV114 @ tc_nat )
| ( SV114
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(1060,plain,
! [SV115: $i] :
( ( ! [SY1156: $i,SY1157: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV115 @ SY1156 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1157 @ SY1156 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV115 ) @ SY1157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(1061,plain,
! [SV116: $i] :
( ( ! [SY1158: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1158 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1158 @ SV116 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1062,plain,
! [SV117: $i] :
( ( ! [SY1159: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1159 @ SV117 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1159 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1063,plain,
! [SV118: $i] :
( ( ! [SY1160: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV118 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SY1160 @ SV118 @ SV118 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY1160 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1064,plain,
! [SV119: $i] :
( ( ! [SY1161: $i,SY1162: $i] :
( ~ ( class_Orderings_Olinorder @ SV119 )
| ( SY1161 = SY1162 )
| ( c_HOL_Oord__class_Oless @ SY1161 @ SY1162 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SY1162 @ SY1161 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(1065,plain,
! [SV120: $i] :
( ( ! [SY1163: $i,SY1164: $i] :
( ~ ( class_Orderings_Olinorder @ SV120 )
| ( c_HOL_Oord__class_Oless @ SY1163 @ SY1164 @ SV120 )
| ( SY1164 = SY1163 )
| ( c_HOL_Oord__class_Oless @ SY1164 @ SY1163 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1066,plain,
! [SV121: $i] :
( ( ! [SY1165: $i,SY1166: $i] :
( ~ ( class_Orderings_Olinorder @ SV121 )
| ( c_HOL_Oord__class_Oless @ SY1165 @ SY1166 @ SV121 )
| ( c_HOL_Oord__class_Oless @ SY1166 @ SY1165 @ SV121 )
| ( SY1166 = SY1165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1067,plain,
! [SV122: $i] :
( ( ! [SY1167: $i] :
( ( c_HOL_Oord__class_Oless @ SV122 @ SY1167 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1167 @ SV122 @ tc_nat )
| ( SY1167 = SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1068,plain,
! [SV123: $i] :
( ( ! [SY1168: $i,SY1169: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SY1168 ) @ SY1169 ) )
| ( c_HOL_Oord__class_Oless @ SY1168 @ SY1169 @ tc_nat )
| ( SY1169 = SY1168 )
| ( c_HOL_Oord__class_Oless @ SY1169 @ SY1168 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1069,plain,
! [SV124: $i] :
( ( ! [SY1170: $i] :
( ( c_HOL_Oord__class_Oless @ SV124 @ SY1170 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1170 @ SV124 @ tc_nat )
| ( SY1170 = SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1070,plain,
! [SV125: $i] :
( ( ! [SY1171: $i,SY1172: $i] :
( ~ ( class_Orderings_Olinorder @ SV125 )
| ( SY1171 = SY1172 )
| ( c_HOL_Oord__class_Oless @ SY1172 @ SY1171 @ SV125 )
| ( c_HOL_Oord__class_Oless @ SY1171 @ SY1172 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(1071,plain,
! [SV126: $i] :
( ( ! [SY1173: $i,SY1174: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV126 )
| ( c_HOL_Oord__class_Oless @ SY1173 @ SY1174 @ SV126 )
| ( c_HOL_Oord__class_Oless @ SY1174 @ SY1173 @ SV126 )
| ( SY1174 = SY1173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1072,plain,
! [SV127: $i] :
( ( ! [SY1175: $i,SY1176: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SY1175 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SY1176 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY1175 @ SY1176 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1073,plain,
! [SV128: $i] :
( ( ! [SY1177: $i] :
( ~ ( class_Orderings_Opreorder @ SV128 )
| ~ ( c_HOL_Oord__class_Oless @ SY1177 @ SY1177 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1074,plain,
! [SV129: $i] :
( ( ! [SY1178: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SY1178 @ SY1178 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1075,plain,
! [SV130: $i] :
( ( ! [SY1179: $i] :
( ~ ( class_Orderings_Oorder @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SY1179 @ SY1179 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1076,plain,
! [SV131: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV131 @ SV131 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1077,plain,
! [SV132: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV132 @ SV132 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1078,plain,
! [SV133: $i] :
( ( ! [SY1180: $i,SY1181: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV133 ) ) @ SY1180 ) @ SY1181 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1180 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV133 @ SY1180 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1181 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1079,plain,
! [SV134: $i] :
( ( ! [SY1182: $i,SY1183: $i,SY1184: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV134 @ SY1182 ) @ SY1183 ) @ SY1184 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ SY1183 ) @ SY1184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1080,plain,
! [SV135: $i] :
( ( ! [SY1185: $i,SY1186: $i,SY1187: $i,SY1188: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SY1185 ) @ SY1186 ) @ SY1187 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SY1185 ) @ SY1188 ) @ SY1187 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SY1185 ) @ SY1186 ) @ SY1188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1081,plain,
! [SV136: $i] :
( ( ! [SY1189: $i,SY1190: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV136 @ SY1189 ) @ SY1190 ) @ SY1190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1082,plain,
! [SV137: $i] :
( ( ! [SY1191: $i,SY1192: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV137 @ SY1191 ) @ SY1192 ) @ SY1192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1083,plain,
! [SV138: $i] :
( ( ! [SY1193: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV138 ) ) @ ( c_Lambda_OdB_OAbs @ SY1193 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV138 ) @ SY1193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1084,plain,
! [SV139: $i] :
( ( ! [SY1194: $i,SY1195: $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 @ SV139 @ SY1194 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1195 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1194 @ 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 @ SV139 ) ) @ SY1194 ) @ SY1195 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1085,plain,
! [SV140: $i] :
( ( ! [SY1196: $i,SY1197: $i,SY1198: $i] :
( ~ ( class_Orderings_Opreorder @ SV140 )
| ( c_HOL_Oord__class_Oless @ SY1196 @ SY1197 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SY1198 @ SY1197 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SY1196 @ SY1198 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1086,plain,
! [SV141: $i] :
( ( ! [SY1199: $i,SY1200: $i,SY1201: $i] :
( ~ ( class_Orderings_Oorder @ SV141 )
| ( c_HOL_Oord__class_Oless @ SY1199 @ SY1200 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SY1199 @ SY1201 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SY1201 @ SY1200 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1087,plain,
! [SV142: $i] :
( ( ( c_Lambda_OdB_OVar @ SV142 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV142 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1088,plain,
! [SV143: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV143 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1089,plain,
! [SV144: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV144 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1090,plain,
! [SV145: $i] :
( ( ! [SY1202: $i,SY1203: $i,SY1204: $i] :
( ( c_Type_Otypings @ SV145 @ SY1202 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1203 @ SV145 @ SY1204 @ SY1202 ) )
| ~ ( c_Type_Otyping @ SV145 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1204 @ SY1202 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1091,plain,
! [SV146: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV146 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV146 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1092,plain,
! [SV147: $i] :
( ( ! [SY1205: $i,SY1206: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV147 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY1205 @ SY1206 @ SV147 @ SV147 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY1205 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY1206 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 @ SV147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1093,plain,
! [SV148: $i] :
( ( ! [SY1207: $i,SY1208: $i,SY1209: $i,SY1210: $i,SY1211: $i,SY1212: $i] :
( ( c_Type_Otypings @ SV148 @ SY1207 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1208 @ SY1209 @ SV148 @ SY1207 ) )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1210 ) @ SY1211 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1209 )
| ~ ( c_Type_Otypings @ SV148 @ SY1211 @ SY1212 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1210 ) @ SY1211 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1207 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1094,plain,
! [SV149: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV149 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1095,plain,
! [SV150: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV150 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1096,plain,
! [SV151: $i] :
( ( ! [SY1213: $i,SY1214: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV151 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1213 @ SV151 @ SY1214 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1213 ) @ SV151 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1097,plain,
! [SV152: $i] :
( ( ! [SY1215: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV152 @ SY1215 ) @ SY1215 )
= ( c_Transitive__Closure_Ortranclp @ SV152 @ SY1215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1098,plain,
! [SV153: $i] :
( ( ! [SY1216: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV153 ) ) @ ( c_Lambda_OdB_OAbs @ SY1216 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV153 ) @ SY1216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1099,plain,
! [SV154: $i] :
( ( ! [SY1217: $i,SY1218: $i,SY1219: $i] :
( ( c_Type_Otyping @ SV154 @ SY1217 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1218 @ SV154 @ SY1217 @ SY1219 ) ) @ SY1218 ) )
| ~ ( c_Type_Otyping @ SV154 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1217 ) @ SY1219 ) @ SY1218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1100,plain,
! [SV155: $i] :
( ( ! [SY1220: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV155 ) @ ( c_Lambda_OdB_OVar @ SY1220 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1101,plain,
! [SV156: $i] :
( ( ! [SY1221: $i,SY1222: $i,SY1223: $i] :
( ( c_Type_Otyping @ SV156 @ SY1221 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1222 @ SV156 @ SY1221 @ SY1223 ) @ SY1222 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV156 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1221 @ SY1223 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1102,plain,
! [SV157: $i] :
( ( ! [SY1224: $i,SY1225: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV157 @ SY1224 ) ) @ ( c_Lambda_Olift @ SY1225 @ SY1224 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV157 ) @ SY1225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1103,plain,
! [SV158: $i] :
( ( ! [SY1226: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV158 ) @ SY1226 )
= ( c_Lambda_OdB_OVar @ SV158 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV158 @ SY1226 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1104,plain,
! [SV159: $i] :
( ( ! [SY1227: $i,SY1228: $i,SY1229: $i] :
( ( c_Type_Otyping @ SV159 @ SY1227 @ SY1228 )
| ~ ( c_Type_Otyping @ SV159 @ SY1229 @ SY1228 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1229 ) @ SY1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1105,plain,
! [SV160: $i] :
( ( ! [SY1230: $i,SY1231: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV160 ) @ SY1230 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1231 ) @ SY1230 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV160 ) @ SY1231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1106,plain,
! [SV161: $i] :
( ( ! [SY1232: $i,SY1233: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SY1232 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SY1233 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1232 ) @ SY1233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1107,plain,
! [SV162: $i] :
( ( ! [SY1234: $i,SY1235: $i,SY1236: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SY1234 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1235 ) @ SY1236 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1234 ) @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV162 ) @ SY1235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1108,plain,
! [SV163: $i] :
( ( ! [SY1237: $i,SY1238: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV163 ) @ SY1237 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1238 ) @ SY1237 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV163 ) @ SY1238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1109,plain,
! [SV164: $i] :
( ( ! [SY1239: $i,SY1240: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SY1239 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SY1240 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1239 ) @ SY1240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1110,plain,
! [SV165: $i] :
( ( ! [SY1241: $i] :
( ( c_HOL_Oord__class_Oless @ SV165 @ SV165 @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV165 ) @ SY1241 @ SV165 )
= SY1241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1111,plain,
! [SV166: $i] :
( ( ! [SY1242: $i,SY1243: $i,SY1244: $i] :
( ( c_Type_Otyping @ SV166 @ SY1242 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1243 @ SV166 @ SY1244 @ SY1242 ) )
| ~ ( c_Type_Otyping @ SV166 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1244 ) @ SY1242 ) @ SY1243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1112,plain,
! [SV167: $i] :
( ( ! [SY1245: $i,SY1246: $i] :
( ( SV167
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1245 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1245 @ SY1246 @ SV167 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1245 ) @ SY1246 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1113,plain,
! [SV168: $i] :
( ( ! [SY1247: $i,SY1248: $i,SY1249: $i,SY1250: $i] :
( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1247 @ SY1248 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1249 )
| ~ ( c_Type_Otypings @ SV168 @ SY1248 @ SY1250 )
| ~ ( c_Type_Otyping @ SV168 @ SY1247 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1250 @ SY1249 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1114,plain,
! [SV169: $i] :
( ( ! [SY1251: $i,SY1252: $i,SY1253: $i] :
( ( c_Type_Otyping @ SV169 @ ( c_Lambda_OdB_OVar @ SY1251 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1252 @ SV169 @ SY1251 @ SY1253 ) @ SY1252 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV169 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1251 ) @ SY1253 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1115,plain,
! [SV170: $i] :
( ( ! [SY1254: $i,SY1255: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV170 ) @ SY1254 @ SY1255 )
= ( c_Lambda_OdB_OVar @ SV170 ) )
| ( SV170 = SY1255 )
| ( c_HOL_Oord__class_Oless @ SY1255 @ SV170 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1116,plain,
! [SV171: $i] :
( ( ! [SY1256: $i,SY1257: $i,SY1258: $i] :
( ( c_Type_Otyping @ SV171 @ SY1256 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1257 @ SV171 @ SY1256 @ SY1258 ) @ SY1257 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV171 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1256 @ SY1258 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1117,plain,
! [SV172: $i] :
( ( ! [SY1259: $i,SY1260: $i,SY1261: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV172 @ SY1259 @ SY1260 ) ) @ ( c_Lambda_Osubst @ SV172 @ SY1261 @ SY1260 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1259 ) @ SY1261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1118,plain,
! [SV173: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SY1262 ) @ SY1263 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV173 @ SY1263 ) ) @ ( c_Lambda_Olift @ SY1262 @ SY1263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1119,plain,
! [SV174: $i] :
( ( ! [SY1264: $i,SY1265: $i,SY1266: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SY1264 @ SY1265 ) ) @ ( c_Lambda_Osubst @ SY1266 @ SY1264 @ SY1265 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV174 ) @ SY1266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1120,plain,
! [SV175: $i] :
( ( ! [SY1267: $i,SY1268: $i,SY1269: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV175 @ SY1267 @ SY1268 ) ) @ ( c_Lambda_Osubst @ SV175 @ SY1269 @ SY1268 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1267 ) @ SY1269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1121,plain,
! [SV176: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1122,plain,
! [SV177: $i] :
( ( ! [SY1270: $i,SY1271: $i,SY1272: $i] :
( ( c_Type_Otyping @ SV177 @ ( c_Lambda_OdB_OAbs @ SY1270 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1271 ) @ SY1272 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1271 @ tc_Type_Otype ) @ SY1270 @ SY1272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1123,plain,
! [SV178: $i] :
( ( ! [SY1273: $i,SY1274: $i,SY1275: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV178 @ SY1273 @ SY1274 @ SY1275 ) @ SY1273 )
= SY1274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1124,plain,
! [SV179: $i] :
( ( ! [SY1276: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV179 @ SY1276 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1125,plain,
! [SV180: $i] :
( ( ! [SY1277: $i,SY1278: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV180 @ SY1277 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1278 @ SY1277 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV180 ) @ SY1278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1126,plain,
! [SV181: $i] :
( ( ! [SY1279: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV181 ) ) @ SY1279 ) ) @ ( c_Lambda_Osubst @ SV181 @ SY1279 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1127,plain,
! [SV182: $i] :
( ( ! [SY1280: $i,SY1281: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV182 @ SY1280 ) ) @ ( c_Lambda_Olift @ SY1281 @ SY1280 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV182 ) @ SY1281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1128,plain,
! [SV183: $i] :
( ( ! [SY1282: $i,SY1283: $i,SY1284: $i,SY1285: $i] :
( ( SV183 = SY1282 )
| ~ ( c_Type_Otyping @ SY1283 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1284 ) @ SY1285 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1282 )
| ~ ( c_Type_Otyping @ SY1283 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1284 ) @ SY1285 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1129,plain,
! [SV184: $i] :
( ( ! [SY1286: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV184 ) @ SY1286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY1286 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1130,plain,
! [SV185: $i] :
( ( ! [SY1287: $i,SY1288: $i,SY1289: $i,SY1290: $i] :
( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1287 ) @ SY1288 ) @ SY1289 )
| ~ ( c_Type_Otyping @ SV185 @ SY1288 @ SY1290 )
| ~ ( c_Type_Otyping @ SV185 @ SY1287 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1290 ) @ SY1289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1131,plain,
! [SV186: $i] :
( ( ! [SY1291: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV186 ) ) @ SY1291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1132,plain,
! [SV187: $i] :
( ( ! [SY1292: $i,SY1293: $i,SY1294: $i,SY1295: $i,SY1296: $i,SY1297: $i] :
( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1292 @ SV187 @ SY1293 @ SY1294 ) @ SY1292 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY1293 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1295 ) @ SY1296 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
| ~ ( c_Type_Otypings @ SY1293 @ SY1296 @ SY1297 )
| ~ ( c_Type_Otyping @ SY1293 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1295 ) @ SY1296 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1294 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1133,plain,
! [SV188: $i] :
( ( ! [SY1298: $i,SY1299: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV188 ) @ SY1298 @ SY1299 )
= ( c_Lambda_OdB_OVar @ SV188 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV188 @ SY1299 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1134,plain,
! [SV189: $i] :
( ( ! [SY1300: $i,SY1301: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV189 @ ( c_Lambda_OdB_OVar @ SY1300 ) @ SY1301 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1135,plain,
! [SV190: $i] :
( ( ! [SY1302: $i,SY1303: $i,SY1304: $i,SY1305: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV190 @ SY1302 @ SY1303 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1304 @ SY1302 ) @ SY1305 )
| ~ ( c_Type_Otyping @ SV190 @ SY1304 @ SY1305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1136,plain,
! [SV191: $i] :
( ( ! [SY1306: $i,SY1307: $i,SY1308: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV191 ) @ SY1306 ) @ SY1307 @ SY1308 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV191 @ SY1307 @ SY1308 ) ) @ ( c_Lambda_Osubst @ SY1306 @ SY1307 @ SY1308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1137,plain,
! [SV192: $i] :
( ( ! [SY1309: $i,SY1310: $i,SY1311: $i] :
( ( c_Type_Otyping @ SV192 @ SY1309 @ SY1310 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1311 ) @ SY1309 ) )
| ~ ( c_Type_Otyping @ SV192 @ SY1311 @ SY1310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1138,plain,
! [SV193: $i] :
( ( ! [SY1312: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV193 ) @ SY1312 @ SV193 )
= SY1312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1139,plain,
! [SV194: $i] :
( ( ! [SY1313: $i,SY1314: $i] :
( ( ( hAPP @ SV194 @ SY1313 )
= SY1314 )
| ~ ( c_Type_Otyping @ SV194 @ ( c_Lambda_OdB_OVar @ SY1313 ) @ SY1314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1140,plain,
! [SV195: $i] :
( ( ! [SY1315: $i,SY1316: $i,SY1317: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV195 @ SY1315 @ SY1316 ) ) @ ( c_Lambda_Osubst @ SY1317 @ SY1315 @ SY1316 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SY1317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1141,plain,
! [SV196: $i] :
( ( ! [SY1318: $i] : ( c_Type_Otyping @ SV196 @ ( c_Lambda_OdB_OVar @ SY1318 ) @ ( hAPP @ SV196 @ SY1318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1142,plain,
! [SV197: $i] :
( ( ! [SY1319: $i,SY1320: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV197 @ SY1319 ) @ SY1320 @ SY1319 )
= SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1143,plain,
! [SV198: $i] :
( ( ! [SY1321: $i,SY1322: $i,SY1323: $i,SY1324: $i,SY1325: $i] :
( ~ ( c_Type_Otyping @ SV198 @ SY1321 @ SY1322 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SY1323 @ SY1322 @ tc_Type_Otype ) @ SY1324 @ SY1325 )
| ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SY1324 @ SY1321 @ SY1323 ) @ SY1325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1144,plain,
! [SV199: $i] :
( ( ! [SY1326: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV199 @ SY1326 ) )
| ~ ( class_Orderings_Opreorder @ SY1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1145,plain,
! [SV200: $i] :
( ( ! [SY1327: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV200 @ SY1327 ) )
| ~ ( class_Orderings_Oorder @ SY1327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1146,plain,
! [SV201: $i] :
( ( ! [SY1328: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV201 ) @ SY1328 ) @ SY1328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1147,plain,
! [SV202: $i] :
( ( ! [SY1329: $i,SY1330: $i] :
( ( SV202 = SY1329 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1330 ) @ SV202 ) @ SY1329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1148,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(1149,plain,
! [SV203: $i] :
( ( ! [SY1331: $i,SY1332: $i,SY1333: $i] :
( ( ( c_List_Oappend @ SV203 @ SY1331 @ SY1332 )
!= ( c_List_Oappend @ SY1333 @ SY1331 @ SY1332 ) )
| ( SV203 = SY1333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1150,plain,
! [SV204: $i] :
( ( ! [SY1334: $i,SY1335: $i,SY1336: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV204 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SY1334 ) @ SY1335 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SY1336 ) @ SY1335 ) )
| ( SY1334 = SY1336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1151,plain,
! [SV205: $i] :
( ( ! [SY1337: $i,SY1338: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SY1337 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1338 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SY1337 )
= SY1338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1152,plain,
! [SV206: $i] :
( ( ! [SY1339: $i,SY1340: $i] :
( ( ( c_List_Olist_ONil @ SV206 )
!= ( c_List_Oappend @ SY1339 @ SY1340 @ SV206 ) )
| ( SY1339
= ( c_List_Olist_ONil @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1153,plain,
! [SV207: $i] :
( ( ! [SY1341: $i,SY1342: $i,SY1343: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV207 ) @ SY1341 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1342 ) @ SY1343 ) )
| ( SY1341 = SY1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1154,plain,
! [SV208: $i] :
( ( ! [SY1344: $i] :
( ( c_Lambda_OdB_OAbs @ SV208 )
!= ( c_Lambda_OdB_OVar @ SY1344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1155,plain,
! [SV209: $i] :
( ( ! [SY1345: $i,SY1346: $i,SY1347: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV209 ) @ SY1345 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1346 ) @ SY1347 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV209 = SY1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1156,plain,
! [SV210: $i] :
( ( ! [SY1348: $i,SY1349: $i] :
( ( c_List_Olist_OCons @ SV210 @ SY1348 @ SY1349 )
!= SY1348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1157,plain,
! [SV211: $i] :
( ( ! [SY1350: $i] :
( ( ( c_Lambda_OdB_OVar @ SV211 )
!= ( c_Lambda_OdB_OVar @ SY1350 ) )
| ( SV211 = SY1350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1158,plain,
! [SV212: $i] :
( ( ! [SY1351: $i,SY1352: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV212 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1351 @ SY1352 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1352
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1159,plain,
! [SV213: $i] :
( ( ! [SY1353: $i,SY1354: $i] :
( ( SV213
!= ( c_List_Oappend @ SY1353 @ SV213 @ SY1354 ) )
| ( SY1353
= ( c_List_Olist_ONil @ SY1354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1160,plain,
! [SV214: $i] :
( ( ! [SY1355: $i,SY1356: $i] :
( ( ( c_List_Oappend @ SV214 @ SY1355 @ SY1356 )
!= ( c_List_Olist_ONil @ SY1356 ) )
| ( SY1355
= ( c_List_Olist_ONil @ SY1356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1161,plain,
! [SV215: $i] :
( ( ! [SY1357: $i,SY1358: $i] :
( ( ( c_Lambda_OdB_OVar @ SV215 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1357 @ SY1358 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV215 )
= SY1357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1162,plain,
! [SV216: $i] :
( ( ! [SY1359: $i] :
( ( c_Lambda_OdB_OVar @ SV216 )
!= ( c_Lambda_OdB_OAbs @ SY1359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1163,plain,
! [SV217: $i] :
( ( ! [SY1360: $i,SY1361: $i] :
( ( c_Lambda_OdB_OAbs @ SV217 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1360 ) @ SY1361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1164,plain,
! [SV218: $i] :
( ( ! [SY1362: $i,SY1363: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SY1362 )
!= ( c_Lambda_OdB_OVar @ SY1363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1165,plain,
! [SV219: $i] :
( ( ! [SY1364: $i,SY1365: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV219 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1364 @ SY1365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV219 )
= SY1364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1166,plain,
! [SV220: $i] :
( ( ! [SY1366: $i,SY1367: $i,SY1368: $i,SY1369: $i] :
( ( ( c_List_Oappend @ SV220 @ ( c_List_Olist_OCons @ SY1366 @ ( c_List_Olist_ONil @ SY1367 ) @ SY1367 ) @ SY1367 )
!= ( c_List_Oappend @ SY1368 @ ( c_List_Olist_OCons @ SY1369 @ ( c_List_Olist_ONil @ SY1367 ) @ SY1367 ) @ SY1367 ) )
| ( SY1366 = SY1369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1167,plain,
! [SV221: $i] :
( ( ! [SY1370: $i,SY1371: $i] :
( ( c_Lambda_OdB_OVar @ SV221 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1370 ) @ SY1371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1168,plain,
! [SV222: $i] :
( ( ! [SY1372: $i,SY1373: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV222 @ SY1372 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1373 @ SY1372 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV222 = SY1373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1169,plain,
! [SV223: $i] :
( ( ! [SY1374: $i,SY1375: $i,SY1376: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV223 ) @ SY1374 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1375 ) @ SY1376 ) )
| ( SV223 = SY1375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1170,plain,
! [SV224: $i] :
( ( ! [SY1377: $i,SY1378: $i,SY1379: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ SY1377 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1378 ) @ SY1379 ) )
| ( SV224 = SY1378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1171,plain,
! [SV225: $i] :
( ( ! [SY1380: $i,SY1381: $i,SY1382: $i,SY1383: $i] :
( ( ( c_List_Oappend @ SV225 @ ( c_List_Olist_OCons @ SY1380 @ ( c_List_Olist_ONil @ SY1381 ) @ SY1381 ) @ SY1381 )
!= ( c_List_Oappend @ SY1382 @ ( c_List_Olist_OCons @ SY1383 @ ( c_List_Olist_ONil @ SY1381 ) @ SY1381 ) @ SY1381 ) )
| ( SV225 = SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1172,plain,
! [SV226: $i] :
( ( ! [SY1384: $i,SY1385: $i,SY1386: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV226 ) ) @ SY1384 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1385 ) @ SY1386 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1173,plain,
! [SV227: $i] :
( ( ! [SY1387: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV227 )
!= ( c_Lambda_OdB_OAbs @ SY1387 ) )
| ( SV227 = SY1387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1174,plain,
! [SV228: $i] :
( ( ! [SY1388: $i,SY1389: $i] :
( ( c_List_Olist_OCons @ SV228 @ SY1388 @ SY1389 )
!= ( c_List_Olist_ONil @ SY1389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1175,plain,
! [SV229: $i] :
( ( ! [SY1390: $i,SY1391: $i,SY1392: $i,SY1393: $i] :
( ( ( c_List_Olist_OCons @ SV229 @ SY1390 @ SY1391 )
!= ( c_List_Olist_OCons @ SY1392 @ SY1393 @ SY1391 ) )
| ( SY1390 = SY1393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1176,plain,
! [SV230: $i] :
( ( ! [SY1394: $i,SY1395: $i] :
( ( SV230
!= ( c_List_Oappend @ SV230 @ SY1394 @ SY1395 ) )
| ( SY1394
= ( c_List_Olist_ONil @ SY1395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1177,plain,
! [SV231: $i] :
( ( ! [SY1396: $i,SY1397: $i] :
( ( ( c_List_Oappend @ SV231 @ SY1396 @ SY1397 )
!= SY1396 )
| ( SV231
= ( c_List_Olist_ONil @ SY1397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1178,plain,
! [SV232: $i] :
( ( ! [SY1398: $i,SY1399: $i] :
( ( ( c_List_Oappend @ SV232 @ SY1398 @ SY1399 )
!= ( c_List_Olist_ONil @ SY1399 ) )
| ( SV232
= ( c_List_Olist_ONil @ SY1399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1179,plain,
! [SV233: $i] :
( ( ! [SY1400: $i,SY1401: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SY1400 )
!= ( c_Lambda_OdB_OAbs @ SY1401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1180,plain,
! [SV234: $i] :
( ( ! [SY1402: $i,SY1403: $i,SY1404: $i,SY1405: $i] :
( ( ( c_List_Olist_OCons @ SV234 @ SY1402 @ SY1403 )
!= ( c_List_Olist_OCons @ SY1404 @ SY1405 @ SY1403 ) )
| ( SV234 = SY1404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1181,plain,
! [SV235: $i] :
( ( ! [SY1406: $i,SY1407: $i,SY1408: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SY1406 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1407 ) @ SY1408 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV235 = SY1407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1182,plain,
! [SV236: $i] :
( ( ! [SY1409: $i,SY1410: $i,SY1411: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SY1409 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1410 ) @ SY1411 ) )
| ( SY1409 = SY1411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1183,plain,
! [SV237: $i] :
( ( ! [SY1412: $i,SY1413: $i,SY1414: $i,SY1415: $i,SY1416: $i,SY1417: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SY1412 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1413 @ SY1414 @ SY1415 ) ) )
| ~ ( c_Type_Otyping @ SY1416 @ SY1414 @ SY1412 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1414 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1416 @ SY1415 @ SY1412 @ tc_Type_Otype ) @ SY1413 @ SY1417 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1184,plain,
! [SV238: $i] :
( ( ! [SY1418: $i,SY1419: $i,SY1420: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SY1418 ) @ SY1419 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SY1418 ) @ SY1420 ) )
| ( SY1419 = SY1420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1185,plain,
! [SV239: $i] :
( ( ! [SY1421: $i,SY1422: $i,SY1423: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV239 )
| ~ ( class_Int_Onumber__ring @ SV239 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SY1421 ) @ SY1422 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SY1421 ) @ SY1423 ) )
| ( SY1422 = SY1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1186,plain,
! [SV240: $i] :
( ( ! [SY1424: $i,SY1425: $i] :
( ( SV240
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SY1424 ) @ SY1425 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SY1424 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SY1424 ) @ ( c_List_Oappend @ SY1425 @ ( c_List_Olist_OCons @ SY1424 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1187,plain,
! [SV241: $i] :
( ( ! [SY1426: $i,SY1427: $i,SY1428: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SY1426 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1427 ) @ SY1428 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1426 = SY1428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1188,plain,
! [SV242: $i] :
( ( ! [SY1429: $i,SY1430: $i] :
( ( c_List_Olist_ONil @ SV242 )
!= ( c_List_Olist_OCons @ SY1429 @ SY1430 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1189,plain,
! [SV243: $i] :
( ( ! [SY1431: $i,SY1432: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV243 )
| ~ ( class_Int_Onumber__ring @ SV243 )
| ( SY1431
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SY1431 ) @ SY1432 ) )
| ( SY1432
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1190,plain,
! [SV244: $i] :
( ( ! [SY1433: $i,SY1434: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV244 @ SY1433 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1434 ) )
| ( SY1433
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1191,plain,
! [SV245: $i] :
( ( ! [SY1435: $i,SY1436: $i,SY1437: $i,SY1438: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV245 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SY1435 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SY1436 ) @ SY1437 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SY1436 ) @ SY1438 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SY1435 ) @ SY1437 )
= SY1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1192,plain,
! [SV246: $i] :
( ( ! [SY1439: $i,SY1440: $i,SY1441: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV246 ) @ SY1439 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1440 ) @ SY1441 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1193,plain,
! [SV247: $i] :
( ( ! [SY1442: $i,SY1443: $i,SY1444: $i,SY1445: $i,SY1446: $i,SY1447: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SY1442 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1443 @ SY1444 @ SY1445 ) ) )
| ~ ( c_Type_Otyping @ SY1446 @ SY1444 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1444 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1446 @ SY1445 @ SV247 @ tc_Type_Otype ) @ SY1443 @ SY1447 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1194,plain,
! [SV248: $i] :
( ( ! [SY1448: $i,SY1449: $i] :
( ( ( c_List_Olist_ONil @ SV248 )
!= ( c_List_Oappend @ SY1448 @ SY1449 @ SV248 ) )
| ( SY1449
= ( c_List_Olist_ONil @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1195,plain,
! [SV249: $i] :
( ( ! [SY1450: $i,SY1451: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV249 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY1450 @ SV249 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1451 @ SV249 ) )
| ( SY1450 = SY1451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1196,plain,
! [SV250: $i] :
( ( ! [SY1452: $i,SY1453: $i] :
( ( ( c_List_Oappend @ SV250 @ SY1452 @ SY1453 )
!= SV250 )
| ( SY1452
= ( c_List_Olist_ONil @ SY1453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1197,plain,
! [SV251: $i] :
( ( ! [SY1454: $i,SY1455: $i,SY1456: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV251 ) @ SY1454 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1455 ) @ SY1456 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1454 = SY1456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1198,plain,
! [SV252: $i] :
( ( ! [SY1457: $i,SY1458: $i] :
( ( ( c_Lambda_OdB_OVar @ SV252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1457 @ SY1458 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1458
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1199,plain,
! [SV253: $i] :
( ( ! [SY1459: $i,SY1460: $i] :
( ( c_List_Olist_OCons @ SV253 @ SY1459 @ SY1460 )
!= ( c_List_Olist_ONil @ SY1460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1200,plain,
! [SV254: $i] :
( ( ! [SY1461: $i,SY1462: $i] :
( SV254
!= ( c_List_Olist_OCons @ SY1461 @ SV254 @ SY1462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1201,plain,
! [SV255: $i] :
( ( ! [SY1463: $i,SY1464: $i,SY1465: $i] :
( ( ( c_List_Oappend @ SV255 @ SY1463 @ SY1464 )
!= ( c_List_Oappend @ SV255 @ SY1465 @ SY1464 ) )
| ( SY1463 = SY1465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1202,plain,
! [SV256: $i] :
( ( ! [SY1466: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV256 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV256 ) @ SY1466 ) @ SY1466 )
!= ( c_HOL_Ozero__class_Ozero @ SV256 ) )
| ( SY1466
= ( c_HOL_Ozero__class_Ozero @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1203,plain,
! [SV257: $i] :
( ( ! [SY1467: $i,SY1468: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV257 @ SY1467 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1468 ) )
| ( SV257
= ( c_Lambda_OdB_OAbs @ SY1468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1204,plain,
! [SV258: $i] :
( ( ! [SY1469: $i,SY1470: $i,SY1471: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV258 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SY1469 ) @ SY1470 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SY1469 ) @ SY1471 ) )
| ( SY1470 = SY1471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1205,plain,
! [SV259: $i,SV1: $i] :
( ( ! [SY1472: $i,SY1473: $i] :
( ( c_List_Oappend @ SV1 @ ( c_List_Oappend @ SV259 @ SY1472 @ SY1473 ) @ SY1473 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV1 @ SV259 @ SY1473 ) @ SY1472 @ SY1473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1206,plain,
! [SV260: $i,SV2: $i] :
( ( ! [SY1474: $i,SY1475: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV2 @ SV260 @ SY1474 ) @ SY1475 @ SY1474 )
= ( c_List_Oappend @ SV2 @ ( c_List_Oappend @ SV260 @ SY1475 @ SY1474 ) @ SY1474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1207,plain,
! [SV261: $i,SV3: $i] :
( ( ! [SY1476: $i,SY1477: $i] :
( ( c_List_Oappend @ SV3 @ ( c_List_Oappend @ SV261 @ SY1476 @ SY1477 ) @ SY1477 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV3 @ SV261 @ SY1477 ) @ SY1476 @ SY1477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1208,plain,
! [SV262: $i,SV4: $i] :
( ( ! [SY1478: $i,SY1479: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV4 @ SV262 @ SY1478 ) @ SY1479 @ SY1478 )
= ( c_List_Oappend @ SV4 @ ( c_List_Oappend @ SV262 @ SY1479 @ SY1478 ) @ SY1478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1209,plain,
! [SV263: $i,SV6: $i] :
( ( ! [SY1480: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV6 ) @ ( c_List_Olist_OCons @ SV263 @ SY1480 @ SV6 ) @ SV6 )
= ( c_List_Olist_OCons @ SV263 @ SY1480 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1210,plain,
! [SV264: $i,SV7: $i] :
( ( ! [SY1481: $i,SY1482: $i] :
( ( c_List_Olistsp @ SV7 @ ( c_List_Oappend @ SV264 @ SY1481 @ SY1482 ) @ SY1482 )
| ~ ( c_List_Olistsp @ SV7 @ SY1481 @ SY1482 )
| ~ ( c_List_Olistsp @ SV7 @ SV264 @ SY1482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1211,plain,
! [SV265: $i,SV8: $i] :
( ( ! [SY1483: $i,SY1484: $i,SY1485: $i,SY1486: $i] :
( ( SV8 = SV265 )
| ( SY1483 = SY1484 )
| ~ ( c_ListOrder_Ostep1 @ SY1485 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SY1483 @ ( c_List_Olist_ONil @ SY1486 ) @ SY1486 ) @ SY1486 ) @ ( c_List_Oappend @ SV265 @ ( c_List_Olist_OCons @ SY1484 @ ( c_List_Olist_ONil @ SY1486 ) @ SY1486 ) @ SY1486 ) @ SY1486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1212,plain,
! [SV266: $i,SV9: $i] :
( ( ! [SY1487: $i,SY1488: $i,SY1489: $i,SY1490: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SV266 ) @ SY1487 ) )
| ( SV266 = SY1487 )
| ~ ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SY1488 @ ( c_List_Olist_OCons @ SV266 @ ( c_List_Olist_ONil @ SY1489 ) @ SY1489 ) @ SY1489 ) @ ( c_List_Oappend @ SY1490 @ ( c_List_Olist_OCons @ SY1487 @ ( c_List_Olist_ONil @ SY1489 ) @ SY1489 ) @ SY1489 ) @ SY1489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1213,plain,
! [SV267: $i,SV10: $i] :
( ( ! [SY1491: $i,SY1492: $i,SY1493: $i,SY1494: $i] :
( ( c_List_Ofoldr @ SV10 @ ( c_List_Oappend @ SV267 @ SY1491 @ SY1492 ) @ SY1493 @ SY1492 @ SY1494 )
= ( c_List_Ofoldr @ SV10 @ SV267 @ ( c_List_Ofoldr @ SV10 @ SY1491 @ SY1493 @ SY1492 @ SY1494 ) @ SY1492 @ SY1494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1214,plain,
! [SV268: $i,SV11: $i] :
( ( SV11
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV268 ) @ SV11 @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1215,plain,
! [SV269: $i,SV12: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV12 ) @ SV269 @ SV12 )
= SV269 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1216,plain,
! [SV270: $i,SV13: $i] :
( ( SV13
= ( c_List_Oappend @ SV13 @ ( c_List_Olist_ONil @ SV270 ) @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1217,plain,
! [SV271: $i,SV14: $i] :
( ( SV14
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV271 ) @ SV14 @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1218,plain,
! [SV272: $i,SV15: $i] :
( ( ( c_List_Oappend @ SV15 @ ( c_List_Olist_ONil @ SV272 ) @ SV272 )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1219,plain,
! [SV273: $i,SV16: $i] :
( ( ! [SY1495: $i,SY1496: $i] :
( ( c_List_Olistsp @ SV16 @ SV273 @ SY1495 )
| ~ ( c_List_Olistsp @ SV16 @ ( c_List_Oappend @ SY1496 @ SV273 @ SY1495 ) @ SY1495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1220,plain,
! [SV274: $i,SV17: $i] :
( ( ! [SY1497: $i,SY1498: $i] :
( ( c_List_Olistsp @ SV17 @ SV274 @ SY1497 )
| ~ ( c_List_Olistsp @ SV17 @ ( c_List_Oappend @ SV274 @ SY1498 @ SY1497 ) @ SY1497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1221,plain,
! [SV275: $i,SV18: $i] :
( ( ! [SY1499: $i,SY1500: $i,SY1501: $i] :
( ( c_ListOrder_Ostep1 @ SV18 @ ( c_List_Oappend @ SV275 @ SY1499 @ SY1500 ) @ ( c_List_Oappend @ SV275 @ SY1501 @ SY1500 ) @ SY1500 )
| ~ ( c_ListOrder_Ostep1 @ SV18 @ SY1499 @ SY1501 @ SY1500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1222,plain,
! [SV276: $i,SV19: $i] :
( ( ! [SY1502: $i,SY1503: $i,SY1504: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV19 @ SV276 @ SY1502 @ SY1503 )
| ( c_ListOrder_Ostep1 @ SV19 @ ( c_List_Oappend @ SV276 @ SY1504 @ SY1503 ) @ ( c_List_Oappend @ SY1502 @ SY1504 @ SY1503 ) @ SY1503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1223,plain,
! [SV277: $i,SV20: $i] :
( ( ! [SY1505: $i,SY1506: $i,SY1507: $i,SY1508: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV277 ) @ SY1505 ) )
| ( c_ListOrder_Ostep1 @ SV20 @ SY1506 @ SY1507 @ SY1508 )
| ~ ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SY1506 @ ( c_List_Olist_OCons @ SV277 @ ( c_List_Olist_ONil @ SY1508 ) @ SY1508 ) @ SY1508 ) @ ( c_List_Oappend @ SY1507 @ ( c_List_Olist_OCons @ SY1505 @ ( c_List_Olist_ONil @ SY1508 ) @ SY1508 ) @ SY1508 ) @ SY1508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1224,plain,
! [SV278: $i,SV21: $i] :
( ( ! [SY1509: $i,SY1510: $i] :
( ( c_Type_Otyping @ SV21 @ SV278 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SY1509 @ SV21 @ SV278 @ SY1510 ) )
| ~ ( c_Type_Otypings @ SV21 @ ( c_List_Oappend @ SY1510 @ ( c_List_Olist_OCons @ SV278 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY1509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1225,plain,
! [SV279: $i,SV22: $i] :
( ( ! [SY1511: $i,SY1512: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV22 @ SV279 @ SY1511 ) @ SY1512 @ SY1511 )
= ( c_List_Olist_OCons @ SV22 @ ( c_List_Oappend @ SV279 @ SY1512 @ SY1511 ) @ SY1511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1226,plain,
! [SV280: $i,SV23: $i] :
( ( ! [SY1513: $i,SY1514: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV23 @ SV280 @ SY1513 ) @ SY1514 @ SY1513 )
= ( c_List_Olist_OCons @ SV23 @ ( c_List_Oappend @ SV280 @ SY1514 @ SY1513 ) @ SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1227,plain,
! [SV281: $i,SV24: $i] :
( ( ! [SY1515: $i,SY1516: $i] :
( ( c_List_Olist_OCons @ SV24 @ ( c_List_Oappend @ SV281 @ SY1515 @ SY1516 ) @ SY1516 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV24 @ SV281 @ SY1516 ) @ SY1515 @ SY1516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1228,plain,
! [SV282: $i,SV25: $i] :
( ( ! [SY1517: $i,SY1518: $i] :
( ( c_List_Olist_OCons @ SV25 @ ( c_List_Oappend @ SV282 @ SY1517 @ SY1518 ) @ SY1518 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV25 @ SV282 @ SY1518 ) @ SY1517 @ SY1518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1229,plain,
! [SV283: $i,SV26: $i] :
( ( ! [SY1519: $i] :
( ( c_List_Olist_OCons @ SV26 @ SV283 @ SY1519 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1519 ) @ ( c_List_Olist_OCons @ SV26 @ SV283 @ SY1519 ) @ SY1519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1230,plain,
! [SV284: $i,SV27: $i] :
( ( ! [SY1520: $i,SY1521: $i,SY1522: $i,SY1523: $i] :
( ( SV27 = SV284 )
| ( c_ListOrder_Ostep1 @ SY1520 @ SV27 @ SV284 @ SY1521 )
| ~ ( c_ListOrder_Ostep1 @ SY1520 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SY1522 @ ( c_List_Olist_ONil @ SY1521 ) @ SY1521 ) @ SY1521 ) @ ( c_List_Oappend @ SV284 @ ( c_List_Olist_OCons @ SY1523 @ ( c_List_Olist_ONil @ SY1521 ) @ SY1521 ) @ SY1521 ) @ SY1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1231,plain,
! [SV285: $i,SV29: $i] :
( ( ! [SY1524: $i,SY1525: $i,SY1526: $i,SY1527: $i] :
( ( c_List_Ofoldl @ SV29 @ SV285 @ ( c_List_Oappend @ SY1524 @ SY1525 @ SY1526 ) @ SY1527 @ SY1526 )
= ( c_List_Ofoldl @ SV29 @ ( c_List_Ofoldl @ SV29 @ SV285 @ SY1524 @ SY1527 @ SY1526 ) @ SY1525 @ SY1527 @ SY1526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1232,plain,
! [SV286: $i,SV30: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV286 ) @ SV286 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV286 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1233,plain,
! [SV287: $i,SV31: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV31 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV287 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV287 ) @ SV287 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1234,plain,
! [SV288: $i,SV32: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV32 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( c_HOL_Ozero__class_Ozero @ SV32 ) ) @ SV288 )
= SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1235,plain,
! [SV289: $i,SV33: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV33 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV289 ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1236,plain,
! [SV290: $i,SV34: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV34 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV290 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) )
= SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1237,plain,
! [SV291: $i,SV35: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV35 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) ) @ SV291 )
= SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1238,plain,
! [SV292: $i,SV36: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV36 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV36 ) @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) )
= SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1239,plain,
! [SV293: $i,SV37: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV37 )
| ~ ( class_Int_Onumber__ring @ SV37 )
| ( SV293
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV293 ) @ ( c_HOL_Ozero__class_Ozero @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1240,plain,
! [SV294: $i,SV38: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV38 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) ) @ SV294 )
= SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1241,plain,
! [SV295: $i,SV39: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV39 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( c_HOL_Ozero__class_Ozero @ SV39 ) ) @ SV295 )
= SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1242,plain,
! [SV296: $i,SV40: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV40 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV296 @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1243,plain,
! [SV297: $i,SV41: $i] :
( ( ! [SY1528: $i,SY1529: $i,SY1530: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SY1528 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY1529 ) @ SY1530 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SY1529 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY1528 ) @ SY1530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1244,plain,
! [SV298: $i,SV42: $i] :
( ( ! [SY1531: $i,SY1532: $i,SY1533: $i,SY1534: $i] :
( ( SV42 = SV298 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1531 @ SV298 ) @ SV42 ) )
| ~ ( c_ListOrder_Ostep1 @ SY1531 @ ( c_List_Olist_OCons @ SV298 @ SY1532 @ SY1533 ) @ ( c_List_Olist_OCons @ SV42 @ SY1534 @ SY1533 ) @ SY1533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1245,plain,
! [SV299: $i,SV43: $i] :
( ( ! [SY1535: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV299 ) @ SY1535 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SY1535 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV299 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1246,plain,
! [SV44: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV44 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV44 )
= ( c_HOL_Ozero__class_Ozero @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1247,plain,
! [SV300: $i,SV45: $i] :
( ( ! [SY1536: $i,SY1537: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV45 @ SV300 @ SV300 ) @ SV300 ) @ SY1536 ) @ SY1537 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV300 ) @ SY1537 ) @ SY1536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1248,plain,
! [SV301: $i,SV46: $i] :
( ( ! [SY1538: $i,SY1539: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SV301 ) @ SY1538 ) @ SY1539 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV46 @ SV301 @ SV301 ) @ SV301 ) @ SY1539 ) @ SY1538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1249,plain,
! [SV302: $i,SV47: $i] :
( ( ! [SY1540: $i,SY1541: $i,SY1542: $i,SY1543: $i] :
( ( c_List_Ofoldl @ SV47 @ SV302 @ ( c_List_Olist_OCons @ SY1540 @ SY1541 @ SY1542 ) @ SY1543 @ SY1542 )
= ( c_List_Ofoldl @ SV47 @ ( hAPP @ ( hAPP @ SV47 @ SV302 ) @ SY1540 ) @ SY1541 @ SY1543 @ SY1542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1250,plain,
! [SV303: $i,SV48: $i] :
( ( ! [SY1544: $i,SY1545: $i] :
( ( c_List_Ofoldr @ SV48 @ ( c_List_Olist_ONil @ SV303 ) @ SY1544 @ SV303 @ SY1545 )
= SY1544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1251,plain,
! [SV304: $i,SV49: $i] :
( ( ! [SY1546: $i,SY1547: $i,SY1548: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV49 @ SV304 ) @ SY1546 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV49 @ SY1547 @ SY1548 ) @ SY1546 ) @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1252,plain,
! [SV305: $i,SV50: $i] :
( ( ! [SY1549: $i,SY1550: $i,SY1551: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV50 @ SV305 @ SY1549 ) @ SY1550 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY1551 ) @ SY1550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1253,plain,
! [SV306: $i,SV51: $i] :
( ( ! [SY1552: $i,SY1553: $i,SY1554: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV306 ) @ SY1552 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV51 @ SY1553 @ SY1554 ) @ SY1552 ) @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1254,plain,
! [SV307: $i,SV52: $i] :
( ( ! [SY1555: $i,SY1556: $i,SY1557: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV52 @ SV307 @ SY1555 ) @ SY1556 ) @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SY1557 ) @ SY1556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1255,plain,
! [SV308: $i,SV53: $i] :
( ( ! [SY1558: $i,SY1559: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV53 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ SY1558 ) ) @ SY1559 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SY1558 ) @ SY1559 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1256,plain,
! [SV309: $i,SV54: $i] :
( ( ! [SY1560: $i,SY1561: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV54 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY1560 ) @ SY1561 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SY1560 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ SY1561 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1257,plain,
! [SV310: $i,SV55: $i] :
( ( ! [SY1562: $i,SY1563: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SY1562 ) ) @ SY1563 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SY1563 ) ) @ SY1562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1258,plain,
! [SV311: $i,SV56: $i] :
( ( ! [SY1564: $i,SY1565: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SY1564 ) @ SY1565 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SY1564 ) ) @ SY1565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1259,plain,
! [SV312: $i,SV57: $i] :
( ( ! [SY1566: $i,SY1567: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV57 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SY1566 ) ) @ SY1567 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SY1566 ) @ SY1567 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1260,plain,
! [SV313: $i,SV58: $i] :
( ( ! [SY1568: $i,SY1569: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV58 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SY1568 ) @ SY1569 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SY1568 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ SY1569 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1261,plain,
! [SV314: $i,SV59: $i] :
( ( ! [SY1570: $i,SY1571: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SY1570 ) ) @ SY1571 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SY1570 ) @ SY1571 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1262,plain,
! [SV315: $i,SV60: $i] :
( ( ! [SY1572: $i,SY1573: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV60 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1572 ) @ SY1573 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SY1572 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SY1573 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1263,plain,
! [SV316: $i,SV61: $i] :
( ( ! [SY1574: $i,SY1575: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV61 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SY1574 ) @ SY1575 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ SY1574 ) ) @ SY1575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1264,plain,
! [SV62: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV62 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) )
= ( c_HOL_Ozero__class_Ozero @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1265,plain,
! [SV317: $i,SV63: $i] :
( ( ! [SY1576: $i,SY1577: $i,SY1578: $i,SY1579: $i] :
( ( SV63 = SV317 )
| ( SY1576 = SY1577 )
| ~ ( c_ListOrder_Ostep1 @ SY1578 @ ( c_List_Olist_OCons @ SV317 @ SY1577 @ SY1579 ) @ ( c_List_Olist_OCons @ SV63 @ SY1576 @ SY1579 ) @ SY1579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1266,plain,
! [SV318: $i,SV64: $i] :
( ( ! [SY1580: $i,SY1581: $i,SY1582: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV64 @ SV318 ) @ SY1580 ) )
| ( c_ListOrder_Ostep1 @ SV64 @ ( c_List_Olist_OCons @ SV318 @ SY1581 @ SY1582 ) @ ( c_List_Olist_OCons @ SY1580 @ SY1581 @ SY1582 ) @ SY1582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1267,plain,
! [SV319: $i,SV65: $i] :
( ( c_List_Olistsp @ SV65 @ ( c_List_Olist_ONil @ SV319 ) @ SV319 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1268,plain,
! [SV320: $i,SV66: $i] :
( ( ! [SY1583: $i,SY1584: $i] :
( ( c_Wellfounded_Oaccp @ SV66 @ SV320 @ SY1583 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SY1583 ) @ SV320 ) @ SY1584 ) )
| ~ ( c_Wellfounded_Oaccp @ SV66 @ SY1584 @ SY1583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1269,plain,
! [SV321: $i,SV67: $i] :
( ( ! [SY1585: $i,SY1586: $i] :
( ( c_Wellfounded_Oaccp @ SV67 @ SV321 @ SY1585 )
| ~ ( c_Wellfounded_Oaccp @ SV67 @ SY1586 @ SY1585 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SY1585 ) @ SV321 ) @ SY1586 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1270,plain,
! [SV68: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV68 @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1271,plain,
! [SV69: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV69 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV69 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1272,plain,
! [SV322: $i,SV70: $i] :
( ( ! [SY1587: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV322 ) @ SY1587 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SY1587 ) @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1273,plain,
! [SV323: $i,SV71: $i] :
( ( ! [SY1588: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV71 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV323 ) @ SY1588 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SY1588 ) @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1274,plain,
! [SV324: $i,SV72: $i] :
( ( ! [SY1589: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SY1589 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SY1589 ) @ SV324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1275,plain,
! [SV325: $i,SV73: $i] :
( ( ! [SY1590: $i,SY1591: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV73 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SY1590 ) @ SY1591 @ SV73 @ SV73 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SY1590 @ SY1591 @ SV73 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1276,plain,
! [SV326: $i,SV74: $i] :
( ( ! [SY1592: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV74 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 @ SY1592 @ SV74 @ SV74 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SY1592 @ SV326 @ SV74 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1277,plain,
! [SV327: $i,SV75: $i] :
( ( ! [SY1593: $i] :
~ ( c_ListOrder_Ostep1 @ SV75 @ ( c_List_Olist_ONil @ SV327 ) @ SY1593 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1278,plain,
! [SV328: $i,SV76: $i] :
( ( ! [SY1594: $i] :
~ ( c_ListOrder_Ostep1 @ SV76 @ SV328 @ ( c_List_Olist_ONil @ SY1594 ) @ SY1594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1279,plain,
! [SV329: $i,SV77: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV77 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV329 @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1280,plain,
! [SV330: $i,SV78: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV78 )
| ( c_HOL_Oord__class_Oless @ SV330 @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ SV330 ) @ SV330 ) @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1281,plain,
! [SV331: $i,SV79: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV79 )
| ( c_HOL_Oord__class_Oless @ SV331 @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV79 ) @ SV331 ) @ SV331 ) @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1282,plain,
! [SV332: $i,SV80: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV80 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV332 ) @ SV332 ) @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ SV332 @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1283,plain,
! [SV333: $i,SV81: $i] :
( ( ! [SY1595: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SV333 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ ( c_HOL_Ozero__class_Ozero @ SV81 ) @ SY1595 @ SV81 @ SV81 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SV333 @ SY1595 @ SV81 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1284,plain,
! [SV334: $i,SV82: $i] :
( ( ! [SY1596: $i,SY1597: $i] :
( ( c_List_Ofoldl @ SV82 @ SV334 @ ( c_List_Olist_ONil @ SY1596 ) @ SY1597 @ SY1596 )
= SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1285,plain,
! [SV335: $i,SV84: $i] :
( ( ! [SY1598: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV335 ) @ SY1598 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SY1598 @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV335 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1286,plain,
! [SV336: $i,SV85: $i] :
( ( ! [SY1599: $i,SY1600: $i,SY1601: $i,SY1602: $i] :
( ( c_ListOrder_Ostep1 @ SV85 @ SV336 @ SY1599 @ SY1600 )
| ( SY1599 = SV336 )
| ~ ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SY1601 @ SV336 @ SY1600 ) @ ( c_List_Olist_OCons @ SY1602 @ SY1599 @ SY1600 ) @ SY1600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1287,plain,
! [SV337: $i,SV86: $i] :
( ( ! [SY1603: $i,SY1604: $i,SY1605: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SY1603 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SY1604 ) @ SY1605 ) @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SY1603 @ SY1605 @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV337 @ SY1604 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1288,plain,
! [SV338: $i,SV87: $i] :
( ( ! [SY1606: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV87 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV338 @ SV87 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1606 @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV338 @ SY1606 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1289,plain,
! [SV339: $i,SV88: $i] :
( ( ! [SY1607: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV339 @ SY1607 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV339 @ SV88 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1607 @ SV88 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1290,plain,
! [SV340: $i,SV89: $i] :
( ( ! [SY1608: $i,SY1609: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SY1608 ) @ SY1609 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ SY1609 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SY1608 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1291,plain,
! [SV341: $i,SV90: $i] :
( ( ! [SY1610: $i,SY1611: $i,SY1612: $i,SY1613: $i] :
( ( c_List_Ofoldr @ SV90 @ ( c_List_Olist_OCons @ SV341 @ SY1610 @ SY1611 ) @ SY1612 @ SY1611 @ SY1613 )
= ( hAPP @ ( hAPP @ SV90 @ SV341 ) @ ( c_List_Ofoldr @ SV90 @ SY1610 @ SY1612 @ SY1611 @ SY1613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1292,plain,
! [SV342: $i,SV91: $i] :
( ( ! [SY1614: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV91 @ SV342 @ SY1614 ) @ SY1614 @ SV342 )
= SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1293,plain,
! [SV343: $i,SV92: $i] :
( ( ! [SY1615: $i,SY1616: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV92 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV343 ) @ SY1615 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SY1616 ) @ SY1615 ) @ SV92 )
| ~ ( c_HOL_Oord__class_Oless @ SV343 @ SY1616 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1294,plain,
! [SV344: $i,SV93: $i] :
( ( ! [SY1617: $i,SY1618: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV344 ) @ SY1617 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY1618 ) @ SY1617 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV344 @ SY1618 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1295,plain,
! [SV345: $i,SV94: $i] :
( ( ! [SY1619: $i,SY1620: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
| ( c_HOL_Oord__class_Oless @ SV345 @ SY1619 @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV345 ) @ SY1620 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SY1619 ) @ SY1620 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1296,plain,
! [SV346: $i,SV95: $i] :
( ( ! [SY1621: $i,SY1622: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SY1621 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SY1622 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SY1621 @ SY1622 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1297,plain,
! [SV347: $i,SV96: $i] :
( ( ! [SY1623: $i,SY1624: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SY1623 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SY1624 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SY1623 @ SY1624 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1298,plain,
! [SV348: $i,SV97: $i] :
( ( ! [SY1625: $i,SY1626: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
| ( c_HOL_Oord__class_Oless @ SV348 @ SY1625 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1626 ) @ SV348 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1626 ) @ SY1625 ) @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1299,plain,
! [SV349: $i,SV98: $i] :
( ( ! [SY1627: $i,SY1628: $i,SY1629: $i,SY1630: $i] :
( ( c_ListOrder_Ostep1 @ SV98 @ SV349 @ SY1627 @ SY1628 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SY1629 ) @ SY1630 ) )
| ~ ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SY1629 @ SV349 @ SY1628 ) @ ( c_List_Olist_OCons @ SY1630 @ SY1627 @ SY1628 ) @ SY1628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1300,plain,
! [SV350: $i,SV99: $i] :
( ( ! [SY1631: $i,SY1632: $i,SY1633: $i] :
( ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_OCons @ SV350 @ SY1631 @ SY1632 ) @ ( c_List_Olist_OCons @ SV350 @ SY1633 @ SY1632 ) @ SY1632 )
| ~ ( c_ListOrder_Ostep1 @ SV99 @ SY1631 @ SY1633 @ SY1632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1301,plain,
! [SV351: $i,SV100: $i] :
( ( ! [SY1634: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV100 @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1634 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV100 @ ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SY1634 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1302,plain,
! [SV352: $i,SV101: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV101 ) @ SV352 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV101 ) @ SV352 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1303,plain,
! [SV353: $i,SV102: $i] :
( ( ! [SY1635: $i] :
( ( ( c_List_Oappend @ SV102 @ ( c_List_Olist_OCons @ SV353 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1635 @ SV102 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV353 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1635 @ ( c_List_Oappend @ SV102 @ ( c_List_Olist_OCons @ SV353 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1304,plain,
! [SV354: $i,SV103: $i] :
( ( ! [SY1636: $i,SY1637: $i] :
( ( c_Wellfounded_Oaccp @ SV103 @ SV354 @ SY1636 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ SV354 ) @ SY1637 ) )
| ~ ( c_Wellfounded_Oaccp @ SV103 @ SY1637 @ SY1636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1305,plain,
! [SV355: $i,SV104: $i] :
( ( ! [SY1638: $i,SY1639: $i] :
( ( c_Wellfounded_Oaccp @ SV104 @ SV355 @ SY1638 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV355 ) @ SY1639 ) )
| ~ ( c_Wellfounded_Oaccp @ SV104 @ SY1639 @ SY1638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1306,plain,
! [SV356: $i,SV105: $i] :
( ( ! [SY1640: $i] :
( ~ ( class_Orderings_Opreorder @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SY1640 @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SY1640 @ SV356 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1307,plain,
! [SV357: $i,SV106: $i] :
( ( ! [SY1641: $i] :
( ~ ( class_Orderings_Opreorder @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SV357 @ SY1641 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SY1641 @ SV357 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1308,plain,
! [SV358: $i,SV107: $i] :
( ( ! [SY1642: $i] :
( ~ ( class_Orderings_Olinorder @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV358 @ SY1642 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SY1642 @ SV358 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1309,plain,
! [SV359: $i,SV108: $i] :
( ( ! [SY1643: $i,SY1644: $i,SY1645: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SY1643 ) @ SY1644 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SY1645 ) @ SY1644 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SY1643 ) @ SY1645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1310,plain,
! [SV360: $i,SV109: $i] :
( ( ! [SY1646: $i,SY1647: $i,SY1648: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SY1646 ) @ SY1647 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SY1648 ) @ SY1647 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SY1646 ) @ SY1648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1311,plain,
! [SV361: $i,SV110: $i] :
( ( ! [SY1649: $i] :
( ~ ( class_Orderings_Oorder @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV361 @ SY1649 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SY1649 @ SV361 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1312,plain,
! [SV362: $i,SV111: $i] :
( ( ! [SY1650: $i,SY1651: $i] :
( ( c_Type_Otypings @ SV111 @ SV362 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1650 @ SV111 @ SY1651 @ SV362 ) )
| ~ ( c_Type_Otyping @ SV111 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1651 ) @ SV362 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1313,plain,
! [SV363: $i,SV112: $i] :
( ( ! [SY1652: $i,SY1653: $i] :
( ( c_Type_Otypings @ SV112 @ SV363 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1652 @ SV112 @ SY1653 @ SV363 ) )
| ~ ( c_Type_Otyping @ SV112 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1653 @ SV363 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1314,plain,
! [SV364: $i,SV113: $i] :
( ( ! [SY1654: $i,SY1655: $i,SY1656: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV113 @ SV364 @ SY1654 @ SY1655 ) @ SY1656 )
= ( hAPP @ SV113 @ SY1656 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1656 @ SV364 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1315,plain,
! [SV114: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV114 @ tc_nat )
= $true )
| ( ( SV114
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1316,plain,
! [SV365: $i,SV115: $i] :
( ( ! [SY1657: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV115 @ SV365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1657 @ SV365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV115 ) @ SY1657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1317,plain,
! [SV366: $i,SV116: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV366 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV366 @ SV116 ) @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1318,plain,
! [SV367: $i,SV117: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV367 @ SV117 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV367 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1319,plain,
! [SV368: $i,SV118: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV118 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV368 @ SV118 @ SV118 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV368 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1320,plain,
! [SV369: $i,SV119: $i] :
( ( ! [SY1658: $i] :
( ~ ( class_Orderings_Olinorder @ SV119 )
| ( SV369 = SY1658 )
| ( c_HOL_Oord__class_Oless @ SV369 @ SY1658 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SY1658 @ SV369 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1321,plain,
! [SV370: $i,SV120: $i] :
( ( ! [SY1659: $i] :
( ~ ( class_Orderings_Olinorder @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV370 @ SY1659 @ SV120 )
| ( SY1659 = SV370 )
| ( c_HOL_Oord__class_Oless @ SY1659 @ SV370 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1322,plain,
! [SV371: $i,SV121: $i] :
( ( ! [SY1660: $i] :
( ~ ( class_Orderings_Olinorder @ SV121 )
| ( c_HOL_Oord__class_Oless @ SV371 @ SY1660 @ SV121 )
| ( c_HOL_Oord__class_Oless @ SY1660 @ SV371 @ SV121 )
| ( SY1660 = SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1323,plain,
! [SV372: $i,SV122: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV122 @ SV372 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV372 @ SV122 @ tc_nat )
| ( SV372 = SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1324,plain,
! [SV373: $i,SV123: $i] :
( ( ! [SY1661: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV373 ) @ SY1661 ) )
| ( c_HOL_Oord__class_Oless @ SV373 @ SY1661 @ tc_nat )
| ( SY1661 = SV373 )
| ( c_HOL_Oord__class_Oless @ SY1661 @ SV373 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1325,plain,
! [SV374: $i,SV124: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV124 @ SV374 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV374 @ SV124 @ tc_nat )
| ( SV374 = SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1326,plain,
! [SV375: $i,SV125: $i] :
( ( ! [SY1662: $i] :
( ~ ( class_Orderings_Olinorder @ SV125 )
| ( SV375 = SY1662 )
| ( c_HOL_Oord__class_Oless @ SY1662 @ SV375 @ SV125 )
| ( c_HOL_Oord__class_Oless @ SV375 @ SY1662 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1327,plain,
! [SV376: $i,SV126: $i] :
( ( ! [SY1663: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV126 )
| ( c_HOL_Oord__class_Oless @ SV376 @ SY1663 @ SV126 )
| ( c_HOL_Oord__class_Oless @ SY1663 @ SV376 @ SV126 )
| ( SY1663 = SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1328,plain,
! [SV377: $i,SV127: $i] :
( ( ! [SY1664: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SV377 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SY1664 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV377 @ SY1664 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1329,plain,
! [SV378: $i,SV128: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV128 )
| ~ ( c_HOL_Oord__class_Oless @ SV378 @ SV378 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1330,plain,
! [SV379: $i,SV129: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV379 @ SV379 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1331,plain,
! [SV380: $i,SV130: $i] :
( ( ~ ( class_Orderings_Oorder @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV380 @ SV380 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1332,plain,
! [SV131: $i] :
( ( c_HOL_Oord__class_Oless @ SV131 @ SV131 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1333,plain,
! [SV132: $i] :
( ( c_HOL_Oord__class_Oless @ SV132 @ SV132 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1334,plain,
! [SV381: $i,SV133: $i] :
( ( ! [SY1665: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV133 ) ) @ SV381 ) @ SY1665 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV381 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV133 @ SV381 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1665 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1335,plain,
! [SV382: $i,SV134: $i] :
( ( ! [SY1666: $i,SY1667: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV134 @ SV382 ) @ SY1666 ) @ SY1667 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ SY1666 ) @ SY1667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1336,plain,
! [SV383: $i,SV135: $i] :
( ( ! [SY1668: $i,SY1669: $i,SY1670: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SY1668 ) @ SY1669 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SY1670 ) @ SY1669 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SY1668 ) @ SY1670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1337,plain,
! [SV384: $i,SV136: $i] :
( ( ! [SY1671: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV136 @ SV384 ) @ SY1671 ) @ SY1671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1338,plain,
! [SV385: $i,SV137: $i] :
( ( ! [SY1672: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV137 @ SV385 ) @ SY1672 ) @ SY1672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1339,plain,
! [SV386: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV138 ) ) @ ( c_Lambda_OdB_OAbs @ SV386 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV138 ) @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1340,plain,
! [SV387: $i,SV139: $i] :
( ( ! [SY1673: $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 @ SV139 @ SV387 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1673 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV387 @ 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 @ SV139 ) ) @ SV387 ) @ SY1673 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1341,plain,
! [SV388: $i,SV140: $i] :
( ( ! [SY1674: $i,SY1675: $i] :
( ~ ( class_Orderings_Opreorder @ SV140 )
| ( c_HOL_Oord__class_Oless @ SV388 @ SY1674 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SY1675 @ SY1674 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV388 @ SY1675 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1342,plain,
! [SV389: $i,SV141: $i] :
( ( ! [SY1676: $i,SY1677: $i] :
( ~ ( class_Orderings_Oorder @ SV141 )
| ( c_HOL_Oord__class_Oless @ SV389 @ SY1676 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV389 @ SY1677 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SY1677 @ SY1676 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1343,plain,
! [SV143: $i] :
( ( c_HOL_Oord__class_Oless @ SV143 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1344,plain,
! [SV144: $i] :
( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1345,plain,
! [SV390: $i,SV145: $i] :
( ( ! [SY1678: $i,SY1679: $i] :
( ( c_Type_Otypings @ SV145 @ SV390 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1678 @ SV145 @ SY1679 @ SV390 ) )
| ~ ( c_Type_Otyping @ SV145 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1679 @ SV390 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1346,plain,
! [SV391: $i,SV147: $i] :
( ( ! [SY1680: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV147 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV391 @ SY1680 @ SV147 @ SV147 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV391 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY1680 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 @ SV147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1347,plain,
! [SV392: $i,SV148: $i] :
( ( ! [SY1681: $i,SY1682: $i,SY1683: $i,SY1684: $i,SY1685: $i] :
( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1681 @ SY1682 @ SV148 @ SV392 ) )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1683 ) @ SY1684 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1682 )
| ~ ( c_Type_Otypings @ SV148 @ SY1684 @ SY1685 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1683 ) @ SY1684 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1348,plain,
! [SV149: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV149 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1349,plain,
! [SV393: $i,SV151: $i] :
( ( ! [SY1686: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV151 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV393 @ SV151 @ SY1686 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV393 ) @ SV151 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1350,plain,
! [SV394: $i,SV152: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV152 @ SV394 ) @ SV394 )
= ( c_Transitive__Closure_Ortranclp @ SV152 @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1351,plain,
! [SV395: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV153 ) ) @ ( c_Lambda_OdB_OAbs @ SV395 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV153 ) @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1352,plain,
! [SV396: $i,SV154: $i] :
( ( ! [SY1687: $i,SY1688: $i] :
( ( c_Type_Otyping @ SV154 @ SV396 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1687 @ SV154 @ SV396 @ SY1688 ) ) @ SY1687 ) )
| ~ ( c_Type_Otyping @ SV154 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SY1688 ) @ SY1687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1353,plain,
! [SV397: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV155 ) @ ( c_Lambda_OdB_OVar @ SV397 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1354,plain,
! [SV398: $i,SV156: $i] :
( ( ! [SY1689: $i,SY1690: $i] :
( ( c_Type_Otyping @ SV156 @ SV398 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1689 @ SV156 @ SV398 @ SY1690 ) @ SY1689 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV156 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV398 @ SY1690 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1355,plain,
! [SV399: $i,SV157: $i] :
( ( ! [SY1691: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV157 @ SV399 ) ) @ ( c_Lambda_Olift @ SY1691 @ SV399 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV157 ) @ SY1691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1356,plain,
! [SV400: $i,SV158: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV158 ) @ SV400 )
= ( c_Lambda_OdB_OVar @ SV158 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV158 @ SV400 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1357,plain,
! [SV401: $i,SV159: $i] :
( ( ! [SY1692: $i,SY1693: $i] :
( ( c_Type_Otyping @ SV159 @ SV401 @ SY1692 )
| ~ ( c_Type_Otyping @ SV159 @ SY1693 @ SY1692 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1693 ) @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1358,plain,
! [SV402: $i,SV160: $i] :
( ( ! [SY1694: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV160 ) @ SV402 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1694 ) @ SV402 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV160 ) @ SY1694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1359,plain,
! [SV403: $i,SV161: $i] :
( ( ! [SY1695: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SV403 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SY1695 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV403 ) @ SY1695 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1360,plain,
! [SV404: $i,SV162: $i] :
( ( ! [SY1696: $i,SY1697: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV404 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1696 ) @ SY1697 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV404 ) @ SY1697 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV162 ) @ SY1696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1361,plain,
! [SV405: $i,SV163: $i] :
( ( ! [SY1698: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV163 ) @ SV405 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1698 ) @ SV405 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV163 ) @ SY1698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1362,plain,
! [SV406: $i,SV164: $i] :
( ( ! [SY1699: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SV406 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SY1699 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV406 ) @ SY1699 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1363,plain,
! [SV407: $i,SV165: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV165 @ SV165 @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV165 ) @ SV407 @ SV165 )
= SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1364,plain,
! [SV408: $i,SV166: $i] :
( ( ! [SY1700: $i,SY1701: $i] :
( ( c_Type_Otyping @ SV166 @ SV408 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1700 @ SV166 @ SY1701 @ SV408 ) )
| ~ ( c_Type_Otyping @ SV166 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1701 ) @ SV408 ) @ SY1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1365,plain,
! [SV409: $i,SV167: $i] :
( ( ! [SY1702: $i] :
( ( SV167
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV409 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV409 @ SY1702 @ SV167 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV409 ) @ SY1702 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1366,plain,
! [SV410: $i,SV168: $i] :
( ( ! [SY1703: $i,SY1704: $i,SY1705: $i] :
( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV410 @ SY1703 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1704 )
| ~ ( c_Type_Otypings @ SV168 @ SY1703 @ SY1705 )
| ~ ( c_Type_Otyping @ SV168 @ SV410 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1705 @ SY1704 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1367,plain,
! [SV411: $i,SV169: $i] :
( ( ! [SY1706: $i,SY1707: $i] :
( ( c_Type_Otyping @ SV169 @ ( c_Lambda_OdB_OVar @ SV411 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1706 @ SV169 @ SV411 @ SY1707 ) @ SY1706 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV169 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV411 ) @ SY1707 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1368,plain,
! [SV412: $i,SV170: $i] :
( ( ! [SY1708: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV170 ) @ SV412 @ SY1708 )
= ( c_Lambda_OdB_OVar @ SV170 ) )
| ( SV170 = SY1708 )
| ( c_HOL_Oord__class_Oless @ SY1708 @ SV170 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1369,plain,
! [SV413: $i,SV171: $i] :
( ( ! [SY1709: $i,SY1710: $i] :
( ( c_Type_Otyping @ SV171 @ SV413 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1709 @ SV171 @ SV413 @ SY1710 ) @ SY1709 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV171 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV413 @ SY1710 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1370,plain,
! [SV414: $i,SV172: $i] :
( ( ! [SY1711: $i,SY1712: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV172 @ SV414 @ SY1711 ) ) @ ( c_Lambda_Osubst @ SV172 @ SY1712 @ SY1711 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV414 ) @ SY1712 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1371,plain,
! [SV415: $i,SV173: $i] :
( ( ! [SY1713: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SV415 ) @ SY1713 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV173 @ SY1713 ) ) @ ( c_Lambda_Olift @ SV415 @ SY1713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1372,plain,
! [SV416: $i,SV174: $i] :
( ( ! [SY1714: $i,SY1715: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV416 @ SY1714 ) ) @ ( c_Lambda_Osubst @ SY1715 @ SV416 @ SY1714 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV174 ) @ SY1715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1373,plain,
! [SV417: $i,SV175: $i] :
( ( ! [SY1716: $i,SY1717: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV175 @ SV417 @ SY1716 ) ) @ ( c_Lambda_Osubst @ SV175 @ SY1717 @ SY1716 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV417 ) @ SY1717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1374,plain,
! [SV418: $i,SV177: $i] :
( ( ! [SY1718: $i,SY1719: $i] :
( ( c_Type_Otyping @ SV177 @ ( c_Lambda_OdB_OAbs @ SV418 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1718 ) @ SY1719 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1718 @ tc_Type_Otype ) @ SV418 @ SY1719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1375,plain,
! [SV419: $i,SV178: $i] :
( ( ! [SY1720: $i,SY1721: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV178 @ SV419 @ SY1720 @ SY1721 ) @ SV419 )
= SY1720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1376,plain,
! [SV420: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV179 @ SV420 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1377,plain,
! [SV421: $i,SV180: $i] :
( ( ! [SY1722: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV180 @ SV421 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1722 @ SV421 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV180 ) @ SY1722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1378,plain,
! [SV422: $i,SV181: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV181 ) ) @ SV422 ) ) @ ( c_Lambda_Osubst @ SV181 @ SV422 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1379,plain,
! [SV423: $i,SV182: $i] :
( ( ! [SY1723: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV182 @ SV423 ) ) @ ( c_Lambda_Olift @ SY1723 @ SV423 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV182 ) @ SY1723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1380,plain,
! [SV424: $i,SV183: $i] :
( ( ! [SY1724: $i,SY1725: $i,SY1726: $i] :
( ( SV183 = SV424 )
| ~ ( c_Type_Otyping @ SY1724 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1725 ) @ SY1726 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV424 )
| ~ ( c_Type_Otyping @ SY1724 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1725 ) @ SY1726 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1381,plain,
! [SV425: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV184 ) @ SV425 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV425 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1382,plain,
! [SV426: $i,SV185: $i] :
( ( ! [SY1727: $i,SY1728: $i,SY1729: $i] :
( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV426 ) @ SY1727 ) @ SY1728 )
| ~ ( c_Type_Otyping @ SV185 @ SY1727 @ SY1729 )
| ~ ( c_Type_Otyping @ SV185 @ SV426 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1729 ) @ SY1728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1383,plain,
! [SV427: $i,SV186: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV186 ) ) @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1384,plain,
! [SV428: $i,SV187: $i] :
( ( ! [SY1730: $i,SY1731: $i,SY1732: $i,SY1733: $i,SY1734: $i] :
( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SY1730 @ SY1731 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY1730 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1732 ) @ SY1733 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
| ~ ( c_Type_Otypings @ SY1730 @ SY1733 @ SY1734 )
| ~ ( c_Type_Otyping @ SY1730 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1732 ) @ SY1733 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1731 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1385,plain,
! [SV429: $i,SV188: $i] :
( ( ! [SY1735: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV188 ) @ SV429 @ SY1735 )
= ( c_Lambda_OdB_OVar @ SV188 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV188 @ SY1735 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1386,plain,
! [SV430: $i,SV189: $i] :
( ( ! [SY1736: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV189 @ ( c_Lambda_OdB_OVar @ SV430 ) @ SY1736 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1387,plain,
! [SV431: $i,SV190: $i] :
( ( ! [SY1737: $i,SY1738: $i,SY1739: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV190 @ SV431 @ SY1737 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1738 @ SV431 ) @ SY1739 )
| ~ ( c_Type_Otyping @ SV190 @ SY1738 @ SY1739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1388,plain,
! [SV432: $i,SV191: $i] :
( ( ! [SY1740: $i,SY1741: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV191 ) @ SV432 ) @ SY1740 @ SY1741 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV191 @ SY1740 @ SY1741 ) ) @ ( c_Lambda_Osubst @ SV432 @ SY1740 @ SY1741 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1389,plain,
! [SV433: $i,SV192: $i] :
( ( ! [SY1742: $i,SY1743: $i] :
( ( c_Type_Otyping @ SV192 @ SV433 @ SY1742 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1743 ) @ SV433 ) )
| ~ ( c_Type_Otyping @ SV192 @ SY1743 @ SY1742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1390,plain,
! [SV434: $i,SV193: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV193 ) @ SV434 @ SV193 )
= SV434 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1391,plain,
! [SV435: $i,SV194: $i] :
( ( ! [SY1744: $i] :
( ( ( hAPP @ SV194 @ SV435 )
= SY1744 )
| ~ ( c_Type_Otyping @ SV194 @ ( c_Lambda_OdB_OVar @ SV435 ) @ SY1744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1392,plain,
! [SV436: $i,SV195: $i] :
( ( ! [SY1745: $i,SY1746: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV195 @ SV436 @ SY1745 ) ) @ ( c_Lambda_Osubst @ SY1746 @ SV436 @ SY1745 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SY1746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1393,plain,
! [SV437: $i,SV196: $i] :
( ( c_Type_Otyping @ SV196 @ ( c_Lambda_OdB_OVar @ SV437 ) @ ( hAPP @ SV196 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1394,plain,
! [SV438: $i,SV197: $i] :
( ( ! [SY1747: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV197 @ SV438 ) @ SY1747 @ SV438 )
= SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1395,plain,
! [SV439: $i,SV198: $i] :
( ( ! [SY1748: $i,SY1749: $i,SY1750: $i,SY1751: $i] :
( ~ ( c_Type_Otyping @ SV198 @ SV439 @ SY1748 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SY1749 @ SY1748 @ tc_Type_Otype ) @ SY1750 @ SY1751 )
| ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SY1750 @ SV439 @ SY1749 ) @ SY1751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1396,plain,
! [SV440: $i,SV199: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV199 @ SV440 ) )
| ~ ( class_Orderings_Opreorder @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1397,plain,
! [SV441: $i,SV200: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV200 @ SV441 ) )
| ~ ( class_Orderings_Oorder @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1398,plain,
! [SV442: $i,SV201: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV201 ) @ SV442 ) @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1399,plain,
! [SV443: $i,SV202: $i] :
( ( ! [SY1752: $i] :
( ( SV202 = SV443 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1752 ) @ SV202 ) @ SV443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1400,plain,
! [SV444: $i,SV203: $i] :
( ( ! [SY1753: $i,SY1754: $i] :
( ( ( c_List_Oappend @ SV203 @ SV444 @ SY1753 )
!= ( c_List_Oappend @ SY1754 @ SV444 @ SY1753 ) )
| ( SV203 = SY1754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1401,plain,
! [SV445: $i,SV204: $i] :
( ( ! [SY1755: $i,SY1756: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV204 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV445 ) @ SY1755 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SY1756 ) @ SY1755 ) )
| ( SV445 = SY1756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1402,plain,
! [SV446: $i,SV205: $i] :
( ( ! [SY1757: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SV446 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1757 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SV446 )
= SY1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1403,plain,
! [SV447: $i,SV206: $i] :
( ( ! [SY1758: $i] :
( ( ( c_List_Olist_ONil @ SV206 )
!= ( c_List_Oappend @ SV447 @ SY1758 @ SV206 ) )
| ( SV447
= ( c_List_Olist_ONil @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1404,plain,
! [SV448: $i,SV207: $i] :
( ( ! [SY1759: $i,SY1760: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV207 ) @ SV448 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1759 ) @ SY1760 ) )
| ( SV448 = SY1760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1405,plain,
! [SV449: $i,SV208: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV208 )
!= ( c_Lambda_OdB_OVar @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1406,plain,
! [SV450: $i,SV209: $i] :
( ( ! [SY1761: $i,SY1762: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV209 ) @ SV450 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1761 ) @ SY1762 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV209 = SY1761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1407,plain,
! [SV451: $i,SV210: $i] :
( ( ! [SY1763: $i] :
( ( c_List_Olist_OCons @ SV210 @ SV451 @ SY1763 )
!= SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1408,plain,
! [SV452: $i,SV211: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV211 )
!= ( c_Lambda_OdB_OVar @ SV452 ) )
| ( SV211 = SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1409,plain,
! [SV453: $i,SV212: $i] :
( ( ! [SY1764: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV212 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV453 @ SY1764 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1764
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1410,plain,
! [SV454: $i,SV213: $i] :
( ( ! [SY1765: $i] :
( ( SV213
!= ( c_List_Oappend @ SV454 @ SV213 @ SY1765 ) )
| ( SV454
= ( c_List_Olist_ONil @ SY1765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1411,plain,
! [SV455: $i,SV214: $i] :
( ( ! [SY1766: $i] :
( ( ( c_List_Oappend @ SV214 @ SV455 @ SY1766 )
!= ( c_List_Olist_ONil @ SY1766 ) )
| ( SV455
= ( c_List_Olist_ONil @ SY1766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1412,plain,
! [SV456: $i,SV215: $i] :
( ( ! [SY1767: $i] :
( ( ( c_Lambda_OdB_OVar @ SV215 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV456 @ SY1767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV215 )
= SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1413,plain,
! [SV457: $i,SV216: $i] :
( ( ( c_Lambda_OdB_OVar @ SV216 )
!= ( c_Lambda_OdB_OAbs @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1414,plain,
! [SV458: $i,SV217: $i] :
( ( ! [SY1768: $i] :
( ( c_Lambda_OdB_OAbs @ SV217 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SY1768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1415,plain,
! [SV459: $i,SV218: $i] :
( ( ! [SY1769: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV459 )
!= ( c_Lambda_OdB_OVar @ SY1769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1416,plain,
! [SV460: $i,SV219: $i] :
( ( ! [SY1770: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV219 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV460 @ SY1770 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV219 )
= SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1417,plain,
! [SV461: $i,SV220: $i] :
( ( ! [SY1771: $i,SY1772: $i,SY1773: $i] :
( ( ( c_List_Oappend @ SV220 @ ( c_List_Olist_OCons @ SV461 @ ( c_List_Olist_ONil @ SY1771 ) @ SY1771 ) @ SY1771 )
!= ( c_List_Oappend @ SY1772 @ ( c_List_Olist_OCons @ SY1773 @ ( c_List_Olist_ONil @ SY1771 ) @ SY1771 ) @ SY1771 ) )
| ( SV461 = SY1773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1418,plain,
! [SV462: $i,SV221: $i] :
( ( ! [SY1774: $i] :
( ( c_Lambda_OdB_OVar @ SV221 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV462 ) @ SY1774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1419,plain,
! [SV463: $i,SV222: $i] :
( ( ! [SY1775: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV222 @ SV463 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1775 @ SV463 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV222 = SY1775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1420,plain,
! [SV464: $i,SV223: $i] :
( ( ! [SY1776: $i,SY1777: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV223 ) @ SV464 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1776 ) @ SY1777 ) )
| ( SV223 = SY1776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1421,plain,
! [SV465: $i,SV224: $i] :
( ( ! [SY1778: $i,SY1779: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ SV465 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1778 ) @ SY1779 ) )
| ( SV224 = SY1778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1422,plain,
! [SV466: $i,SV225: $i] :
( ( ! [SY1780: $i,SY1781: $i,SY1782: $i] :
( ( ( c_List_Oappend @ SV225 @ ( c_List_Olist_OCons @ SV466 @ ( c_List_Olist_ONil @ SY1780 ) @ SY1780 ) @ SY1780 )
!= ( c_List_Oappend @ SY1781 @ ( c_List_Olist_OCons @ SY1782 @ ( c_List_Olist_ONil @ SY1780 ) @ SY1780 ) @ SY1780 ) )
| ( SV225 = SY1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1423,plain,
! [SV467: $i,SV226: $i] :
( ( ! [SY1783: $i,SY1784: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV226 ) ) @ SV467 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1783 ) @ SY1784 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1424,plain,
! [SV468: $i,SV227: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV227 )
!= ( c_Lambda_OdB_OAbs @ SV468 ) )
| ( SV227 = SV468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1425,plain,
! [SV469: $i,SV228: $i] :
( ( ! [SY1785: $i] :
( ( c_List_Olist_OCons @ SV228 @ SV469 @ SY1785 )
!= ( c_List_Olist_ONil @ SY1785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1426,plain,
! [SV470: $i,SV229: $i] :
( ( ! [SY1786: $i,SY1787: $i,SY1788: $i] :
( ( ( c_List_Olist_OCons @ SV229 @ SV470 @ SY1786 )
!= ( c_List_Olist_OCons @ SY1787 @ SY1788 @ SY1786 ) )
| ( SV470 = SY1788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1427,plain,
! [SV471: $i,SV230: $i] :
( ( ! [SY1789: $i] :
( ( SV230
!= ( c_List_Oappend @ SV230 @ SV471 @ SY1789 ) )
| ( SV471
= ( c_List_Olist_ONil @ SY1789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1428,plain,
! [SV472: $i,SV231: $i] :
( ( ! [SY1790: $i] :
( ( ( c_List_Oappend @ SV231 @ SV472 @ SY1790 )
!= SV472 )
| ( SV231
= ( c_List_Olist_ONil @ SY1790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1429,plain,
! [SV473: $i,SV232: $i] :
( ( ! [SY1791: $i] :
( ( ( c_List_Oappend @ SV232 @ SV473 @ SY1791 )
!= ( c_List_Olist_ONil @ SY1791 ) )
| ( SV232
= ( c_List_Olist_ONil @ SY1791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1430,plain,
! [SV474: $i,SV233: $i] :
( ( ! [SY1792: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SV474 )
!= ( c_Lambda_OdB_OAbs @ SY1792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1431,plain,
! [SV475: $i,SV234: $i] :
( ( ! [SY1793: $i,SY1794: $i,SY1795: $i] :
( ( ( c_List_Olist_OCons @ SV234 @ SV475 @ SY1793 )
!= ( c_List_Olist_OCons @ SY1794 @ SY1795 @ SY1793 ) )
| ( SV234 = SY1794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1432,plain,
! [SV476: $i,SV235: $i] :
( ( ! [SY1796: $i,SY1797: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV476 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1796 ) @ SY1797 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV235 = SY1796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1433,plain,
! [SV477: $i,SV236: $i] :
( ( ! [SY1798: $i,SY1799: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV477 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1798 ) @ SY1799 ) )
| ( SV477 = SY1799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1434,plain,
! [SV478: $i,SV237: $i] :
( ( ! [SY1800: $i,SY1801: $i,SY1802: $i,SY1803: $i,SY1804: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1800 @ SY1801 @ SY1802 ) ) )
| ~ ( c_Type_Otyping @ SY1803 @ SY1801 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1803 @ SY1802 @ SV478 @ tc_Type_Otype ) @ SY1800 @ SY1804 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1435,plain,
! [SV479: $i,SV238: $i] :
( ( ! [SY1805: $i,SY1806: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SY1805 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SY1806 ) )
| ( SY1805 = SY1806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1436,plain,
! [SV480: $i,SV239: $i] :
( ( ! [SY1807: $i,SY1808: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV239 )
| ~ ( class_Int_Onumber__ring @ SV239 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SY1807 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SY1808 ) )
| ( SY1807 = SY1808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1437,plain,
! [SV481: $i,SV240: $i] :
( ( ! [SY1809: $i] :
( ( SV240
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 ) @ SY1809 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 ) @ ( c_List_Oappend @ SY1809 @ ( c_List_Olist_OCons @ SV481 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1438,plain,
! [SV482: $i,SV241: $i] :
( ( ! [SY1810: $i,SY1811: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV482 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1810 ) @ SY1811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV482 = SY1811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1439,plain,
! [SV483: $i,SV242: $i] :
( ( ! [SY1812: $i] :
( ( c_List_Olist_ONil @ SV242 )
!= ( c_List_Olist_OCons @ SV483 @ SY1812 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1440,plain,
! [SV484: $i,SV243: $i] :
( ( ! [SY1813: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV243 )
| ~ ( class_Int_Onumber__ring @ SV243 )
| ( SV484
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SV484 ) @ SY1813 ) )
| ( SY1813
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1441,plain,
! [SV485: $i,SV244: $i] :
( ( ! [SY1814: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV244 @ SV485 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1814 ) )
| ( SV485
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1442,plain,
! [SV486: $i,SV245: $i] :
( ( ! [SY1815: $i,SY1816: $i,SY1817: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV245 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SY1815 ) @ SY1816 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SY1815 ) @ SY1817 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ SY1816 )
= SY1817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1443,plain,
! [SV487: $i,SV246: $i] :
( ( ! [SY1818: $i,SY1819: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV246 ) @ SV487 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1818 ) @ SY1819 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1444,plain,
! [SV488: $i,SV247: $i] :
( ( ! [SY1820: $i,SY1821: $i,SY1822: $i,SY1823: $i,SY1824: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1820 @ SY1821 @ SY1822 ) ) )
| ~ ( c_Type_Otyping @ SY1823 @ SY1821 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1821 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1823 @ SY1822 @ SV247 @ tc_Type_Otype ) @ SY1820 @ SY1824 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1820 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1445,plain,
! [SV489: $i,SV248: $i] :
( ( ! [SY1825: $i] :
( ( ( c_List_Olist_ONil @ SV248 )
!= ( c_List_Oappend @ SV489 @ SY1825 @ SV248 ) )
| ( SY1825
= ( c_List_Olist_ONil @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1446,plain,
! [SV490: $i,SV249: $i] :
( ( ! [SY1826: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV249 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV490 @ SV249 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1826 @ SV249 ) )
| ( SV490 = SY1826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1447,plain,
! [SV491: $i,SV250: $i] :
( ( ! [SY1827: $i] :
( ( ( c_List_Oappend @ SV250 @ SV491 @ SY1827 )
!= SV250 )
| ( SV491
= ( c_List_Olist_ONil @ SY1827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1448,plain,
! [SV492: $i,SV251: $i] :
( ( ! [SY1828: $i,SY1829: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV251 ) @ SV492 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1828 ) @ SY1829 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV492 = SY1829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1449,plain,
! [SV493: $i,SV252: $i] :
( ( ! [SY1830: $i] :
( ( ( c_Lambda_OdB_OVar @ SV252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV493 @ SY1830 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1830
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1450,plain,
! [SV494: $i,SV253: $i] :
( ( ! [SY1831: $i] :
( ( c_List_Olist_OCons @ SV253 @ SV494 @ SY1831 )
!= ( c_List_Olist_ONil @ SY1831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1451,plain,
! [SV495: $i,SV254: $i] :
( ( ! [SY1832: $i] :
( SV254
!= ( c_List_Olist_OCons @ SV495 @ SV254 @ SY1832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1452,plain,
! [SV496: $i,SV255: $i] :
( ( ! [SY1833: $i,SY1834: $i] :
( ( ( c_List_Oappend @ SV255 @ SV496 @ SY1833 )
!= ( c_List_Oappend @ SV255 @ SY1834 @ SY1833 ) )
| ( SV496 = SY1834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1453,plain,
! [SV497: $i,SV256: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV256 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV256 ) @ SV497 ) @ SV497 )
!= ( c_HOL_Ozero__class_Ozero @ SV256 ) )
| ( SV497
= ( c_HOL_Ozero__class_Ozero @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1454,plain,
! [SV498: $i,SV257: $i] :
( ( ! [SY1835: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV257 @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1835 ) )
| ( SV257
= ( c_Lambda_OdB_OAbs @ SY1835 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1455,plain,
! [SV499: $i,SV258: $i] :
( ( ! [SY1836: $i,SY1837: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV258 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SY1836 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SY1837 ) )
| ( SY1836 = SY1837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1456,plain,
! [SV500: $i,SV259: $i,SV1: $i] :
( ( ! [SY1838: $i] :
( ( c_List_Oappend @ SV1 @ ( c_List_Oappend @ SV259 @ SV500 @ SY1838 ) @ SY1838 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV1 @ SV259 @ SY1838 ) @ SV500 @ SY1838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1457,plain,
! [SV501: $i,SV260: $i,SV2: $i] :
( ( ! [SY1839: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV2 @ SV260 @ SV501 ) @ SY1839 @ SV501 )
= ( c_List_Oappend @ SV2 @ ( c_List_Oappend @ SV260 @ SY1839 @ SV501 ) @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1458,plain,
! [SV502: $i,SV261: $i,SV3: $i] :
( ( ! [SY1840: $i] :
( ( c_List_Oappend @ SV3 @ ( c_List_Oappend @ SV261 @ SV502 @ SY1840 ) @ SY1840 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV3 @ SV261 @ SY1840 ) @ SV502 @ SY1840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1459,plain,
! [SV503: $i,SV262: $i,SV4: $i] :
( ( ! [SY1841: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV4 @ SV262 @ SV503 ) @ SY1841 @ SV503 )
= ( c_List_Oappend @ SV4 @ ( c_List_Oappend @ SV262 @ SY1841 @ SV503 ) @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1460,plain,
! [SV504: $i,SV263: $i,SV6: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV6 ) @ ( c_List_Olist_OCons @ SV263 @ SV504 @ SV6 ) @ SV6 )
= ( c_List_Olist_OCons @ SV263 @ SV504 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1461,plain,
! [SV505: $i,SV264: $i,SV7: $i] :
( ( ! [SY1842: $i] :
( ( c_List_Olistsp @ SV7 @ ( c_List_Oappend @ SV264 @ SV505 @ SY1842 ) @ SY1842 )
| ~ ( c_List_Olistsp @ SV7 @ SV505 @ SY1842 )
| ~ ( c_List_Olistsp @ SV7 @ SV264 @ SY1842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1462,plain,
! [SV506: $i,SV265: $i,SV8: $i] :
( ( ! [SY1843: $i,SY1844: $i,SY1845: $i] :
( ( SV8 = SV265 )
| ( SV506 = SY1843 )
| ~ ( c_ListOrder_Ostep1 @ SY1844 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SY1845 ) @ SY1845 ) @ SY1845 ) @ ( c_List_Oappend @ SV265 @ ( c_List_Olist_OCons @ SY1843 @ ( c_List_Olist_ONil @ SY1845 ) @ SY1845 ) @ SY1845 ) @ SY1845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1463,plain,
! [SV507: $i,SV266: $i,SV9: $i] :
( ( ! [SY1846: $i,SY1847: $i,SY1848: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SV266 ) @ SV507 ) )
| ( SV266 = SV507 )
| ~ ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SY1846 @ ( c_List_Olist_OCons @ SV266 @ ( c_List_Olist_ONil @ SY1847 ) @ SY1847 ) @ SY1847 ) @ ( c_List_Oappend @ SY1848 @ ( c_List_Olist_OCons @ SV507 @ ( c_List_Olist_ONil @ SY1847 ) @ SY1847 ) @ SY1847 ) @ SY1847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1464,plain,
! [SV508: $i,SV267: $i,SV10: $i] :
( ( ! [SY1849: $i,SY1850: $i,SY1851: $i] :
( ( c_List_Ofoldr @ SV10 @ ( c_List_Oappend @ SV267 @ SV508 @ SY1849 ) @ SY1850 @ SY1849 @ SY1851 )
= ( c_List_Ofoldr @ SV10 @ SV267 @ ( c_List_Ofoldr @ SV10 @ SV508 @ SY1850 @ SY1849 @ SY1851 ) @ SY1849 @ SY1851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1465,plain,
! [SV509: $i,SV273: $i,SV16: $i] :
( ( ! [SY1852: $i] :
( ( c_List_Olistsp @ SV16 @ SV273 @ SV509 )
| ~ ( c_List_Olistsp @ SV16 @ ( c_List_Oappend @ SY1852 @ SV273 @ SV509 ) @ SV509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1466,plain,
! [SV510: $i,SV274: $i,SV17: $i] :
( ( ! [SY1853: $i] :
( ( c_List_Olistsp @ SV17 @ SV274 @ SV510 )
| ~ ( c_List_Olistsp @ SV17 @ ( c_List_Oappend @ SV274 @ SY1853 @ SV510 ) @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1467,plain,
! [SV511: $i,SV275: $i,SV18: $i] :
( ( ! [SY1854: $i,SY1855: $i] :
( ( c_ListOrder_Ostep1 @ SV18 @ ( c_List_Oappend @ SV275 @ SV511 @ SY1854 ) @ ( c_List_Oappend @ SV275 @ SY1855 @ SY1854 ) @ SY1854 )
| ~ ( c_ListOrder_Ostep1 @ SV18 @ SV511 @ SY1855 @ SY1854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1468,plain,
! [SV512: $i,SV276: $i,SV19: $i] :
( ( ! [SY1856: $i,SY1857: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV19 @ SV276 @ SV512 @ SY1856 )
| ( c_ListOrder_Ostep1 @ SV19 @ ( c_List_Oappend @ SV276 @ SY1857 @ SY1856 ) @ ( c_List_Oappend @ SV512 @ SY1857 @ SY1856 ) @ SY1856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1469,plain,
! [SV513: $i,SV277: $i,SV20: $i] :
( ( ! [SY1858: $i,SY1859: $i,SY1860: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV277 ) @ SV513 ) )
| ( c_ListOrder_Ostep1 @ SV20 @ SY1858 @ SY1859 @ SY1860 )
| ~ ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SY1858 @ ( c_List_Olist_OCons @ SV277 @ ( c_List_Olist_ONil @ SY1860 ) @ SY1860 ) @ SY1860 ) @ ( c_List_Oappend @ SY1859 @ ( c_List_Olist_OCons @ SV513 @ ( c_List_Olist_ONil @ SY1860 ) @ SY1860 ) @ SY1860 ) @ SY1860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1470,plain,
! [SV514: $i,SV278: $i,SV21: $i] :
( ( ! [SY1861: $i] :
( ( c_Type_Otyping @ SV21 @ SV278 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV514 @ SV21 @ SV278 @ SY1861 ) )
| ~ ( c_Type_Otypings @ SV21 @ ( c_List_Oappend @ SY1861 @ ( c_List_Olist_OCons @ SV278 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1471,plain,
! [SV515: $i,SV279: $i,SV22: $i] :
( ( ! [SY1862: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV22 @ SV279 @ SV515 ) @ SY1862 @ SV515 )
= ( c_List_Olist_OCons @ SV22 @ ( c_List_Oappend @ SV279 @ SY1862 @ SV515 ) @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1472,plain,
! [SV516: $i,SV280: $i,SV23: $i] :
( ( ! [SY1863: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV23 @ SV280 @ SV516 ) @ SY1863 @ SV516 )
= ( c_List_Olist_OCons @ SV23 @ ( c_List_Oappend @ SV280 @ SY1863 @ SV516 ) @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1473,plain,
! [SV517: $i,SV281: $i,SV24: $i] :
( ( ! [SY1864: $i] :
( ( c_List_Olist_OCons @ SV24 @ ( c_List_Oappend @ SV281 @ SV517 @ SY1864 ) @ SY1864 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV24 @ SV281 @ SY1864 ) @ SV517 @ SY1864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1474,plain,
! [SV518: $i,SV282: $i,SV25: $i] :
( ( ! [SY1865: $i] :
( ( c_List_Olist_OCons @ SV25 @ ( c_List_Oappend @ SV282 @ SV518 @ SY1865 ) @ SY1865 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV25 @ SV282 @ SY1865 ) @ SV518 @ SY1865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1475,plain,
! [SV519: $i,SV283: $i,SV26: $i] :
( ( ( c_List_Olist_OCons @ SV26 @ SV283 @ SV519 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV519 ) @ ( c_List_Olist_OCons @ SV26 @ SV283 @ SV519 ) @ SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1476,plain,
! [SV520: $i,SV284: $i,SV27: $i] :
( ( ! [SY1866: $i,SY1867: $i,SY1868: $i] :
( ( SV27 = SV284 )
| ( c_ListOrder_Ostep1 @ SV520 @ SV27 @ SV284 @ SY1866 )
| ~ ( c_ListOrder_Ostep1 @ SV520 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SY1867 @ ( c_List_Olist_ONil @ SY1866 ) @ SY1866 ) @ SY1866 ) @ ( c_List_Oappend @ SV284 @ ( c_List_Olist_OCons @ SY1868 @ ( c_List_Olist_ONil @ SY1866 ) @ SY1866 ) @ SY1866 ) @ SY1866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1477,plain,
! [SV521: $i,SV285: $i,SV29: $i] :
( ( ! [SY1869: $i,SY1870: $i,SY1871: $i] :
( ( c_List_Ofoldl @ SV29 @ SV285 @ ( c_List_Oappend @ SV521 @ SY1869 @ SY1870 ) @ SY1871 @ SY1870 )
= ( c_List_Ofoldl @ SV29 @ ( c_List_Ofoldl @ SV29 @ SV285 @ SV521 @ SY1871 @ SY1870 ) @ SY1869 @ SY1871 @ SY1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1478,plain,
! [SV286: $i,SV30: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV30 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV286 ) @ SV286 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV286 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1479,plain,
! [SV287: $i,SV31: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV31 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV287 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV287 ) @ SV287 ) @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1480,plain,
! [SV288: $i,SV32: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV32 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( c_HOL_Ozero__class_Ozero @ SV32 ) ) @ SV288 )
= SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1481,plain,
! [SV289: $i,SV33: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV33 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV289 ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1482,plain,
! [SV290: $i,SV34: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV34 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV290 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) )
= SV290 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1483,plain,
! [SV291: $i,SV35: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV35 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) ) @ SV291 )
= SV291 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1484,plain,
! [SV292: $i,SV36: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV36 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV36 ) @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) )
= SV292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1485,plain,
! [SV293: $i,SV37: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV37 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV37 )
| ( SV293
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV293 ) @ ( c_HOL_Ozero__class_Ozero @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1486,plain,
! [SV294: $i,SV38: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV38 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) ) @ SV294 )
= SV294 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1487,plain,
! [SV295: $i,SV39: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV39 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( c_HOL_Ozero__class_Ozero @ SV39 ) ) @ SV295 )
= SV295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1488,plain,
! [SV296: $i,SV40: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV40 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV296 @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1489,plain,
! [SV522: $i,SV297: $i,SV41: $i] :
( ( ! [SY1872: $i,SY1873: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV522 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SY1872 ) @ SY1873 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SY1872 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV522 ) @ SY1873 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1490,plain,
! [SV523: $i,SV298: $i,SV42: $i] :
( ( ! [SY1874: $i,SY1875: $i,SY1876: $i] :
( ( SV42 = SV298 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV298 ) @ SV42 ) )
| ~ ( c_ListOrder_Ostep1 @ SV523 @ ( c_List_Olist_OCons @ SV298 @ SY1874 @ SY1875 ) @ ( c_List_Olist_OCons @ SV42 @ SY1876 @ SY1875 ) @ SY1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1491,plain,
! [SV524: $i,SV299: $i,SV43: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV299 ) @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV524 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV299 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1492,plain,
! [SV44: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV44 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV44 )
= ( c_HOL_Ozero__class_Ozero @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1493,plain,
! [SV525: $i,SV300: $i,SV45: $i] :
( ( ! [SY1877: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV45 @ SV300 @ SV300 ) @ SV300 ) @ SV525 ) @ SY1877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV300 ) @ SY1877 ) @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1494,plain,
! [SV526: $i,SV301: $i,SV46: $i] :
( ( ! [SY1878: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SV301 ) @ SV526 ) @ SY1878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV46 @ SV301 @ SV301 ) @ SV301 ) @ SY1878 ) @ SV526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1495,plain,
! [SV527: $i,SV302: $i,SV47: $i] :
( ( ! [SY1879: $i,SY1880: $i,SY1881: $i] :
( ( c_List_Ofoldl @ SV47 @ SV302 @ ( c_List_Olist_OCons @ SV527 @ SY1879 @ SY1880 ) @ SY1881 @ SY1880 )
= ( c_List_Ofoldl @ SV47 @ ( hAPP @ ( hAPP @ SV47 @ SV302 ) @ SV527 ) @ SY1879 @ SY1881 @ SY1880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1496,plain,
! [SV528: $i,SV303: $i,SV48: $i] :
( ( ! [SY1882: $i] :
( ( c_List_Ofoldr @ SV48 @ ( c_List_Olist_ONil @ SV303 ) @ SV528 @ SV303 @ SY1882 )
= SV528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1497,plain,
! [SV529: $i,SV304: $i,SV49: $i] :
( ( ! [SY1883: $i,SY1884: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV49 @ SV304 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV49 @ SY1883 @ SY1884 ) @ SV529 ) @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1498,plain,
! [SV530: $i,SV305: $i,SV50: $i] :
( ( ! [SY1885: $i,SY1886: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV50 @ SV305 @ SV530 ) @ SY1885 ) @ SY1886 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY1886 ) @ SY1885 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1499,plain,
! [SV531: $i,SV306: $i,SV51: $i] :
( ( ! [SY1887: $i,SY1888: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV306 ) @ SV531 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV51 @ SY1887 @ SY1888 ) @ SV531 ) @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1500,plain,
! [SV532: $i,SV307: $i,SV52: $i] :
( ( ! [SY1889: $i,SY1890: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV52 @ SV307 @ SV532 ) @ SY1889 ) @ SY1890 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SY1890 ) @ SY1889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1501,plain,
! [SV533: $i,SV308: $i,SV53: $i] :
( ( ! [SY1891: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV53 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ SV533 ) ) @ SY1891 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV533 ) @ SY1891 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1502,plain,
! [SV534: $i,SV309: $i,SV54: $i] :
( ( ! [SY1892: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV54 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV534 ) @ SY1892 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV534 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ SY1892 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1503,plain,
! [SV535: $i,SV310: $i,SV55: $i] :
( ( ! [SY1893: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SV535 ) ) @ SY1893 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SY1893 ) ) @ SV535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1504,plain,
! [SV536: $i,SV311: $i,SV56: $i] :
( ( ! [SY1894: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV536 ) @ SY1894 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SV536 ) ) @ SY1894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1505,plain,
! [SV537: $i,SV312: $i,SV57: $i] :
( ( ! [SY1895: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV57 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SV537 ) ) @ SY1895 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV537 ) @ SY1895 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1506,plain,
! [SV538: $i,SV313: $i,SV58: $i] :
( ( ! [SY1896: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV58 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV538 ) @ SY1896 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ SY1896 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1507,plain,
! [SV539: $i,SV314: $i,SV59: $i] :
( ( ! [SY1897: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SV539 ) ) @ SY1897 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV539 ) @ SY1897 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1508,plain,
! [SV540: $i,SV315: $i,SV60: $i] :
( ( ! [SY1898: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV60 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV540 ) @ SY1898 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SY1898 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1509,plain,
! [SV541: $i,SV316: $i,SV61: $i] :
( ( ! [SY1899: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV61 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV541 ) @ SY1899 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ SV541 ) ) @ SY1899 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1510,plain,
! [SV62: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV62 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) )
= ( c_HOL_Ozero__class_Ozero @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1511,plain,
! [SV542: $i,SV317: $i,SV63: $i] :
( ( ! [SY1900: $i,SY1901: $i,SY1902: $i] :
( ( SV63 = SV317 )
| ( SV542 = SY1900 )
| ~ ( c_ListOrder_Ostep1 @ SY1901 @ ( c_List_Olist_OCons @ SV317 @ SY1900 @ SY1902 ) @ ( c_List_Olist_OCons @ SV63 @ SV542 @ SY1902 ) @ SY1902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1512,plain,
! [SV543: $i,SV318: $i,SV64: $i] :
( ( ! [SY1903: $i,SY1904: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV64 @ SV318 ) @ SV543 ) )
| ( c_ListOrder_Ostep1 @ SV64 @ ( c_List_Olist_OCons @ SV318 @ SY1903 @ SY1904 ) @ ( c_List_Olist_OCons @ SV543 @ SY1903 @ SY1904 ) @ SY1904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1513,plain,
! [SV544: $i,SV320: $i,SV66: $i] :
( ( ! [SY1905: $i] :
( ( c_Wellfounded_Oaccp @ SV66 @ SV320 @ SV544 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV544 ) @ SV320 ) @ SY1905 ) )
| ~ ( c_Wellfounded_Oaccp @ SV66 @ SY1905 @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1514,plain,
! [SV545: $i,SV321: $i,SV67: $i] :
( ( ! [SY1906: $i] :
( ( c_Wellfounded_Oaccp @ SV67 @ SV321 @ SV545 )
| ~ ( c_Wellfounded_Oaccp @ SV67 @ SY1906 @ SV545 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV545 ) @ SV321 ) @ SY1906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1515,plain,
! [SV68: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV68 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV68 @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1516,plain,
! [SV69: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV69 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1517,plain,
! [SV546: $i,SV322: $i,SV70: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV322 ) @ SV546 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV546 ) @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1518,plain,
! [SV547: $i,SV323: $i,SV71: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV71 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV323 ) @ SV547 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV547 ) @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1519,plain,
! [SV548: $i,SV324: $i,SV72: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV548 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV548 ) @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1520,plain,
! [SV549: $i,SV325: $i,SV73: $i] :
( ( ! [SY1907: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV73 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV549 ) @ SY1907 @ SV73 @ SV73 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV549 @ SY1907 @ SV73 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1521,plain,
! [SV550: $i,SV326: $i,SV74: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV74 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 @ SV550 @ SV74 @ SV74 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV550 @ SV326 @ SV74 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1522,plain,
! [SV551: $i,SV327: $i,SV75: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV75 @ ( c_List_Olist_ONil @ SV327 ) @ SV551 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1523,plain,
! [SV552: $i,SV328: $i,SV76: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV76 @ SV328 @ ( c_List_Olist_ONil @ SV552 ) @ SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1524,plain,
! [SV329: $i,SV77: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV77 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV329 @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1525,plain,
! [SV330: $i,SV78: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV78 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV330 @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ SV330 ) @ SV330 ) @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1526,plain,
! [SV331: $i,SV79: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV79 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV331 @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV79 ) @ SV331 ) @ SV331 ) @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1527,plain,
! [SV332: $i,SV80: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV80 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV332 ) @ SV332 ) @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ SV332 @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1528,plain,
! [SV553: $i,SV333: $i,SV81: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SV333 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ ( c_HOL_Ozero__class_Ozero @ SV81 ) @ SV553 @ SV81 @ SV81 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SV333 @ SV553 @ SV81 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1529,plain,
! [SV554: $i,SV334: $i,SV82: $i] :
( ( ! [SY1908: $i] :
( ( c_List_Ofoldl @ SV82 @ SV334 @ ( c_List_Olist_ONil @ SV554 ) @ SY1908 @ SV554 )
= SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1530,plain,
! [SV555: $i,SV335: $i,SV84: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV335 ) @ SV555 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV555 @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV335 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1531,plain,
! [SV556: $i,SV336: $i,SV85: $i] :
( ( ! [SY1909: $i,SY1910: $i,SY1911: $i] :
( ( c_ListOrder_Ostep1 @ SV85 @ SV336 @ SV556 @ SY1909 )
| ( SV556 = SV336 )
| ~ ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SY1910 @ SV336 @ SY1909 ) @ ( c_List_Olist_OCons @ SY1911 @ SV556 @ SY1909 ) @ SY1909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1532,plain,
! [SV557: $i,SV337: $i,SV86: $i] :
( ( ! [SY1912: $i,SY1913: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SY1912 ) @ SY1913 ) @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SY1913 @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV337 @ SY1912 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1533,plain,
! [SV558: $i,SV338: $i,SV87: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV87 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV338 @ SV87 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV558 @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV338 @ SV558 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1534,plain,
! [SV559: $i,SV339: $i,SV88: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV339 @ SV559 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV339 @ SV88 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV559 @ SV88 ) @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1535,plain,
! [SV560: $i,SV340: $i,SV89: $i] :
( ( ! [SY1914: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV560 ) @ SY1914 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ SY1914 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV560 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1536,plain,
! [SV561: $i,SV341: $i,SV90: $i] :
( ( ! [SY1915: $i,SY1916: $i,SY1917: $i] :
( ( c_List_Ofoldr @ SV90 @ ( c_List_Olist_OCons @ SV341 @ SV561 @ SY1915 ) @ SY1916 @ SY1915 @ SY1917 )
= ( hAPP @ ( hAPP @ SV90 @ SV341 ) @ ( c_List_Ofoldr @ SV90 @ SV561 @ SY1916 @ SY1915 @ SY1917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1537,plain,
! [SV562: $i,SV342: $i,SV91: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV91 @ SV342 @ SV562 ) @ SV562 @ SV342 )
= SV91 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1538,plain,
! [SV563: $i,SV343: $i,SV92: $i] :
( ( ! [SY1918: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV92 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV343 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SY1918 ) @ SV563 ) @ SV92 )
| ~ ( c_HOL_Oord__class_Oless @ SV343 @ SY1918 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1539,plain,
! [SV564: $i,SV344: $i,SV93: $i] :
( ( ! [SY1919: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV344 ) @ SV564 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY1919 ) @ SV564 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV344 @ SY1919 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1540,plain,
! [SV565: $i,SV345: $i,SV94: $i] :
( ( ! [SY1920: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
| ( c_HOL_Oord__class_Oless @ SV345 @ SV565 @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV345 ) @ SY1920 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV565 ) @ SY1920 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1541,plain,
! [SV566: $i,SV346: $i,SV95: $i] :
( ( ! [SY1921: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SY1921 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV566 @ SY1921 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1542,plain,
! [SV567: $i,SV347: $i,SV96: $i] :
( ( ! [SY1922: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV567 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SY1922 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ SY1922 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1543,plain,
! [SV568: $i,SV348: $i,SV97: $i] :
( ( ! [SY1923: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
| ( c_HOL_Oord__class_Oless @ SV348 @ SV568 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1923 ) @ SV348 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY1923 ) @ SV568 ) @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1544,plain,
! [SV569: $i,SV349: $i,SV98: $i] :
( ( ! [SY1924: $i,SY1925: $i,SY1926: $i] :
( ( c_ListOrder_Ostep1 @ SV98 @ SV349 @ SV569 @ SY1924 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SY1925 ) @ SY1926 ) )
| ~ ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SY1925 @ SV349 @ SY1924 ) @ ( c_List_Olist_OCons @ SY1926 @ SV569 @ SY1924 ) @ SY1924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1545,plain,
! [SV570: $i,SV350: $i,SV99: $i] :
( ( ! [SY1927: $i,SY1928: $i] :
( ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_OCons @ SV350 @ SV570 @ SY1927 ) @ ( c_List_Olist_OCons @ SV350 @ SY1928 @ SY1927 ) @ SY1927 )
| ~ ( c_ListOrder_Ostep1 @ SV99 @ SV570 @ SY1928 @ SY1927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1546,plain,
! [SV571: $i,SV351: $i,SV100: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV100 @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV571 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV100 @ ( c_List_Oappend @ SV351 @ ( c_List_Olist_OCons @ SV571 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1547,plain,
! [SV572: $i,SV353: $i,SV102: $i] :
( ( ( ( c_List_Oappend @ SV102 @ ( c_List_Olist_OCons @ SV353 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV572 @ SV102 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV353 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV572 @ ( c_List_Oappend @ SV102 @ ( c_List_Olist_OCons @ SV353 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1548,plain,
! [SV573: $i,SV354: $i,SV103: $i] :
( ( ! [SY1929: $i] :
( ( c_Wellfounded_Oaccp @ SV103 @ SV354 @ SV573 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ SV354 ) @ SY1929 ) )
| ~ ( c_Wellfounded_Oaccp @ SV103 @ SY1929 @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1549,plain,
! [SV574: $i,SV355: $i,SV104: $i] :
( ( ! [SY1930: $i] :
( ( c_Wellfounded_Oaccp @ SV104 @ SV355 @ SV574 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV355 ) @ SY1930 ) )
| ~ ( c_Wellfounded_Oaccp @ SV104 @ SY1930 @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1550,plain,
! [SV575: $i,SV356: $i,SV105: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV575 @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV356 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1551,plain,
! [SV576: $i,SV357: $i,SV106: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SV357 @ SV576 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV357 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1552,plain,
! [SV577: $i,SV358: $i,SV107: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV358 @ SV577 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV358 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1553,plain,
! [SV578: $i,SV359: $i,SV108: $i] :
( ( ! [SY1931: $i,SY1932: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SY1931 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SY1932 ) @ SY1931 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SY1932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1554,plain,
! [SV579: $i,SV360: $i,SV109: $i] :
( ( ! [SY1933: $i,SY1934: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV579 ) @ SY1933 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SY1934 ) @ SY1933 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SV579 ) @ SY1934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1555,plain,
! [SV580: $i,SV361: $i,SV110: $i] :
( ( ~ ( class_Orderings_Oorder @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV361 @ SV580 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV580 @ SV361 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1556,plain,
! [SV581: $i,SV362: $i,SV111: $i] :
( ( ! [SY1935: $i] :
( ( c_Type_Otypings @ SV111 @ SV362 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV581 @ SV111 @ SY1935 @ SV362 ) )
| ~ ( c_Type_Otyping @ SV111 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1935 ) @ SV362 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1557,plain,
! [SV582: $i,SV363: $i,SV112: $i] :
( ( ! [SY1936: $i] :
( ( c_Type_Otypings @ SV112 @ SV363 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV582 @ SV112 @ SY1936 @ SV363 ) )
| ~ ( c_Type_Otyping @ SV112 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1936 @ SV363 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1558,plain,
! [SV583: $i,SV364: $i,SV113: $i] :
( ( ! [SY1937: $i,SY1938: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV113 @ SV364 @ SV583 @ SY1937 ) @ SY1938 )
= ( hAPP @ SV113 @ SY1938 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1938 @ SV364 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1559,plain,
! [SV584: $i,SV365: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV115 @ SV365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV584 @ SV365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV115 ) @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1560,plain,
! [SV366: $i,SV116: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV116 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV366 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV366 @ SV116 ) @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1561,plain,
! [SV367: $i,SV117: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV117 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV367 @ SV117 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV367 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1562,plain,
! [SV368: $i,SV118: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV118 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV368 @ SV118 @ SV118 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV368 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1563,plain,
! [SV585: $i,SV369: $i,SV119: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV119 )
| ( SV369 = SV585 )
| ( c_HOL_Oord__class_Oless @ SV369 @ SV585 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV585 @ SV369 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1564,plain,
! [SV586: $i,SV370: $i,SV120: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV370 @ SV586 @ SV120 )
| ( SV586 = SV370 )
| ( c_HOL_Oord__class_Oless @ SV586 @ SV370 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1565,plain,
! [SV587: $i,SV371: $i,SV121: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV121 )
| ( c_HOL_Oord__class_Oless @ SV371 @ SV587 @ SV121 )
| ( c_HOL_Oord__class_Oless @ SV587 @ SV371 @ SV121 )
| ( SV587 = SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1566,plain,
! [SV372: $i,SV122: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV122 @ SV372 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV372 @ SV122 @ tc_nat )
| ( SV372 = SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1567,plain,
! [SV588: $i,SV373: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV373 ) @ SV588 ) )
| ( c_HOL_Oord__class_Oless @ SV373 @ SV588 @ tc_nat )
| ( SV588 = SV373 )
| ( c_HOL_Oord__class_Oless @ SV588 @ SV373 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1568,plain,
! [SV374: $i,SV124: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV124 @ SV374 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV374 @ SV124 @ tc_nat )
| ( SV374 = SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1569,plain,
! [SV589: $i,SV375: $i,SV125: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV125 )
| ( SV375 = SV589 )
| ( c_HOL_Oord__class_Oless @ SV589 @ SV375 @ SV125 )
| ( c_HOL_Oord__class_Oless @ SV375 @ SV589 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1570,plain,
! [SV590: $i,SV376: $i,SV126: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV126 )
| ( c_HOL_Oord__class_Oless @ SV376 @ SV590 @ SV126 )
| ( c_HOL_Oord__class_Oless @ SV590 @ SV376 @ SV126 )
| ( SV590 = SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1571,plain,
! [SV591: $i,SV377: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SV377 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SV591 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV377 @ SV591 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1572,plain,
! [SV378: $i,SV128: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV128 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV378 @ SV378 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1573,plain,
! [SV379: $i,SV129: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV129 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV379 @ SV379 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1574,plain,
! [SV380: $i,SV130: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV130 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV380 @ SV380 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1575,plain,
! [SV592: $i,SV381: $i,SV133: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV133 ) ) @ SV381 ) @ SV592 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV381 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV133 @ SV381 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV592 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1576,plain,
! [SV593: $i,SV382: $i,SV134: $i] :
( ( ! [SY1939: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV134 @ SV382 ) @ SV593 ) @ SY1939 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ SV593 ) @ SY1939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1577,plain,
! [SV594: $i,SV383: $i,SV135: $i] :
( ( ! [SY1940: $i,SY1941: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SY1940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SY1941 ) @ SY1940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SY1941 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1578,plain,
! [SV595: $i,SV384: $i,SV136: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV136 @ SV384 ) @ SV595 ) @ SV595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1579,plain,
! [SV596: $i,SV385: $i,SV137: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV137 @ SV385 ) @ SV596 ) @ SV596 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1580,plain,
! [SV386: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV138 ) ) @ ( c_Lambda_OdB_OAbs @ SV386 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV138 ) @ SV386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1581,plain,
! [SV597: $i,SV387: $i,SV139: $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 @ SV139 @ SV387 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV387 @ 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 @ SV139 ) ) @ SV387 ) @ SV597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1582,plain,
! [SV598: $i,SV388: $i,SV140: $i] :
( ( ! [SY1942: $i] :
( ~ ( class_Orderings_Opreorder @ SV140 )
| ( c_HOL_Oord__class_Oless @ SV388 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SY1942 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV388 @ SY1942 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1583,plain,
! [SV599: $i,SV389: $i,SV141: $i] :
( ( ! [SY1943: $i] :
( ~ ( class_Orderings_Oorder @ SV141 )
| ( c_HOL_Oord__class_Oless @ SV389 @ SV599 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV389 @ SY1943 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SY1943 @ SV599 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1584,plain,
! [SV600: $i,SV390: $i,SV145: $i] :
( ( ! [SY1944: $i] :
( ( c_Type_Otypings @ SV145 @ SV390 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV600 @ SV145 @ SY1944 @ SV390 ) )
| ~ ( c_Type_Otyping @ SV145 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1944 @ SV390 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1585,plain,
! [SV601: $i,SV391: $i,SV147: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV147 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV391 @ SV601 @ SV147 @ SV147 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV391 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV601 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1586,plain,
! [SV602: $i,SV392: $i,SV148: $i] :
( ( ! [SY1945: $i,SY1946: $i,SY1947: $i,SY1948: $i] :
( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SY1945 @ SV148 @ SV392 ) )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1946 ) @ SY1947 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1945 )
| ~ ( c_Type_Otypings @ SV148 @ SY1947 @ SY1948 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1946 ) @ SY1947 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1587,plain,
! [SV149: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV149 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1588,plain,
! [SV603: $i,SV393: $i,SV151: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV151 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV393 @ SV151 @ SV603 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV393 ) @ SV151 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1589,plain,
! [SV395: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV153 ) ) @ ( c_Lambda_OdB_OAbs @ SV395 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV153 ) @ SV395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1590,plain,
! [SV604: $i,SV396: $i,SV154: $i] :
( ( ! [SY1949: $i] :
( ( c_Type_Otyping @ SV154 @ SV396 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV604 @ SV154 @ SV396 @ SY1949 ) ) @ SV604 ) )
| ~ ( c_Type_Otyping @ SV154 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SY1949 ) @ SV604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1591,plain,
! [SV397: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV155 ) @ ( c_Lambda_OdB_OVar @ SV397 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1592,plain,
! [SV605: $i,SV398: $i,SV156: $i] :
( ( ! [SY1950: $i] :
( ( c_Type_Otyping @ SV156 @ SV398 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV605 @ SV156 @ SV398 @ SY1950 ) @ SV605 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV156 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV398 @ SY1950 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1593,plain,
! [SV606: $i,SV399: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV157 @ SV399 ) ) @ ( c_Lambda_Olift @ SV606 @ SV399 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV157 ) @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1594,plain,
! [SV400: $i,SV158: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV158 ) @ SV400 )
= ( c_Lambda_OdB_OVar @ SV158 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV158 @ SV400 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1595,plain,
! [SV607: $i,SV401: $i,SV159: $i] :
( ( ! [SY1951: $i] :
( ( c_Type_Otyping @ SV159 @ SV401 @ SV607 )
| ~ ( c_Type_Otyping @ SV159 @ SY1951 @ SV607 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1951 ) @ SV401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1596,plain,
! [SV608: $i,SV402: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV160 ) @ SV402 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SV402 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV160 ) @ SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1597,plain,
! [SV609: $i,SV403: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SV403 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SV609 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV403 ) @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1598,plain,
! [SV610: $i,SV404: $i,SV162: $i] :
( ( ! [SY1952: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV404 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SY1952 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV404 ) @ SY1952 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV162 ) @ SV610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1599,plain,
! [SV611: $i,SV405: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV163 ) @ SV405 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV611 ) @ SV405 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV163 ) @ SV611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1600,plain,
! [SV612: $i,SV406: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SV406 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SV612 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV406 ) @ SV612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1601,plain,
! [SV407: $i,SV165: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV165 @ SV165 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV165 ) @ SV407 @ SV165 )
= SV407 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1602,plain,
! [SV613: $i,SV408: $i,SV166: $i] :
( ( ! [SY1953: $i] :
( ( c_Type_Otyping @ SV166 @ SV408 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV613 @ SV166 @ SY1953 @ SV408 ) )
| ~ ( c_Type_Otyping @ SV166 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1953 ) @ SV408 ) @ SV613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1603,plain,
! [SV614: $i,SV409: $i,SV167: $i] :
( ( ( SV167
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV409 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV409 @ SV614 @ SV167 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV409 ) @ SV614 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1604,plain,
! [SV615: $i,SV410: $i,SV168: $i] :
( ( ! [SY1954: $i,SY1955: $i] :
( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV410 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1954 )
| ~ ( c_Type_Otypings @ SV168 @ SV615 @ SY1955 )
| ~ ( c_Type_Otyping @ SV168 @ SV410 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1955 @ SY1954 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1605,plain,
! [SV616: $i,SV411: $i,SV169: $i] :
( ( ! [SY1956: $i] :
( ( c_Type_Otyping @ SV169 @ ( c_Lambda_OdB_OVar @ SV411 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV616 @ SV169 @ SV411 @ SY1956 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV169 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV411 ) @ SY1956 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1606,plain,
! [SV617: $i,SV412: $i,SV170: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV170 ) @ SV412 @ SV617 )
= ( c_Lambda_OdB_OVar @ SV170 ) )
| ( SV170 = SV617 )
| ( c_HOL_Oord__class_Oless @ SV617 @ SV170 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1607,plain,
! [SV618: $i,SV413: $i,SV171: $i] :
( ( ! [SY1957: $i] :
( ( c_Type_Otyping @ SV171 @ SV413 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV618 @ SV171 @ SV413 @ SY1957 ) @ SV618 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV171 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV413 @ SY1957 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1608,plain,
! [SV619: $i,SV414: $i,SV172: $i] :
( ( ! [SY1958: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV172 @ SV414 @ SV619 ) ) @ ( c_Lambda_Osubst @ SV172 @ SY1958 @ SV619 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV414 ) @ SY1958 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1609,plain,
! [SV620: $i,SV415: $i,SV173: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SV415 ) @ SV620 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV173 @ SV620 ) ) @ ( c_Lambda_Olift @ SV415 @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1610,plain,
! [SV621: $i,SV416: $i,SV174: $i] :
( ( ! [SY1959: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV416 @ SV621 ) ) @ ( c_Lambda_Osubst @ SY1959 @ SV416 @ SV621 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV174 ) @ SY1959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1611,plain,
! [SV622: $i,SV417: $i,SV175: $i] :
( ( ! [SY1960: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV175 @ SV417 @ SV622 ) ) @ ( c_Lambda_Osubst @ SV175 @ SY1960 @ SV622 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV417 ) @ SY1960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1612,plain,
! [SV623: $i,SV418: $i,SV177: $i] :
( ( ! [SY1961: $i] :
( ( c_Type_Otyping @ SV177 @ ( c_Lambda_OdB_OAbs @ SV418 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV623 ) @ SY1961 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV623 @ tc_Type_Otype ) @ SV418 @ SY1961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1613,plain,
! [SV624: $i,SV419: $i,SV178: $i] :
( ( ! [SY1962: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV178 @ SV419 @ SV624 @ SY1962 ) @ SV419 )
= SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1614,plain,
! [SV420: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV179 @ SV420 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1615,plain,
! [SV625: $i,SV421: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV180 @ SV421 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV625 @ SV421 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV180 ) @ SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1616,plain,
! [SV626: $i,SV423: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV182 @ SV423 ) ) @ ( c_Lambda_Olift @ SV626 @ SV423 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV182 ) @ SV626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1617,plain,
! [SV627: $i,SV424: $i,SV183: $i] :
( ( ! [SY1963: $i,SY1964: $i] :
( ( SV183 = SV424 )
| ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1963 ) @ SY1964 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV424 )
| ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1963 ) @ SY1964 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1618,plain,
! [SV425: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV184 ) @ SV425 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV425 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1619,plain,
! [SV628: $i,SV426: $i,SV185: $i] :
( ( ! [SY1965: $i,SY1966: $i] :
( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV426 ) @ SV628 ) @ SY1965 )
| ~ ( c_Type_Otyping @ SV185 @ SV628 @ SY1966 )
| ~ ( c_Type_Otyping @ SV185 @ SV426 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1966 ) @ SY1965 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1620,plain,
! [SV427: $i,SV186: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV186 ) ) @ SV427 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1621,plain,
! [SV629: $i,SV428: $i,SV187: $i] :
( ( ! [SY1967: $i,SY1968: $i,SY1969: $i,SY1970: $i] :
( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SY1967 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1968 ) @ SY1969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
| ~ ( c_Type_Otypings @ SV629 @ SY1969 @ SY1970 )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1968 ) @ SY1969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1967 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1622,plain,
! [SV630: $i,SV429: $i,SV188: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV188 ) @ SV429 @ SV630 )
= ( c_Lambda_OdB_OVar @ SV188 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV188 @ SV630 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1623,plain,
! [SV631: $i,SV430: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV189 @ ( c_Lambda_OdB_OVar @ SV430 ) @ SV631 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1624,plain,
! [SV632: $i,SV431: $i,SV190: $i] :
( ( ! [SY1971: $i,SY1972: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV190 @ SV431 @ SV632 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1971 @ SV431 ) @ SY1972 )
| ~ ( c_Type_Otyping @ SV190 @ SY1971 @ SY1972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1625,plain,
! [SV633: $i,SV432: $i,SV191: $i] :
( ( ! [SY1973: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV191 ) @ SV432 ) @ SV633 @ SY1973 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV191 @ SV633 @ SY1973 ) ) @ ( c_Lambda_Osubst @ SV432 @ SV633 @ SY1973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1626,plain,
! [SV634: $i,SV433: $i,SV192: $i] :
( ( ! [SY1974: $i] :
( ( c_Type_Otyping @ SV192 @ SV433 @ SV634 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1974 ) @ SV433 ) )
| ~ ( c_Type_Otyping @ SV192 @ SY1974 @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1627,plain,
! [SV635: $i,SV435: $i,SV194: $i] :
( ( ( ( hAPP @ SV194 @ SV435 )
= SV635 )
| ~ ( c_Type_Otyping @ SV194 @ ( c_Lambda_OdB_OVar @ SV435 ) @ SV635 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1628,plain,
! [SV636: $i,SV436: $i,SV195: $i] :
( ( ! [SY1975: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV195 @ SV436 @ SV636 ) ) @ ( c_Lambda_Osubst @ SY1975 @ SV436 @ SV636 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SY1975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1629,plain,
! [SV637: $i,SV438: $i,SV197: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV197 @ SV438 ) @ SV637 @ SV438 )
= SV197 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1630,plain,
! [SV638: $i,SV439: $i,SV198: $i] :
( ( ! [SY1976: $i,SY1977: $i,SY1978: $i] :
( ~ ( c_Type_Otyping @ SV198 @ SV439 @ SV638 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SY1976 @ SV638 @ tc_Type_Otype ) @ SY1977 @ SY1978 )
| ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SY1977 @ SV439 @ SY1976 ) @ SY1978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1631,plain,
! [SV440: $i,SV199: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV199 @ SV440 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1632,plain,
! [SV441: $i,SV200: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV200 @ SV441 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1633,plain,
! [SV639: $i,SV443: $i,SV202: $i] :
( ( ( SV202 = SV443 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV639 ) @ SV202 ) @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1634,plain,
! [SV640: $i,SV444: $i,SV203: $i] :
( ( ! [SY1979: $i] :
( ( ( c_List_Oappend @ SV203 @ SV444 @ SV640 )
!= ( c_List_Oappend @ SY1979 @ SV444 @ SV640 ) )
| ( SV203 = SY1979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1635,plain,
! [SV641: $i,SV445: $i,SV204: $i] :
( ( ! [SY1980: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV204 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV445 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SY1980 ) @ SV641 ) )
| ( SV445 = SY1980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1636,plain,
! [SV642: $i,SV446: $i,SV205: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SV446 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV642 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SV446 )
= SV642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1637,plain,
! [SV643: $i,SV447: $i,SV206: $i] :
( ( ( ( c_List_Olist_ONil @ SV206 )
!= ( c_List_Oappend @ SV447 @ SV643 @ SV206 ) )
| ( SV447
= ( c_List_Olist_ONil @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1638,plain,
! [SV644: $i,SV448: $i,SV207: $i] :
( ( ! [SY1981: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV207 ) @ SV448 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV644 ) @ SY1981 ) )
| ( SV448 = SY1981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1639,plain,
! [SV449: $i,SV208: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV208 )
= ( c_Lambda_OdB_OVar @ SV449 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1640,plain,
! [SV645: $i,SV450: $i,SV209: $i] :
( ( ! [SY1982: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV209 ) @ SV450 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV645 ) @ SY1982 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV209 = SV645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1641,plain,
! [SV646: $i,SV451: $i,SV210: $i] :
( ( ( c_List_Olist_OCons @ SV210 @ SV451 @ SV646 )
!= SV451 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1642,plain,
! [SV452: $i,SV211: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV211 )
!= ( c_Lambda_OdB_OVar @ SV452 ) )
= $true )
| ( ( SV211 = SV452 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1643,plain,
! [SV647: $i,SV453: $i,SV212: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV212 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV453 @ SV647 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV647
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1644,plain,
! [SV648: $i,SV454: $i,SV213: $i] :
( ( ( SV213
!= ( c_List_Oappend @ SV454 @ SV213 @ SV648 ) )
| ( SV454
= ( c_List_Olist_ONil @ SV648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1645,plain,
! [SV649: $i,SV455: $i,SV214: $i] :
( ( ( ( c_List_Oappend @ SV214 @ SV455 @ SV649 )
!= ( c_List_Olist_ONil @ SV649 ) )
| ( SV455
= ( c_List_Olist_ONil @ SV649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1646,plain,
! [SV650: $i,SV456: $i,SV215: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV215 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV456 @ SV650 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV215 )
= SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1647,plain,
! [SV457: $i,SV216: $i] :
( ( ( c_Lambda_OdB_OVar @ SV216 )
= ( c_Lambda_OdB_OAbs @ SV457 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1648,plain,
! [SV651: $i,SV458: $i,SV217: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV217 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV651 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1649,plain,
! [SV652: $i,SV459: $i,SV218: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV459 )
!= ( c_Lambda_OdB_OVar @ SV652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1650,plain,
! [SV653: $i,SV460: $i,SV219: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV219 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV460 @ SV653 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV219 )
= SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1651,plain,
! [SV654: $i,SV461: $i,SV220: $i] :
( ( ! [SY1983: $i,SY1984: $i] :
( ( ( c_List_Oappend @ SV220 @ ( c_List_Olist_OCons @ SV461 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 )
!= ( c_List_Oappend @ SY1983 @ ( c_List_Olist_OCons @ SY1984 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 ) )
| ( SV461 = SY1984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1652,plain,
! [SV655: $i,SV462: $i,SV221: $i] :
( ( ( c_Lambda_OdB_OVar @ SV221 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV462 ) @ SV655 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1653,plain,
! [SV656: $i,SV463: $i,SV222: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV222 @ SV463 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV656 @ SV463 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV222 = SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1654,plain,
! [SV657: $i,SV464: $i,SV223: $i] :
( ( ! [SY1985: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV223 ) @ SV464 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV657 ) @ SY1985 ) )
| ( SV223 = SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1655,plain,
! [SV658: $i,SV465: $i,SV224: $i] :
( ( ! [SY1986: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ SV465 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV658 ) @ SY1986 ) )
| ( SV224 = SV658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1656,plain,
! [SV659: $i,SV466: $i,SV225: $i] :
( ( ! [SY1987: $i,SY1988: $i] :
( ( ( c_List_Oappend @ SV225 @ ( c_List_Olist_OCons @ SV466 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 )
!= ( c_List_Oappend @ SY1987 @ ( c_List_Olist_OCons @ SY1988 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 ) )
| ( SV225 = SY1987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1657,plain,
! [SV660: $i,SV467: $i,SV226: $i] :
( ( ! [SY1989: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV226 ) ) @ SV467 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV660 ) @ SY1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1658,plain,
! [SV468: $i,SV227: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV227 )
!= ( c_Lambda_OdB_OAbs @ SV468 ) )
= $true )
| ( ( SV227 = SV468 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1659,plain,
! [SV661: $i,SV469: $i,SV228: $i] :
( ( ( c_List_Olist_OCons @ SV228 @ SV469 @ SV661 )
!= ( c_List_Olist_ONil @ SV661 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1660,plain,
! [SV662: $i,SV470: $i,SV229: $i] :
( ( ! [SY1990: $i,SY1991: $i] :
( ( ( c_List_Olist_OCons @ SV229 @ SV470 @ SV662 )
!= ( c_List_Olist_OCons @ SY1990 @ SY1991 @ SV662 ) )
| ( SV470 = SY1991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1661,plain,
! [SV663: $i,SV471: $i,SV230: $i] :
( ( ( SV230
!= ( c_List_Oappend @ SV230 @ SV471 @ SV663 ) )
| ( SV471
= ( c_List_Olist_ONil @ SV663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1662,plain,
! [SV664: $i,SV472: $i,SV231: $i] :
( ( ( ( c_List_Oappend @ SV231 @ SV472 @ SV664 )
!= SV472 )
| ( SV231
= ( c_List_Olist_ONil @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1663,plain,
! [SV665: $i,SV473: $i,SV232: $i] :
( ( ( ( c_List_Oappend @ SV232 @ SV473 @ SV665 )
!= ( c_List_Olist_ONil @ SV665 ) )
| ( SV232
= ( c_List_Olist_ONil @ SV665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1664,plain,
! [SV666: $i,SV474: $i,SV233: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SV474 )
!= ( c_Lambda_OdB_OAbs @ SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1665,plain,
! [SV667: $i,SV475: $i,SV234: $i] :
( ( ! [SY1992: $i,SY1993: $i] :
( ( ( c_List_Olist_OCons @ SV234 @ SV475 @ SV667 )
!= ( c_List_Olist_OCons @ SY1992 @ SY1993 @ SV667 ) )
| ( SV234 = SY1992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1666,plain,
! [SV668: $i,SV476: $i,SV235: $i] :
( ( ! [SY1994: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV476 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV668 ) @ SY1994 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV235 = SV668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1667,plain,
! [SV669: $i,SV477: $i,SV236: $i] :
( ( ! [SY1995: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV477 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV669 ) @ SY1995 ) )
| ( SV477 = SY1995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1668,plain,
! [SV670: $i,SV478: $i,SV237: $i] :
( ( ! [SY1996: $i,SY1997: $i,SY1998: $i,SY1999: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SY1996 @ SY1997 ) ) )
| ~ ( c_Type_Otyping @ SY1998 @ SY1996 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1996 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1998 @ SY1997 @ SV478 @ tc_Type_Otype ) @ SV670 @ SY1999 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1669,plain,
! [SV671: $i,SV479: $i,SV238: $i] :
( ( ! [SY2000: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV671 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SY2000 ) )
| ( SV671 = SY2000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1670,plain,
! [SV672: $i,SV480: $i,SV239: $i] :
( ( ! [SY2001: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV239 )
| ~ ( class_Int_Onumber__ring @ SV239 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV672 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SY2001 ) )
| ( SV672 = SY2001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1671,plain,
! [SV673: $i,SV481: $i,SV240: $i] :
( ( ( SV240
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 ) @ SV673 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 ) @ ( c_List_Oappend @ SV673 @ ( c_List_Olist_OCons @ SV481 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1672,plain,
! [SV674: $i,SV482: $i,SV241: $i] :
( ( ! [SY2002: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV482 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV674 ) @ SY2002 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV482 = SY2002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1673,plain,
! [SV675: $i,SV483: $i,SV242: $i] :
( ( ( c_List_Olist_ONil @ SV242 )
!= ( c_List_Olist_OCons @ SV483 @ SV675 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1674,plain,
! [SV676: $i,SV484: $i,SV243: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV243 )
| ~ ( class_Int_Onumber__ring @ SV243 )
| ( SV484
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SV484 ) @ SV676 ) )
| ( SV676
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1675,plain,
! [SV677: $i,SV485: $i,SV244: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV244 @ SV485 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV677 ) )
| ( SV485
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1676,plain,
! [SV678: $i,SV486: $i,SV245: $i] :
( ( ! [SY2003: $i,SY2004: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV245 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SY2003 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SY2004 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ SY2003 )
= SY2004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1677,plain,
! [SV679: $i,SV487: $i,SV246: $i] :
( ( ! [SY2005: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV246 ) @ SV487 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV679 ) @ SY2005 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1678,plain,
! [SV680: $i,SV488: $i,SV247: $i] :
( ( ! [SY2006: $i,SY2007: $i,SY2008: $i,SY2009: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SY2006 @ SY2007 ) ) )
| ~ ( c_Type_Otyping @ SY2008 @ SY2006 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2006 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2008 @ SY2007 @ SV247 @ tc_Type_Otype ) @ SV680 @ SY2009 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1679,plain,
! [SV681: $i,SV489: $i,SV248: $i] :
( ( ( ( c_List_Olist_ONil @ SV248 )
!= ( c_List_Oappend @ SV489 @ SV681 @ SV248 ) )
| ( SV681
= ( c_List_Olist_ONil @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1680,plain,
! [SV682: $i,SV490: $i,SV249: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV249 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV490 @ SV249 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV682 @ SV249 ) )
| ( SV490 = SV682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1681,plain,
! [SV683: $i,SV491: $i,SV250: $i] :
( ( ( ( c_List_Oappend @ SV250 @ SV491 @ SV683 )
!= SV250 )
| ( SV491
= ( c_List_Olist_ONil @ SV683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1682,plain,
! [SV684: $i,SV492: $i,SV251: $i] :
( ( ! [SY2010: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV251 ) @ SV492 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV684 ) @ SY2010 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV492 = SY2010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1683,plain,
! [SV685: $i,SV493: $i,SV252: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV493 @ SV685 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV685
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1684,plain,
! [SV686: $i,SV494: $i,SV253: $i] :
( ( ( c_List_Olist_OCons @ SV253 @ SV494 @ SV686 )
!= ( c_List_Olist_ONil @ SV686 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1685,plain,
! [SV687: $i,SV495: $i,SV254: $i] :
( ( SV254
!= ( c_List_Olist_OCons @ SV495 @ SV254 @ SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1686,plain,
! [SV688: $i,SV496: $i,SV255: $i] :
( ( ! [SY2011: $i] :
( ( ( c_List_Oappend @ SV255 @ SV496 @ SV688 )
!= ( c_List_Oappend @ SV255 @ SY2011 @ SV688 ) )
| ( SV496 = SY2011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1687,plain,
! [SV497: $i,SV256: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV256 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV256 ) @ SV497 ) @ SV497 )
!= ( c_HOL_Ozero__class_Ozero @ SV256 ) )
| ( SV497
= ( c_HOL_Ozero__class_Ozero @ SV256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1688,plain,
! [SV689: $i,SV498: $i,SV257: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV257 @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV689 ) )
| ( SV257
= ( c_Lambda_OdB_OAbs @ SV689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1689,plain,
! [SV690: $i,SV499: $i,SV258: $i] :
( ( ! [SY2012: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV258 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV690 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SY2012 ) )
| ( SV690 = SY2012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1690,plain,
! [SV691: $i,SV500: $i,SV259: $i,SV1: $i] :
( ( ( c_List_Oappend @ SV1 @ ( c_List_Oappend @ SV259 @ SV500 @ SV691 ) @ SV691 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV1 @ SV259 @ SV691 ) @ SV500 @ SV691 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1691,plain,
! [SV692: $i,SV501: $i,SV260: $i,SV2: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV2 @ SV260 @ SV501 ) @ SV692 @ SV501 )
= ( c_List_Oappend @ SV2 @ ( c_List_Oappend @ SV260 @ SV692 @ SV501 ) @ SV501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1692,plain,
! [SV693: $i,SV502: $i,SV261: $i,SV3: $i] :
( ( ( c_List_Oappend @ SV3 @ ( c_List_Oappend @ SV261 @ SV502 @ SV693 ) @ SV693 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV3 @ SV261 @ SV693 ) @ SV502 @ SV693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1693,plain,
! [SV694: $i,SV503: $i,SV262: $i,SV4: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV4 @ SV262 @ SV503 ) @ SV694 @ SV503 )
= ( c_List_Oappend @ SV4 @ ( c_List_Oappend @ SV262 @ SV694 @ SV503 ) @ SV503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1694,plain,
! [SV695: $i,SV505: $i,SV264: $i,SV7: $i] :
( ( ( c_List_Olistsp @ SV7 @ ( c_List_Oappend @ SV264 @ SV505 @ SV695 ) @ SV695 )
| ~ ( c_List_Olistsp @ SV7 @ SV505 @ SV695 )
| ~ ( c_List_Olistsp @ SV7 @ SV264 @ SV695 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1695,plain,
! [SV696: $i,SV506: $i,SV265: $i,SV8: $i] :
( ( ! [SY2013: $i,SY2014: $i] :
( ( SV8 = SV265 )
| ( SV506 = SV696 )
| ~ ( c_ListOrder_Ostep1 @ SY2013 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SY2014 ) @ SY2014 ) @ SY2014 ) @ ( c_List_Oappend @ SV265 @ ( c_List_Olist_OCons @ SV696 @ ( c_List_Olist_ONil @ SY2014 ) @ SY2014 ) @ SY2014 ) @ SY2014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1696,plain,
! [SV697: $i,SV507: $i,SV266: $i,SV9: $i] :
( ( ! [SY2015: $i,SY2016: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SV266 ) @ SV507 ) )
| ( SV266 = SV507 )
| ~ ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SV697 @ ( c_List_Olist_OCons @ SV266 @ ( c_List_Olist_ONil @ SY2015 ) @ SY2015 ) @ SY2015 ) @ ( c_List_Oappend @ SY2016 @ ( c_List_Olist_OCons @ SV507 @ ( c_List_Olist_ONil @ SY2015 ) @ SY2015 ) @ SY2015 ) @ SY2015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1697,plain,
! [SV698: $i,SV508: $i,SV267: $i,SV10: $i] :
( ( ! [SY2017: $i,SY2018: $i] :
( ( c_List_Ofoldr @ SV10 @ ( c_List_Oappend @ SV267 @ SV508 @ SV698 ) @ SY2017 @ SV698 @ SY2018 )
= ( c_List_Ofoldr @ SV10 @ SV267 @ ( c_List_Ofoldr @ SV10 @ SV508 @ SY2017 @ SV698 @ SY2018 ) @ SV698 @ SY2018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1698,plain,
! [SV699: $i,SV509: $i,SV273: $i,SV16: $i] :
( ( ( c_List_Olistsp @ SV16 @ SV273 @ SV509 )
| ~ ( c_List_Olistsp @ SV16 @ ( c_List_Oappend @ SV699 @ SV273 @ SV509 ) @ SV509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1699,plain,
! [SV700: $i,SV510: $i,SV274: $i,SV17: $i] :
( ( ( c_List_Olistsp @ SV17 @ SV274 @ SV510 )
| ~ ( c_List_Olistsp @ SV17 @ ( c_List_Oappend @ SV274 @ SV700 @ SV510 ) @ SV510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1700,plain,
! [SV701: $i,SV511: $i,SV275: $i,SV18: $i] :
( ( ! [SY2019: $i] :
( ( c_ListOrder_Ostep1 @ SV18 @ ( c_List_Oappend @ SV275 @ SV511 @ SV701 ) @ ( c_List_Oappend @ SV275 @ SY2019 @ SV701 ) @ SV701 )
| ~ ( c_ListOrder_Ostep1 @ SV18 @ SV511 @ SY2019 @ SV701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1701,plain,
! [SV702: $i,SV512: $i,SV276: $i,SV19: $i] :
( ( ! [SY2020: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV19 @ SV276 @ SV512 @ SV702 )
| ( c_ListOrder_Ostep1 @ SV19 @ ( c_List_Oappend @ SV276 @ SY2020 @ SV702 ) @ ( c_List_Oappend @ SV512 @ SY2020 @ SV702 ) @ SV702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1702,plain,
! [SV703: $i,SV513: $i,SV277: $i,SV20: $i] :
( ( ! [SY2021: $i,SY2022: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV277 ) @ SV513 ) )
| ( c_ListOrder_Ostep1 @ SV20 @ SV703 @ SY2021 @ SY2022 )
| ~ ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SV703 @ ( c_List_Olist_OCons @ SV277 @ ( c_List_Olist_ONil @ SY2022 ) @ SY2022 ) @ SY2022 ) @ ( c_List_Oappend @ SY2021 @ ( c_List_Olist_OCons @ SV513 @ ( c_List_Olist_ONil @ SY2022 ) @ SY2022 ) @ SY2022 ) @ SY2022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1703,plain,
! [SV704: $i,SV514: $i,SV278: $i,SV21: $i] :
( ( ( c_Type_Otyping @ SV21 @ SV278 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV514 @ SV21 @ SV278 @ SV704 ) )
| ~ ( c_Type_Otypings @ SV21 @ ( c_List_Oappend @ SV704 @ ( c_List_Olist_OCons @ SV278 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1704,plain,
! [SV705: $i,SV515: $i,SV279: $i,SV22: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV22 @ SV279 @ SV515 ) @ SV705 @ SV515 )
= ( c_List_Olist_OCons @ SV22 @ ( c_List_Oappend @ SV279 @ SV705 @ SV515 ) @ SV515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1705,plain,
! [SV706: $i,SV516: $i,SV280: $i,SV23: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV23 @ SV280 @ SV516 ) @ SV706 @ SV516 )
= ( c_List_Olist_OCons @ SV23 @ ( c_List_Oappend @ SV280 @ SV706 @ SV516 ) @ SV516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1706,plain,
! [SV707: $i,SV517: $i,SV281: $i,SV24: $i] :
( ( ( c_List_Olist_OCons @ SV24 @ ( c_List_Oappend @ SV281 @ SV517 @ SV707 ) @ SV707 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV24 @ SV281 @ SV707 ) @ SV517 @ SV707 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1707,plain,
! [SV708: $i,SV518: $i,SV282: $i,SV25: $i] :
( ( ( c_List_Olist_OCons @ SV25 @ ( c_List_Oappend @ SV282 @ SV518 @ SV708 ) @ SV708 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV25 @ SV282 @ SV708 ) @ SV518 @ SV708 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1708,plain,
! [SV709: $i,SV520: $i,SV284: $i,SV27: $i] :
( ( ! [SY2023: $i,SY2024: $i] :
( ( SV27 = SV284 )
| ( c_ListOrder_Ostep1 @ SV520 @ SV27 @ SV284 @ SV709 )
| ~ ( c_ListOrder_Ostep1 @ SV520 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SY2023 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ ( c_List_Oappend @ SV284 @ ( c_List_Olist_OCons @ SY2024 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ SV709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1709,plain,
! [SV710: $i,SV521: $i,SV285: $i,SV29: $i] :
( ( ! [SY2025: $i,SY2026: $i] :
( ( c_List_Ofoldl @ SV29 @ SV285 @ ( c_List_Oappend @ SV521 @ SV710 @ SY2025 ) @ SY2026 @ SY2025 )
= ( c_List_Ofoldl @ SV29 @ ( c_List_Ofoldl @ SV29 @ SV285 @ SV521 @ SY2026 @ SY2025 ) @ SV710 @ SY2026 @ SY2025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1710,plain,
! [SV286: $i,SV30: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV30 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV286 ) @ SV286 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV286 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1711,plain,
! [SV287: $i,SV31: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV31 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV287 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV287 ) @ SV287 ) @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1712,plain,
! [SV288: $i,SV32: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV32 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV32 ) @ ( c_HOL_Ozero__class_Ozero @ SV32 ) ) @ SV288 )
= SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1713,plain,
! [SV289: $i,SV33: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV33 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV33 ) @ SV289 ) @ ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1714,plain,
! [SV290: $i,SV34: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV34 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV290 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) )
= SV290 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1715,plain,
! [SV291: $i,SV35: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV35 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) ) @ SV291 )
= SV291 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1716,plain,
! [SV292: $i,SV36: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV36 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV36 ) @ SV292 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) )
= SV292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1717,plain,
! [SV293: $i,SV37: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV37 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV37 )
| ( SV293
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV293 ) @ ( c_HOL_Ozero__class_Ozero @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1718,plain,
! [SV294: $i,SV38: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV38 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) ) @ SV294 )
= SV294 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1719,plain,
! [SV295: $i,SV39: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV39 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV39 ) @ ( c_HOL_Ozero__class_Ozero @ SV39 ) ) @ SV295 )
= SV295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1720,plain,
! [SV296: $i,SV40: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV40 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV296 @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1721,plain,
! [SV711: $i,SV522: $i,SV297: $i,SV41: $i] :
( ( ! [SY2027: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV522 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV711 ) @ SY2027 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV711 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV522 ) @ SY2027 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1722,plain,
! [SV712: $i,SV523: $i,SV298: $i,SV42: $i] :
( ( ! [SY2028: $i,SY2029: $i] :
( ( SV42 = SV298 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV298 ) @ SV42 ) )
| ~ ( c_ListOrder_Ostep1 @ SV523 @ ( c_List_Olist_OCons @ SV298 @ SV712 @ SY2028 ) @ ( c_List_Olist_OCons @ SV42 @ SY2029 @ SY2028 ) @ SY2028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1723,plain,
! [SV524: $i,SV299: $i,SV43: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV299 ) @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV524 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV299 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1724,plain,
! [SV713: $i,SV525: $i,SV300: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV45 @ SV300 @ SV300 ) @ SV300 ) @ SV525 ) @ SV713 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV300 ) @ SV713 ) @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1725,plain,
! [SV714: $i,SV526: $i,SV301: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SV301 ) @ SV526 ) @ SV714 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV46 @ SV301 @ SV301 ) @ SV301 ) @ SV714 ) @ SV526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1726,plain,
! [SV715: $i,SV527: $i,SV302: $i,SV47: $i] :
( ( ! [SY2030: $i,SY2031: $i] :
( ( c_List_Ofoldl @ SV47 @ SV302 @ ( c_List_Olist_OCons @ SV527 @ SV715 @ SY2030 ) @ SY2031 @ SY2030 )
= ( c_List_Ofoldl @ SV47 @ ( hAPP @ ( hAPP @ SV47 @ SV302 ) @ SV527 ) @ SV715 @ SY2031 @ SY2030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1727,plain,
! [SV716: $i,SV528: $i,SV303: $i,SV48: $i] :
( ( ( c_List_Ofoldr @ SV48 @ ( c_List_Olist_ONil @ SV303 ) @ SV528 @ SV303 @ SV716 )
= SV528 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1728,plain,
! [SV717: $i,SV529: $i,SV304: $i,SV49: $i] :
( ( ! [SY2032: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV49 @ SV304 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV49 @ SV717 @ SY2032 ) @ SV529 ) @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1729,plain,
! [SV718: $i,SV530: $i,SV305: $i,SV50: $i] :
( ( ! [SY2033: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV50 @ SV305 @ SV530 ) @ SV718 ) @ SY2033 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY2033 ) @ SV718 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1730,plain,
! [SV719: $i,SV531: $i,SV306: $i,SV51: $i] :
( ( ! [SY2034: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV306 ) @ SV531 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV51 @ SV719 @ SY2034 ) @ SV531 ) @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1731,plain,
! [SV720: $i,SV532: $i,SV307: $i,SV52: $i] :
( ( ! [SY2035: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV52 @ SV307 @ SV532 ) @ SV720 ) @ SY2035 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SY2035 ) @ SV720 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1732,plain,
! [SV721: $i,SV533: $i,SV308: $i,SV53: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV53 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ SV533 ) ) @ SV721 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV533 ) @ SV721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1733,plain,
! [SV722: $i,SV534: $i,SV309: $i,SV54: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV54 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV534 ) @ SV722 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV534 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ SV722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1734,plain,
! [SV723: $i,SV535: $i,SV310: $i,SV55: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SV535 ) ) @ SV723 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SV723 ) ) @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1735,plain,
! [SV724: $i,SV536: $i,SV311: $i,SV56: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV536 ) @ SV724 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SV536 ) ) @ SV724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1736,plain,
! [SV725: $i,SV537: $i,SV312: $i,SV57: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV57 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SV537 ) ) @ SV725 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV537 ) @ SV725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1737,plain,
! [SV726: $i,SV538: $i,SV313: $i,SV58: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV58 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV538 ) @ SV726 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ SV726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1738,plain,
! [SV727: $i,SV539: $i,SV314: $i,SV59: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SV539 ) ) @ SV727 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV539 ) @ SV727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1739,plain,
! [SV728: $i,SV540: $i,SV315: $i,SV60: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV60 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV540 ) @ SV728 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SV728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1740,plain,
! [SV729: $i,SV541: $i,SV316: $i,SV61: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV61 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV541 ) @ SV729 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ SV541 ) ) @ SV729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1741,plain,
! [SV730: $i,SV542: $i,SV317: $i,SV63: $i] :
( ( ! [SY2036: $i,SY2037: $i] :
( ( SV63 = SV317 )
| ( SV542 = SV730 )
| ~ ( c_ListOrder_Ostep1 @ SY2036 @ ( c_List_Olist_OCons @ SV317 @ SV730 @ SY2037 ) @ ( c_List_Olist_OCons @ SV63 @ SV542 @ SY2037 ) @ SY2037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1742,plain,
! [SV731: $i,SV543: $i,SV318: $i,SV64: $i] :
( ( ! [SY2038: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV64 @ SV318 ) @ SV543 ) )
| ( c_ListOrder_Ostep1 @ SV64 @ ( c_List_Olist_OCons @ SV318 @ SV731 @ SY2038 ) @ ( c_List_Olist_OCons @ SV543 @ SV731 @ SY2038 ) @ SY2038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1743,plain,
! [SV732: $i,SV544: $i,SV320: $i,SV66: $i] :
( ( ( c_Wellfounded_Oaccp @ SV66 @ SV320 @ SV544 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV544 ) @ SV320 ) @ SV732 ) )
| ~ ( c_Wellfounded_Oaccp @ SV66 @ SV732 @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1744,plain,
! [SV733: $i,SV545: $i,SV321: $i,SV67: $i] :
( ( ( c_Wellfounded_Oaccp @ SV67 @ SV321 @ SV545 )
| ~ ( c_Wellfounded_Oaccp @ SV67 @ SV733 @ SV545 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV545 ) @ SV321 ) @ SV733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1745,plain,
! [SV546: $i,SV322: $i,SV70: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV322 ) @ SV546 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV546 ) @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1746,plain,
! [SV547: $i,SV323: $i,SV71: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV71 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV323 ) @ SV547 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV547 ) @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1747,plain,
! [SV548: $i,SV324: $i,SV72: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV548 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV548 ) @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1748,plain,
! [SV734: $i,SV549: $i,SV325: $i,SV73: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV73 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV549 ) @ SV734 @ SV73 @ SV73 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV549 @ SV734 @ SV73 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1749,plain,
! [SV550: $i,SV326: $i,SV74: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV74 ) )
= $true )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 @ SV550 @ SV74 @ SV74 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV550 @ SV326 @ SV74 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1750,plain,
! [SV551: $i,SV327: $i,SV75: $i] :
( ( c_ListOrder_Ostep1 @ SV75 @ ( c_List_Olist_ONil @ SV327 ) @ SV551 @ SV327 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1751,plain,
! [SV552: $i,SV328: $i,SV76: $i] :
( ( c_ListOrder_Ostep1 @ SV76 @ SV328 @ ( c_List_Olist_ONil @ SV552 ) @ SV552 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1752,plain,
! [SV329: $i,SV77: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV77 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV329 @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1753,plain,
! [SV330: $i,SV78: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV78 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV330 @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ SV330 ) @ SV330 ) @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1754,plain,
! [SV331: $i,SV79: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV79 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV331 @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV79 ) @ SV331 ) @ SV331 ) @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1755,plain,
! [SV332: $i,SV80: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV80 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV332 ) @ SV332 ) @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ SV332 @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1756,plain,
! [SV553: $i,SV333: $i,SV81: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV81 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SV333 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ ( c_HOL_Ozero__class_Ozero @ SV81 ) @ SV553 @ SV81 @ SV81 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SV333 @ SV553 @ SV81 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1757,plain,
! [SV735: $i,SV554: $i,SV334: $i,SV82: $i] :
( ( ( c_List_Ofoldl @ SV82 @ SV334 @ ( c_List_Olist_ONil @ SV554 ) @ SV735 @ SV554 )
= SV334 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1758,plain,
! [SV555: $i,SV335: $i,SV84: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV335 ) @ SV555 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV555 @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV335 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1759,plain,
! [SV736: $i,SV556: $i,SV336: $i,SV85: $i] :
( ( ! [SY2039: $i,SY2040: $i] :
( ( c_ListOrder_Ostep1 @ SV85 @ SV336 @ SV556 @ SV736 )
| ( SV556 = SV336 )
| ~ ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SY2039 @ SV336 @ SV736 ) @ ( c_List_Olist_OCons @ SY2040 @ SV556 @ SV736 ) @ SV736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1760,plain,
! [SV737: $i,SV557: $i,SV337: $i,SV86: $i] :
( ( ! [SY2041: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV737 ) @ SY2041 ) @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SY2041 @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV337 @ SV737 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1761,plain,
! [SV558: $i,SV338: $i,SV87: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV87 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV338 @ SV87 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV558 @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV338 @ SV558 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1762,plain,
! [SV559: $i,SV339: $i,SV88: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV88 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV339 @ SV559 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV339 @ SV88 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV559 @ SV88 ) @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1763,plain,
! [SV738: $i,SV560: $i,SV340: $i,SV89: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV560 ) @ SV738 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ SV738 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV560 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1764,plain,
! [SV739: $i,SV561: $i,SV341: $i,SV90: $i] :
( ( ! [SY2042: $i,SY2043: $i] :
( ( c_List_Ofoldr @ SV90 @ ( c_List_Olist_OCons @ SV341 @ SV561 @ SV739 ) @ SY2042 @ SV739 @ SY2043 )
= ( hAPP @ ( hAPP @ SV90 @ SV341 ) @ ( c_List_Ofoldr @ SV90 @ SV561 @ SY2042 @ SV739 @ SY2043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1765,plain,
! [SV740: $i,SV563: $i,SV343: $i,SV92: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV92 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV343 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV740 ) @ SV563 ) @ SV92 )
| ~ ( c_HOL_Oord__class_Oless @ SV343 @ SV740 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1766,plain,
! [SV741: $i,SV564: $i,SV344: $i,SV93: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV344 ) @ SV564 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV741 ) @ SV564 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV344 @ SV741 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1767,plain,
! [SV742: $i,SV565: $i,SV345: $i,SV94: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
| ( c_HOL_Oord__class_Oless @ SV345 @ SV565 @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV345 ) @ SV742 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV565 ) @ SV742 ) @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1768,plain,
! [SV743: $i,SV566: $i,SV346: $i,SV95: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV743 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV566 @ SV743 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1769,plain,
! [SV744: $i,SV567: $i,SV347: $i,SV96: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV567 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV744 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ SV744 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1770,plain,
! [SV745: $i,SV568: $i,SV348: $i,SV97: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
| ( c_HOL_Oord__class_Oless @ SV348 @ SV568 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV348 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV568 ) @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1771,plain,
! [SV746: $i,SV569: $i,SV349: $i,SV98: $i] :
( ( ! [SY2044: $i,SY2045: $i] :
( ( c_ListOrder_Ostep1 @ SV98 @ SV349 @ SV569 @ SV746 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SY2044 ) @ SY2045 ) )
| ~ ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SY2044 @ SV349 @ SV746 ) @ ( c_List_Olist_OCons @ SY2045 @ SV569 @ SV746 ) @ SV746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1772,plain,
! [SV747: $i,SV570: $i,SV350: $i,SV99: $i] :
( ( ! [SY2046: $i] :
( ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_OCons @ SV350 @ SV570 @ SV747 ) @ ( c_List_Olist_OCons @ SV350 @ SY2046 @ SV747 ) @ SV747 )
| ~ ( c_ListOrder_Ostep1 @ SV99 @ SV570 @ SY2046 @ SV747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1773,plain,
! [SV572: $i,SV353: $i,SV102: $i] :
( ( ( ( c_List_Oappend @ SV102 @ ( c_List_Olist_OCons @ SV353 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV572 @ SV102 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV353 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV572 @ ( c_List_Oappend @ SV102 @ ( c_List_Olist_OCons @ SV353 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1774,plain,
! [SV748: $i,SV573: $i,SV354: $i,SV103: $i] :
( ( ( c_Wellfounded_Oaccp @ SV103 @ SV354 @ SV573 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ SV354 ) @ SV748 ) )
| ~ ( c_Wellfounded_Oaccp @ SV103 @ SV748 @ SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1775,plain,
! [SV749: $i,SV574: $i,SV355: $i,SV104: $i] :
( ( ( c_Wellfounded_Oaccp @ SV104 @ SV355 @ SV574 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV355 ) @ SV749 ) )
| ~ ( c_Wellfounded_Oaccp @ SV104 @ SV749 @ SV574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1776,plain,
! [SV575: $i,SV356: $i,SV105: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV105 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV575 @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV356 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1777,plain,
! [SV576: $i,SV357: $i,SV106: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV106 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV357 @ SV576 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV357 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1778,plain,
! [SV577: $i,SV358: $i,SV107: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV107 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV358 @ SV577 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV358 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1552]) ).
thf(1779,plain,
! [SV750: $i,SV578: $i,SV359: $i,SV108: $i] :
( ( ! [SY2047: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV750 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SY2047 ) @ SV750 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SY2047 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1780,plain,
! [SV751: $i,SV579: $i,SV360: $i,SV109: $i] :
( ( ! [SY2048: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV579 ) @ SV751 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SY2048 ) @ SV751 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SV579 ) @ SY2048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1781,plain,
! [SV580: $i,SV361: $i,SV110: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV110 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV361 @ SV580 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV580 @ SV361 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1782,plain,
! [SV752: $i,SV581: $i,SV362: $i,SV111: $i] :
( ( ( c_Type_Otypings @ SV111 @ SV362 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV581 @ SV111 @ SV752 @ SV362 ) )
| ~ ( c_Type_Otyping @ SV111 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV752 ) @ SV362 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1783,plain,
! [SV753: $i,SV582: $i,SV363: $i,SV112: $i] :
( ( ( c_Type_Otypings @ SV112 @ SV363 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV582 @ SV112 @ SV753 @ SV363 ) )
| ~ ( c_Type_Otyping @ SV112 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV753 @ SV363 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1784,plain,
! [SV754: $i,SV583: $i,SV364: $i,SV113: $i] :
( ( ! [SY2049: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV113 @ SV364 @ SV583 @ SV754 ) @ SY2049 )
= ( hAPP @ SV113 @ SY2049 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2049 @ SV364 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1785,plain,
! [SV584: $i,SV365: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV115 @ SV365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV584 @ SV365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV115 ) @ SV584 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1786,plain,
! [SV366: $i,SV116: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV116 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV366 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV366 @ SV116 ) @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1787,plain,
! [SV367: $i,SV117: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV117 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV367 @ SV117 ) @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV367 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1788,plain,
! [SV368: $i,SV118: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV118 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV368 @ SV118 @ SV118 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV368 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1789,plain,
! [SV585: $i,SV369: $i,SV119: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV119 ) )
= $true )
| ( ( ( SV369 = SV585 )
| ( c_HOL_Oord__class_Oless @ SV369 @ SV585 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV585 @ SV369 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1790,plain,
! [SV586: $i,SV370: $i,SV120: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV120 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV370 @ SV586 @ SV120 )
| ( SV586 = SV370 )
| ( c_HOL_Oord__class_Oless @ SV586 @ SV370 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1791,plain,
! [SV587: $i,SV371: $i,SV121: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV121 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV371 @ SV587 @ SV121 )
| ( c_HOL_Oord__class_Oless @ SV587 @ SV371 @ SV121 )
| ( SV587 = SV371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1792,plain,
! [SV122: $i,SV372: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV372 @ SV122 @ tc_nat )
= $true )
| ( ( SV372 = SV122 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV122 @ SV372 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1793,plain,
! [SV588: $i,SV373: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV373 ) @ SV588 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV373 @ SV588 @ tc_nat )
| ( SV588 = SV373 )
| ( c_HOL_Oord__class_Oless @ SV588 @ SV373 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1794,plain,
! [SV124: $i,SV374: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV374 @ SV124 @ tc_nat )
= $true )
| ( ( SV374 = SV124 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV124 @ SV374 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1795,plain,
! [SV589: $i,SV375: $i,SV125: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV125 ) )
= $true )
| ( ( ( SV375 = SV589 )
| ( c_HOL_Oord__class_Oless @ SV589 @ SV375 @ SV125 )
| ( c_HOL_Oord__class_Oless @ SV375 @ SV589 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1796,plain,
! [SV590: $i,SV376: $i,SV126: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV126 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV376 @ SV590 @ SV126 )
| ( c_HOL_Oord__class_Oless @ SV590 @ SV376 @ SV126 )
| ( SV590 = SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1797,plain,
! [SV591: $i,SV377: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SV377 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SV591 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV377 @ SV591 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1798,plain,
! [SV378: $i,SV128: $i] :
( ( ( class_Orderings_Opreorder @ SV128 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV378 @ SV378 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1799,plain,
! [SV379: $i,SV129: $i] :
( ( ( class_Orderings_Olinorder @ SV129 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV379 @ SV379 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1800,plain,
! [SV380: $i,SV130: $i] :
( ( ( class_Orderings_Oorder @ SV130 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV380 @ SV380 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1801,plain,
! [SV592: $i,SV381: $i,SV133: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV133 ) ) @ SV381 ) @ SV592 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV381 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV133 @ SV381 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV592 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1802,plain,
! [SV755: $i,SV593: $i,SV382: $i,SV134: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV134 @ SV382 ) @ SV593 ) @ SV755 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ SV593 ) @ SV755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1803,plain,
! [SV756: $i,SV594: $i,SV383: $i,SV135: $i] :
( ( ! [SY2050: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV756 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SY2050 ) @ SV756 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SY2050 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1804,plain,
! [SV386: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV138 ) @ SV386 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV138 ) ) @ ( c_Lambda_OdB_OAbs @ SV386 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1805,plain,
! [SV597: $i,SV387: $i,SV139: $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 @ SV139 @ SV387 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV597 @ 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 ) @ SV387 @ 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 @ SV139 ) ) @ SV387 ) @ SV597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1806,plain,
! [SV757: $i,SV598: $i,SV388: $i,SV140: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV140 )
| ( c_HOL_Oord__class_Oless @ SV388 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV757 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV757 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1807,plain,
! [SV758: $i,SV599: $i,SV389: $i,SV141: $i] :
( ( ~ ( class_Orderings_Oorder @ SV141 )
| ( c_HOL_Oord__class_Oless @ SV389 @ SV599 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV758 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV758 @ SV599 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1808,plain,
! [SV759: $i,SV600: $i,SV390: $i,SV145: $i] :
( ( ( c_Type_Otypings @ SV145 @ SV390 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV600 @ SV145 @ SV759 @ SV390 ) )
| ~ ( c_Type_Otyping @ SV145 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV759 @ SV390 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1809,plain,
! [SV601: $i,SV391: $i,SV147: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV147 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV391 @ SV601 @ SV147 @ SV147 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV391 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV601 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1810,plain,
! [SV760: $i,SV602: $i,SV392: $i,SV148: $i] :
( ( ! [SY2051: $i,SY2052: $i,SY2053: $i] :
( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2051 ) @ SY2052 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
| ~ ( c_Type_Otypings @ SV148 @ SY2052 @ SY2053 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2051 ) @ SY2052 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1811,plain,
! [SV603: $i,SV393: $i,SV151: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV151 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV393 @ SV151 @ SV603 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV393 ) @ SV151 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV603 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1812,plain,
! [SV395: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV153 ) @ SV395 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV153 ) ) @ ( c_Lambda_OdB_OAbs @ SV395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1813,plain,
! [SV761: $i,SV604: $i,SV396: $i,SV154: $i] :
( ( ( c_Type_Otyping @ SV154 @ SV396 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV604 @ SV154 @ SV396 @ SV761 ) ) @ SV604 ) )
| ~ ( c_Type_Otyping @ SV154 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SV761 ) @ SV604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1814,plain,
! [SV397: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV155 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV155 ) @ ( c_Lambda_OdB_OVar @ SV397 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1815,plain,
! [SV762: $i,SV605: $i,SV398: $i,SV156: $i] :
( ( ( c_Type_Otyping @ SV156 @ SV398 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV605 @ SV156 @ SV398 @ SV762 ) @ SV605 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV156 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV398 @ SV762 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1816,plain,
! [SV606: $i,SV399: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV157 @ SV399 ) ) @ ( c_Lambda_Olift @ SV606 @ SV399 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV157 ) @ SV606 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1817,plain,
! [SV400: $i,SV158: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV158 @ SV400 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV158 ) @ SV400 )
= ( c_Lambda_OdB_OVar @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1818,plain,
! [SV763: $i,SV607: $i,SV401: $i,SV159: $i] :
( ( ( c_Type_Otyping @ SV159 @ SV401 @ SV607 )
| ~ ( c_Type_Otyping @ SV159 @ SV763 @ SV607 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV763 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1819,plain,
! [SV608: $i,SV402: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV160 ) @ SV402 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SV402 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV160 ) @ SV608 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1820,plain,
! [SV609: $i,SV403: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SV403 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SV609 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV403 ) @ SV609 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1821,plain,
! [SV764: $i,SV610: $i,SV404: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV404 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SV764 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV404 ) @ SV764 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV162 ) @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1822,plain,
! [SV611: $i,SV405: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV163 ) @ SV405 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV611 ) @ SV405 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV163 ) @ SV611 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1823,plain,
! [SV612: $i,SV406: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SV406 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SV612 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV406 ) @ SV612 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1824,plain,
! [SV765: $i,SV613: $i,SV408: $i,SV166: $i] :
( ( ( c_Type_Otyping @ SV166 @ SV408 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV613 @ SV166 @ SV765 @ SV408 ) )
| ~ ( c_Type_Otyping @ SV166 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV765 ) @ SV408 ) @ SV613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1825,plain,
! [SV614: $i,SV409: $i,SV167: $i] :
( ( ( SV167
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV409 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV409 @ SV614 @ SV167 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV409 ) @ SV614 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV167 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1603]) ).
thf(1826,plain,
! [SV766: $i,SV615: $i,SV410: $i,SV168: $i] :
( ( ! [SY2054: $i] :
( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV410 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV766 )
| ~ ( c_Type_Otypings @ SV168 @ SV615 @ SY2054 )
| ~ ( c_Type_Otyping @ SV168 @ SV410 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY2054 @ SV766 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1827,plain,
! [SV767: $i,SV616: $i,SV411: $i,SV169: $i] :
( ( ( c_Type_Otyping @ SV169 @ ( c_Lambda_OdB_OVar @ SV411 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV616 @ SV169 @ SV411 @ SV767 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV169 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV411 ) @ SV767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1828,plain,
! [SV617: $i,SV412: $i,SV170: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV170 ) @ SV412 @ SV617 )
= ( c_Lambda_OdB_OVar @ SV170 ) )
= $true )
| ( ( ( SV170 = SV617 )
| ( c_HOL_Oord__class_Oless @ SV617 @ SV170 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1829,plain,
! [SV768: $i,SV618: $i,SV413: $i,SV171: $i] :
( ( ( c_Type_Otyping @ SV171 @ SV413 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV618 @ SV171 @ SV413 @ SV768 ) @ SV618 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV171 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV413 @ SV768 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV618 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1830,plain,
! [SV769: $i,SV619: $i,SV414: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV172 @ SV414 @ SV619 ) ) @ ( c_Lambda_Osubst @ SV172 @ SV769 @ SV619 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV414 ) @ SV769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1831,plain,
! [SV770: $i,SV621: $i,SV416: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV416 @ SV621 ) ) @ ( c_Lambda_Osubst @ SV770 @ SV416 @ SV621 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV174 ) @ SV770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1832,plain,
! [SV771: $i,SV622: $i,SV417: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV175 @ SV417 @ SV622 ) ) @ ( c_Lambda_Osubst @ SV175 @ SV771 @ SV622 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV417 ) @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1833,plain,
! [SV772: $i,SV623: $i,SV418: $i,SV177: $i] :
( ( ( c_Type_Otyping @ SV177 @ ( c_Lambda_OdB_OAbs @ SV418 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV623 ) @ SV772 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV623 @ tc_Type_Otype ) @ SV418 @ SV772 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1834,plain,
! [SV773: $i,SV624: $i,SV419: $i,SV178: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV178 @ SV419 @ SV624 @ SV773 ) @ SV419 )
= SV624 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1835,plain,
! [SV420: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV179 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV179 @ SV420 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1836,plain,
! [SV625: $i,SV421: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV180 @ SV421 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV625 @ SV421 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV180 ) @ SV625 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1837,plain,
! [SV626: $i,SV423: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV182 @ SV423 ) ) @ ( c_Lambda_Olift @ SV626 @ SV423 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV182 ) @ SV626 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1838,plain,
! [SV774: $i,SV627: $i,SV424: $i,SV183: $i] :
( ( ! [SY2055: $i] :
( ( SV183 = SV424 )
| ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SY2055 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV424 )
| ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SY2055 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1839,plain,
! [SV184: $i,SV425: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV425 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV184 ) @ SV425 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1840,plain,
! [SV775: $i,SV628: $i,SV426: $i,SV185: $i] :
( ( ! [SY2056: $i] :
( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV426 ) @ SV628 ) @ SV775 )
| ~ ( c_Type_Otyping @ SV185 @ SV628 @ SY2056 )
| ~ ( c_Type_Otyping @ SV185 @ SV426 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY2056 ) @ SV775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1841,plain,
! [SV776: $i,SV629: $i,SV428: $i,SV187: $i] :
( ( ! [SY2057: $i,SY2058: $i,SY2059: $i] :
( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2057 ) @ SY2058 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
| ~ ( c_Type_Otypings @ SV629 @ SY2058 @ SY2059 )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2057 ) @ SY2058 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1842,plain,
! [SV630: $i,SV429: $i,SV188: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV188 ) @ SV429 @ SV630 )
= ( c_Lambda_OdB_OVar @ SV188 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV188 @ SV630 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1843,plain,
! [SV631: $i,SV430: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV189 @ ( c_Lambda_OdB_OVar @ SV430 ) @ SV631 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV189 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1844,plain,
! [SV777: $i,SV632: $i,SV431: $i,SV190: $i] :
( ( ! [SY2060: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV190 @ SV431 @ SV632 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV777 @ SV431 ) @ SY2060 )
| ~ ( c_Type_Otyping @ SV190 @ SV777 @ SY2060 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1845,plain,
! [SV778: $i,SV633: $i,SV432: $i,SV191: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV191 ) @ SV432 ) @ SV633 @ SV778 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV191 @ SV633 @ SV778 ) ) @ ( c_Lambda_Osubst @ SV432 @ SV633 @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1846,plain,
! [SV779: $i,SV634: $i,SV433: $i,SV192: $i] :
( ( ( c_Type_Otyping @ SV192 @ SV433 @ SV634 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV779 ) @ SV433 ) )
| ~ ( c_Type_Otyping @ SV192 @ SV779 @ SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1847,plain,
! [SV635: $i,SV435: $i,SV194: $i] :
( ( ( ( hAPP @ SV194 @ SV435 )
= SV635 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV194 @ ( c_Lambda_OdB_OVar @ SV435 ) @ SV635 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1848,plain,
! [SV780: $i,SV636: $i,SV436: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV195 @ SV436 @ SV636 ) ) @ ( c_Lambda_Osubst @ SV780 @ SV436 @ SV636 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SV780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1849,plain,
! [SV781: $i,SV638: $i,SV439: $i,SV198: $i] :
( ( ! [SY2061: $i,SY2062: $i] :
( ~ ( c_Type_Otyping @ SV198 @ SV439 @ SV638 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SV781 @ SV638 @ tc_Type_Otype ) @ SY2061 @ SY2062 )
| ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SY2061 @ SV439 @ SV781 ) @ SY2062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1850,plain,
! [SV199: $i,SV440: $i] :
( ( ( class_Orderings_Opreorder @ SV440 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV199 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1851,plain,
! [SV200: $i,SV441: $i] :
( ( ( class_Orderings_Oorder @ SV441 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV200 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1852,plain,
! [SV639: $i,SV443: $i,SV202: $i] :
( ( ( SV202 = SV443 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV639 ) @ SV202 ) @ SV443 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1853,plain,
! [SV782: $i,SV640: $i,SV444: $i,SV203: $i] :
( ( ( ( c_List_Oappend @ SV203 @ SV444 @ SV640 )
!= ( c_List_Oappend @ SV782 @ SV444 @ SV640 ) )
| ( SV203 = SV782 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1854,plain,
! [SV783: $i,SV641: $i,SV445: $i,SV204: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV204 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV445 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV783 ) @ SV641 ) )
| ( SV445 = SV783 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1855,plain,
! [SV642: $i,SV446: $i,SV205: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SV446 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV642 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SV446 )
= SV642 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1856,plain,
! [SV643: $i,SV447: $i,SV206: $i] :
( ( ( ( c_List_Olist_ONil @ SV206 )
!= ( c_List_Oappend @ SV447 @ SV643 @ SV206 ) )
= $true )
| ( ( SV447
= ( c_List_Olist_ONil @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1857,plain,
! [SV784: $i,SV644: $i,SV448: $i,SV207: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV207 ) @ SV448 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV644 ) @ SV784 ) )
| ( SV448 = SV784 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1858,plain,
! [SV785: $i,SV645: $i,SV450: $i,SV209: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV209 ) @ SV450 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV645 ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV209 = SV645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1859,plain,
! [SV646: $i,SV451: $i,SV210: $i] :
( ( ( c_List_Olist_OCons @ SV210 @ SV451 @ SV646 )
= SV451 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1860,plain,
! [SV452: $i,SV211: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV211 )
= ( c_Lambda_OdB_OVar @ SV452 ) )
= $false )
| ( ( SV211 = SV452 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1861,plain,
! [SV647: $i,SV453: $i,SV212: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV212 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV453 @ SV647 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV647
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1862,plain,
! [SV648: $i,SV454: $i,SV213: $i] :
( ( ( SV213
!= ( c_List_Oappend @ SV454 @ SV213 @ SV648 ) )
= $true )
| ( ( SV454
= ( c_List_Olist_ONil @ SV648 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1863,plain,
! [SV649: $i,SV455: $i,SV214: $i] :
( ( ( ( c_List_Oappend @ SV214 @ SV455 @ SV649 )
!= ( c_List_Olist_ONil @ SV649 ) )
= $true )
| ( ( SV455
= ( c_List_Olist_ONil @ SV649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1864,plain,
! [SV650: $i,SV456: $i,SV215: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV215 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV456 @ SV650 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV215 )
= SV456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1865,plain,
! [SV651: $i,SV458: $i,SV217: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV217 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV651 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1866,plain,
! [SV652: $i,SV459: $i,SV218: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV218 ) @ SV459 )
= ( c_Lambda_OdB_OVar @ SV652 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1867,plain,
! [SV653: $i,SV460: $i,SV219: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV219 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV460 @ SV653 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV219 )
= SV460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1868,plain,
! [SV786: $i,SV654: $i,SV461: $i,SV220: $i] :
( ( ! [SY2063: $i] :
( ( ( c_List_Oappend @ SV220 @ ( c_List_Olist_OCons @ SV461 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 )
!= ( c_List_Oappend @ SV786 @ ( c_List_Olist_OCons @ SY2063 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 ) )
| ( SV461 = SY2063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1869,plain,
! [SV655: $i,SV462: $i,SV221: $i] :
( ( ( c_Lambda_OdB_OVar @ SV221 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV462 ) @ SV655 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1870,plain,
! [SV656: $i,SV463: $i,SV222: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV222 @ SV463 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV656 @ SV463 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV222 = SV656 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1871,plain,
! [SV787: $i,SV657: $i,SV464: $i,SV223: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV223 ) @ SV464 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV657 ) @ SV787 ) )
| ( SV223 = SV657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1872,plain,
! [SV788: $i,SV658: $i,SV465: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ SV465 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV658 ) @ SV788 ) )
| ( SV224 = SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1873,plain,
! [SV789: $i,SV659: $i,SV466: $i,SV225: $i] :
( ( ! [SY2064: $i] :
( ( ( c_List_Oappend @ SV225 @ ( c_List_Olist_OCons @ SV466 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 )
!= ( c_List_Oappend @ SV789 @ ( c_List_Olist_OCons @ SY2064 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 ) )
| ( SV225 = SV789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1874,plain,
! [SV790: $i,SV660: $i,SV467: $i,SV226: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV226 ) ) @ SV467 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV660 ) @ SV790 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1875,plain,
! [SV468: $i,SV227: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV227 )
= ( c_Lambda_OdB_OAbs @ SV468 ) )
= $false )
| ( ( SV227 = SV468 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1876,plain,
! [SV661: $i,SV469: $i,SV228: $i] :
( ( ( c_List_Olist_OCons @ SV228 @ SV469 @ SV661 )
= ( c_List_Olist_ONil @ SV661 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1877,plain,
! [SV791: $i,SV662: $i,SV470: $i,SV229: $i] :
( ( ! [SY2065: $i] :
( ( ( c_List_Olist_OCons @ SV229 @ SV470 @ SV662 )
!= ( c_List_Olist_OCons @ SV791 @ SY2065 @ SV662 ) )
| ( SV470 = SY2065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1878,plain,
! [SV663: $i,SV471: $i,SV230: $i] :
( ( ( SV230
!= ( c_List_Oappend @ SV230 @ SV471 @ SV663 ) )
= $true )
| ( ( SV471
= ( c_List_Olist_ONil @ SV663 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1879,plain,
! [SV664: $i,SV472: $i,SV231: $i] :
( ( ( ( c_List_Oappend @ SV231 @ SV472 @ SV664 )
!= SV472 )
= $true )
| ( ( SV231
= ( c_List_Olist_ONil @ SV664 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1880,plain,
! [SV665: $i,SV473: $i,SV232: $i] :
( ( ( ( c_List_Oappend @ SV232 @ SV473 @ SV665 )
!= ( c_List_Olist_ONil @ SV665 ) )
= $true )
| ( ( SV232
= ( c_List_Olist_ONil @ SV665 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(1881,plain,
! [SV666: $i,SV474: $i,SV233: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV233 ) @ SV474 )
= ( c_Lambda_OdB_OAbs @ SV666 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1882,plain,
! [SV792: $i,SV667: $i,SV475: $i,SV234: $i] :
( ( ! [SY2066: $i] :
( ( ( c_List_Olist_OCons @ SV234 @ SV475 @ SV667 )
!= ( c_List_Olist_OCons @ SV792 @ SY2066 @ SV667 ) )
| ( SV234 = SV792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1883,plain,
! [SV793: $i,SV668: $i,SV476: $i,SV235: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV476 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV668 ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV235 = SV668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1884,plain,
! [SV794: $i,SV669: $i,SV477: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV477 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV669 ) @ SV794 ) )
| ( SV477 = SV794 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1885,plain,
! [SV795: $i,SV670: $i,SV478: $i,SV237: $i] :
( ( ! [SY2067: $i,SY2068: $i,SY2069: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SY2067 ) ) )
| ~ ( c_Type_Otyping @ SY2068 @ SV795 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2068 @ SY2067 @ SV478 @ tc_Type_Otype ) @ SV670 @ SY2069 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1886,plain,
! [SV796: $i,SV671: $i,SV479: $i,SV238: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV671 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV796 ) )
| ( SV671 = SV796 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1887,plain,
! [SV797: $i,SV672: $i,SV480: $i,SV239: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV239 )
| ~ ( class_Int_Onumber__ring @ SV239 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV672 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV797 ) )
| ( SV672 = SV797 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1888,plain,
! [SV673: $i,SV481: $i,SV240: $i] :
( ( ( SV240
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 ) @ SV673 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 ) @ ( c_List_Oappend @ SV673 @ ( c_List_Olist_OCons @ SV481 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1889,plain,
! [SV798: $i,SV674: $i,SV482: $i,SV241: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV482 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV674 ) @ SV798 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV482 = SV798 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1890,plain,
! [SV675: $i,SV483: $i,SV242: $i] :
( ( ( c_List_Olist_ONil @ SV242 )
= ( c_List_Olist_OCons @ SV483 @ SV675 @ SV242 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1891,plain,
! [SV676: $i,SV484: $i,SV243: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV243 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV243 )
| ( SV484
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SV484 ) @ SV676 ) )
| ( SV676
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1892,plain,
! [SV677: $i,SV485: $i,SV244: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV244 @ SV485 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV677 ) )
= $true )
| ( ( SV485
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1893,plain,
! [SV799: $i,SV678: $i,SV486: $i,SV245: $i] :
( ( ! [SY2070: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV245 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV799 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SY2070 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ SV799 )
= SY2070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1894,plain,
! [SV800: $i,SV679: $i,SV487: $i,SV246: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV246 ) @ SV487 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV679 ) @ SV800 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(1895,plain,
! [SV801: $i,SV680: $i,SV488: $i,SV247: $i] :
( ( ! [SY2071: $i,SY2072: $i,SY2073: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SY2071 ) ) )
| ~ ( c_Type_Otyping @ SY2072 @ SV801 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2072 @ SY2071 @ SV247 @ tc_Type_Otype ) @ SV680 @ SY2073 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1896,plain,
! [SV681: $i,SV489: $i,SV248: $i] :
( ( ( ( c_List_Olist_ONil @ SV248 )
!= ( c_List_Oappend @ SV489 @ SV681 @ SV248 ) )
= $true )
| ( ( SV681
= ( c_List_Olist_ONil @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1897,plain,
! [SV682: $i,SV490: $i,SV249: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV249 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV490 @ SV249 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV682 @ SV249 ) )
| ( SV490 = SV682 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1898,plain,
! [SV683: $i,SV491: $i,SV250: $i] :
( ( ( ( c_List_Oappend @ SV250 @ SV491 @ SV683 )
!= SV250 )
= $true )
| ( ( SV491
= ( c_List_Olist_ONil @ SV683 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1899,plain,
! [SV802: $i,SV684: $i,SV492: $i,SV251: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV251 ) @ SV492 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV684 ) @ SV802 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV492 = SV802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1900,plain,
! [SV685: $i,SV493: $i,SV252: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV252 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV493 @ SV685 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV685
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1901,plain,
! [SV686: $i,SV494: $i,SV253: $i] :
( ( ( c_List_Olist_OCons @ SV253 @ SV494 @ SV686 )
= ( c_List_Olist_ONil @ SV686 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1902,plain,
! [SV687: $i,SV495: $i,SV254: $i] :
( ( SV254
= ( c_List_Olist_OCons @ SV495 @ SV254 @ SV687 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1903,plain,
! [SV803: $i,SV688: $i,SV496: $i,SV255: $i] :
( ( ( ( c_List_Oappend @ SV255 @ SV496 @ SV688 )
!= ( c_List_Oappend @ SV255 @ SV803 @ SV688 ) )
| ( SV496 = SV803 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1904,plain,
! [SV497: $i,SV256: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV256 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV256 ) @ SV497 ) @ SV497 )
!= ( c_HOL_Ozero__class_Ozero @ SV256 ) )
| ( SV497
= ( c_HOL_Ozero__class_Ozero @ SV256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1905,plain,
! [SV689: $i,SV498: $i,SV257: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV257 @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV689 ) )
= $true )
| ( ( SV257
= ( c_Lambda_OdB_OAbs @ SV689 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1906,plain,
! [SV804: $i,SV690: $i,SV499: $i,SV258: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV258 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV690 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV804 ) )
| ( SV690 = SV804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1907,plain,
! [SV695: $i,SV505: $i,SV264: $i,SV7: $i] :
( ( ( c_List_Olistsp @ SV7 @ ( c_List_Oappend @ SV264 @ SV505 @ SV695 ) @ SV695 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV7 @ SV505 @ SV695 )
| ~ ( c_List_Olistsp @ SV7 @ SV264 @ SV695 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1908,plain,
! [SV805: $i,SV696: $i,SV506: $i,SV265: $i,SV8: $i] :
( ( ! [SY2074: $i] :
( ( SV8 = SV265 )
| ( SV506 = SV696 )
| ~ ( c_ListOrder_Ostep1 @ SV805 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SY2074 ) @ SY2074 ) @ SY2074 ) @ ( c_List_Oappend @ SV265 @ ( c_List_Olist_OCons @ SV696 @ ( c_List_Olist_ONil @ SY2074 ) @ SY2074 ) @ SY2074 ) @ SY2074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1909,plain,
! [SV806: $i,SV697: $i,SV507: $i,SV266: $i,SV9: $i] :
( ( ! [SY2075: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SV266 ) @ SV507 ) )
| ( SV266 = SV507 )
| ~ ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SV697 @ ( c_List_Olist_OCons @ SV266 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ ( c_List_Oappend @ SY2075 @ ( c_List_Olist_OCons @ SV507 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ SV806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(1910,plain,
! [SV807: $i,SV698: $i,SV508: $i,SV267: $i,SV10: $i] :
( ( ! [SY2076: $i] :
( ( c_List_Ofoldr @ SV10 @ ( c_List_Oappend @ SV267 @ SV508 @ SV698 ) @ SV807 @ SV698 @ SY2076 )
= ( c_List_Ofoldr @ SV10 @ SV267 @ ( c_List_Ofoldr @ SV10 @ SV508 @ SV807 @ SV698 @ SY2076 ) @ SV698 @ SY2076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1911,plain,
! [SV699: $i,SV509: $i,SV273: $i,SV16: $i] :
( ( ( c_List_Olistsp @ SV16 @ SV273 @ SV509 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV16 @ ( c_List_Oappend @ SV699 @ SV273 @ SV509 ) @ SV509 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1912,plain,
! [SV700: $i,SV510: $i,SV274: $i,SV17: $i] :
( ( ( c_List_Olistsp @ SV17 @ SV274 @ SV510 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV17 @ ( c_List_Oappend @ SV274 @ SV700 @ SV510 ) @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1913,plain,
! [SV808: $i,SV701: $i,SV511: $i,SV275: $i,SV18: $i] :
( ( ( c_ListOrder_Ostep1 @ SV18 @ ( c_List_Oappend @ SV275 @ SV511 @ SV701 ) @ ( c_List_Oappend @ SV275 @ SV808 @ SV701 ) @ SV701 )
| ~ ( c_ListOrder_Ostep1 @ SV18 @ SV511 @ SV808 @ SV701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(1914,plain,
! [SV809: $i,SV702: $i,SV512: $i,SV276: $i,SV19: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV19 @ SV276 @ SV512 @ SV702 )
| ( c_ListOrder_Ostep1 @ SV19 @ ( c_List_Oappend @ SV276 @ SV809 @ SV702 ) @ ( c_List_Oappend @ SV512 @ SV809 @ SV702 ) @ SV702 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(1915,plain,
! [SV810: $i,SV703: $i,SV513: $i,SV277: $i,SV20: $i] :
( ( ! [SY2077: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV277 ) @ SV513 ) )
| ( c_ListOrder_Ostep1 @ SV20 @ SV703 @ SV810 @ SY2077 )
| ~ ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SV703 @ ( c_List_Olist_OCons @ SV277 @ ( c_List_Olist_ONil @ SY2077 ) @ SY2077 ) @ SY2077 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV513 @ ( c_List_Olist_ONil @ SY2077 ) @ SY2077 ) @ SY2077 ) @ SY2077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1916,plain,
! [SV704: $i,SV514: $i,SV278: $i,SV21: $i] :
( ( ( c_Type_Otyping @ SV21 @ SV278 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV514 @ SV21 @ SV278 @ SV704 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV21 @ ( c_List_Oappend @ SV704 @ ( c_List_Olist_OCons @ SV278 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1917,plain,
! [SV811: $i,SV709: $i,SV520: $i,SV284: $i,SV27: $i] :
( ( ! [SY2078: $i] :
( ( SV27 = SV284 )
| ( c_ListOrder_Ostep1 @ SV520 @ SV27 @ SV284 @ SV709 )
| ~ ( c_ListOrder_Ostep1 @ SV520 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ ( c_List_Oappend @ SV284 @ ( c_List_Olist_OCons @ SY2078 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ SV709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1918,plain,
! [SV812: $i,SV710: $i,SV521: $i,SV285: $i,SV29: $i] :
( ( ! [SY2079: $i] :
( ( c_List_Ofoldl @ SV29 @ SV285 @ ( c_List_Oappend @ SV521 @ SV710 @ SV812 ) @ SY2079 @ SV812 )
= ( c_List_Ofoldl @ SV29 @ ( c_List_Ofoldl @ SV29 @ SV285 @ SV521 @ SY2079 @ SV812 ) @ SV710 @ SY2079 @ SV812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1919,plain,
! [SV286: $i,SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV286 ) @ SV286 ) @ SV30 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV286 @ SV30 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1920,plain,
! [SV287: $i,SV31: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV287 @ SV31 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV287 ) @ SV287 ) @ SV31 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1921,plain,
! [SV293: $i,SV37: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV37 ) )
= $true )
| ( ( SV293
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV293 ) @ ( c_HOL_Ozero__class_Ozero @ SV37 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1922,plain,
! [SV40: $i,SV296: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV296 @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1923,plain,
! [SV813: $i,SV711: $i,SV522: $i,SV297: $i,SV41: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV41 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV522 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV711 ) @ SV813 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV711 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV522 ) @ SV813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1924,plain,
! [SV814: $i,SV712: $i,SV523: $i,SV298: $i,SV42: $i] :
( ( ! [SY2080: $i] :
( ( SV42 = SV298 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV298 ) @ SV42 ) )
| ~ ( c_ListOrder_Ostep1 @ SV523 @ ( c_List_Olist_OCons @ SV298 @ SV712 @ SV814 ) @ ( c_List_Olist_OCons @ SV42 @ SY2080 @ SV814 ) @ SV814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(1925,plain,
! [SV524: $i,SV299: $i,SV43: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV299 ) @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV524 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV299 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1926,plain,
! [SV713: $i,SV525: $i,SV300: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV45 @ SV300 @ SV300 ) @ SV300 ) @ SV525 ) @ SV713 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV300 ) @ SV713 ) @ SV525 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1927,plain,
! [SV714: $i,SV526: $i,SV301: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SV301 ) @ SV526 ) @ SV714 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV46 @ SV301 @ SV301 ) @ SV301 ) @ SV714 ) @ SV526 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1928,plain,
! [SV815: $i,SV715: $i,SV527: $i,SV302: $i,SV47: $i] :
( ( ! [SY2081: $i] :
( ( c_List_Ofoldl @ SV47 @ SV302 @ ( c_List_Olist_OCons @ SV527 @ SV715 @ SV815 ) @ SY2081 @ SV815 )
= ( c_List_Ofoldl @ SV47 @ ( hAPP @ ( hAPP @ SV47 @ SV302 ) @ SV527 ) @ SV715 @ SY2081 @ SV815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1929,plain,
! [SV816: $i,SV717: $i,SV529: $i,SV304: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV49 @ SV304 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV49 @ SV717 @ SV816 ) @ SV529 ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(1930,plain,
! [SV817: $i,SV718: $i,SV530: $i,SV305: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV50 @ SV305 @ SV530 ) @ SV718 ) @ SV817 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV817 ) @ SV718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1931,plain,
! [SV818: $i,SV719: $i,SV531: $i,SV306: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV306 ) @ SV531 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV51 @ SV719 @ SV818 ) @ SV531 ) @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(1932,plain,
! [SV819: $i,SV720: $i,SV532: $i,SV307: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV52 @ SV307 @ SV532 ) @ SV720 ) @ SV819 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV819 ) @ SV720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1933,plain,
! [SV721: $i,SV533: $i,SV308: $i,SV53: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV53 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ SV533 ) ) @ SV721 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV533 ) @ SV721 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1934,plain,
! [SV722: $i,SV534: $i,SV309: $i,SV54: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV54 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV534 ) @ SV722 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV534 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ SV722 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1935,plain,
! [SV723: $i,SV535: $i,SV310: $i,SV55: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SV535 ) ) @ SV723 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SV723 ) ) @ SV535 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1936,plain,
! [SV724: $i,SV536: $i,SV311: $i,SV56: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV536 ) @ SV724 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SV536 ) ) @ SV724 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(1937,plain,
! [SV725: $i,SV537: $i,SV312: $i,SV57: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV57 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SV537 ) ) @ SV725 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV537 ) @ SV725 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1938,plain,
! [SV726: $i,SV538: $i,SV313: $i,SV58: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV58 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV538 ) @ SV726 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ SV726 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(1939,plain,
! [SV727: $i,SV539: $i,SV314: $i,SV59: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV59 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SV539 ) ) @ SV727 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV539 ) @ SV727 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1940,plain,
! [SV728: $i,SV540: $i,SV315: $i,SV60: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV60 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV540 ) @ SV728 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SV728 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1941,plain,
! [SV729: $i,SV541: $i,SV316: $i,SV61: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV61 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV541 ) @ SV729 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ SV541 ) ) @ SV729 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1942,plain,
! [SV820: $i,SV730: $i,SV542: $i,SV317: $i,SV63: $i] :
( ( ! [SY2082: $i] :
( ( SV63 = SV317 )
| ( SV542 = SV730 )
| ~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Olist_OCons @ SV317 @ SV730 @ SY2082 ) @ ( c_List_Olist_OCons @ SV63 @ SV542 @ SY2082 ) @ SY2082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1943,plain,
! [SV821: $i,SV731: $i,SV543: $i,SV318: $i,SV64: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV64 @ SV318 ) @ SV543 ) )
| ( c_ListOrder_Ostep1 @ SV64 @ ( c_List_Olist_OCons @ SV318 @ SV731 @ SV821 ) @ ( c_List_Olist_OCons @ SV543 @ SV731 @ SV821 ) @ SV821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1944,plain,
! [SV732: $i,SV544: $i,SV320: $i,SV66: $i] :
( ( ( c_Wellfounded_Oaccp @ SV66 @ SV320 @ SV544 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV544 ) @ SV320 ) @ SV732 ) )
| ~ ( c_Wellfounded_Oaccp @ SV66 @ SV732 @ SV544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1743]) ).
thf(1945,plain,
! [SV733: $i,SV545: $i,SV321: $i,SV67: $i] :
( ( ( c_Wellfounded_Oaccp @ SV67 @ SV321 @ SV545 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV67 @ SV733 @ SV545 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV545 ) @ SV321 ) @ SV733 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(1946,plain,
! [SV546: $i,SV322: $i,SV70: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV322 ) @ SV546 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV70 ) @ SV546 ) @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1947,plain,
! [SV547: $i,SV323: $i,SV71: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV71 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV323 ) @ SV547 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV71 ) @ SV547 ) @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1948,plain,
! [SV548: $i,SV324: $i,SV72: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV324 ) @ SV548 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV72 ) @ SV548 ) @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1949,plain,
! [SV734: $i,SV549: $i,SV325: $i,SV73: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV73 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV549 ) @ SV734 @ SV73 @ SV73 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV549 @ SV734 @ SV73 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1950,plain,
! [SV550: $i,SV326: $i,SV74: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV74 )
= $false )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV326 @ SV550 @ SV74 @ SV74 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV74 ) @ SV550 @ SV326 @ SV74 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1951,plain,
! [SV329: $i,SV77: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV329 @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1952,plain,
! [SV78: $i,SV330: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV330 @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ SV330 ) @ SV330 ) @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1953,plain,
! [SV79: $i,SV331: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV331 @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV79 ) @ SV331 ) @ SV331 ) @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1954,plain,
! [SV332: $i,SV80: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV332 ) @ SV332 ) @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV332 @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1955,plain,
! [SV553: $i,SV333: $i,SV81: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV81 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SV333 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ ( c_HOL_Ozero__class_Ozero @ SV81 ) @ SV553 @ SV81 @ SV81 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV81 ) @ SV333 @ SV553 @ SV81 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1956,plain,
! [SV555: $i,SV335: $i,SV84: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV335 ) @ SV555 ) @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV555 @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV335 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1957,plain,
! [SV822: $i,SV736: $i,SV556: $i,SV336: $i,SV85: $i] :
( ( ! [SY2083: $i] :
( ( c_ListOrder_Ostep1 @ SV85 @ SV336 @ SV556 @ SV736 )
| ( SV556 = SV336 )
| ~ ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SV822 @ SV336 @ SV736 ) @ ( c_List_Olist_OCons @ SY2083 @ SV556 @ SV736 ) @ SV736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(1958,plain,
! [SV823: $i,SV737: $i,SV557: $i,SV337: $i,SV86: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV737 ) @ SV823 ) @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV823 @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV337 @ SV737 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(1959,plain,
! [SV558: $i,SV338: $i,SV87: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV87 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV338 @ SV87 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV558 @ SV87 ) @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV338 @ SV558 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1960,plain,
! [SV559: $i,SV339: $i,SV88: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV88 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV339 @ SV559 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV339 @ SV88 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV559 @ SV88 ) @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1961,plain,
! [SV738: $i,SV560: $i,SV340: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV89 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV560 ) @ SV738 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ SV738 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV560 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(1962,plain,
! [SV824: $i,SV739: $i,SV561: $i,SV341: $i,SV90: $i] :
( ( ! [SY2084: $i] :
( ( c_List_Ofoldr @ SV90 @ ( c_List_Olist_OCons @ SV341 @ SV561 @ SV739 ) @ SV824 @ SV739 @ SY2084 )
= ( hAPP @ ( hAPP @ SV90 @ SV341 ) @ ( c_List_Ofoldr @ SV90 @ SV561 @ SV824 @ SV739 @ SY2084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(1963,plain,
! [SV740: $i,SV563: $i,SV343: $i,SV92: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV92 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV343 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV740 ) @ SV563 ) @ SV92 )
| ~ ( c_HOL_Oord__class_Oless @ SV343 @ SV740 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1964,plain,
! [SV741: $i,SV564: $i,SV344: $i,SV93: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV344 ) @ SV564 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV741 ) @ SV564 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV344 @ SV741 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1965,plain,
! [SV742: $i,SV565: $i,SV345: $i,SV94: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV345 @ SV565 @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV345 ) @ SV742 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV565 ) @ SV742 ) @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(1966,plain,
! [SV743: $i,SV566: $i,SV346: $i,SV95: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV95 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV743 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV566 @ SV743 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1967,plain,
! [SV744: $i,SV567: $i,SV347: $i,SV96: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV567 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV744 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ SV744 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1968,plain,
! [SV745: $i,SV568: $i,SV348: $i,SV97: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV348 @ SV568 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV348 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV568 ) @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1969,plain,
! [SV825: $i,SV746: $i,SV569: $i,SV349: $i,SV98: $i] :
( ( ! [SY2085: $i] :
( ( c_ListOrder_Ostep1 @ SV98 @ SV349 @ SV569 @ SV746 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV825 ) @ SY2085 ) )
| ~ ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SV825 @ SV349 @ SV746 ) @ ( c_List_Olist_OCons @ SY2085 @ SV569 @ SV746 ) @ SV746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(1970,plain,
! [SV826: $i,SV747: $i,SV570: $i,SV350: $i,SV99: $i] :
( ( ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_OCons @ SV350 @ SV570 @ SV747 ) @ ( c_List_Olist_OCons @ SV350 @ SV826 @ SV747 ) @ SV747 )
| ~ ( c_ListOrder_Ostep1 @ SV99 @ SV570 @ SV826 @ SV747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1971,plain,
! [SV748: $i,SV573: $i,SV354: $i,SV103: $i] :
( ( ( c_Wellfounded_Oaccp @ SV103 @ SV354 @ SV573 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ SV354 ) @ SV748 ) )
| ~ ( c_Wellfounded_Oaccp @ SV103 @ SV748 @ SV573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1972,plain,
! [SV749: $i,SV574: $i,SV355: $i,SV104: $i] :
( ( ( c_Wellfounded_Oaccp @ SV104 @ SV355 @ SV574 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV355 ) @ SV749 ) )
| ~ ( c_Wellfounded_Oaccp @ SV104 @ SV749 @ SV574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1973,plain,
! [SV575: $i,SV356: $i,SV105: $i] :
( ( ( class_Orderings_Opreorder @ SV105 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV575 @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV356 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1974,plain,
! [SV576: $i,SV357: $i,SV106: $i] :
( ( ( class_Orderings_Opreorder @ SV106 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV357 @ SV576 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV357 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1975,plain,
! [SV577: $i,SV358: $i,SV107: $i] :
( ( ( class_Orderings_Olinorder @ SV107 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV358 @ SV577 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV358 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1976,plain,
! [SV827: $i,SV750: $i,SV578: $i,SV359: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV750 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SV827 ) @ SV750 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(1977,plain,
! [SV828: $i,SV751: $i,SV579: $i,SV360: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV579 ) @ SV751 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV828 ) @ SV751 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SV579 ) @ SV828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(1978,plain,
! [SV580: $i,SV361: $i,SV110: $i] :
( ( ( class_Orderings_Oorder @ SV110 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV361 @ SV580 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV580 @ SV361 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1979,plain,
! [SV752: $i,SV581: $i,SV362: $i,SV111: $i] :
( ( ( c_Type_Otypings @ SV111 @ SV362 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV581 @ SV111 @ SV752 @ SV362 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV111 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV752 ) @ SV362 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV581 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(1980,plain,
! [SV753: $i,SV582: $i,SV363: $i,SV112: $i] :
( ( ( c_Type_Otypings @ SV112 @ SV363 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV582 @ SV112 @ SV753 @ SV363 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV112 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV753 @ SV363 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(1981,plain,
! [SV829: $i,SV754: $i,SV583: $i,SV364: $i,SV113: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV113 @ SV364 @ SV583 @ SV754 ) @ SV829 )
= ( hAPP @ SV113 @ SV829 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV829 @ SV364 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(1982,plain,
! [SV365: $i,SV584: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV115 ) @ SV584 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV115 @ SV365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV584 @ SV365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1983,plain,
! [SV116: $i,SV366: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV366 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV366 @ SV116 ) @ SV116 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(1984,plain,
! [SV367: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV367 @ SV117 ) @ SV117 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV367 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(1985,plain,
! [SV585: $i,SV369: $i,SV119: $i] :
( ( ( class_Orderings_Olinorder @ SV119 )
= $false )
| ( ( ( SV369 = SV585 )
| ( c_HOL_Oord__class_Oless @ SV369 @ SV585 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV585 @ SV369 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1986,plain,
! [SV586: $i,SV370: $i,SV120: $i] :
( ( ( class_Orderings_Olinorder @ SV120 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV370 @ SV586 @ SV120 )
| ( SV586 = SV370 )
| ( c_HOL_Oord__class_Oless @ SV586 @ SV370 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1987,plain,
! [SV587: $i,SV371: $i,SV121: $i] :
( ( ( class_Orderings_Olinorder @ SV121 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV371 @ SV587 @ SV121 )
| ( c_HOL_Oord__class_Oless @ SV587 @ SV371 @ SV121 )
| ( SV587 = SV371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1988,plain,
! [SV123: $i,SV588: $i,SV373: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV373 @ SV588 @ tc_nat )
= $true )
| ( ( ( SV588 = SV373 )
| ( c_HOL_Oord__class_Oless @ SV588 @ SV373 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV373 ) @ SV588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1989,plain,
! [SV589: $i,SV375: $i,SV125: $i] :
( ( ( class_Orderings_Olinorder @ SV125 )
= $false )
| ( ( ( SV375 = SV589 )
| ( c_HOL_Oord__class_Oless @ SV589 @ SV375 @ SV125 )
| ( c_HOL_Oord__class_Oless @ SV375 @ SV589 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1990,plain,
! [SV590: $i,SV376: $i,SV126: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV126 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV376 @ SV590 @ SV126 )
| ( c_HOL_Oord__class_Oless @ SV590 @ SV376 @ SV126 )
| ( SV590 = SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1991,plain,
! [SV127: $i,SV591: $i,SV377: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV377 @ SV591 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SV377 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV127 @ SV591 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1992,plain,
! [SV128: $i,SV378: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV378 @ SV378 @ SV128 )
= $false )
| ( ( class_Orderings_Opreorder @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1993,plain,
! [SV129: $i,SV379: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV379 @ SV379 @ SV129 )
= $false )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1994,plain,
! [SV130: $i,SV380: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV380 @ SV380 @ SV130 )
= $false )
| ( ( class_Orderings_Oorder @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1995,plain,
! [SV592: $i,SV133: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV381 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV133 @ SV381 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV592 @ 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 @ SV133 ) ) @ SV381 ) @ SV592 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1996,plain,
! [SV755: $i,SV593: $i,SV382: $i,SV134: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV134 @ SV382 ) @ SV593 ) @ SV755 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ SV593 ) @ SV755 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(1997,plain,
! [SV830: $i,SV756: $i,SV594: $i,SV383: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV756 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV830 ) @ SV756 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(1998,plain,
! [SV597: $i,SV387: $i,SV139: $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 @ SV139 @ SV387 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV597 @ 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 ) @ SV387 @ 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 @ SV139 ) ) @ SV387 ) @ SV597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1999,plain,
! [SV757: $i,SV598: $i,SV388: $i,SV140: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV140 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV388 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV757 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV757 @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(2000,plain,
! [SV758: $i,SV599: $i,SV389: $i,SV141: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV141 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV389 @ SV599 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV758 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV758 @ SV599 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(2001,plain,
! [SV759: $i,SV600: $i,SV390: $i,SV145: $i] :
( ( ( c_Type_Otypings @ SV145 @ SV390 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV600 @ SV145 @ SV759 @ SV390 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV145 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV759 @ SV390 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(2002,plain,
! [SV601: $i,SV391: $i,SV147: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV147 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV391 @ SV601 @ SV147 @ SV147 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV391 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV601 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(2003,plain,
! [SV831: $i,SV760: $i,SV602: $i,SV392: $i,SV148: $i] :
( ( ! [SY2086: $i,SY2087: $i] :
( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SY2086 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
| ~ ( c_Type_Otypings @ SV148 @ SY2086 @ SY2087 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SY2086 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2004,plain,
! [SV603: $i,SV151: $i,SV393: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV393 ) @ SV151 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV603 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV151 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV393 @ SV151 @ SV603 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(2005,plain,
! [SV761: $i,SV604: $i,SV396: $i,SV154: $i] :
( ( ( c_Type_Otyping @ SV154 @ SV396 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV604 @ SV154 @ SV396 @ SV761 ) ) @ SV604 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV154 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SV761 ) @ SV604 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(2006,plain,
! [SV762: $i,SV605: $i,SV398: $i,SV156: $i] :
( ( ( c_Type_Otyping @ SV156 @ SV398 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV605 @ SV156 @ SV398 @ SV762 ) @ SV605 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV156 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV398 @ SV762 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV605 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(2007,plain,
! [SV399: $i,SV606: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV157 ) @ SV606 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV157 @ SV399 ) ) @ ( c_Lambda_Olift @ SV606 @ SV399 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(2008,plain,
! [SV763: $i,SV607: $i,SV401: $i,SV159: $i] :
( ( ( c_Type_Otyping @ SV159 @ SV401 @ SV607 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV159 @ SV763 @ SV607 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV763 ) @ SV401 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(2009,plain,
! [SV402: $i,SV608: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV160 ) @ SV608 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV160 ) @ SV402 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SV402 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(2010,plain,
! [SV161: $i,SV609: $i,SV403: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV403 ) @ SV609 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SV403 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV161 ) @ SV609 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(2011,plain,
! [SV764: $i,SV610: $i,SV404: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV404 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SV764 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV404 ) @ SV764 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV162 ) @ SV610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2012,plain,
! [SV405: $i,SV611: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV163 ) @ SV611 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV163 ) @ SV405 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV611 ) @ SV405 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(2013,plain,
! [SV164: $i,SV612: $i,SV406: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV406 ) @ SV612 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SV406 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV164 ) @ SV612 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(2014,plain,
! [SV765: $i,SV613: $i,SV408: $i,SV166: $i] :
( ( ( c_Type_Otyping @ SV166 @ SV408 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV613 @ SV166 @ SV765 @ SV408 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV166 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV765 ) @ SV408 ) @ SV613 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(2015,plain,
! [SV167: $i,SV614: $i,SV409: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV409 ) @ SV614 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV167 ) )
= $false )
| ( ( SV167
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV409 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV409 @ SV614 @ SV167 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(2016,plain,
! [SV832: $i,SV766: $i,SV615: $i,SV410: $i,SV168: $i] :
( ( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV410 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV766 )
| ~ ( c_Type_Otypings @ SV168 @ SV615 @ SV832 )
| ~ ( c_Type_Otyping @ SV168 @ SV410 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV832 @ SV766 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2017,plain,
! [SV767: $i,SV616: $i,SV411: $i,SV169: $i] :
( ( ( c_Type_Otyping @ SV169 @ ( c_Lambda_OdB_OVar @ SV411 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV616 @ SV169 @ SV411 @ SV767 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV169 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV411 ) @ SV767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2018,plain,
! [SV412: $i,SV617: $i,SV170: $i] :
( ( ( SV170 = SV617 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV617 @ SV170 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV170 ) @ SV412 @ SV617 )
= ( c_Lambda_OdB_OVar @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2019,plain,
! [SV768: $i,SV618: $i,SV413: $i,SV171: $i] :
( ( ( c_Type_Otyping @ SV171 @ SV413 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV618 @ SV171 @ SV413 @ SV768 ) @ SV618 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV171 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV413 @ SV768 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2020,plain,
! [SV769: $i,SV619: $i,SV414: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV172 @ SV414 @ SV619 ) ) @ ( c_Lambda_Osubst @ SV172 @ SV769 @ SV619 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV414 ) @ SV769 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2021,plain,
! [SV770: $i,SV621: $i,SV416: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV416 @ SV621 ) ) @ ( c_Lambda_Osubst @ SV770 @ SV416 @ SV621 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV174 ) @ SV770 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(2022,plain,
! [SV771: $i,SV622: $i,SV417: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV175 @ SV417 @ SV622 ) ) @ ( c_Lambda_Osubst @ SV175 @ SV771 @ SV622 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV417 ) @ SV771 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2023,plain,
! [SV772: $i,SV623: $i,SV418: $i,SV177: $i] :
( ( ( c_Type_Otyping @ SV177 @ ( c_Lambda_OdB_OAbs @ SV418 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV623 ) @ SV772 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV623 @ tc_Type_Otype ) @ SV418 @ SV772 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2024,plain,
! [SV421: $i,SV625: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV180 ) @ SV625 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV180 @ SV421 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV625 @ SV421 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(2025,plain,
! [SV423: $i,SV626: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV182 ) @ SV626 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV182 @ SV423 ) ) @ ( c_Lambda_Olift @ SV626 @ SV423 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(2026,plain,
! [SV833: $i,SV774: $i,SV627: $i,SV424: $i,SV183: $i] :
( ( ( SV183 = SV424 )
| ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV424 )
| ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2027,plain,
! [SV834: $i,SV775: $i,SV628: $i,SV426: $i,SV185: $i] :
( ( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV426 ) @ SV628 ) @ SV775 )
| ~ ( c_Type_Otyping @ SV185 @ SV628 @ SV834 )
| ~ ( c_Type_Otyping @ SV185 @ SV426 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV834 ) @ SV775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2028,plain,
! [SV835: $i,SV776: $i,SV629: $i,SV428: $i,SV187: $i] :
( ( ! [SY2088: $i,SY2089: $i] :
( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SY2088 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
| ~ ( c_Type_Otypings @ SV629 @ SY2088 @ SY2089 )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SY2088 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2029,plain,
! [SV429: $i,SV630: $i,SV188: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV188 @ SV630 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV188 ) @ SV429 @ SV630 )
= ( c_Lambda_OdB_OVar @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(2030,plain,
! [SV631: $i,SV430: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV189 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV189 @ ( c_Lambda_OdB_OVar @ SV430 ) @ SV631 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(2031,plain,
! [SV836: $i,SV777: $i,SV632: $i,SV431: $i,SV190: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV190 @ SV431 @ SV632 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV777 @ SV431 ) @ SV836 )
| ~ ( c_Type_Otyping @ SV190 @ SV777 @ SV836 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2032,plain,
! [SV779: $i,SV634: $i,SV433: $i,SV192: $i] :
( ( ( c_Type_Otyping @ SV192 @ SV433 @ SV634 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV779 ) @ SV433 ) )
| ~ ( c_Type_Otyping @ SV192 @ SV779 @ SV634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(2033,plain,
! [SV635: $i,SV435: $i,SV194: $i] :
( ( ( c_Type_Otyping @ SV194 @ ( c_Lambda_OdB_OVar @ SV435 ) @ SV635 )
= $false )
| ( ( ( hAPP @ SV194 @ SV435 )
= SV635 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(2034,plain,
! [SV780: $i,SV636: $i,SV436: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV195 @ SV436 @ SV636 ) ) @ ( c_Lambda_Osubst @ SV780 @ SV436 @ SV636 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SV780 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2035,plain,
! [SV837: $i,SV781: $i,SV638: $i,SV439: $i,SV198: $i] :
( ( ! [SY2090: $i] :
( ~ ( c_Type_Otyping @ SV198 @ SV439 @ SV638 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SV781 @ SV638 @ tc_Type_Otype ) @ SV837 @ SY2090 )
| ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SV837 @ SV439 @ SV781 ) @ SY2090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2036,plain,
! [SV443: $i,SV202: $i,SV639: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV639 ) @ SV202 ) @ SV443 ) )
= $false )
| ( ( SV202 = SV443 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2037,plain,
! [SV782: $i,SV640: $i,SV444: $i,SV203: $i] :
( ( ( ( c_List_Oappend @ SV203 @ SV444 @ SV640 )
!= ( c_List_Oappend @ SV782 @ SV444 @ SV640 ) )
= $true )
| ( ( SV203 = SV782 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2038,plain,
! [SV783: $i,SV641: $i,SV445: $i,SV204: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV204 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV445 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV783 ) @ SV641 ) )
| ( SV445 = SV783 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(2039,plain,
! [SV642: $i,SV446: $i,SV205: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SV446 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV642 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV205 ) @ SV446 )
= SV642 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(2040,plain,
! [SV643: $i,SV447: $i,SV206: $i] :
( ( ( ( c_List_Olist_ONil @ SV206 )
= ( c_List_Oappend @ SV447 @ SV643 @ SV206 ) )
= $false )
| ( ( SV447
= ( c_List_Olist_ONil @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(2041,plain,
! [SV784: $i,SV644: $i,SV448: $i,SV207: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV207 ) @ SV448 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV644 ) @ SV784 ) )
= $true )
| ( ( SV448 = SV784 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(2042,plain,
! [SV785: $i,SV645: $i,SV450: $i,SV209: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV209 ) @ SV450 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV645 ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV209 = SV645 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(2043,plain,
! [SV647: $i,SV453: $i,SV212: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV212 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV453 @ SV647 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV647
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(2044,plain,
! [SV648: $i,SV454: $i,SV213: $i] :
( ( ( SV213
= ( c_List_Oappend @ SV454 @ SV213 @ SV648 ) )
= $false )
| ( ( SV454
= ( c_List_Olist_ONil @ SV648 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(2045,plain,
! [SV649: $i,SV455: $i,SV214: $i] :
( ( ( ( c_List_Oappend @ SV214 @ SV455 @ SV649 )
= ( c_List_Olist_ONil @ SV649 ) )
= $false )
| ( ( SV455
= ( c_List_Olist_ONil @ SV649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2046,plain,
! [SV650: $i,SV456: $i,SV215: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV215 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV456 @ SV650 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV215 )
= SV456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2047,plain,
! [SV653: $i,SV460: $i,SV219: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV219 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV460 @ SV653 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV219 )
= SV460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2048,plain,
! [SV838: $i,SV786: $i,SV654: $i,SV461: $i,SV220: $i] :
( ( ( ( c_List_Oappend @ SV220 @ ( c_List_Olist_OCons @ SV461 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 )
!= ( c_List_Oappend @ SV786 @ ( c_List_Olist_OCons @ SV838 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 ) )
| ( SV461 = SV838 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2049,plain,
! [SV656: $i,SV463: $i,SV222: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV222 @ SV463 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV656 @ SV463 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV222 = SV656 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2050,plain,
! [SV787: $i,SV657: $i,SV464: $i,SV223: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV223 ) @ SV464 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV657 ) @ SV787 ) )
= $true )
| ( ( SV223 = SV657 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2051,plain,
! [SV788: $i,SV658: $i,SV465: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ SV465 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV658 ) @ SV788 ) )
= $true )
| ( ( SV224 = SV658 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2052,plain,
! [SV839: $i,SV789: $i,SV659: $i,SV466: $i,SV225: $i] :
( ( ( ( c_List_Oappend @ SV225 @ ( c_List_Olist_OCons @ SV466 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 )
!= ( c_List_Oappend @ SV789 @ ( c_List_Olist_OCons @ SV839 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 ) )
| ( SV225 = SV789 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2053,plain,
! [SV790: $i,SV660: $i,SV467: $i,SV226: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV226 ) ) @ SV467 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV660 ) @ SV790 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(2054,plain,
! [SV840: $i,SV791: $i,SV662: $i,SV470: $i,SV229: $i] :
( ( ( ( c_List_Olist_OCons @ SV229 @ SV470 @ SV662 )
!= ( c_List_Olist_OCons @ SV791 @ SV840 @ SV662 ) )
| ( SV470 = SV840 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2055,plain,
! [SV663: $i,SV471: $i,SV230: $i] :
( ( ( SV230
= ( c_List_Oappend @ SV230 @ SV471 @ SV663 ) )
= $false )
| ( ( SV471
= ( c_List_Olist_ONil @ SV663 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2056,plain,
! [SV664: $i,SV472: $i,SV231: $i] :
( ( ( ( c_List_Oappend @ SV231 @ SV472 @ SV664 )
= SV472 )
= $false )
| ( ( SV231
= ( c_List_Olist_ONil @ SV664 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2057,plain,
! [SV665: $i,SV473: $i,SV232: $i] :
( ( ( ( c_List_Oappend @ SV232 @ SV473 @ SV665 )
= ( c_List_Olist_ONil @ SV665 ) )
= $false )
| ( ( SV232
= ( c_List_Olist_ONil @ SV665 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2058,plain,
! [SV841: $i,SV792: $i,SV667: $i,SV475: $i,SV234: $i] :
( ( ( ( c_List_Olist_OCons @ SV234 @ SV475 @ SV667 )
!= ( c_List_Olist_OCons @ SV792 @ SV841 @ SV667 ) )
| ( SV234 = SV792 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2059,plain,
! [SV793: $i,SV668: $i,SV476: $i,SV235: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV476 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV668 ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV235 = SV668 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2060,plain,
! [SV794: $i,SV669: $i,SV477: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV477 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV669 ) @ SV794 ) )
= $true )
| ( ( SV477 = SV794 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2061,plain,
! [SV842: $i,SV795: $i,SV670: $i,SV478: $i,SV237: $i] :
( ( ! [SY2091: $i,SY2092: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
| ~ ( c_Type_Otyping @ SY2091 @ SV795 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2091 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SY2092 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2062,plain,
! [SV796: $i,SV671: $i,SV479: $i,SV238: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV671 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV796 ) )
| ( SV671 = SV796 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(2063,plain,
! [SV797: $i,SV672: $i,SV480: $i,SV239: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV239 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV239 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV672 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV797 ) )
| ( SV672 = SV797 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2064,plain,
! [SV673: $i,SV481: $i,SV240: $i] :
( ( ( SV240
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 ) @ SV673 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV240 ) @ SV481 ) @ ( c_List_Oappend @ SV673 @ ( c_List_Olist_OCons @ SV481 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2065,plain,
! [SV798: $i,SV674: $i,SV482: $i,SV241: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV482 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV674 ) @ SV798 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV482 = SV798 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2066,plain,
! [SV676: $i,SV484: $i,SV243: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV243 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV243 )
| ( SV484
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SV484 ) @ SV676 ) )
| ( SV676
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2067,plain,
! [SV677: $i,SV485: $i,SV244: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV244 @ SV485 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV677 ) )
= $false )
| ( ( SV485
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(2068,plain,
! [SV843: $i,SV799: $i,SV678: $i,SV486: $i,SV245: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV245 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV799 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV843 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ SV799 )
= SV843 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2069,plain,
! [SV800: $i,SV679: $i,SV487: $i,SV246: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV246 ) @ SV487 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV679 ) @ SV800 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(2070,plain,
! [SV844: $i,SV801: $i,SV680: $i,SV488: $i,SV247: $i] :
( ( ! [SY2093: $i,SY2094: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
| ~ ( c_Type_Otyping @ SY2093 @ SV801 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY2093 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SY2094 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2071,plain,
! [SV681: $i,SV489: $i,SV248: $i] :
( ( ( ( c_List_Olist_ONil @ SV248 )
= ( c_List_Oappend @ SV489 @ SV681 @ SV248 ) )
= $false )
| ( ( SV681
= ( c_List_Olist_ONil @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(2072,plain,
! [SV682: $i,SV490: $i,SV249: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV249 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV490 @ SV249 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV682 @ SV249 ) )
| ( SV490 = SV682 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(2073,plain,
! [SV683: $i,SV491: $i,SV250: $i] :
( ( ( ( c_List_Oappend @ SV250 @ SV491 @ SV683 )
= SV250 )
= $false )
| ( ( SV491
= ( c_List_Olist_ONil @ SV683 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2074,plain,
! [SV802: $i,SV684: $i,SV492: $i,SV251: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV251 ) @ SV492 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV684 ) @ SV802 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV492 = SV802 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2075,plain,
! [SV685: $i,SV493: $i,SV252: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV252 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV493 @ SV685 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV685
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(2076,plain,
! [SV803: $i,SV688: $i,SV496: $i,SV255: $i] :
( ( ( ( c_List_Oappend @ SV255 @ SV496 @ SV688 )
!= ( c_List_Oappend @ SV255 @ SV803 @ SV688 ) )
= $true )
| ( ( SV496 = SV803 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2077,plain,
! [SV497: $i,SV256: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV256 ) @ SV497 ) @ SV497 )
!= ( c_HOL_Ozero__class_Ozero @ SV256 ) )
= $true )
| ( ( SV497
= ( c_HOL_Ozero__class_Ozero @ SV256 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2078,plain,
! [SV689: $i,SV498: $i,SV257: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV257 @ SV498 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV689 ) )
= $false )
| ( ( SV257
= ( c_Lambda_OdB_OAbs @ SV689 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(2079,plain,
! [SV804: $i,SV690: $i,SV499: $i,SV258: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV258 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV690 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV804 ) )
| ( SV690 = SV804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2080,plain,
! [SV264: $i,SV695: $i,SV505: $i,SV7: $i] :
( ( ( ~ ( c_List_Olistsp @ SV7 @ SV505 @ SV695 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV7 @ SV264 @ SV695 ) )
= $true )
| ( ( c_List_Olistsp @ SV7 @ ( c_List_Oappend @ SV264 @ SV505 @ SV695 ) @ SV695 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2081,plain,
! [SV845: $i,SV805: $i,SV696: $i,SV506: $i,SV265: $i,SV8: $i] :
( ( ( SV8 = SV265 )
| ( SV506 = SV696 )
| ~ ( c_ListOrder_Ostep1 @ SV805 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SV845 ) @ SV845 ) @ SV845 ) @ ( c_List_Oappend @ SV265 @ ( c_List_Olist_OCons @ SV696 @ ( c_List_Olist_ONil @ SV845 ) @ SV845 ) @ SV845 ) @ SV845 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2082,plain,
! [SV846: $i,SV806: $i,SV697: $i,SV507: $i,SV266: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SV266 ) @ SV507 ) )
| ( SV266 = SV507 )
| ~ ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SV697 @ ( c_List_Olist_OCons @ SV266 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV507 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2083,plain,
! [SV847: $i,SV807: $i,SV698: $i,SV508: $i,SV267: $i,SV10: $i] :
( ( ( c_List_Ofoldr @ SV10 @ ( c_List_Oappend @ SV267 @ SV508 @ SV698 ) @ SV807 @ SV698 @ SV847 )
= ( c_List_Ofoldr @ SV10 @ SV267 @ ( c_List_Ofoldr @ SV10 @ SV508 @ SV807 @ SV698 @ SV847 ) @ SV698 @ SV847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2084,plain,
! [SV509: $i,SV273: $i,SV699: $i,SV16: $i] :
( ( ( c_List_Olistsp @ SV16 @ ( c_List_Oappend @ SV699 @ SV273 @ SV509 ) @ SV509 )
= $false )
| ( ( c_List_Olistsp @ SV16 @ SV273 @ SV509 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(2085,plain,
! [SV510: $i,SV700: $i,SV274: $i,SV17: $i] :
( ( ( c_List_Olistsp @ SV17 @ ( c_List_Oappend @ SV274 @ SV700 @ SV510 ) @ SV510 )
= $false )
| ( ( c_List_Olistsp @ SV17 @ SV274 @ SV510 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2086,plain,
! [SV808: $i,SV701: $i,SV511: $i,SV275: $i,SV18: $i] :
( ( ( c_ListOrder_Ostep1 @ SV18 @ ( c_List_Oappend @ SV275 @ SV511 @ SV701 ) @ ( c_List_Oappend @ SV275 @ SV808 @ SV701 ) @ SV701 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV18 @ SV511 @ SV808 @ SV701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(2087,plain,
! [SV809: $i,SV702: $i,SV512: $i,SV276: $i,SV19: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV19 @ SV276 @ SV512 @ SV702 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV19 @ ( c_List_Oappend @ SV276 @ SV809 @ SV702 ) @ ( c_List_Oappend @ SV512 @ SV809 @ SV702 ) @ SV702 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2088,plain,
! [SV848: $i,SV810: $i,SV703: $i,SV513: $i,SV277: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV277 ) @ SV513 ) )
| ( c_ListOrder_Ostep1 @ SV20 @ SV703 @ SV810 @ SV848 )
| ~ ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SV703 @ ( c_List_Olist_OCons @ SV277 @ ( c_List_Olist_ONil @ SV848 ) @ SV848 ) @ SV848 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV513 @ ( c_List_Olist_ONil @ SV848 ) @ SV848 ) @ SV848 ) @ SV848 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2089,plain,
! [SV514: $i,SV278: $i,SV704: $i,SV21: $i] :
( ( ( c_Type_Otypings @ SV21 @ ( c_List_Oappend @ SV704 @ ( c_List_Olist_OCons @ SV278 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV514 )
= $false )
| ( ( c_Type_Otyping @ SV21 @ SV278 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV514 @ SV21 @ SV278 @ SV704 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2090,plain,
! [SV849: $i,SV811: $i,SV709: $i,SV520: $i,SV284: $i,SV27: $i] :
( ( ( SV27 = SV284 )
| ( c_ListOrder_Ostep1 @ SV520 @ SV27 @ SV284 @ SV709 )
| ~ ( c_ListOrder_Ostep1 @ SV520 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ ( c_List_Oappend @ SV284 @ ( c_List_Olist_OCons @ SV849 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ SV709 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2091,plain,
! [SV850: $i,SV812: $i,SV710: $i,SV521: $i,SV285: $i,SV29: $i] :
( ( ( c_List_Ofoldl @ SV29 @ SV285 @ ( c_List_Oappend @ SV521 @ SV710 @ SV812 ) @ SV850 @ SV812 )
= ( c_List_Ofoldl @ SV29 @ ( c_List_Ofoldl @ SV29 @ SV285 @ SV521 @ SV850 @ SV812 ) @ SV710 @ SV850 @ SV812 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2092,plain,
! [SV286: $i,SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV286 @ SV30 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ SV286 ) @ SV286 ) @ SV30 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2093,plain,
! [SV287: $i,SV31: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ SV287 ) @ SV287 ) @ SV31 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV287 @ SV31 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2094,plain,
! [SV293: $i,SV37: $i] :
( ( ( class_Int_Onumber__ring @ SV37 )
= $false )
| ( ( SV293
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV293 ) @ ( c_HOL_Ozero__class_Ozero @ SV37 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(2095,plain,
! [SV813: $i,SV711: $i,SV522: $i,SV297: $i,SV41: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV41 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV522 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV711 ) @ SV813 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV711 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV522 ) @ SV813 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2096,plain,
! [SV851: $i,SV814: $i,SV712: $i,SV523: $i,SV298: $i,SV42: $i] :
( ( ( SV42 = SV298 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV298 ) @ SV42 ) )
| ~ ( c_ListOrder_Ostep1 @ SV523 @ ( c_List_Olist_OCons @ SV298 @ SV712 @ SV814 ) @ ( c_List_Olist_OCons @ SV42 @ SV851 @ SV814 ) @ SV814 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2097,plain,
! [SV524: $i,SV299: $i,SV43: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV299 ) @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV524 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV299 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2098,plain,
! [SV525: $i,SV713: $i,SV300: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV300 ) @ SV713 ) @ SV525 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV45 @ SV300 @ SV300 ) @ SV300 ) @ SV525 ) @ SV713 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2099,plain,
! [SV526: $i,SV714: $i,SV301: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV46 @ SV301 @ SV301 ) @ SV301 ) @ SV714 ) @ SV526 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SV301 ) @ SV526 ) @ SV714 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(2100,plain,
! [SV852: $i,SV815: $i,SV715: $i,SV527: $i,SV302: $i,SV47: $i] :
( ( ( c_List_Ofoldl @ SV47 @ SV302 @ ( c_List_Olist_OCons @ SV527 @ SV715 @ SV815 ) @ SV852 @ SV815 )
= ( c_List_Ofoldl @ SV47 @ ( hAPP @ ( hAPP @ SV47 @ SV302 ) @ SV527 ) @ SV715 @ SV852 @ SV815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2101,plain,
! [SV816: $i,SV717: $i,SV529: $i,SV304: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV49 @ SV304 ) @ SV529 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV49 @ SV717 @ SV816 ) @ SV529 ) @ SV304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2102,plain,
! [SV817: $i,SV718: $i,SV530: $i,SV305: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV50 @ SV305 @ SV530 ) @ SV718 ) @ SV817 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV817 ) @ SV718 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2103,plain,
! [SV818: $i,SV719: $i,SV531: $i,SV306: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV306 ) @ SV531 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV51 @ SV719 @ SV818 ) @ SV531 ) @ SV306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2104,plain,
! [SV819: $i,SV720: $i,SV532: $i,SV307: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV52 @ SV307 @ SV532 ) @ SV720 ) @ SV819 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV819 ) @ SV720 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2105,plain,
! [SV721: $i,SV533: $i,SV308: $i,SV53: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV53 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ SV533 ) ) @ SV721 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV308 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV53 ) @ SV533 ) @ SV721 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2106,plain,
! [SV722: $i,SV534: $i,SV309: $i,SV54: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV54 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV534 ) @ SV722 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV534 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV54 ) @ SV309 ) @ SV722 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2107,plain,
! [SV723: $i,SV535: $i,SV310: $i,SV55: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SV535 ) ) @ SV723 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV55 ) @ SV310 ) @ SV723 ) ) @ SV535 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2108,plain,
! [SV724: $i,SV536: $i,SV311: $i,SV56: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV56 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV536 ) @ SV724 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ SV311 ) @ SV536 ) ) @ SV724 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2109,plain,
! [SV725: $i,SV537: $i,SV312: $i,SV57: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV57 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ SV537 ) ) @ SV725 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV312 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV57 ) @ SV537 ) @ SV725 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2110,plain,
! [SV726: $i,SV538: $i,SV313: $i,SV58: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV58 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV538 ) @ SV726 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV538 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV58 ) @ SV313 ) @ SV726 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2111,plain,
! [SV727: $i,SV539: $i,SV314: $i,SV59: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV59 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ SV539 ) ) @ SV727 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV314 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ SV539 ) @ SV727 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2112,plain,
! [SV728: $i,SV540: $i,SV315: $i,SV60: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV60 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV540 ) @ SV728 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV540 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV60 ) @ SV315 ) @ SV728 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2113,plain,
! [SV729: $i,SV541: $i,SV316: $i,SV61: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV61 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV541 ) @ SV729 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ SV316 ) @ SV541 ) ) @ SV729 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2114,plain,
! [SV853: $i,SV820: $i,SV730: $i,SV542: $i,SV317: $i,SV63: $i] :
( ( ( SV63 = SV317 )
| ( SV542 = SV730 )
| ~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Olist_OCons @ SV317 @ SV730 @ SV853 ) @ ( c_List_Olist_OCons @ SV63 @ SV542 @ SV853 ) @ SV853 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2115,plain,
! [SV821: $i,SV731: $i,SV543: $i,SV318: $i,SV64: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV64 @ SV318 ) @ SV543 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV64 @ ( c_List_Olist_OCons @ SV318 @ SV731 @ SV821 ) @ ( c_List_Olist_OCons @ SV543 @ SV731 @ SV821 ) @ SV821 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(2116,plain,
! [SV732: $i,SV320: $i,SV544: $i,SV66: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV544 ) @ SV320 ) @ SV732 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV66 @ SV732 @ SV544 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV66 @ SV320 @ SV544 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(2117,plain,
! [SV321: $i,SV545: $i,SV733: $i,SV67: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV67 @ SV733 @ SV545 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV545 ) @ SV321 ) @ SV733 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV67 @ SV321 @ SV545 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2118,plain,
! [SV734: $i,SV549: $i,SV325: $i,SV73: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV73 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ SV549 ) @ SV734 @ SV73 @ SV73 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV325 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV73 ) @ SV549 @ SV734 @ SV73 @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2119,plain,
! [SV77: $i,SV329: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV329 @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV77 ) @ SV329 ) @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2120,plain,
! [SV330: $i,SV78: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV78 ) @ SV330 ) @ SV330 ) @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV330 @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV78 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2121,plain,
! [SV331: $i,SV79: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV79 ) @ SV331 ) @ SV331 ) @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV331 @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV79 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2122,plain,
! [SV80: $i,SV332: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV332 @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV332 ) @ SV332 ) @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV80 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2123,plain,
! [SV555: $i,SV335: $i,SV84: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV335 ) @ SV555 ) @ SV84 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV555 @ SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV335 @ SV84 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2124,plain,
! [SV854: $i,SV822: $i,SV736: $i,SV556: $i,SV336: $i,SV85: $i] :
( ( ( c_ListOrder_Ostep1 @ SV85 @ SV336 @ SV556 @ SV736 )
| ( SV556 = SV336 )
| ~ ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SV822 @ SV336 @ SV736 ) @ ( c_List_Olist_OCons @ SV854 @ SV556 @ SV736 ) @ SV736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2125,plain,
! [SV823: $i,SV737: $i,SV557: $i,SV337: $i,SV86: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV737 ) @ SV823 ) @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV823 @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV337 @ SV737 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2126,plain,
! [SV558: $i,SV87: $i,SV338: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV338 @ SV87 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV558 @ SV87 ) @ SV87 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV338 @ SV558 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2127,plain,
! [SV88: $i,SV559: $i,SV339: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV339 @ SV559 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV339 @ SV88 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV559 @ SV88 ) @ SV88 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2128,plain,
! [SV738: $i,SV560: $i,SV340: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV89 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV560 ) @ SV738 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ SV738 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV560 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2129,plain,
! [SV855: $i,SV824: $i,SV739: $i,SV561: $i,SV341: $i,SV90: $i] :
( ( ( c_List_Ofoldr @ SV90 @ ( c_List_Olist_OCons @ SV341 @ SV561 @ SV739 ) @ SV824 @ SV739 @ SV855 )
= ( hAPP @ ( hAPP @ SV90 @ SV341 ) @ ( c_List_Ofoldr @ SV90 @ SV561 @ SV824 @ SV739 @ SV855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2130,plain,
! [SV740: $i,SV563: $i,SV343: $i,SV92: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV92 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV343 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV740 ) @ SV563 ) @ SV92 )
| ~ ( c_HOL_Oord__class_Oless @ SV343 @ SV740 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2131,plain,
! [SV741: $i,SV564: $i,SV344: $i,SV93: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV344 ) @ SV564 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV741 ) @ SV564 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV344 @ SV741 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2132,plain,
! [SV742: $i,SV565: $i,SV345: $i,SV94: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV345 @ SV565 @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV345 ) @ SV742 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV565 ) @ SV742 ) @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2133,plain,
! [SV743: $i,SV566: $i,SV346: $i,SV95: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV95 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV743 ) @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ SV566 @ SV743 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2134,plain,
! [SV744: $i,SV567: $i,SV347: $i,SV96: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV567 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV744 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ SV744 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2135,plain,
! [SV745: $i,SV568: $i,SV348: $i,SV97: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV348 @ SV568 @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV348 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV568 ) @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2136,plain,
! [SV856: $i,SV825: $i,SV746: $i,SV569: $i,SV349: $i,SV98: $i] :
( ( ( c_ListOrder_Ostep1 @ SV98 @ SV349 @ SV569 @ SV746 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV825 ) @ SV856 ) )
| ~ ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SV825 @ SV349 @ SV746 ) @ ( c_List_Olist_OCons @ SV856 @ SV569 @ SV746 ) @ SV746 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2137,plain,
! [SV826: $i,SV747: $i,SV570: $i,SV350: $i,SV99: $i] :
( ( ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_OCons @ SV350 @ SV570 @ SV747 ) @ ( c_List_Olist_OCons @ SV350 @ SV826 @ SV747 ) @ SV747 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV99 @ SV570 @ SV826 @ SV747 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(2138,plain,
! [SV573: $i,SV748: $i,SV354: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ SV354 ) @ SV748 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV103 @ SV748 @ SV573 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV103 @ SV354 @ SV573 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2139,plain,
! [SV574: $i,SV749: $i,SV355: $i,SV104: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV355 ) @ SV749 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV104 @ SV749 @ SV574 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV104 @ SV355 @ SV574 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2140,plain,
! [SV105: $i,SV575: $i,SV356: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV575 @ SV105 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV356 @ SV105 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2141,plain,
! [SV106: $i,SV576: $i,SV357: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV357 @ SV576 @ SV106 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV357 @ SV106 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1974]) ).
thf(2142,plain,
! [SV107: $i,SV577: $i,SV358: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV358 @ SV577 @ SV107 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV358 @ SV107 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2143,plain,
! [SV827: $i,SV750: $i,SV578: $i,SV359: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV750 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SV827 ) @ SV750 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV827 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2144,plain,
! [SV828: $i,SV751: $i,SV579: $i,SV360: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV579 ) @ SV751 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV828 ) @ SV751 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SV579 ) @ SV828 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1977]) ).
thf(2145,plain,
! [SV110: $i,SV580: $i,SV361: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV361 @ SV580 @ SV110 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV580 @ SV361 @ SV110 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2146,plain,
! [SV581: $i,SV362: $i,SV752: $i,SV111: $i] :
( ( ( c_Type_Otyping @ SV111 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV752 ) @ SV362 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV581 )
= $false )
| ( ( c_Type_Otypings @ SV111 @ SV362 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV581 @ SV111 @ SV752 @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2147,plain,
! [SV582: $i,SV363: $i,SV753: $i,SV112: $i] :
( ( ( c_Type_Otyping @ SV112 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV753 @ SV363 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV582 )
= $false )
| ( ( c_Type_Otypings @ SV112 @ SV363 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV582 @ SV112 @ SV753 @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2148,plain,
! [SV829: $i,SV754: $i,SV583: $i,SV364: $i,SV113: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV113 @ SV364 @ SV583 @ SV754 ) @ SV829 )
= ( hAPP @ SV113 @ SV829 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV829 @ SV364 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2149,plain,
! [SV366: $i,SV116: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV366 @ SV116 ) @ SV116 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV366 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2150,plain,
! [SV117: $i,SV367: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV367 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV367 @ SV117 ) @ SV117 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2151,plain,
! [SV119: $i,SV585: $i,SV369: $i] :
( ( ( SV369 = SV585 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV369 @ SV585 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV585 @ SV369 @ SV119 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2152,plain,
! [SV120: $i,SV586: $i,SV370: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV370 @ SV586 @ SV120 )
= $true )
| ( ( ( SV586 = SV370 )
| ( c_HOL_Oord__class_Oless @ SV586 @ SV370 @ SV120 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2153,plain,
! [SV121: $i,SV587: $i,SV371: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV371 @ SV587 @ SV121 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV587 @ SV371 @ SV121 )
| ( SV587 = SV371 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2154,plain,
! [SV123: $i,SV373: $i,SV588: $i] :
( ( ( SV588 = SV373 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV588 @ SV373 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV373 @ SV588 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV373 ) @ SV588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2155,plain,
! [SV125: $i,SV589: $i,SV375: $i] :
( ( ( SV375 = SV589 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV589 @ SV375 @ SV125 )
| ( c_HOL_Oord__class_Oless @ SV375 @ SV589 @ SV125 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2156,plain,
! [SV126: $i,SV590: $i,SV376: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV376 @ SV590 @ SV126 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV590 @ SV376 @ SV126 )
| ( SV590 = SV376 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2157,plain,
! [SV592: $i,SV133: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV381 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV133 @ SV381 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV592 @ 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 @ SV133 ) ) @ SV381 ) @ SV592 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2158,plain,
! [SV382: $i,SV755: $i,SV593: $i,SV134: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ SV593 ) @ SV755 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV134 @ SV382 ) @ SV593 ) @ SV755 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2159,plain,
! [SV830: $i,SV756: $i,SV594: $i,SV383: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV756 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV830 ) @ SV756 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV830 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2160,plain,
! [SV597: $i,SV139: $i,SV387: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV387 @ 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 @ SV139 ) ) @ SV387 ) @ SV597 @ 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 @ SV139 @ SV387 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2161,plain,
! [SV757: $i,SV598: $i,SV388: $i,SV140: $i] :
( ( ( class_Orderings_Opreorder @ SV140 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV388 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV757 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV757 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2162,plain,
! [SV758: $i,SV599: $i,SV389: $i,SV141: $i] :
( ( ( class_Orderings_Oorder @ SV141 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV389 @ SV599 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV758 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV758 @ SV599 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2163,plain,
! [SV600: $i,SV390: $i,SV759: $i,SV145: $i] :
( ( ( c_Type_Otyping @ SV145 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV759 @ SV390 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV600 )
= $false )
| ( ( c_Type_Otypings @ SV145 @ SV390 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV600 @ SV145 @ SV759 @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2164,plain,
! [SV857: $i,SV831: $i,SV760: $i,SV602: $i,SV392: $i,SV148: $i] :
( ( ! [SY2095: $i] :
( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
| ~ ( c_Type_Otypings @ SV148 @ SV857 @ SY2095 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2165,plain,
! [SV604: $i,SV761: $i,SV396: $i,SV154: $i] :
( ( ( c_Type_Otyping @ SV154 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SV761 ) @ SV604 )
= $false )
| ( ( c_Type_Otyping @ SV154 @ SV396 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV604 @ SV154 @ SV396 @ SV761 ) ) @ SV604 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2166,plain,
! [SV605: $i,SV762: $i,SV398: $i,SV156: $i] :
( ( ( c_Type_Otyping @ SV156 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV398 @ SV762 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV605 )
= $false )
| ( ( c_Type_Otyping @ SV156 @ SV398 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV605 @ SV156 @ SV398 @ SV762 ) @ SV605 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2167,plain,
! [SV401: $i,SV607: $i,SV763: $i,SV159: $i] :
( ( ( ~ ( c_Type_Otyping @ SV159 @ SV763 @ SV607 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV763 ) @ SV401 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV159 @ SV401 @ SV607 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2168,plain,
! [SV610: $i,SV162: $i,SV764: $i,SV404: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV404 ) @ SV764 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV162 ) @ SV610 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV404 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SV764 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2169,plain,
! [SV613: $i,SV408: $i,SV765: $i,SV166: $i] :
( ( ( c_Type_Otyping @ SV166 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV765 ) @ SV408 ) @ SV613 )
= $false )
| ( ( c_Type_Otyping @ SV166 @ SV408 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV613 @ SV166 @ SV765 @ SV408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2170,plain,
! [SV832: $i,SV766: $i,SV615: $i,SV410: $i,SV168: $i] :
( ( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV410 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV766 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV168 @ SV615 @ SV832 )
| ~ ( c_Type_Otyping @ SV168 @ SV410 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV832 @ SV766 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2171,plain,
! [SV616: $i,SV767: $i,SV411: $i,SV169: $i] :
( ( ( c_Type_Otyping @ SV169 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV411 ) @ SV767 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV616 )
= $false )
| ( ( c_Type_Otyping @ SV169 @ ( c_Lambda_OdB_OVar @ SV411 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV616 @ SV169 @ SV411 @ SV767 ) @ SV616 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2172,plain,
! [SV618: $i,SV768: $i,SV413: $i,SV171: $i] :
( ( ( c_Type_Otyping @ SV171 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV413 @ SV768 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV618 )
= $false )
| ( ( c_Type_Otyping @ SV171 @ SV413 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV618 @ SV171 @ SV413 @ SV768 ) @ SV618 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2173,plain,
! [SV619: $i,SV172: $i,SV769: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV414 ) @ SV769 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV172 @ SV414 @ SV619 ) ) @ ( c_Lambda_Osubst @ SV172 @ SV769 @ SV619 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2174,plain,
! [SV621: $i,SV416: $i,SV770: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV174 ) @ SV770 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV174 @ SV416 @ SV621 ) ) @ ( c_Lambda_Osubst @ SV770 @ SV416 @ SV621 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2175,plain,
! [SV622: $i,SV175: $i,SV771: $i,SV417: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV417 ) @ SV771 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV175 @ SV417 @ SV622 ) ) @ ( c_Lambda_Osubst @ SV175 @ SV771 @ SV622 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2176,plain,
! [SV772: $i,SV418: $i,SV623: $i,SV177: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV177 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV623 @ tc_Type_Otype ) @ SV418 @ SV772 )
= $false )
| ( ( c_Type_Otyping @ SV177 @ ( c_Lambda_OdB_OAbs @ SV418 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV623 ) @ SV772 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2177,plain,
! [SV833: $i,SV774: $i,SV627: $i,SV424: $i,SV183: $i] :
( ( ( SV183 = SV424 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV424 )
| ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2178,plain,
! [SV834: $i,SV775: $i,SV628: $i,SV426: $i,SV185: $i] :
( ( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV426 ) @ SV628 ) @ SV775 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV185 @ SV628 @ SV834 )
| ~ ( c_Type_Otyping @ SV185 @ SV426 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV834 ) @ SV775 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2179,plain,
! [SV858: $i,SV835: $i,SV776: $i,SV629: $i,SV428: $i,SV187: $i] :
( ( ! [SY2096: $i] :
( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
| ~ ( c_Type_Otypings @ SV629 @ SV858 @ SY2096 )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2180,plain,
! [SV836: $i,SV777: $i,SV632: $i,SV431: $i,SV190: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV190 @ SV431 @ SV632 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV777 @ SV431 ) @ SV836 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV190 @ SV777 @ SV836 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2181,plain,
! [SV634: $i,SV192: $i,SV433: $i,SV779: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV779 ) @ SV433 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV192 @ SV779 @ SV634 ) )
= $true )
| ( ( c_Type_Otyping @ SV192 @ SV433 @ SV634 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2182,plain,
! [SV636: $i,SV436: $i,SV780: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV195 ) @ SV780 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV195 @ SV436 @ SV636 ) ) @ ( c_Lambda_Osubst @ SV780 @ SV436 @ SV636 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2183,plain,
! [SV859: $i,SV837: $i,SV781: $i,SV638: $i,SV439: $i,SV198: $i] :
( ( ~ ( c_Type_Otyping @ SV198 @ SV439 @ SV638 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SV781 @ SV638 @ tc_Type_Otype ) @ SV837 @ SV859 )
| ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SV837 @ SV439 @ SV781 ) @ SV859 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2184,plain,
! [SV782: $i,SV640: $i,SV444: $i,SV203: $i] :
( ( ( ( c_List_Oappend @ SV203 @ SV444 @ SV640 )
= ( c_List_Oappend @ SV782 @ SV444 @ SV640 ) )
= $false )
| ( ( SV203 = SV782 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2185,plain,
! [SV783: $i,SV641: $i,SV445: $i,SV204: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV204 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV445 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV783 ) @ SV641 ) )
| ( SV445 = SV783 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2186,plain,
! [SV784: $i,SV644: $i,SV448: $i,SV207: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV207 ) @ SV448 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV644 ) @ SV784 ) )
= $false )
| ( ( SV448 = SV784 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2187,plain,
! [SV785: $i,SV645: $i,SV450: $i,SV209: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV209 ) @ SV450 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV645 ) @ SV785 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV209 = SV645 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2188,plain,
! [SV838: $i,SV786: $i,SV654: $i,SV461: $i,SV220: $i] :
( ( ( ( c_List_Oappend @ SV220 @ ( c_List_Olist_OCons @ SV461 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 )
!= ( c_List_Oappend @ SV786 @ ( c_List_Olist_OCons @ SV838 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 ) )
= $true )
| ( ( SV461 = SV838 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2189,plain,
! [SV787: $i,SV657: $i,SV464: $i,SV223: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV223 ) @ SV464 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV657 ) @ SV787 ) )
= $false )
| ( ( SV223 = SV657 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2190,plain,
! [SV788: $i,SV658: $i,SV465: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV224 ) @ SV465 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV658 ) @ SV788 ) )
= $false )
| ( ( SV224 = SV658 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2191,plain,
! [SV839: $i,SV789: $i,SV659: $i,SV466: $i,SV225: $i] :
( ( ( ( c_List_Oappend @ SV225 @ ( c_List_Olist_OCons @ SV466 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 )
!= ( c_List_Oappend @ SV789 @ ( c_List_Olist_OCons @ SV839 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 ) )
= $true )
| ( ( SV225 = SV789 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2192,plain,
! [SV840: $i,SV791: $i,SV662: $i,SV470: $i,SV229: $i] :
( ( ( ( c_List_Olist_OCons @ SV229 @ SV470 @ SV662 )
!= ( c_List_Olist_OCons @ SV791 @ SV840 @ SV662 ) )
= $true )
| ( ( SV470 = SV840 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2193,plain,
! [SV841: $i,SV792: $i,SV667: $i,SV475: $i,SV234: $i] :
( ( ( ( c_List_Olist_OCons @ SV234 @ SV475 @ SV667 )
!= ( c_List_Olist_OCons @ SV792 @ SV841 @ SV667 ) )
= $true )
| ( ( SV234 = SV792 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2194,plain,
! [SV793: $i,SV668: $i,SV476: $i,SV235: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV235 ) @ SV476 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV668 ) @ SV793 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV235 = SV668 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2195,plain,
! [SV794: $i,SV669: $i,SV477: $i,SV236: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV236 ) @ SV477 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV669 ) @ SV794 ) )
= $false )
| ( ( SV477 = SV794 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2196,plain,
! [SV860: $i,SV842: $i,SV795: $i,SV670: $i,SV478: $i,SV237: $i] :
( ( ! [SY2097: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
| ~ ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SY2097 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2197,plain,
! [SV796: $i,SV671: $i,SV479: $i,SV238: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV671 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV796 ) )
| ( SV671 = SV796 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2198,plain,
! [SV797: $i,SV672: $i,SV480: $i,SV239: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV239 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV239 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV672 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV797 ) )
| ( SV672 = SV797 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2199,plain,
! [SV798: $i,SV674: $i,SV482: $i,SV241: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV241 ) @ SV482 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV674 ) @ SV798 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV482 = SV798 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2200,plain,
! [SV676: $i,SV484: $i,SV243: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV243 ) )
= $true )
| ( ( ( SV484
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SV484 ) @ SV676 ) )
| ( SV676
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2201,plain,
! [SV843: $i,SV799: $i,SV678: $i,SV486: $i,SV245: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV245 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV799 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV843 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ SV799 )
= SV843 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2068]) ).
thf(2202,plain,
! [SV861: $i,SV844: $i,SV801: $i,SV680: $i,SV488: $i,SV247: $i] :
( ( ! [SY2098: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
| ~ ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SY2098 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2203,plain,
! [SV682: $i,SV249: $i,SV490: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV490 @ SV249 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV682 @ SV249 ) )
= $true )
| ( ( SV490 = SV682 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2072]) ).
thf(2204,plain,
! [SV802: $i,SV684: $i,SV492: $i,SV251: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV251 ) @ SV492 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV684 ) @ SV802 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV492 = SV802 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2205,plain,
! [SV803: $i,SV688: $i,SV496: $i,SV255: $i] :
( ( ( ( c_List_Oappend @ SV255 @ SV496 @ SV688 )
= ( c_List_Oappend @ SV255 @ SV803 @ SV688 ) )
= $false )
| ( ( SV496 = SV803 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2206,plain,
! [SV497: $i,SV256: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV256 ) @ SV497 ) @ SV497 )
= ( c_HOL_Ozero__class_Ozero @ SV256 ) )
= $false )
| ( ( SV497
= ( c_HOL_Ozero__class_Ozero @ SV256 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2207,plain,
! [SV804: $i,SV690: $i,SV499: $i,SV258: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV258 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV690 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV804 ) )
| ( SV690 = SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2208,plain,
! [SV264: $i,SV695: $i,SV505: $i,SV7: $i] :
( ( ( c_List_Olistsp @ SV7 @ SV505 @ SV695 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV7 @ SV264 @ SV695 ) )
= $true )
| ( ( c_List_Olistsp @ SV7 @ ( c_List_Oappend @ SV264 @ SV505 @ SV695 ) @ SV695 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2209,plain,
! [SV845: $i,SV805: $i,SV696: $i,SV506: $i,SV265: $i,SV8: $i] :
( ( ( SV8 = SV265 )
= $true )
| ( ( ( SV506 = SV696 )
| ~ ( c_ListOrder_Ostep1 @ SV805 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SV845 ) @ SV845 ) @ SV845 ) @ ( c_List_Oappend @ SV265 @ ( c_List_Olist_OCons @ SV696 @ ( c_List_Olist_ONil @ SV845 ) @ SV845 ) @ SV845 ) @ SV845 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2210,plain,
! [SV846: $i,SV806: $i,SV697: $i,SV507: $i,SV266: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SV266 ) @ SV507 ) )
= $true )
| ( ( ( SV266 = SV507 )
| ~ ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SV697 @ ( c_List_Olist_OCons @ SV266 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV507 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ SV806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2211,plain,
! [SV275: $i,SV701: $i,SV808: $i,SV511: $i,SV18: $i] :
( ( ( c_ListOrder_Ostep1 @ SV18 @ SV511 @ SV808 @ SV701 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV18 @ ( c_List_Oappend @ SV275 @ SV511 @ SV701 ) @ ( c_List_Oappend @ SV275 @ SV808 @ SV701 ) @ SV701 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2212,plain,
! [SV809: $i,SV702: $i,SV512: $i,SV276: $i,SV19: $i] :
( ( ( c_ListOrder_Ostep1 @ SV19 @ SV276 @ SV512 @ SV702 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV19 @ ( c_List_Oappend @ SV276 @ SV809 @ SV702 ) @ ( c_List_Oappend @ SV512 @ SV809 @ SV702 ) @ SV702 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2213,plain,
! [SV848: $i,SV810: $i,SV703: $i,SV513: $i,SV277: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV277 ) @ SV513 ) )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV20 @ SV703 @ SV810 @ SV848 )
| ~ ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SV703 @ ( c_List_Olist_OCons @ SV277 @ ( c_List_Olist_ONil @ SV848 ) @ SV848 ) @ SV848 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV513 @ ( c_List_Olist_ONil @ SV848 ) @ SV848 ) @ SV848 ) @ SV848 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2214,plain,
! [SV849: $i,SV811: $i,SV709: $i,SV520: $i,SV284: $i,SV27: $i] :
( ( ( SV27 = SV284 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV520 @ SV27 @ SV284 @ SV709 )
| ~ ( c_ListOrder_Ostep1 @ SV520 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ ( c_List_Oappend @ SV284 @ ( c_List_Olist_OCons @ SV849 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ SV709 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2215,plain,
! [SV813: $i,SV711: $i,SV522: $i,SV297: $i,SV41: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV41 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV522 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV711 ) @ SV813 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV297 ) @ SV711 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV41 ) @ SV522 ) @ SV813 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2216,plain,
! [SV851: $i,SV814: $i,SV712: $i,SV523: $i,SV298: $i,SV42: $i] :
( ( ( SV42 = SV298 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV298 ) @ SV42 ) )
| ~ ( c_ListOrder_Ostep1 @ SV523 @ ( c_List_Olist_OCons @ SV298 @ SV712 @ SV814 ) @ ( c_List_Olist_OCons @ SV42 @ SV851 @ SV814 ) @ SV814 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2217,plain,
! [SV299: $i,SV43: $i,SV524: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV524 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV299 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV299 ) @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2218,plain,
! [SV304: $i,SV529: $i,SV816: $i,SV717: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV49 @ SV717 @ SV816 ) @ SV529 ) @ SV304 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV49 @ SV304 ) @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2219,plain,
! [SV530: $i,SV305: $i,SV718: $i,SV817: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV817 ) @ SV718 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV50 @ SV305 @ SV530 ) @ SV718 ) @ SV817 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2220,plain,
! [SV306: $i,SV531: $i,SV818: $i,SV719: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV51 @ SV719 @ SV818 ) @ SV531 ) @ SV306 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV306 ) @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2221,plain,
! [SV532: $i,SV307: $i,SV720: $i,SV819: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV52 @ SV819 ) @ SV720 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV52 @ SV307 @ SV532 ) @ SV720 ) @ SV819 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2222,plain,
! [SV853: $i,SV820: $i,SV730: $i,SV542: $i,SV317: $i,SV63: $i] :
( ( ( SV63 = SV317 )
= $true )
| ( ( ( SV542 = SV730 )
| ~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Olist_OCons @ SV317 @ SV730 @ SV853 ) @ ( c_List_Olist_OCons @ SV63 @ SV542 @ SV853 ) @ SV853 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2223,plain,
! [SV821: $i,SV731: $i,SV543: $i,SV318: $i,SV64: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV64 @ SV318 ) @ SV543 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV64 @ ( c_List_Olist_OCons @ SV318 @ SV731 @ SV821 ) @ ( c_List_Olist_OCons @ SV543 @ SV731 @ SV821 ) @ SV821 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2224,plain,
! [SV732: $i,SV320: $i,SV544: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV544 ) @ SV320 ) @ SV732 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV66 @ SV732 @ SV544 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV66 @ SV320 @ SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2225,plain,
! [SV321: $i,SV545: $i,SV733: $i,SV67: $i] :
( ( ( c_Wellfounded_Oaccp @ SV67 @ SV733 @ SV545 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV545 ) @ SV321 ) @ SV733 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV67 @ SV321 @ SV545 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2226,plain,
! [SV335: $i,SV555: $i,SV84: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV555 @ SV84 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV335 @ SV84 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV335 ) @ SV555 ) @ SV84 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2227,plain,
! [SV854: $i,SV822: $i,SV736: $i,SV556: $i,SV336: $i,SV85: $i] :
( ( ( c_ListOrder_Ostep1 @ SV85 @ SV336 @ SV556 @ SV736 )
= $true )
| ( ( ( SV556 = SV336 )
| ~ ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SV822 @ SV336 @ SV736 ) @ ( c_List_Olist_OCons @ SV854 @ SV556 @ SV736 ) @ SV736 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2228,plain,
! [SV823: $i,SV737: $i,SV557: $i,SV337: $i,SV86: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV737 ) @ SV823 ) @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV823 @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV337 @ SV737 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2229,plain,
! [SV87: $i,SV558: $i,SV338: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV338 @ SV558 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV338 @ SV87 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV558 @ SV87 ) @ SV87 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2230,plain,
! [SV559: $i,SV88: $i,SV339: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV339 @ SV88 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV559 @ SV88 ) @ SV88 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV339 @ SV559 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2231,plain,
! [SV738: $i,SV560: $i,SV89: $i,SV340: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV560 ) @ SV738 ) @ SV89 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV340 @ SV738 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV560 @ SV89 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2232,plain,
! [SV740: $i,SV563: $i,SV343: $i,SV92: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV343 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV740 ) @ SV563 ) @ SV92 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV343 @ SV740 @ SV92 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2233,plain,
! [SV741: $i,SV564: $i,SV344: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV344 ) @ SV564 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV741 ) @ SV564 ) @ SV93 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV344 @ SV741 @ SV93 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2234,plain,
! [SV742: $i,SV94: $i,SV565: $i,SV345: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV345 @ SV565 @ SV94 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV345 ) @ SV742 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV565 ) @ SV742 ) @ SV94 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2235,plain,
! [SV743: $i,SV566: $i,SV346: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV743 ) @ SV95 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV566 @ SV743 @ SV95 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2236,plain,
! [SV744: $i,SV567: $i,SV347: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV567 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV744 ) @ SV96 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV567 @ SV744 @ SV96 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2237,plain,
! [SV745: $i,SV97: $i,SV568: $i,SV348: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV348 @ SV568 @ SV97 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV348 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV568 ) @ SV97 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2238,plain,
! [SV856: $i,SV825: $i,SV746: $i,SV569: $i,SV349: $i,SV98: $i] :
( ( ( c_ListOrder_Ostep1 @ SV98 @ SV349 @ SV569 @ SV746 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV825 ) @ SV856 ) )
| ~ ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SV825 @ SV349 @ SV746 ) @ ( c_List_Olist_OCons @ SV856 @ SV569 @ SV746 ) @ SV746 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2239,plain,
! [SV350: $i,SV747: $i,SV826: $i,SV570: $i,SV99: $i] :
( ( ( c_ListOrder_Ostep1 @ SV99 @ SV570 @ SV826 @ SV747 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV99 @ ( c_List_Olist_OCons @ SV350 @ SV570 @ SV747 ) @ ( c_List_Olist_OCons @ SV350 @ SV826 @ SV747 ) @ SV747 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2240,plain,
! [SV573: $i,SV748: $i,SV354: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ SV354 ) @ SV748 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV103 @ SV748 @ SV573 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV103 @ SV354 @ SV573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2241,plain,
! [SV574: $i,SV749: $i,SV355: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV355 ) @ SV749 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV104 @ SV749 @ SV574 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV104 @ SV355 @ SV574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2242,plain,
! [SV105: $i,SV575: $i,SV356: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV356 @ SV575 @ SV105 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV575 @ SV356 @ SV105 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2243,plain,
! [SV106: $i,SV576: $i,SV357: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV357 @ SV576 @ SV106 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV576 @ SV357 @ SV106 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2244,plain,
! [SV107: $i,SV577: $i,SV358: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV358 @ SV577 @ SV107 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV577 @ SV358 @ SV107 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2245,plain,
! [SV578: $i,SV359: $i,SV750: $i,SV827: $i,SV108: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SV827 ) @ SV750 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV827 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV750 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2246,plain,
! [SV579: $i,SV751: $i,SV828: $i,SV360: $i,SV109: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV828 ) @ SV751 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SV579 ) @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV579 ) @ SV751 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2247,plain,
! [SV110: $i,SV580: $i,SV361: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV361 @ SV580 @ SV110 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV580 @ SV361 @ SV110 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2248,plain,
! [SV754: $i,SV583: $i,SV113: $i,SV364: $i,SV829: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV829 @ SV364 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( c_Type_Oshift @ SV113 @ SV364 @ SV583 @ SV754 ) @ SV829 )
= ( hAPP @ SV113 @ SV829 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2249,plain,
! [SV119: $i,SV585: $i,SV369: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV369 @ SV585 @ SV119 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV585 @ SV369 @ SV119 )
= $true )
| ( ( SV369 = SV585 )
= $true )
| ( ( class_Orderings_Olinorder @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2250,plain,
! [SV120: $i,SV370: $i,SV586: $i] :
( ( ( SV586 = SV370 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV586 @ SV370 @ SV120 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV370 @ SV586 @ SV120 )
= $true )
| ( ( class_Orderings_Olinorder @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2251,plain,
! [SV121: $i,SV371: $i,SV587: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV587 @ SV371 @ SV121 )
= $true )
| ( ( SV587 = SV371 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV371 @ SV587 @ SV121 )
= $true )
| ( ( class_Orderings_Olinorder @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2252,plain,
! [SV125: $i,SV375: $i,SV589: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV589 @ SV375 @ SV125 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV375 @ SV589 @ SV125 )
= $true )
| ( ( SV375 = SV589 )
= $true )
| ( ( class_Orderings_Olinorder @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2253,plain,
! [SV126: $i,SV376: $i,SV590: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV590 @ SV376 @ SV126 )
= $true )
| ( ( SV590 = SV376 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV376 @ SV590 @ SV126 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2254,plain,
! [SV592: $i,SV381: $i,SV133: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV133 @ SV381 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV592 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV381 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV133 ) ) @ SV381 ) @ SV592 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2255,plain,
! [SV594: $i,SV756: $i,SV830: $i,SV383: $i,SV135: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV830 ) @ SV756 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV830 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV756 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2256,plain,
! [SV597: $i,SV139: $i,SV387: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV387 @ 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 @ SV139 ) ) @ SV387 ) @ SV597 @ 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 @ SV139 @ SV387 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2257,plain,
! [SV757: $i,SV140: $i,SV598: $i,SV388: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV388 @ SV598 @ SV140 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV757 @ SV598 @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV757 @ SV140 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2161]) ).
thf(2258,plain,
! [SV758: $i,SV141: $i,SV599: $i,SV389: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV389 @ SV599 @ SV141 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV758 @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ SV758 @ SV599 @ SV141 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2259,plain,
! [SV862: $i,SV857: $i,SV831: $i,SV760: $i,SV602: $i,SV392: $i,SV148: $i] :
( ( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
| ~ ( c_Type_Otypings @ SV148 @ SV857 @ SV862 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2260,plain,
! [SV401: $i,SV607: $i,SV763: $i,SV159: $i] :
( ( ( c_Type_Otyping @ SV159 @ SV763 @ SV607 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV763 ) @ SV401 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV159 @ SV401 @ SV607 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2261,plain,
! [SV610: $i,SV162: $i,SV764: $i,SV404: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV404 ) @ SV764 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV162 ) @ SV610 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV404 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SV764 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2262,plain,
! [SV766: $i,SV410: $i,SV832: $i,SV615: $i,SV168: $i] :
( ( ( ~ ( c_Type_Otypings @ SV168 @ SV615 @ SV832 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV168 @ SV410 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV832 @ SV766 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV410 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV766 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2263,plain,
! [SV183: $i,SV424: $i,SV833: $i,SV774: $i,SV627: $i] :
( ( ( ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV424 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 ) )
= $true )
| ( ( SV183 = SV424 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2264,plain,
! [SV775: $i,SV426: $i,SV834: $i,SV628: $i,SV185: $i] :
( ( ( ~ ( c_Type_Otyping @ SV185 @ SV628 @ SV834 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV185 @ SV426 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV834 ) @ SV775 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV426 ) @ SV628 ) @ SV775 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2265,plain,
! [SV863: $i,SV858: $i,SV835: $i,SV776: $i,SV629: $i,SV428: $i,SV187: $i] :
( ( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
| ~ ( c_Type_Otypings @ SV629 @ SV858 @ SV863 )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2266,plain,
! [SV632: $i,SV431: $i,SV836: $i,SV777: $i,SV190: $i] :
( ( ( c_Type_Otyping @ SV190 @ SV777 @ SV836 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV190 @ SV431 @ SV632 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV777 @ SV431 ) @ SV836 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2267,plain,
! [SV634: $i,SV192: $i,SV433: $i,SV779: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV779 ) @ SV433 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV192 @ SV779 @ SV634 ) )
= $true )
| ( ( c_Type_Otyping @ SV192 @ SV433 @ SV634 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2268,plain,
! [SV859: $i,SV837: $i,SV781: $i,SV638: $i,SV439: $i,SV198: $i] :
( ( ( ~ ( c_Type_Otyping @ SV198 @ SV439 @ SV638 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SV781 @ SV638 @ tc_Type_Otype ) @ SV837 @ SV859 )
| ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SV837 @ SV439 @ SV781 ) @ SV859 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2269,plain,
! [SV783: $i,SV641: $i,SV445: $i,SV204: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV445 ) @ SV641 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV783 ) @ SV641 ) )
= $true )
| ( ( SV445 = SV783 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2270,plain,
! [SV838: $i,SV786: $i,SV654: $i,SV461: $i,SV220: $i] :
( ( ( ( c_List_Oappend @ SV220 @ ( c_List_Olist_OCons @ SV461 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 )
= ( c_List_Oappend @ SV786 @ ( c_List_Olist_OCons @ SV838 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 ) )
= $false )
| ( ( SV461 = SV838 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2271,plain,
! [SV839: $i,SV789: $i,SV659: $i,SV466: $i,SV225: $i] :
( ( ( ( c_List_Oappend @ SV225 @ ( c_List_Olist_OCons @ SV466 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 )
= ( c_List_Oappend @ SV789 @ ( c_List_Olist_OCons @ SV839 @ ( c_List_Olist_ONil @ SV659 ) @ SV659 ) @ SV659 ) )
= $false )
| ( ( SV225 = SV789 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2272,plain,
! [SV840: $i,SV791: $i,SV662: $i,SV470: $i,SV229: $i] :
( ( ( ( c_List_Olist_OCons @ SV229 @ SV470 @ SV662 )
= ( c_List_Olist_OCons @ SV791 @ SV840 @ SV662 ) )
= $false )
| ( ( SV470 = SV840 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2273,plain,
! [SV841: $i,SV792: $i,SV667: $i,SV475: $i,SV234: $i] :
( ( ( ( c_List_Olist_OCons @ SV234 @ SV475 @ SV667 )
= ( c_List_Olist_OCons @ SV792 @ SV841 @ SV667 ) )
= $false )
| ( ( SV234 = SV792 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2274,plain,
! [SV864: $i,SV860: $i,SV842: $i,SV795: $i,SV670: $i,SV478: $i,SV237: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
| ~ ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2275,plain,
! [SV796: $i,SV671: $i,SV479: $i,SV238: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV671 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV796 ) )
= $true )
| ( ( SV671 = SV796 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2276,plain,
! [SV797: $i,SV672: $i,SV480: $i,SV239: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV239 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV672 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV797 ) )
| ( SV672 = SV797 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2277,plain,
! [SV676: $i,SV484: $i,SV243: $i] :
( ( ( class_Int_Onumber__ring @ SV243 )
= $false )
| ( ( ( SV484
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SV484 ) @ SV676 ) )
| ( SV676
= ( c_HOL_Ozero__class_Ozero @ SV243 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2278,plain,
! [SV843: $i,SV799: $i,SV678: $i,SV486: $i,SV245: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV245 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV799 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV843 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ SV799 )
= SV843 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2279,plain,
! [SV865: $i,SV861: $i,SV844: $i,SV801: $i,SV680: $i,SV488: $i,SV247: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
| ~ ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2280,plain,
! [SV682: $i,SV249: $i,SV490: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV490 @ SV249 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV682 @ SV249 ) )
= $false )
| ( ( SV490 = SV682 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2281,plain,
! [SV804: $i,SV690: $i,SV499: $i,SV258: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV690 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV804 ) )
= $true )
| ( ( SV690 = SV804 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2282,plain,
! [SV505: $i,SV695: $i,SV264: $i,SV7: $i] :
( ( ( c_List_Olistsp @ SV7 @ SV264 @ SV695 )
= $false )
| ( ( c_List_Olistsp @ SV7 @ SV505 @ SV695 )
= $false )
| ( ( c_List_Olistsp @ SV7 @ ( c_List_Oappend @ SV264 @ SV505 @ SV695 ) @ SV695 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2283,plain,
! [SV265: $i,SV845: $i,SV8: $i,SV805: $i,SV696: $i,SV506: $i] :
( ( ( SV506 = SV696 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV805 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SV845 ) @ SV845 ) @ SV845 ) @ ( c_List_Oappend @ SV265 @ ( c_List_Olist_OCons @ SV696 @ ( c_List_Olist_ONil @ SV845 ) @ SV845 ) @ SV845 ) @ SV845 ) )
= $true )
| ( ( SV8 = SV265 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2284,plain,
! [SV846: $i,SV806: $i,SV697: $i,SV9: $i,SV507: $i,SV266: $i] :
( ( ( SV266 = SV507 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SV697 @ ( c_List_Olist_OCons @ SV266 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV507 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ SV806 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SV266 ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2285,plain,
! [SV513: $i,SV277: $i,SV848: $i,SV810: $i,SV703: $i,SV20: $i] :
( ( ( c_ListOrder_Ostep1 @ SV20 @ SV703 @ SV810 @ SV848 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SV703 @ ( c_List_Olist_OCons @ SV277 @ ( c_List_Olist_ONil @ SV848 ) @ SV848 ) @ SV848 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV513 @ ( c_List_Olist_ONil @ SV848 ) @ SV848 ) @ SV848 ) @ SV848 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV277 ) @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2286,plain,
! [SV849: $i,SV811: $i,SV709: $i,SV284: $i,SV27: $i,SV520: $i] :
( ( ( c_ListOrder_Ostep1 @ SV520 @ SV27 @ SV284 @ SV709 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV520 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ ( c_List_Oappend @ SV284 @ ( c_List_Olist_OCons @ SV849 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ SV709 ) )
= $true )
| ( ( SV27 = SV284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2287,plain,
! [SV851: $i,SV814: $i,SV712: $i,SV42: $i,SV298: $i,SV523: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV298 ) @ SV42 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV523 @ ( c_List_Olist_OCons @ SV298 @ SV712 @ SV814 ) @ ( c_List_Olist_OCons @ SV42 @ SV851 @ SV814 ) @ SV814 ) )
= $true )
| ( ( SV42 = SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2288,plain,
! [SV299: $i,SV43: $i,SV524: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV524 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV299 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV299 ) @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2289,plain,
! [SV63: $i,SV853: $i,SV317: $i,SV820: $i,SV730: $i,SV542: $i] :
( ( ( SV542 = SV730 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Olist_OCons @ SV317 @ SV730 @ SV853 ) @ ( c_List_Olist_OCons @ SV63 @ SV542 @ SV853 ) @ SV853 ) )
= $true )
| ( ( SV63 = SV317 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2290,plain,
! [SV320: $i,SV544: $i,SV732: $i,SV66: $i] :
( ( ( c_Wellfounded_Oaccp @ SV66 @ SV732 @ SV544 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV66 @ SV544 ) @ SV320 ) @ SV732 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV66 @ SV320 @ SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2291,plain,
! [SV733: $i,SV321: $i,SV545: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV67 @ SV545 ) @ SV321 ) @ SV733 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV67 @ SV733 @ SV545 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV67 @ SV321 @ SV545 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2292,plain,
! [SV335: $i,SV555: $i,SV84: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV555 @ SV84 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV335 @ SV84 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV335 ) @ SV555 ) @ SV84 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2293,plain,
! [SV854: $i,SV736: $i,SV822: $i,SV85: $i,SV336: $i,SV556: $i] :
( ( ( SV556 = SV336 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SV822 @ SV336 @ SV736 ) @ ( c_List_Olist_OCons @ SV854 @ SV556 @ SV736 ) @ SV736 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV85 @ SV336 @ SV556 @ SV736 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2294,plain,
! [SV823: $i,SV737: $i,SV557: $i,SV337: $i,SV86: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV737 ) @ SV823 ) @ SV86 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV823 @ SV86 )
| ~ ( c_HOL_Oord__class_Oless @ SV337 @ SV737 @ SV86 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2295,plain,
! [SV560: $i,SV89: $i,SV738: $i,SV340: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV340 @ SV738 @ SV89 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV560 @ SV89 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV560 ) @ SV738 ) @ SV89 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2296,plain,
! [SV563: $i,SV92: $i,SV740: $i,SV343: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV343 @ SV740 @ SV92 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV343 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV92 ) @ SV740 ) @ SV563 ) @ SV92 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2297,plain,
! [SV564: $i,SV93: $i,SV741: $i,SV344: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV344 @ SV741 @ SV93 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV344 ) @ SV564 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV741 ) @ SV564 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2298,plain,
! [SV565: $i,SV742: $i,SV345: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV345 ) @ SV742 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV565 ) @ SV742 ) @ SV94 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV345 @ SV565 @ SV94 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2299,plain,
! [SV346: $i,SV95: $i,SV743: $i,SV566: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV566 @ SV743 @ SV95 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV566 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV346 ) @ SV743 ) @ SV95 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2300,plain,
! [SV347: $i,SV96: $i,SV744: $i,SV567: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV567 @ SV744 @ SV96 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV567 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV347 ) @ SV744 ) @ SV96 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2301,plain,
! [SV568: $i,SV348: $i,SV745: $i,SV97: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV348 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV745 ) @ SV568 ) @ SV97 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV348 @ SV568 @ SV97 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2302,plain,
! [SV569: $i,SV746: $i,SV349: $i,SV856: $i,SV825: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV825 ) @ SV856 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SV825 @ SV349 @ SV746 ) @ ( c_List_Olist_OCons @ SV856 @ SV569 @ SV746 ) @ SV746 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV98 @ SV349 @ SV569 @ SV746 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2303,plain,
! [SV354: $i,SV573: $i,SV748: $i,SV103: $i] :
( ( ( c_Wellfounded_Oaccp @ SV103 @ SV748 @ SV573 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ SV354 ) @ SV748 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV103 @ SV354 @ SV573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2304,plain,
! [SV355: $i,SV574: $i,SV749: $i,SV104: $i] :
( ( ( c_Wellfounded_Oaccp @ SV104 @ SV749 @ SV574 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV104 @ SV355 ) @ SV749 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV104 @ SV355 @ SV574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2305,plain,
! [SV105: $i,SV356: $i,SV575: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV575 @ SV356 @ SV105 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV356 @ SV575 @ SV105 )
= $false )
| ( ( class_Orderings_Opreorder @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2306,plain,
! [SV106: $i,SV357: $i,SV576: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV576 @ SV357 @ SV106 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV357 @ SV576 @ SV106 )
= $false )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2307,plain,
! [SV107: $i,SV358: $i,SV577: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV577 @ SV358 @ SV107 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV358 @ SV577 @ SV107 )
= $false )
| ( ( class_Orderings_Olinorder @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2308,plain,
! [SV578: $i,SV359: $i,SV750: $i,SV827: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SV827 ) @ SV750 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV827 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV750 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2309,plain,
! [SV579: $i,SV751: $i,SV828: $i,SV360: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV828 ) @ SV751 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SV579 ) @ SV828 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV579 ) @ SV751 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2310,plain,
! [SV110: $i,SV361: $i,SV580: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV580 @ SV361 @ SV110 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV361 @ SV580 @ SV110 )
= $false )
| ( ( class_Orderings_Oorder @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2311,plain,
! [SV594: $i,SV756: $i,SV830: $i,SV383: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV830 ) @ SV756 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV830 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV756 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2312,plain,
! [SV388: $i,SV140: $i,SV598: $i,SV757: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV757 @ SV598 @ SV140 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV757 @ SV140 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV388 @ SV598 @ SV140 )
= $true )
| ( ( class_Orderings_Opreorder @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2313,plain,
! [SV599: $i,SV141: $i,SV758: $i,SV389: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV758 @ SV141 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV758 @ SV599 @ SV141 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV389 @ SV599 @ SV141 )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2314,plain,
! [SV862: $i,SV857: $i,SV831: $i,SV760: $i,SV602: $i,SV392: $i,SV148: $i] :
( ( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
| ~ ( c_Type_Otypings @ SV148 @ SV857 @ SV862 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2315,plain,
! [SV607: $i,SV159: $i,SV401: $i,SV763: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV763 ) @ SV401 ) )
= $false )
| ( ( c_Type_Otyping @ SV159 @ SV763 @ SV607 )
= $false )
| ( ( c_Type_Otyping @ SV159 @ SV401 @ SV607 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2316,plain,
! [SV764: $i,SV404: $i,SV610: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV162 ) @ SV610 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV404 ) @ SV764 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV404 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SV764 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2317,plain,
! [SV766: $i,SV410: $i,SV832: $i,SV615: $i,SV168: $i] :
( ( ( c_Type_Otypings @ SV168 @ SV615 @ SV832 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV168 @ SV410 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV832 @ SV766 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV410 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2318,plain,
! [SV183: $i,SV424: $i,SV833: $i,SV774: $i,SV627: $i] :
( ( ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV424 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 ) )
= $true )
| ( ( SV183 = SV424 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2319,plain,
! [SV775: $i,SV426: $i,SV834: $i,SV628: $i,SV185: $i] :
( ( ( c_Type_Otyping @ SV185 @ SV628 @ SV834 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV185 @ SV426 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV834 ) @ SV775 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV426 ) @ SV628 ) @ SV775 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2320,plain,
! [SV863: $i,SV858: $i,SV835: $i,SV776: $i,SV629: $i,SV428: $i,SV187: $i] :
( ( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
| ~ ( c_Type_Otypings @ SV629 @ SV858 @ SV863 )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2321,plain,
! [SV433: $i,SV634: $i,SV779: $i,SV192: $i] :
( ( ( c_Type_Otyping @ SV192 @ SV779 @ SV634 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV779 ) @ SV433 ) )
= $false )
| ( ( c_Type_Otyping @ SV192 @ SV433 @ SV634 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2322,plain,
! [SV859: $i,SV837: $i,SV781: $i,SV638: $i,SV439: $i,SV198: $i] :
( ( ( c_Type_Otyping @ SV198 @ SV439 @ SV638 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SV781 @ SV638 @ tc_Type_Otype ) @ SV837 @ SV859 )
| ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SV837 @ SV439 @ SV781 ) @ SV859 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2323,plain,
! [SV783: $i,SV641: $i,SV445: $i,SV204: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV445 ) @ SV641 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV204 ) @ SV783 ) @ SV641 ) )
= $false )
| ( ( SV445 = SV783 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2324,plain,
! [SV864: $i,SV860: $i,SV842: $i,SV795: $i,SV670: $i,SV478: $i,SV237: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
| ~ ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2325,plain,
! [SV796: $i,SV671: $i,SV479: $i,SV238: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV671 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV238 ) @ SV479 ) @ SV796 ) )
= $false )
| ( ( SV671 = SV796 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2326,plain,
! [SV797: $i,SV672: $i,SV480: $i,SV239: $i] :
( ( ( class_Int_Onumber__ring @ SV239 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV672 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV797 ) )
| ( SV672 = SV797 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2327,plain,
! [SV676: $i,SV243: $i,SV484: $i] :
( ( ( SV484
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SV484 ) @ SV676 ) )
= $true )
| ( ( SV676
= ( c_HOL_Ozero__class_Ozero @ SV243 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV243 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2328,plain,
! [SV843: $i,SV799: $i,SV678: $i,SV486: $i,SV245: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV799 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV843 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ SV799 )
= SV843 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2329,plain,
! [SV865: $i,SV861: $i,SV844: $i,SV801: $i,SV680: $i,SV488: $i,SV247: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
| ~ ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2279]) ).
thf(2330,plain,
! [SV804: $i,SV690: $i,SV499: $i,SV258: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV690 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV258 ) @ SV499 ) @ SV804 ) )
= $false )
| ( ( SV690 = SV804 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2331,plain,
! [SV696: $i,SV265: $i,SV845: $i,SV506: $i,SV8: $i,SV805: $i] :
( ( ( c_ListOrder_Ostep1 @ SV805 @ ( c_List_Oappend @ SV8 @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SV845 ) @ SV845 ) @ SV845 ) @ ( c_List_Oappend @ SV265 @ ( c_List_Olist_OCons @ SV696 @ ( c_List_Olist_ONil @ SV845 ) @ SV845 ) @ SV845 ) @ SV845 )
= $false )
| ( ( SV506 = SV696 )
= $true )
| ( ( SV8 = SV265 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2332,plain,
! [SV507: $i,SV846: $i,SV806: $i,SV266: $i,SV697: $i,SV9: $i] :
( ( ( c_ListOrder_Ostep1 @ SV9 @ ( c_List_Oappend @ SV697 @ ( c_List_Olist_OCons @ SV266 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV507 @ ( c_List_Olist_ONil @ SV806 ) @ SV806 ) @ SV806 ) @ SV806 )
= $false )
| ( ( SV266 = SV507 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV9 @ SV266 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2333,plain,
! [SV513: $i,SV810: $i,SV848: $i,SV277: $i,SV703: $i,SV20: $i] :
( ( ( c_ListOrder_Ostep1 @ SV20 @ ( c_List_Oappend @ SV703 @ ( c_List_Olist_OCons @ SV277 @ ( c_List_Olist_ONil @ SV848 ) @ SV848 ) @ SV848 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV513 @ ( c_List_Olist_ONil @ SV848 ) @ SV848 ) @ SV848 ) @ SV848 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV20 @ SV703 @ SV810 @ SV848 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV277 ) @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2334,plain,
! [SV849: $i,SV284: $i,SV709: $i,SV811: $i,SV27: $i,SV520: $i] :
( ( ( c_ListOrder_Ostep1 @ SV520 @ ( c_List_Oappend @ SV27 @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ ( c_List_Oappend @ SV284 @ ( c_List_Olist_OCons @ SV849 @ ( c_List_Olist_ONil @ SV709 ) @ SV709 ) @ SV709 ) @ SV709 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV520 @ SV27 @ SV284 @ SV709 )
= $true )
| ( ( SV27 = SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2335,plain,
! [SV851: $i,SV42: $i,SV814: $i,SV712: $i,SV298: $i,SV523: $i] :
( ( ( c_ListOrder_Ostep1 @ SV523 @ ( c_List_Olist_OCons @ SV298 @ SV712 @ SV814 ) @ ( c_List_Olist_OCons @ SV42 @ SV851 @ SV814 ) @ SV814 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV523 @ SV298 ) @ SV42 ) )
= $true )
| ( ( SV42 = SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2336,plain,
! [SV524: $i,SV43: $i,SV299: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV299 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV524 @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV43 ) @ SV299 ) @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV43 ) @ SV43 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2337,plain,
! [SV542: $i,SV63: $i,SV853: $i,SV730: $i,SV317: $i,SV820: $i] :
( ( ( c_ListOrder_Ostep1 @ SV820 @ ( c_List_Olist_OCons @ SV317 @ SV730 @ SV853 ) @ ( c_List_Olist_OCons @ SV63 @ SV542 @ SV853 ) @ SV853 )
= $false )
| ( ( SV542 = SV730 )
= $true )
| ( ( SV63 = SV317 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2338,plain,
! [SV555: $i,SV335: $i,SV84: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV335 @ SV84 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ SV555 @ SV84 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV84 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV84 ) @ SV335 ) @ SV555 ) @ SV84 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2339,plain,
! [SV556: $i,SV854: $i,SV736: $i,SV336: $i,SV822: $i,SV85: $i] :
( ( ( c_ListOrder_Ostep1 @ SV85 @ ( c_List_Olist_OCons @ SV822 @ SV336 @ SV736 ) @ ( c_List_Olist_OCons @ SV854 @ SV556 @ SV736 ) @ SV736 )
= $false )
| ( ( SV556 = SV336 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV85 @ SV336 @ SV556 @ SV736 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2340,plain,
! [SV737: $i,SV337: $i,SV86: $i,SV823: $i,SV557: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV823 @ SV86 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV337 @ SV737 @ SV86 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV737 ) @ SV823 ) @ SV86 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2341,plain,
! [SV560: $i,SV89: $i,SV738: $i,SV340: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV340 @ SV738 @ SV89 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV560 @ SV89 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV560 ) @ SV738 ) @ SV89 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2342,plain,
! [SV569: $i,SV856: $i,SV746: $i,SV349: $i,SV825: $i,SV98: $i] :
( ( ( c_ListOrder_Ostep1 @ SV98 @ ( c_List_Olist_OCons @ SV825 @ SV349 @ SV746 ) @ ( c_List_Olist_OCons @ SV856 @ SV569 @ SV746 ) @ SV746 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ SV825 ) @ SV856 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV98 @ SV349 @ SV569 @ SV746 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2343,plain,
! [SV750: $i,SV827: $i,SV578: $i,SV359: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV827 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV108 @ SV827 ) @ SV750 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV108 @ SV359 ) @ SV578 ) @ SV750 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2344,plain,
! [SV751: $i,SV360: $i,SV828: $i,SV579: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV109 @ SV579 ) @ SV828 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV828 ) @ SV751 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV109 @ SV360 ) @ SV579 ) @ SV751 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2345,plain,
! [SV756: $i,SV830: $i,SV594: $i,SV383: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV830 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV830 ) @ SV756 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV135 @ SV383 ) @ SV594 ) @ SV756 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2346,plain,
! [SV388: $i,SV140: $i,SV598: $i,SV757: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV757 @ SV598 @ SV140 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV757 @ SV140 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV388 @ SV598 @ SV140 )
= $true )
| ( ( class_Orderings_Opreorder @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2347,plain,
! [SV599: $i,SV141: $i,SV758: $i,SV389: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV389 @ SV758 @ SV141 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV758 @ SV599 @ SV141 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV389 @ SV599 @ SV141 )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2348,plain,
! [SV602: $i,SV392: $i,SV862: $i,SV760: $i,SV857: $i,SV831: $i,SV148: $i] :
( ( ( ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV148 @ SV857 @ SV862 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) )
= $true )
| ( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2349,plain,
! [SV615: $i,SV766: $i,SV832: $i,SV410: $i,SV168: $i] :
( ( ( c_Type_Otyping @ SV168 @ SV410 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV832 @ SV766 @ tc_Type_Otype @ tc_Type_Otype ) )
= $false )
| ( ( c_Type_Otypings @ SV168 @ SV615 @ SV832 )
= $false )
| ( ( c_Type_Otyping @ SV168 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV410 @ SV615 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2350,plain,
! [SV424: $i,SV183: $i,SV833: $i,SV774: $i,SV627: $i] :
( ( ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV183 )
= $false )
| ( ( c_Type_Otyping @ SV627 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV774 ) @ SV833 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV424 )
= $false )
| ( ( SV183 = SV424 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2351,plain,
! [SV628: $i,SV775: $i,SV834: $i,SV426: $i,SV185: $i] :
( ( ( c_Type_Otyping @ SV185 @ SV426 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV834 ) @ SV775 ) )
= $false )
| ( ( c_Type_Otyping @ SV185 @ SV628 @ SV834 )
= $false )
| ( ( c_Type_Otyping @ SV185 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV426 ) @ SV628 ) @ SV775 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2352,plain,
! [SV428: $i,SV776: $i,SV863: $i,SV187: $i,SV858: $i,SV835: $i,SV629: $i] :
( ( ( ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV629 @ SV858 @ SV863 )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) )
= $true )
| ( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2353,plain,
! [SV439: $i,SV859: $i,SV837: $i,SV638: $i,SV781: $i,SV198: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SV781 @ SV638 @ tc_Type_Otype ) @ SV837 @ SV859 ) )
= $true )
| ( ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SV837 @ SV439 @ SV781 ) @ SV859 )
= $true )
| ( ( c_Type_Otyping @ SV198 @ SV439 @ SV638 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2354,plain,
! [SV864: $i,SV860: $i,SV842: $i,SV795: $i,SV670: $i,SV478: $i,SV237: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
| ~ ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2355,plain,
! [SV797: $i,SV672: $i,SV480: $i,SV239: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV672 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV797 ) )
= $true )
| ( ( SV672 = SV797 )
= $true )
| ( ( class_Int_Onumber__ring @ SV239 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2356,plain,
! [SV676: $i,SV243: $i,SV484: $i] :
( ( ( SV484
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV243 ) @ SV484 ) @ SV676 ) )
= $false )
| ( ( SV676
= ( c_HOL_Ozero__class_Ozero @ SV243 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV243 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2357,plain,
! [SV843: $i,SV799: $i,SV678: $i,SV486: $i,SV245: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV799 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV678 ) @ SV843 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV245 ) @ SV486 ) @ SV799 )
= SV843 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2358,plain,
! [SV865: $i,SV861: $i,SV844: $i,SV801: $i,SV680: $i,SV488: $i,SV247: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
| ~ ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2359,plain,
! [SV737: $i,SV337: $i,SV86: $i,SV823: $i,SV557: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV557 @ SV823 @ SV86 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV337 @ SV737 @ SV86 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV737 ) @ SV823 ) @ SV86 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2360,plain,
! [SV738: $i,SV340: $i,SV560: $i,SV89: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV560 @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV340 @ SV738 @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV340 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV89 ) @ SV560 ) @ SV738 ) @ SV89 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2361,plain,
! [SV598: $i,SV140: $i,SV757: $i,SV388: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV388 @ SV757 @ SV140 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV757 @ SV598 @ SV140 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV388 @ SV598 @ SV140 )
= $true )
| ( ( class_Orderings_Opreorder @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2362,plain,
! [SV389: $i,SV141: $i,SV599: $i,SV758: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV758 @ SV599 @ SV141 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV389 @ SV758 @ SV141 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV389 @ SV599 @ SV141 )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2363,plain,
! [SV602: $i,SV392: $i,SV862: $i,SV760: $i,SV857: $i,SV831: $i,SV148: $i] :
( ( ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV148 @ SV857 @ SV862 )
| ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) )
= $true )
| ( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2364,plain,
! [SV428: $i,SV776: $i,SV863: $i,SV187: $i,SV858: $i,SV835: $i,SV629: $i] :
( ( ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV629 @ SV858 @ SV863 )
| ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) )
= $true )
| ( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2365,plain,
! [SV439: $i,SV859: $i,SV837: $i,SV638: $i,SV781: $i,SV198: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV198 @ SV781 @ SV638 @ tc_Type_Otype ) @ SV837 @ SV859 )
= $false )
| ( ( c_Type_Otyping @ SV198 @ ( c_Lambda_Osubst @ SV837 @ SV439 @ SV781 ) @ SV859 )
= $true )
| ( ( c_Type_Otyping @ SV198 @ SV439 @ SV638 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2366,plain,
! [SV237: $i,SV864: $i,SV478: $i,SV860: $i,SV842: $i,SV795: $i,SV670: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2367,plain,
! [SV797: $i,SV672: $i,SV480: $i,SV239: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV672 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV239 ) @ SV480 ) @ SV797 ) )
= $false )
| ( ( SV672 = SV797 )
= $true )
| ( ( class_Int_Onumber__ring @ SV239 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2368,plain,
! [SV488: $i,SV865: $i,SV247: $i,SV861: $i,SV844: $i,SV801: $i,SV680: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2369,plain,
! [SV823: $i,SV557: $i,SV86: $i,SV737: $i,SV337: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV337 @ SV737 @ SV86 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV557 @ SV823 @ SV86 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV337 ) @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV86 ) @ SV737 ) @ SV823 ) @ SV86 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2370,plain,
! [SV760: $i,SV602: $i,SV392: $i,SV831: $i,SV862: $i,SV857: $i,SV148: $i] :
( ( ( ~ ( c_Type_Otypings @ SV148 @ SV857 @ SV862 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) )
= $true )
| ( ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
= $false )
| ( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2371,plain,
! [SV187: $i,SV428: $i,SV776: $i,SV835: $i,SV863: $i,SV858: $i,SV629: $i] :
( ( ( ~ ( c_Type_Otypings @ SV629 @ SV858 @ SV863 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) )
= $true )
| ( ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
= $false )
| ( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2372,plain,
! [SV237: $i,SV864: $i,SV670: $i,SV842: $i,SV478: $i,SV795: $i,SV860: $i] :
( ( ( ~ ( c_Type_Otyping @ SV860 @ SV795 @ SV478 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2373,plain,
! [SV488: $i,SV865: $i,SV680: $i,SV844: $i,SV247: $i,SV801: $i,SV861: $i] :
( ( ( ~ ( c_Type_Otyping @ SV861 @ SV801 @ SV247 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2374,plain,
! [SV760: $i,SV602: $i,SV392: $i,SV831: $i,SV862: $i,SV857: $i,SV148: $i] :
( ( ( c_Type_Otypings @ SV148 @ SV857 @ SV862 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 ) )
= $true )
| ( ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
= $false )
| ( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2375,plain,
! [SV187: $i,SV428: $i,SV776: $i,SV835: $i,SV863: $i,SV858: $i,SV629: $i] :
( ( ( c_Type_Otypings @ SV629 @ SV858 @ SV863 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 ) )
= $true )
| ( ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
= $false )
| ( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2376,plain,
! [SV237: $i,SV864: $i,SV670: $i,SV842: $i,SV478: $i,SV795: $i,SV860: $i] :
( ( ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2377,plain,
! [SV488: $i,SV865: $i,SV680: $i,SV844: $i,SV247: $i,SV801: $i,SV861: $i] :
( ( ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2378,plain,
! [SV760: $i,SV862: $i,SV602: $i,SV392: $i,SV857: $i,SV831: $i,SV148: $i] :
( ( ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV392 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV602 )
= $false )
| ( ( c_Type_Otypings @ SV148 @ SV857 @ SV862 )
= $false )
| ( ( c_Type_Otyping @ SV148 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV831 ) @ SV857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV760 )
= $false )
| ( ( c_Type_Otypings @ SV148 @ SV392 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV602 @ SV760 @ SV148 @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2379,plain,
! [SV187: $i,SV863: $i,SV428: $i,SV776: $i,SV858: $i,SV835: $i,SV629: $i] :
( ( ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV428 )
= $false )
| ( ( c_Type_Otypings @ SV629 @ SV858 @ SV863 )
= $false )
| ( ( c_Type_Otyping @ SV629 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV835 ) @ SV858 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV187 )
= $false )
| ( ( SV187
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV428 @ SV187 @ SV629 @ SV776 ) @ SV428 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2380,plain,
! [SV237: $i,SV864: $i,SV670: $i,SV478: $i,SV842: $i,SV860: $i,SV795: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2381,plain,
! [SV488: $i,SV865: $i,SV680: $i,SV247: $i,SV844: $i,SV861: $i,SV801: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2382,plain,
! [SV237: $i,SV864: $i,SV670: $i,SV478: $i,SV842: $i,SV860: $i,SV795: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2383,plain,
! [SV488: $i,SV865: $i,SV680: $i,SV247: $i,SV844: $i,SV861: $i,SV801: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2384,plain,
! [SV237: $i,SV795: $i,SV864: $i,SV670: $i,SV478: $i,SV842: $i,SV860: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
= $false )
| ( ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2385,plain,
! [SV488: $i,SV801: $i,SV865: $i,SV680: $i,SV247: $i,SV844: $i,SV861: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
= $false )
| ( ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2386,plain,
! [SV237: $i,SV795: $i,SV864: $i,SV670: $i,SV478: $i,SV842: $i,SV860: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
= $false )
| ( ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2387,plain,
! [SV488: $i,SV801: $i,SV865: $i,SV680: $i,SV247: $i,SV844: $i,SV861: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
= $false )
| ( ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2388,plain,
! [SV237: $i,SV795: $i,SV864: $i,SV478: $i,SV842: $i,SV860: $i,SV670: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV670 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV860 @ SV842 @ SV478 @ tc_Type_Otype ) @ SV670 @ SV864 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV795 ) )
= $false )
| ( ( c_Type_Otyping @ SV860 @ SV795 @ SV478 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV670 @ SV795 @ SV842 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV237 ) @ SV478 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2389,plain,
! [SV488: $i,SV801: $i,SV865: $i,SV247: $i,SV844: $i,SV861: $i,SV680: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV680 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV861 @ SV844 @ SV247 @ tc_Type_Otype ) @ SV680 @ SV865 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV801 ) )
= $false )
| ( ( c_Type_Otyping @ SV861 @ SV801 @ SV247 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV680 @ SV801 @ SV844 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV247 ) @ SV488 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2390,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[677,2389,2388,2379,2378,2369,2367,2365,2362,2361,2360,2357,2356,2351,2350,2349,2345,2344,2343,2342,2339,2338,2337,2336,2335,2334,2333,2332,2331,2330,2325,2323,2321,2316,2315,2310,2307,2306,2305,2304,2303,2301,2300,2299,2298,2297,2296,2291,2290,2282,2280,2273,2272,2271,2270,2266,2256,2254,2253,2252,2251,2250,2249,2248,2239,2230,2229,2223,2221,2220,2219,2218,2215,2212,2211,2206,2205,2204,2199,2195,2194,2190,2189,2187,2186,2184,2182,2176,2175,2174,2173,2172,2171,2169,2166,2165,2163,2158,2154,2150,2149,2147,2146,2129,2122,2121,2120,2119,2118,2113,2112,2111,2110,2109,2108,2107,2106,2105,2100,2099,2098,2094,2093,2092,2091,2089,2085,2084,2083,2078,2075,2073,2071,2069,2067,2064,2057,2056,2055,2053,2049,2047,2046,2045,2044,2043,2040,2039,2036,2033,2030,2029,2025,2024,2018,2015,2013,2012,2010,2009,2007,2004,2002,1994,1993,1992,1991,1982,1955,1950,1948,1947,1946,1922,1902,1901,1890,1881,1876,1875,1869,1866,1865,1860,1859,1851,1850,1845,1839,1835,1834,1817,1814,1812,1804,1794,1792,1788,1773,1757,1751,1750,1727,1719,1718,1716,1715,1714,1713,1712,1707,1706,1705,1704,1693,1692,1691,1690,1647,1639,1629,1620,1609,1601,1587,1579,1578,1546,1537,1516,1515,1510,1492,1475,1460,1398,1393,1390,1378,1350,1344,1343,1333,1332,1315,1302,1267,1218,1217,1216,1215,1214,1148,1121,1095,1091,1087,1058,1027,972,949,944,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,864,863,860,856,855,854,850,820,818,817,816,812,807,788,772]) ).
thf(2391,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL799-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 12:36:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.82/6.57 ..
% 37.82/6.57
% 37.82/6.57 No.of.Axioms: 294
% 37.82/6.57
% 37.82/6.57 Length.of.Defs: 0
% 37.82/6.57
% 37.82/6.57 Contains.Choice.Funs: false
% 37.82/6.57 .......................................................................................
% 37.82/6.57
% 37.82/6.57 ********************************
% 37.82/6.57 * All subproblems solved! *
% 37.82/6.57 ********************************
% 37.82/6.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:294,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2390,loop_count:0,foatp_calls:1,translation:fof_full)
% 37.82/6.57
% 37.82/6.57 %**** Beginning of derivation protocol ****
% 37.82/6.57 % SZS output start CNFRefutation
% See solution above
% 37.82/6.58
% 37.82/6.58 %**** End of derivation protocol ****
% 37.82/6.58 %**** no. of clauses in derivation: 2391 ****
% 37.82/6.58 %**** clause counter: 2390 ****
% 37.82/6.58
% 37.82/6.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:294,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2390,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------