%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL788-1 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:30:33 AM UTC 2026
% Result : Unsatisfiable 23.78s 4.17s
% Output : CNFRefutation 23.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 243
% Syntax : Number of formulae : 1920 (1497 unt; 0 typ; 0 def)
% Number of atoms : 7886 (4340 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 25630 (1364 ~;1800 |; 0 &;22466 @)
% ( 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 : 69 ( 66 usr; 24 con; 0-5 aty)
% Number of variables : 7216 ( 0 ^;7216 !; 0 ?;7216 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
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_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_Obutlast,type,
c_List_Obutlast: $i > $i > $i ).
thf(tp_c_List_Oconcat__map,type,
c_List_Oconcat__map: $i > $i > $i > $i > $i ).
thf(tp_c_List_OdropWhile,type,
c_List_OdropWhile: $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_Ohd,type,
c_List_Ohd: $i > $i > $i ).
thf(tp_c_List_Olast,type,
c_List_Olast: $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_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i > $i ).
thf(tp_c_List_Orotate1,type,
c_List_Orotate1: $i > $i > $i ).
thf(tp_c_List_Osko__List__XCons__eq__append__conv__1__1,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xappend__eq__Cons__conv__1__1,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xsplit__list__first__prop__iff__1__5,type,
c_List_Osko__List__Xsplit__list__first__prop__iff__1__5: $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xsplit__list__last__prop__iff__1__5,type,
c_List_Osko__List__Xsplit__list__last__prop__iff__1__5: $i > $i > $i > $i ).
thf(tp_c_List_Osplice,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(tp_c_List_OtakeWhile,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(tp_c_List_Otl,type,
c_List_Otl: $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__Xtype__induct__1__1,type,
c_Type_Osko__Type__Xtype__induct__1__1: $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_OAtom,type,
c_Type_Otype_OAtom: $i > $i ).
thf(tp_c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
thf(tp_c_Type_Otype_Otype__case,type,
c_Type_Otype_Otype__case: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otype_Otype__rec,type,
c_Type_Otype_Otype__rec: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_c_Type_Otypings,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i > $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_Type_Otype,type,
tc_Type_Otype: $i ).
thf(tp_tc_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 )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
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_CHAINED_0_01) ).
thf(4,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(5,axiom,
! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
thf(6,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_1) ).
thf(7,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).
thf(8,axiom,
! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
thf(9,axiom,
! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).
thf(10,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(11,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(12,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(13,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(14,axiom,
! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_0) ).
thf(15,axiom,
! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_1) ).
thf(16,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(17,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(18,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(19,axiom,
! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
thf(20,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(21,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(22,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(23,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(24,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(25,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(26,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(27,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(28,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(29,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(30,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(31,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(32,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(33,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(34,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(35,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(36,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(37,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(38,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(39,axiom,
! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
thf(40,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(41,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(42,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(43,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(44,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(45,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(46,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(47,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
thf(48,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(49,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
thf(50,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(51,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(52,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(53,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(54,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(55,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(56,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(57,axiom,
! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_2) ).
thf(58,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(59,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(60,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(61,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(62,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(63,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(64,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(65,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).
thf(66,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_0) ).
thf(67,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(68,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(69,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(70,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(71,axiom,
! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
thf(72,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(73,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(74,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
thf(75,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(76,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(77,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(78,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(79,axiom,
! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(80,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(81,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(82,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(83,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(84,axiom,
! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(85,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(86,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(87,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(88,axiom,
! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(89,axiom,
! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(90,axiom,
! [V_x: $i,V_xs: $i,T_b: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_b ) @ T_b ) @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(91,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(92,axiom,
! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(93,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(94,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(95,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(96,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(97,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(98,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(99,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(100,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(101,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(102,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(103,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(104,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(105,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(106,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(107,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(108,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(109,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(110,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(111,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(112,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(113,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(114,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(115,axiom,
! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(116,axiom,
! [V_P: $i,V_xs: $i,V_x: $i,V_l: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).
thf(117,axiom,
! [V_P: $i,V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ V_P @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_a ) @ T_a ) @ T_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ V_P @ V_x @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_6) ).
thf(118,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( hAPP @ V_f @ V_x ) @ ( c_List_Oconcat__map @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat__map_Osimps_I2_J_0) ).
thf(119,axiom,
! [V_P: $i,V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ V_P @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_a ) @ T_a ) @ T_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ V_P @ V_xb @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_6) ).
thf(120,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(121,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(122,axiom,
! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(123,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(124,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b )
= ( c_List_Ofoldr @ ( c_COMBC @ V_f @ T_a @ T_b @ T_a ) @ ( c_List_Orev @ V_xs @ T_b ) @ V_a @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr_0) ).
thf(125,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(126,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(127,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(128,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(129,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).
thf(130,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(131,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(132,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(133,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(134,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(135,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(136,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(137,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(138,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(139,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(140,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(141,axiom,
! [T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(142,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(143,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(144,axiom,
! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(145,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(146,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(147,axiom,
! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(148,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(149,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(150,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(151,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(152,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(153,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(154,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(155,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(156,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(157,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(158,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_0) ).
thf(159,axiom,
! [V_xs: $i,V_P: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( V_xs
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_2) ).
thf(160,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
thf(161,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(162,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(163,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(164,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(165,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat__map_Osimps_I1_J_0) ).
thf(166,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(167,axiom,
! [V_f: $i,V_xs: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a )
= ( c_List_Ofoldl @ ( c_COMBC @ V_f @ T_b @ T_a @ T_a ) @ V_a @ ( c_List_Orev @ V_xs @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
thf(168,axiom,
! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(169,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(170,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(171,axiom,
! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(172,axiom,
! [V_P: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
thf(173,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(174,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(175,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(176,axiom,
! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(177,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(178,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(179,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(180,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(181,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(182,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(183,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(184,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(185,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(186,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(187,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(188,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).
thf(189,axiom,
! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(190,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(191,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(192,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(193,axiom,
! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(194,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(195,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(196,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(197,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(198,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(199,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(200,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(201,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(202,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(203,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(204,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(205,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(206,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__dropWhile__id_0) ).
thf(207,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(208,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(209,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(210,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(211,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).
thf(212,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).
thf(213,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(214,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(215,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(216,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(217,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(218,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(219,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).
thf(220,axiom,
! [V_P: $i,T_a: $i] :
( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).
thf(221,axiom,
c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
thf(222,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(223,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(224,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(225,axiom,
! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(226,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(227,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(228,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ohd @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a ) ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).
thf(229,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(230,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(231,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(232,axiom,
! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(233,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(234,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(235,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__replicate_0) ).
thf(236,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(237,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(238,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__replicate_0) ).
thf(239,axiom,
! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(240,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(241,axiom,
! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(242,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(243,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[242]) ).
thf(244,negated_conjecture,
( 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_conjecture_0) ).
thf(245,plain,
$false = $false,
inference(unfold_def,[status(thm)],[243]) ).
thf(246,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(247,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(248,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)],[3]) ).
thf(249,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(250,plain,
( ( ! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(251,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(252,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(253,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(254,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(255,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)],[10]) ).
thf(256,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)],[11]) ).
thf(257,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)],[12]) ).
thf(258,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)],[13]) ).
thf(259,plain,
( ( ! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(260,plain,
( ( ! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(261,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)],[16]) ).
thf(262,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)],[17]) ).
thf(263,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)],[18]) ).
thf(264,plain,
( ( ! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(265,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)],[20]) ).
thf(266,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)],[21]) ).
thf(267,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)],[22]) ).
thf(268,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)],[23]) ).
thf(269,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)],[24]) ).
thf(270,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)],[25]) ).
thf(271,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)],[26]) ).
thf(272,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)],[27]) ).
thf(273,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)],[28]) ).
thf(274,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)],[29]) ).
thf(275,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)],[30]) ).
thf(276,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)],[31]) ).
thf(277,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)],[32]) ).
thf(278,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)],[33]) ).
thf(279,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)],[34]) ).
thf(280,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)],[35]) ).
thf(281,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)],[36]) ).
thf(282,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)],[37]) ).
thf(283,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)],[38]) ).
thf(284,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(285,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)],[40]) ).
thf(286,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)],[41]) ).
thf(287,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)],[42]) ).
thf(288,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)],[43]) ).
thf(289,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)],[44]) ).
thf(290,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)],[45]) ).
thf(291,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)],[46]) ).
thf(292,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(293,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)],[48]) ).
thf(294,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(295,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)],[50]) ).
thf(296,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)],[51]) ).
thf(297,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)],[52]) ).
thf(298,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)],[53]) ).
thf(299,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)],[54]) ).
thf(300,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)],[55]) ).
thf(301,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)],[56]) ).
thf(302,plain,
( ( ! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(303,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)],[58]) ).
thf(304,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)],[59]) ).
thf(305,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)],[60]) ).
thf(306,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)],[61]) ).
thf(307,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)],[62]) ).
thf(308,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)],[63]) ).
thf(309,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)],[64]) ).
thf(310,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(311,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(312,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)],[67]) ).
thf(313,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)],[68]) ).
thf(314,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)],[69]) ).
thf(315,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)],[70]) ).
thf(316,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(317,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)],[72]) ).
thf(318,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)],[73]) ).
thf(319,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(320,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)],[75]) ).
thf(321,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)],[76]) ).
thf(322,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)],[77]) ).
thf(323,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(324,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(325,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(326,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(327,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)],[82]) ).
thf(328,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)],[83]) ).
thf(329,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(330,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(331,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(332,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)],[87]) ).
thf(333,plain,
( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(334,plain,
( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(335,plain,
( ( ! [V_x: $i,V_xs: $i,T_b: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_b ) @ T_b ) @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(336,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)],[91]) ).
thf(337,plain,
( ( ! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(338,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)],[93]) ).
thf(339,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)],[94]) ).
thf(340,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)],[95]) ).
thf(341,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)],[96]) ).
thf(342,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)],[97]) ).
thf(343,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)],[98]) ).
thf(344,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)],[99]) ).
thf(345,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)],[100]) ).
thf(346,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)],[101]) ).
thf(347,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)],[102]) ).
thf(348,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)],[103]) ).
thf(349,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)],[104]) ).
thf(350,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)],[105]) ).
thf(351,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(352,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(353,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(354,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(355,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(356,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(357,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(358,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(359,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(360,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(361,plain,
( ( ! [V_P: $i,V_xs: $i,V_x: $i,V_l: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(362,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ V_P @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_a ) @ T_a ) @ T_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ V_P @ V_x @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(363,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( hAPP @ V_f @ V_x ) @ ( c_List_Oconcat__map @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(364,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ V_P @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_a ) @ T_a ) @ T_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ V_P @ V_xb @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(365,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)],[120]) ).
thf(366,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(367,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(368,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)],[123]) ).
thf(369,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b )
= ( c_List_Ofoldr @ ( c_COMBC @ V_f @ T_a @ T_b @ T_a ) @ ( c_List_Orev @ V_xs @ T_b ) @ V_a @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(370,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(371,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(372,plain,
( ( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(373,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)],[128]) ).
thf(374,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(375,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(376,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)],[131]) ).
thf(377,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)],[132]) ).
thf(378,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)],[133]) ).
thf(379,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(380,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)],[135]) ).
thf(381,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)],[136]) ).
thf(382,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)],[137]) ).
thf(383,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)],[138]) ).
thf(384,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)],[139]) ).
thf(385,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(386,plain,
( ( ! [T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(387,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)],[142]) ).
thf(388,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)],[143]) ).
thf(389,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(390,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(391,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(392,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(393,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(394,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)],[149]) ).
thf(395,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(396,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(397,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(398,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)],[153]) ).
thf(399,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)],[154]) ).
thf(400,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)],[155]) ).
thf(401,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)],[156]) ).
thf(402,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)],[157]) ).
thf(403,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(404,plain,
( ( ! [V_xs: $i,V_P: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( V_xs
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(405,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(406,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)],[161]) ).
thf(407,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(408,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(409,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)],[164]) ).
thf(410,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(411,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(412,plain,
( ( ! [V_f: $i,V_xs: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a )
= ( c_List_Ofoldl @ ( c_COMBC @ V_f @ T_b @ T_a @ T_a ) @ V_a @ ( c_List_Orev @ V_xs @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(413,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(414,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)],[169]) ).
thf(415,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)],[170]) ).
thf(416,plain,
( ( ! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(417,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(418,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)],[173]) ).
thf(419,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)],[174]) ).
thf(420,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)],[175]) ).
thf(421,plain,
( ( ! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(422,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)],[177]) ).
thf(423,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(424,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)],[179]) ).
thf(425,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(426,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)],[181]) ).
thf(427,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(428,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)],[183]) ).
thf(429,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(430,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(431,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(432,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(433,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(434,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(435,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(436,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(437,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(438,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(439,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(440,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(441,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)],[196]) ).
thf(442,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)],[197]) ).
thf(443,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)],[198]) ).
thf(444,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)],[199]) ).
thf(445,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)],[200]) ).
thf(446,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)],[201]) ).
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)],[202]) ).
thf(448,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(449,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(450,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)],[205]) ).
thf(451,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(452,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)],[207]) ).
thf(453,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)],[208]) ).
thf(454,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)],[209]) ).
thf(455,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)],[210]) ).
thf(456,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(457,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(458,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)],[213]) ).
thf(459,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)],[214]) ).
thf(460,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(461,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)],[216]) ).
thf(462,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)],[217]) ).
thf(463,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)],[218]) ).
thf(464,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(465,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(466,plain,
( ( c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(467,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)],[222]) ).
thf(468,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)],[223]) ).
thf(469,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)],[224]) ).
thf(470,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(471,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)],[226]) ).
thf(472,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)],[227]) ).
thf(473,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ohd @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a ) ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(474,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)],[229]) ).
thf(475,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)],[230]) ).
thf(476,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)],[231]) ).
thf(477,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(478,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(479,plain,
( ( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(480,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(481,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)],[236]) ).
thf(482,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(483,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(484,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(485,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(486,plain,
( ( ! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(487,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)],[244]) ).
thf(488,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[245]) ).
thf(489,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)],[487]) ).
thf(490,plain,
( ( ! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(491,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(492,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(493,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(494,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(495,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)],[481]) ).
thf(496,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(497,plain,
( ( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(498,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(499,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(500,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)],[476]) ).
thf(501,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)],[475]) ).
thf(502,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)],[474]) ).
thf(503,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ohd @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a ) ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(504,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)],[472]) ).
thf(505,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)],[471]) ).
thf(506,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(507,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)],[469]) ).
thf(508,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)],[468]) ).
thf(509,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)],[467]) ).
thf(510,plain,
( ( c_Type_Otyping @ v_ea______ @ v_ua______ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(511,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(512,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(513,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)],[463]) ).
thf(514,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)],[462]) ).
thf(515,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)],[461]) ).
thf(516,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(517,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)],[459]) ).
thf(518,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)],[458]) ).
thf(519,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(520,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(521,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)],[455]) ).
thf(522,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)],[454]) ).
thf(523,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)],[453]) ).
thf(524,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)],[452]) ).
thf(525,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(526,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)],[450]) ).
thf(527,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(528,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(529,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(530,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)],[446]) ).
thf(531,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)],[445]) ).
thf(532,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)],[444]) ).
thf(533,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)],[443]) ).
thf(534,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)],[442]) ).
thf(535,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)],[441]) ).
thf(536,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(537,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(538,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(539,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(540,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(541,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(542,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(543,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(544,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(545,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(546,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(547,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(548,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)],[428]) ).
thf(549,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(550,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)],[426]) ).
thf(551,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(552,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)],[424]) ).
thf(553,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(554,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)],[422]) ).
thf(555,plain,
( ( ! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(556,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)],[420]) ).
thf(557,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)],[419]) ).
thf(558,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)],[418]) ).
thf(559,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(560,plain,
( ( ! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(561,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)],[415]) ).
thf(562,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)],[414]) ).
thf(563,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(564,plain,
( ( ! [V_f: $i,V_xs: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a )
= ( c_List_Ofoldl @ ( c_COMBC @ V_f @ T_b @ T_a @ T_a ) @ V_a @ ( c_List_Orev @ V_xs @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(565,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(566,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(567,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)],[409]) ).
thf(568,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(569,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(570,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)],[406]) ).
thf(571,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(572,plain,
( ( ! [V_xs: $i,V_P: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( V_xs
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(573,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(574,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)],[402]) ).
thf(575,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)],[401]) ).
thf(576,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)],[400]) ).
thf(577,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)],[399]) ).
thf(578,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)],[398]) ).
thf(579,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(580,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(581,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(582,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)],[394]) ).
thf(583,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(584,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(585,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(586,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(587,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(588,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)],[388]) ).
thf(589,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)],[387]) ).
thf(590,plain,
( ( ! [T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(591,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(592,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)],[384]) ).
thf(593,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)],[383]) ).
thf(594,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)],[382]) ).
thf(595,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)],[381]) ).
thf(596,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)],[380]) ).
thf(597,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(598,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)],[378]) ).
thf(599,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)],[377]) ).
thf(600,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)],[376]) ).
thf(601,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(602,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(603,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)],[373]) ).
thf(604,plain,
( ( v_rs____
= ( c_List_Olist_OCons @ v_a____ @ v_as____ @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(605,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(606,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)],[370]) ).
thf(607,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,T_a: $i,T_b: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b )
= ( c_List_Ofoldr @ ( c_COMBC @ V_f @ T_a @ T_b @ T_a ) @ ( c_List_Orev @ V_xs @ T_b ) @ V_a @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(608,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)],[368]) ).
thf(609,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(610,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(611,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)],[365]) ).
thf(612,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ V_P @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_a ) @ T_a ) @ T_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ V_P @ V_xb @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(613,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( hAPP @ V_f @ V_x ) @ ( c_List_Oconcat__map @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(614,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ V_P @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_a ) @ T_a ) @ T_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ V_P @ V_x @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(615,plain,
( ( ! [V_P: $i,V_xs: $i,V_x: $i,V_l: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(616,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_zs
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(617,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(618,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(619,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(620,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(621,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(622,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(623,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(624,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(625,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(626,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)],[350]) ).
thf(627,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)],[349]) ).
thf(628,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)],[348]) ).
thf(629,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)],[347]) ).
thf(630,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)],[346]) ).
thf(631,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)],[345]) ).
thf(632,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)],[344]) ).
thf(633,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)],[343]) ).
thf(634,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)],[342]) ).
thf(635,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)],[341]) ).
thf(636,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)],[340]) ).
thf(637,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)],[339]) ).
thf(638,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)],[338]) ).
thf(639,plain,
( ( ! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(640,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)],[336]) ).
thf(641,plain,
( ( ! [V_x: $i,V_xs: $i,T_b: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_b ) @ T_b ) @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(642,plain,
( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(643,plain,
( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(644,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)],[332]) ).
thf(645,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(646,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a )
= V_ys )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(647,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a )
= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(648,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)],[328]) ).
thf(649,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)],[327]) ).
thf(650,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(651,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(652,plain,
( ( ! [V_ys: $i,V_zs: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_zs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( V_ys
= ( c_List_Olist_OCons @ V_x @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(653,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i,V_zs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Oappend @ V_ys @ V_zs @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ V_x @ V_xs @ V_ys @ V_zs @ T_a ) @ V_zs @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(654,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)],[322]) ).
thf(655,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)],[321]) ).
thf(656,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)],[320]) ).
thf(657,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(658,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)],[318]) ).
thf(659,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)],[317]) ).
thf(660,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(661,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)],[315]) ).
thf(662,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)],[314]) ).
thf(663,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)],[313]) ).
thf(664,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)],[312]) ).
thf(665,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(666,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(667,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)],[309]) ).
thf(668,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)],[308]) ).
thf(669,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)],[307]) ).
thf(670,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)],[306]) ).
thf(671,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)],[305]) ).
thf(672,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)],[304]) ).
thf(673,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)],[303]) ).
thf(674,plain,
( ( ! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(675,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)],[301]) ).
thf(676,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)],[300]) ).
thf(677,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)],[299]) ).
thf(678,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)],[298]) ).
thf(679,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)],[297]) ).
thf(680,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)],[296]) ).
thf(681,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)],[295]) ).
thf(682,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(683,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)],[293]) ).
thf(684,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(685,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)],[291]) ).
thf(686,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)],[290]) ).
thf(687,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)],[289]) ).
thf(688,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)],[288]) ).
thf(689,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)],[287]) ).
thf(690,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)],[286]) ).
thf(691,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)],[285]) ).
thf(692,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(693,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)],[283]) ).
thf(694,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)],[282]) ).
thf(695,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)],[281]) ).
thf(696,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)],[280]) ).
thf(697,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)],[279]) ).
thf(698,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)],[278]) ).
thf(699,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)],[277]) ).
thf(700,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)],[276]) ).
thf(701,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)],[275]) ).
thf(702,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)],[274]) ).
thf(703,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)],[273]) ).
thf(704,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)],[272]) ).
thf(705,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)],[271]) ).
thf(706,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)],[270]) ).
thf(707,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)],[269]) ).
thf(708,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)],[268]) ).
thf(709,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)],[267]) ).
thf(710,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)],[266]) ).
thf(711,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)],[265]) ).
thf(712,plain,
( ( ! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(713,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)],[263]) ).
thf(714,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)],[262]) ).
thf(715,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)],[261]) ).
thf(716,plain,
( ( ! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(717,plain,
( ( ! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(718,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)],[258]) ).
thf(719,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)],[257]) ).
thf(720,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)],[256]) ).
thf(721,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)],[255]) ).
thf(722,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(723,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(724,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(725,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(726,plain,
( ( ! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(727,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(728,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)],[248]) ).
thf(729,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(730,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(731,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[488]) ).
thf(732,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)],[714]) ).
thf(733,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ SX3 @ SX1 ) )
| ( SX0
= ( c_List_Oappend @ ( c_List_Orev @ SX3 @ SX1 ) @ ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(734,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX3 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SX3 @ SX4 @ SX0 @ SX1 @ SX2 ) @ SX2 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(735,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)],[524]) ).
thf(736,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)],[531]) ).
thf(737,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)],[659]) ).
thf(738,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(739,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SX0 @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX2 )
= SX3 )
| ( SX3
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(740,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( SX0
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ SX1 @ SX0 @ SX2 ) @ ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) @ SX2 ) )
| ( ( c_List_OdropWhile @ SX1 @ SX0 @ SX2 )
= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(741,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(742,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)],[700]) ).
thf(743,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)],[705]) ).
thf(744,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)],[606]) ).
thf(745,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(746,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)],[676]) ).
thf(747,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(748,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)],[608]) ).
thf(749,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)],[504]) ).
thf(750,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)],[489]) ).
thf(751,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Type_Otype_OAtom @ SX0 )
!= ( c_Type_Otype_OAtom @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(752,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX2
= ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(753,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)],[694]) ).
thf(754,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Type_Otype_OAtom @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[726]) ).
thf(755,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SX0 @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX2 )
= SX3 )
| ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(756,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(757,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)],[636]) ).
thf(758,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SX3 @ SX4 @ SX0 @ SX1 @ SX2 ) @ SX1 @ SX2 )
= SX4 )
| ( SX1
= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(759,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)],[713]) ).
thf(760,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)],[675]) ).
thf(761,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)],[599]) ).
thf(762,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)],[693]) ).
thf(763,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)],[517]) ).
thf(764,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)],[518]) ).
thf(765,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 )
!= ( c_Type_Otype_OAtom @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[712]) ).
thf(766,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)],[699]) ).
thf(767,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_OdropWhile @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX1
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SX0 @ SX1 @ SX2 ) @ ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(768,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)],[695]) ).
thf(769,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)],[703]) ).
thf(770,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(771,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)],[637]) ).
thf(772,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oreplicate @ SX1 @ SX2 @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(773,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oreplicate @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(774,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oreplicate @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(775,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)],[628]) ).
thf(776,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(777,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[716]) ).
thf(778,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)],[687]) ).
thf(779,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orotate1 @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(780,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)],[697]) ).
thf(781,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)],[698]) ).
thf(782,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX3 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SX3 @ SX4 @ SX0 @ SX1 @ SX2 ) @ SX2 ) )
| ( SX1
= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(783,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)],[574]) ).
thf(784,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)],[688]) ).
thf(785,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( SX1
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SX0 @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX4 @ SX2 ) )
| ( SX3
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(786,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)],[702]) ).
thf(787,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)],[629]) ).
thf(788,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)],[706]) ).
thf(789,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(790,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[717]) ).
thf(791,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)],[502]) ).
thf(792,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)],[690]) ).
thf(793,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)],[523]) ).
thf(794,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_OdropWhile @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(795,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SX3 @ SX4 @ SX0 @ SX1 @ SX2 ) @ SX1 @ SX2 )
= SX4 )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(796,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)],[522]) ).
thf(797,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)],[667]) ).
thf(798,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)],[529]) ).
thf(799,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(800,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)],[689]) ).
thf(801,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(802,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( SX1
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SX0 @ SX1 @ SX3 @ SX4 @ SX2 ) @ SX4 @ SX2 ) )
| ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(803,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)],[686]) ).
thf(804,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)],[627]) ).
thf(805,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)],[668]) ).
thf(806,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Orev @ SX1 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(807,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)],[521]) ).
thf(808,plain,
! [SV1: $i] :
( ( ! [SY796: $i] :
( ( c_List_Olist_ONil @ SV1 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY796 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(809,plain,
! [SV2: $i] :
( ( ! [SY797: $i,SY798: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV2 @ SY797 @ SY798 ) @ SY798 )
= SY797 )
| ( SV2
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(810,plain,
! [SV3: $i] :
( ( ! [SY799: $i,SY800: $i,SY801: $i] :
( ( c_Type_Otyping @ SV3 @ SY799 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SY800 @ SV3 @ SY799 @ SY801 ) )
| ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SY801 @ ( c_List_Olist_OCons @ SY799 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(811,plain,
! [SV4: $i] :
( ( ! [SY802: $i,SY803: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV4 @ SY802 @ SY803 ) @ SY803 )
= SY802 )
| ( SV4
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(812,plain,
! [SV5: $i] :
( ( ! [SY804: $i,SY805: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV5 @ SY804 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY805 @ SY804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(813,plain,
! [SV6: $i] :
( ( ! [SY806: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV6 @ SY806 )
= ( c_List_Olist_ONil @ SY806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(814,plain,
! [SV7: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV7 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(815,plain,
! [SV8: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV8 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(816,plain,
! [SV9: $i] :
( ( ! [SY807: $i,SY808: $i] :
( ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV9 @ SY807 @ SY808 ) @ SY808 ) ) )
| ( ( c_List_OdropWhile @ SV9 @ SY807 @ SY808 )
= ( c_List_Olist_ONil @ SY808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(817,plain,
! [SV10: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV10 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV10 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(818,plain,
! [SV11: $i] :
( ( ! [SY809: $i,SY810: $i,SY811: $i,SY812: $i,SY813: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV11 @ SY809 @ SY810 @ SY811 ) @ SY812 ) @ SY813 )
= ( hAPP @ ( hAPP @ SV11 @ SY813 ) @ SY812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(819,plain,
! [SV12: $i] :
( ( ! [SY814: $i,SY815: $i,SY816: $i] :
( ( c_List_Olistsp @ SV12 @ SY814 @ SY815 )
| ~ ( c_List_Olistsp @ SV12 @ ( c_List_Oappend @ SY814 @ SY816 @ SY815 ) @ SY815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(820,plain,
! [SV13: $i] :
( ( ! [SY817: $i,SY818: $i,SY819: $i] :
( ( c_List_Olistsp @ SV13 @ SY817 @ SY818 )
| ~ ( c_List_Olistsp @ SV13 @ ( c_List_Oappend @ SY819 @ SY817 @ SY818 ) @ SY818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(821,plain,
! [SV14: $i] :
( ( ! [SY820: $i] : ( c_List_Olistsp @ SV14 @ ( c_List_Olist_ONil @ SY820 ) @ SY820 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(822,plain,
! [SV15: $i] :
( ( ! [SY821: $i] :
( ( c_List_OdropWhile @ SV15 @ ( c_List_Olist_ONil @ SY821 ) @ SY821 )
= ( c_List_Olist_ONil @ SY821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(823,plain,
! [SV16: $i] :
( ( ! [SY822: $i,SY823: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV16 ) ) @ SY822 ) @ SY823 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY822 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV16 @ SY822 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY823 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(824,plain,
! [SV17: $i] :
( ( ! [SY824: $i,SY825: $i,SY826: $i,SY827: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV17 @ SY824 @ SY825 ) @ ( c_List_Olist_OCons @ SY826 @ SY827 @ SY825 ) @ SY825 )
= ( c_List_Olist_OCons @ SV17 @ ( c_List_Olist_OCons @ SY826 @ ( c_List_Osplice @ SY824 @ SY827 @ SY825 ) @ SY825 ) @ SY825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(825,plain,
! [SV18: $i] :
( ( ! [SY828: $i,SY829: $i,SY830: $i] :
( ( ( c_List_OdropWhile @ SV18 @ ( c_List_Olist_OCons @ SY828 @ SY829 @ SY830 ) @ SY830 )
= ( c_List_OdropWhile @ SV18 @ SY829 @ SY830 ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ SY828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(826,plain,
! [SV19: $i] :
( ( ! [SY831: $i,SY832: $i,SY833: $i] :
( ( ( c_List_OdropWhile @ SV19 @ ( c_List_Olist_OCons @ SY831 @ SY832 @ SY833 ) @ SY833 )
= ( c_List_Olist_OCons @ SY831 @ SY832 @ SY833 ) )
| ( hBOOL @ ( hAPP @ SV19 @ SY831 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(827,plain,
! [SV20: $i] :
( ( ! [SY834: $i,SY835: $i] :
( ( c_List_Oappend @ ( c_List_OtakeWhile @ SV20 @ SY834 @ SY835 ) @ ( c_List_OdropWhile @ SV20 @ SY834 @ SY835 ) @ SY835 )
= SY834 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(828,plain,
! [SV21: $i] :
( ( ! [SY836: $i,SY837: $i,SY838: $i] :
( ( c_List_Olistsp @ SV21 @ ( c_List_Oappend @ SY836 @ SY837 @ SY838 ) @ SY838 )
| ~ ( c_List_Olistsp @ SV21 @ SY837 @ SY838 )
| ~ ( c_List_Olistsp @ SV21 @ SY836 @ SY838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(829,plain,
! [SV22: $i] :
( ( ! [SY839: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ SV22 ) @ SY839 @ SV22 )
= SY839 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(830,plain,
! [SV23: $i] :
( ( ! [SY840: $i] :
( ( c_List_Osplice @ SV23 @ ( c_List_Olist_ONil @ SY840 ) @ SY840 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(831,plain,
! [SV24: $i] :
( ( ! [SY841: $i,SY842: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV24 @ SY841 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY842 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV24 @ ( c_List_Oappend @ SY841 @ ( c_List_Olist_OCons @ SY842 @ ( 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)],[530]) ).
thf(832,plain,
! [SV25: $i] :
( ( ! [SY843: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV25 ) @ SY843 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV25 ) @ SY843 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(833,plain,
! [SV26: $i] :
( ( ! [SY844: $i,SY845: $i] :
( ( ( c_List_Oappend @ SV26 @ ( c_List_Olist_OCons @ SY844 @ ( 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 @ SY845 @ SV26 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY844 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY845 @ ( c_List_Oappend @ SV26 @ ( c_List_Olist_OCons @ SY844 @ ( 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)],[534]) ).
thf(834,plain,
! [SV27: $i] :
( ( ! [SY846: $i,SY847: $i,SY848: $i] :
( ( c_Type_Otyping @ SV27 @ ( c_Lambda_OdB_OAbs @ SY846 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY847 ) @ SY848 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV27 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY847 @ tc_Type_Otype ) @ SY846 @ SY848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(835,plain,
! [SV28: $i] :
( ( ! [SY849: $i,SY850: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV28 @ SY849 @ SY850 ) @ ( c_List_Olist_ONil @ SY850 ) @ SY850 )
= ( c_List_Olist_OCons @ SV28 @ SY849 @ SY850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(836,plain,
! [SV29: $i] :
( ( ! [SY851: $i,SY852: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV29 @ SY851 @ SY852 ) @ SY852 )
= ( c_List_Olist_OCons @ SV29 @ ( c_List_Obutlast @ SY851 @ SY852 ) @ SY852 ) )
| ( SY851
= ( c_List_Olist_ONil @ SY852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(837,plain,
! [SV30: $i] :
( ( ! [SY853: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ SV30 @ ( c_List_Olist_ONil @ SY853 ) @ SY853 ) @ SY853 )
= SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(838,plain,
! [SV31: $i] :
( ( ! [SY854: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV31 @ ( c_List_Olist_ONil @ SY854 ) @ SY854 ) @ SY854 )
= ( c_List_Olist_ONil @ SY854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(839,plain,
! [SV32: $i] :
( ( ! [SY855: $i,SY856: $i,SY857: $i] :
( ( ( c_List_OtakeWhile @ SV32 @ ( c_List_Olist_OCons @ SY855 @ SY856 @ SY857 ) @ SY857 )
= ( c_List_Olist_ONil @ SY857 ) )
| ( hBOOL @ ( hAPP @ SV32 @ SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(840,plain,
! [SV33: $i] :
( ( ! [SY858: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV33 @ ( c_List_Olist_ONil @ SY858 ) @ SY858 ) @ SY858 )
= ( c_List_Olist_OCons @ SV33 @ ( c_List_Olist_ONil @ SY858 ) @ SY858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(841,plain,
! [SV34: $i] :
( ( ! [SY859: $i,SY860: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV34 @ SY859 @ SY860 ) @ SY860 )
= ( c_List_Olast @ SY859 @ SY860 ) )
| ( SY859
= ( c_List_Olist_ONil @ SY860 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(842,plain,
! [SV35: $i] :
( ( ! [SY861: $i] :
( ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_ONil @ SY861 ) @ SY861 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_ONil @ SY861 ) @ SY861 ) @ SY861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(843,plain,
! [SV36: $i] :
( ( ! [SY862: $i,SY863: $i,SY864: $i,SY865: $i,SY866: $i,SY867: $i] :
( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY862 @ SV36 @ SY863 @ SY864 ) @ SY862 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY863 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY865 ) @ SY866 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
| ~ ( c_Type_Otypings @ SY863 @ SY866 @ SY867 )
| ~ ( c_Type_Otyping @ SY863 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY865 ) @ SY866 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY864 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(844,plain,
! [SV37: $i] :
( ( ! [SY868: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV37 @ SY868 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV37 @ SY868 ) @ ( c_List_Olist_ONil @ SY868 ) @ SY868 ) @ SY868 )
= SV37 )
| ( SV37
= ( c_List_Olist_ONil @ SY868 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(845,plain,
! [SV38: $i] :
( ( ! [SY869: $i,SY870: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV38 @ SY869 @ SY870 ) @ SY870 )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(846,plain,
! [SV39: $i] :
( ( ! [SY871: $i,SY872: $i,SY873: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV39 ) @ SY871 ) @ SY872 @ SY873 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV39 @ SY872 @ SY873 ) ) @ ( c_Lambda_Osubst @ SY871 @ SY872 @ SY873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(847,plain,
! [SV40: $i] :
( ( ( c_List_Olist_ONil @ SV40 )
= ( c_List_Orev @ ( c_List_Olist_ONil @ SV40 ) @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(848,plain,
! [SV41: $i] :
( ( ! [SY874: $i,SY875: $i,SY876: $i] :
( ( c_Type_Otypings @ SV41 @ SY874 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY875 @ SV41 @ SY876 @ SY874 ) )
| ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY876 ) @ SY874 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(849,plain,
! [SV42: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ SV42 ) @ SV42 )
= ( c_List_Olist_ONil @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(850,plain,
! [SV43: $i] :
( ( ! [SY877: $i,SY878: $i,SY879: $i,SY880: $i] :
( ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_OCons @ SY877 @ SY878 @ SY879 ) @ ( c_List_Olist_OCons @ SY877 @ SY880 @ SY879 ) @ SY879 )
| ~ ( c_ListOrder_Ostep1 @ SV43 @ SY878 @ SY880 @ SY879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(851,plain,
! [SV44: $i] :
( ( ! [SY881: $i,SY882: $i,SY883: $i,SY884: $i,SY885: $i] :
( ( c_ListOrder_Ostep1 @ SV44 @ SY881 @ SY882 @ SY883 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SY884 ) @ SY885 ) )
| ~ ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SY884 @ SY881 @ SY883 ) @ ( c_List_Olist_OCons @ SY885 @ SY882 @ SY883 ) @ SY883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(852,plain,
! [SV45: $i] :
( ( ! [SY886: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV45 ) @ SY886 @ SV45 )
= SY886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(853,plain,
! [SV46: $i] :
( ( ! [SY887: $i] :
( ( c_List_OtakeWhile @ SV46 @ ( c_List_Olist_ONil @ SY887 ) @ SY887 )
= ( c_List_Olist_ONil @ SY887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(854,plain,
! [SV47: $i] :
( ( ( c_List_Otl @ ( c_List_Olist_ONil @ SV47 ) @ SV47 )
= ( c_List_Olist_ONil @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(855,plain,
! [SV48: $i] :
( ( ! [SY888: $i,SY889: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV48 @ ( c_Lambda_OdB_OVar @ SY888 ) @ SY889 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(856,plain,
! [SV49: $i] :
( ( ! [SY890: $i,SY891: $i,SY892: $i] :
( ( c_Type_Otypings @ SV49 @ SY890 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY891 @ SV49 @ SY892 @ SY890 ) )
| ~ ( c_Type_Otyping @ SV49 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY892 @ SY890 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(857,plain,
! [SV50: $i] :
( ( ! [SY893: $i,SY894: $i,SY895: $i,SY896: $i] :
( ( c_List_Ofoldr @ SV50 @ SY893 @ SY894 @ SY895 @ SY896 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV50 @ SY895 @ SY896 @ SY896 ) @ SY894 @ ( c_List_Orev @ SY893 @ SY895 ) @ SY896 @ SY895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(858,plain,
! [SV51: $i] :
( ( ! [SY897: $i,SY898: $i] :
( ( c_List_Oconcat__map @ SV51 @ ( c_List_Olist_ONil @ SY897 ) @ SY897 @ SY898 )
= ( c_List_Olist_ONil @ SY898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(859,plain,
! [SV52: $i] :
( ( ! [SY899: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV52 ) @ SY899 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY899 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(860,plain,
! [SV53: $i] :
( ( ! [SY900: $i,SY901: $i,SY902: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV53 @ SY900 @ SY901 ) @ ( c_List_Oreplicate @ SY902 @ SY900 @ SY901 ) @ SY901 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY902 @ SY900 @ SY901 ) @ ( c_List_Oreplicate @ SV53 @ SY900 @ SY901 ) @ SY901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(861,plain,
! [SV54: $i] :
( ( ! [SY903: $i,SY904: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ SV54 @ SY903 @ SY904 ) @ SY904 )
= SY903 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(862,plain,
! [SV55: $i] :
( ( ! [SY905: $i,SY906: $i,SY907: $i,SY908: $i,SY909: $i] :
( ( c_ListOrder_Ostep1 @ SV55 @ SY905 @ SY906 @ SY907 )
| ( SY906 = SY905 )
| ~ ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SY908 @ SY905 @ SY907 ) @ ( c_List_Olist_OCons @ SY909 @ SY906 @ SY907 ) @ SY907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(863,plain,
! [SV56: $i] :
( ( ! [SY910: $i,SY911: $i,SY912: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV56 @ SY910 @ SY911 ) @ SY912 @ SY911 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY912 @ SY911 ) @ ( c_List_Osplice @ SY910 @ ( c_List_Otl @ SY912 @ SY911 ) @ SY911 ) @ SY911 ) @ SY911 ) )
| ( SY912
= ( c_List_Olist_ONil @ SY911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(864,plain,
! [SV57: $i] :
( ( ! [SY913: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV57 @ SY913 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(865,plain,
! [SV58: $i] :
( ( ! [SY914: $i,SY915: $i,SY916: $i] :
( ( c_List_Ofoldl @ SV58 @ SY914 @ ( c_List_Olist_ONil @ SY915 ) @ SY916 @ SY915 )
= SY914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(866,plain,
! [SV59: $i] :
( ( ! [SY917: $i,SY918: $i] :
~ ( c_ListOrder_Ostep1 @ SV59 @ SY917 @ ( c_List_Olist_ONil @ SY918 ) @ SY918 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(867,plain,
! [SV60: $i] :
( ( ! [SY919: $i,SY920: $i] :
~ ( c_ListOrder_Ostep1 @ SV60 @ ( c_List_Olist_ONil @ SY919 ) @ SY920 @ SY919 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(868,plain,
! [SV61: $i] :
( ( ! [SY921: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ SV61 @ SY921 ) @ SY921 )
= ( c_List_Olast @ SV61 @ SY921 ) )
| ( SV61
= ( c_List_Olist_ONil @ SY921 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(869,plain,
! [SV62: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(870,plain,
! [SV63: $i] :
( ( ! [SY922: $i,SY923: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV63 @ SY922 @ SY923 ) @ SY923 )
= ( c_List_Oreplicate @ SV63 @ SY922 @ SY923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(871,plain,
! [SV64: $i] :
( ( ! [SY924: $i,SY925: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV64 ) @ SY924 ) @ SY925 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV64 @ SY925 ) ) @ ( c_Lambda_Olift @ SY924 @ SY925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(872,plain,
! [SV65: $i] :
( ( ! [SY926: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV65 @ SY926 ) @ SY926 )
= SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(873,plain,
! [SV66: $i] :
( ( ! [SY927: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV66 @ SY927 ) @ SY927 )
= SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(874,plain,
! [SV67: $i] :
( ( ! [SY928: $i] :
( SV67
= ( c_List_Orev @ ( c_List_Orev @ SV67 @ SY928 ) @ SY928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(875,plain,
! [SV68: $i] :
( ( ! [SY929: $i,SY930: $i,SY931: $i,SY932: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SY929 ) @ SY930 ) )
| ( c_ListOrder_Ostep1 @ SV68 @ ( c_List_Olist_OCons @ SY929 @ SY931 @ SY932 ) @ ( c_List_Olist_OCons @ SY930 @ SY931 @ SY932 ) @ SY932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(876,plain,
! [SV69: $i] :
( ( ! [SY933: $i,SY934: $i,SY935: $i,SY936: $i,SY937: $i] :
( ( SV69 = SY933 )
| ( SY934 = SY935 )
| ~ ( c_ListOrder_Ostep1 @ SY936 @ ( c_List_Olist_OCons @ SY933 @ SY935 @ SY937 ) @ ( c_List_Olist_OCons @ SV69 @ SY934 @ SY937 ) @ SY937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(877,plain,
! [SV70: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ SV70 ) @ SV70 )
= ( c_List_Olist_ONil @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(878,plain,
! [SV71: $i] :
( ( ! [SY938: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ SV71 @ SY938 ) @ SY938 )
= ( c_List_Ohd @ SV71 @ SY938 ) )
| ( SV71
= ( c_List_Olist_ONil @ SY938 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(879,plain,
! [SV72: $i] :
( ( ! [SY939: $i,SY940: $i,SY941: $i,SY942: $i] :
( ( c_ListOrder_Ostep1 @ SV72 @ ( c_List_Oappend @ SY939 @ SY940 @ SY941 ) @ ( c_List_Oappend @ SY939 @ SY942 @ SY941 ) @ SY941 )
| ~ ( c_ListOrder_Ostep1 @ SV72 @ SY940 @ SY942 @ SY941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(880,plain,
! [SV73: $i] :
( ( ! [SY943: $i,SY944: $i,SY945: $i,SY946: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV73 @ SY943 @ SY944 @ SY945 )
| ( c_ListOrder_Ostep1 @ SV73 @ ( c_List_Oappend @ SY943 @ SY946 @ SY945 ) @ ( c_List_Oappend @ SY944 @ SY946 @ SY945 ) @ SY945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(881,plain,
! [SV74: $i] :
( ( ( c_Lambda_OdB_OVar @ SV74 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV74 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(882,plain,
! [SV75: $i] :
( ( ! [SY947: $i,SY948: $i,SY949: $i] :
( ( c_Type_Otypings @ SV75 @ SY947 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY948 @ SV75 @ SY949 @ SY947 ) )
| ~ ( c_Type_Otyping @ SV75 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY949 @ SY947 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(883,plain,
! [SV76: $i] :
( ( ! [SY950: $i,SY951: $i,SY952: $i,SY953: $i,SY954: $i] :
( ( c_List_Ofoldl @ SV76 @ SY950 @ ( c_List_Olist_OCons @ SY951 @ SY952 @ SY953 ) @ SY954 @ SY953 )
= ( c_List_Ofoldl @ SV76 @ ( hAPP @ ( hAPP @ SV76 @ SY950 ) @ SY951 ) @ SY952 @ SY954 @ SY953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(884,plain,
! [SV77: $i] :
( ( ! [SY955: $i] :
( ( ( c_List_Orotate1 @ SV77 @ SY955 )
= ( c_List_Oappend @ ( c_List_Otl @ SV77 @ SY955 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV77 @ SY955 ) @ ( c_List_Olist_ONil @ SY955 ) @ SY955 ) @ SY955 ) )
| ( SV77
= ( c_List_Olist_ONil @ SY955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(885,plain,
! [SV78: $i] :
( ( ! [SY956: $i,SY957: $i,SY958: $i,SY959: $i,SY960: $i] :
( ( SV78 = SY956 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY957 @ SY956 ) @ SV78 ) )
| ~ ( c_ListOrder_Ostep1 @ SY957 @ ( c_List_Olist_OCons @ SY956 @ SY958 @ SY959 ) @ ( c_List_Olist_OCons @ SV78 @ SY960 @ SY959 ) @ SY959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(886,plain,
! [SV79: $i] :
( ( ! [SY961: $i,SY962: $i,SY963: $i,SY964: $i,SY965: $i,SY966: $i] :
( ( c_Type_Otypings @ SV79 @ SY961 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY962 @ SY963 @ SV79 @ SY961 ) )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY964 ) @ SY965 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY963 )
| ~ ( c_Type_Otypings @ SV79 @ SY965 @ SY966 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY964 ) @ SY965 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY961 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(887,plain,
! [SV80: $i] :
( ( ! [SY967: $i,SY968: $i,SY969: $i] :
( ( ( c_List_OtakeWhile @ SV80 @ ( c_List_Olist_OCons @ SY967 @ SY968 @ SY969 ) @ SY969 )
= ( c_List_Olist_OCons @ SY967 @ ( c_List_OtakeWhile @ SV80 @ SY968 @ SY969 ) @ SY969 ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ SY967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(888,plain,
! [SV81: $i] :
( ( ! [SY970: $i,SY971: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV81 @ SY970 ) @ SY971 @ SY970 )
= SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(889,plain,
! [SV82: $i] :
( ( ! [SY972: $i,SY973: $i,SY974: $i,SY975: $i] :
( ( c_List_Ofoldl @ SV82 @ SY972 @ SY973 @ SY974 @ SY975 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV82 @ SY974 @ SY975 @ SY974 ) @ ( c_List_Orev @ SY973 @ SY975 ) @ SY972 @ SY975 @ SY974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(890,plain,
! [SV83: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_ONil @ SV83 ) @ SV83 )
= ( c_List_Olist_ONil @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(891,plain,
! [SV84: $i] :
( ( ! [SY976: $i,SY977: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV84 @ SY976 @ SY977 ) @ SY977 )
= ( c_List_Oappend @ ( c_List_Orev @ SY976 @ SY977 ) @ ( c_List_Orev @ SV84 @ SY977 ) @ SY977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(892,plain,
! [SV85: $i] :
( ( ! [SY978: $i,SY979: $i,SY980: $i,SY981: $i,SY982: $i] :
( ( c_List_Ofoldl @ SV85 @ SY978 @ ( c_List_Oappend @ SY979 @ SY980 @ SY981 ) @ SY982 @ SY981 )
= ( c_List_Ofoldl @ SV85 @ ( c_List_Ofoldl @ SV85 @ SY978 @ SY979 @ SY982 @ SY981 ) @ SY980 @ SY982 @ SY981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(893,plain,
! [SV86: $i] :
( ( ! [SY983: $i,SY984: $i,SY985: $i,SY986: $i] :
( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ ( c_List_Oappend @ SY983 @ ( c_List_Olist_OCons @ SY984 @ SY985 @ SY986 ) @ SY986 ) @ SY986 ) ) )
| ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ SY985 @ SY986 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV86 @ SY984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(894,plain,
! [SV87: $i] :
( ( ! [SY987: $i,SY988: $i,SY989: $i,SY990: $i] :
( ( c_List_Oconcat__map @ SV87 @ ( c_List_Olist_OCons @ SY987 @ SY988 @ SY989 ) @ SY989 @ SY990 )
= ( c_List_Oappend @ ( hAPP @ SV87 @ SY987 ) @ ( c_List_Oconcat__map @ SV87 @ SY988 @ SY989 @ SY990 ) @ SY990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(895,plain,
! [SV88: $i] :
( ( ! [SY991: $i,SY992: $i,SY993: $i,SY994: $i] :
( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ ( c_List_Oappend @ SY991 @ ( c_List_Olist_OCons @ SY992 @ SY993 @ SY994 ) @ SY994 ) @ SY994 ) ) )
| ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ SY991 @ SY994 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV88 @ SY992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(896,plain,
! [SV89: $i] :
( ( ! [SY995: $i,SY996: $i,SY997: $i,SY998: $i] :
( ( ( c_List_OtakeWhile @ SV89 @ ( c_List_Oappend @ SY995 @ ( c_List_Olist_OCons @ SY996 @ SY997 @ SY998 ) @ SY998 ) @ SY998 )
= ( c_List_OtakeWhile @ SV89 @ SY995 @ SY998 ) )
| ( hBOOL @ ( hAPP @ SV89 @ SY996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(897,plain,
! [SV90: $i] :
( ( ! [SY999: $i,SY1000: $i,SY1001: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV90 @ SY999 @ SY1000 ) @ ( c_List_Olist_OCons @ SY999 @ SY1001 @ SY1000 ) @ SY1000 )
= ( c_List_Olist_OCons @ SY999 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV90 @ SY999 @ SY1000 ) @ SY1001 @ SY1000 ) @ SY1000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(898,plain,
! [SV91: $i] :
( ( ! [SY1002: $i,SY1003: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ SV91 @ SY1002 @ SY1003 ) @ SY1003 )
= ( c_List_Ohd @ SV91 @ SY1003 ) )
| ( SV91
= ( c_List_Olist_ONil @ SY1003 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(899,plain,
! [SV92: $i] :
( ( ! [SY1004: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV92 @ ( c_List_Olist_ONil @ SY1004 ) @ SY1004 ) @ SY1004 )
= ( c_List_Obutlast @ SV92 @ SY1004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(900,plain,
! [SV93: $i] :
( ( ! [SY1005: $i,SY1006: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ SV93 @ SY1005 @ SY1006 ) @ SY1006 )
= ( c_List_Oappend @ ( c_List_Otl @ SV93 @ SY1006 ) @ SY1005 @ SY1006 ) )
| ( SV93
= ( c_List_Olist_ONil @ SY1006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(901,plain,
! [SV94: $i] :
( ( ! [SY1007: $i,SY1008: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV94 @ SY1007 @ SY1008 ) @ SY1008 )
= ( c_List_Olast @ SY1007 @ SY1008 ) )
| ( SY1007
= ( c_List_Olist_ONil @ SY1008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(902,plain,
! [SV95: $i] :
( ( ! [SY1009: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV95 @ ( c_List_Olist_ONil @ SY1009 ) @ SY1009 ) @ SY1009 )
= ( c_List_Olast @ SV95 @ SY1009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(903,plain,
! [SV96: $i] :
( ( ! [SY1010: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ SV96 ) @ SY1010 @ SV96 ) @ SV96 )
= ( c_List_Ohd @ SY1010 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(904,plain,
! [SV97: $i] :
( ( ! [SY1011: $i,SY1012: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV97 @ SY1011 @ SY1012 ) @ SY1012 )
= ( c_List_Oappend @ SV97 @ ( c_List_Obutlast @ SY1011 @ SY1012 ) @ SY1012 ) )
| ( SY1011
= ( c_List_Olist_ONil @ SY1012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(905,plain,
! [SV98: $i] :
( ( ! [SY1013: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV98 ) @ ( c_Lambda_OdB_OVar @ SY1013 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(906,plain,
! [SV99: $i] :
( ( ! [SY1014: $i,SY1015: $i,SY1016: $i] :
( ( c_Type_Otyping @ SV99 @ SY1014 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1015 @ SV99 @ SY1016 @ SY1014 ) )
| ~ ( c_Type_Otyping @ SV99 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1016 ) @ SY1014 ) @ SY1015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(907,plain,
! [SV100: $i] :
( ( ! [SY1017: $i,SY1018: $i,SY1019: $i] :
( ( c_Type_Otyping @ SV100 @ SY1017 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1018 @ SV100 @ SY1017 @ SY1019 ) @ SY1018 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1017 @ SY1019 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(908,plain,
! [SV101: $i] :
( ( ! [SY1020: $i,SY1021: $i,SY1022: $i,SY1023: $i] :
( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1020 @ SY1021 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1022 )
| ~ ( c_Type_Otypings @ SV101 @ SY1021 @ SY1023 )
| ~ ( c_Type_Otyping @ SV101 @ SY1020 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1023 @ SY1022 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(909,plain,
! [SV102: $i] :
( ( ! [SY1024: $i,SY1025: $i,SY1026: $i] :
( ( c_Type_Otyping @ SV102 @ SY1024 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1025 @ SV102 @ SY1024 @ SY1026 ) @ SY1025 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV102 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1024 @ SY1026 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(910,plain,
! [SV103: $i] :
( ( ! [SY1027: $i,SY1028: $i,SY1029: $i,SY1030: $i,SY1031: $i] :
( ~ ( c_Type_Otyping @ SV103 @ SY1027 @ SY1028 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SY1029 @ SY1028 @ tc_Type_Otype ) @ SY1030 @ SY1031 )
| ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SY1030 @ SY1027 @ SY1029 ) @ SY1031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(911,plain,
! [SV104: $i] :
( ( ! [SY1032: $i,SY1033: $i,SY1034: $i,SY1035: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV104 @ SY1032 @ SY1033 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1034 @ SY1032 ) @ SY1035 )
| ~ ( c_Type_Otyping @ SV104 @ SY1034 @ SY1035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(912,plain,
! [SV105: $i] :
( ( ! [SY1036: $i,SY1037: $i,SY1038: $i] :
( ( c_Type_Otyping @ SV105 @ ( c_Lambda_OdB_OVar @ SY1036 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1037 @ SV105 @ SY1036 @ SY1038 ) @ SY1037 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV105 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1036 ) @ SY1038 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(913,plain,
! [SV106: $i] :
( ( ! [SY1039: $i,SY1040: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV106 @ SY1039 @ SY1040 ) @ ( c_List_Olist_OCons @ SY1039 @ ( c_List_Olist_ONil @ SY1040 ) @ SY1040 ) @ SY1040 )
= ( c_List_Olist_OCons @ SY1039 @ ( c_List_Oreplicate @ SV106 @ SY1039 @ SY1040 ) @ SY1040 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(914,plain,
! [SV107: $i] :
( ( ! [SY1041: $i,SY1042: $i,SY1043: $i,SY1044: $i,SY1045: $i] :
( ( SV107 = SY1041 )
| ( c_ListOrder_Ostep1 @ SY1042 @ SV107 @ SY1041 @ SY1043 )
| ~ ( c_ListOrder_Ostep1 @ SY1042 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SY1044 @ ( c_List_Olist_ONil @ SY1043 ) @ SY1043 ) @ SY1043 ) @ ( c_List_Oappend @ SY1041 @ ( c_List_Olist_OCons @ SY1045 @ ( c_List_Olist_ONil @ SY1043 ) @ SY1043 ) @ SY1043 ) @ SY1043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(915,plain,
! [SV108: $i] :
( ( ! [SY1046: $i,SY1047: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV108 @ SY1046 @ SY1047 ) @ SY1047 )
= ( c_List_Oappend @ SY1046 @ ( c_List_Olist_OCons @ SV108 @ ( c_List_Olist_ONil @ SY1047 ) @ SY1047 ) @ SY1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(916,plain,
! [SV109: $i] :
( ( ! [SY1048: $i,SY1049: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV109 @ SY1048 ) @ ( c_List_Olist_OCons @ SY1049 @ ( c_List_Olist_ONil @ SY1048 ) @ SY1048 ) @ SY1048 ) @ SY1048 )
= ( c_List_Olist_OCons @ SY1049 @ SV109 @ SY1048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(917,plain,
! [SV110: $i] :
( ( ! [SY1050: $i,SY1051: $i,SY1052: $i,SY1053: $i,SY1054: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SY1050 ) @ SY1051 ) )
| ( c_ListOrder_Ostep1 @ SV110 @ SY1052 @ SY1053 @ SY1054 )
| ~ ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SY1052 @ ( c_List_Olist_OCons @ SY1050 @ ( c_List_Olist_ONil @ SY1054 ) @ SY1054 ) @ SY1054 ) @ ( c_List_Oappend @ SY1053 @ ( c_List_Olist_OCons @ SY1051 @ ( c_List_Olist_ONil @ SY1054 ) @ SY1054 ) @ SY1054 ) @ SY1054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(918,plain,
! [SV111: $i] :
( ( ! [SY1055: $i,SY1056: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV111 @ SY1055 @ SY1056 ) @ SY1056 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1055 @ SY1056 ) @ ( c_List_Olist_OCons @ SV111 @ ( c_List_Olist_ONil @ SY1056 ) @ SY1056 ) @ SY1056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(919,plain,
! [SV112: $i] :
( ( ! [SY1057: $i,SY1058: $i,SY1059: $i,SY1060: $i,SY1061: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SY1057 ) @ SY1058 ) )
| ( SY1057 = SY1058 )
| ~ ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SY1059 @ ( c_List_Olist_OCons @ SY1057 @ ( c_List_Olist_ONil @ SY1060 ) @ SY1060 ) @ SY1060 ) @ ( c_List_Oappend @ SY1061 @ ( c_List_Olist_OCons @ SY1058 @ ( c_List_Olist_ONil @ SY1060 ) @ SY1060 ) @ SY1060 ) @ SY1060 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(920,plain,
! [SV113: $i] :
( ( ! [SY1062: $i,SY1063: $i,SY1064: $i,SY1065: $i,SY1066: $i] :
( ( SV113 = SY1062 )
| ( SY1063 = SY1064 )
| ~ ( c_ListOrder_Ostep1 @ SY1065 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SY1063 @ ( c_List_Olist_ONil @ SY1066 ) @ SY1066 ) @ SY1066 ) @ ( c_List_Oappend @ SY1062 @ ( c_List_Olist_OCons @ SY1064 @ ( c_List_Olist_ONil @ SY1066 ) @ SY1066 ) @ SY1066 ) @ SY1066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(921,plain,
! [SV114: $i] :
( ( ! [SY1067: $i,SY1068: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV114 @ ( c_List_Olist_OCons @ SY1067 @ ( c_List_Olist_ONil @ SY1068 ) @ SY1068 ) @ SY1068 ) @ SY1068 )
= SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(922,plain,
! [SV115: $i] :
( ( ! [SY1069: $i,SY1070: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV115 @ ( c_List_Olist_OCons @ SY1069 @ ( c_List_Olist_ONil @ SY1070 ) @ SY1070 ) @ SY1070 ) @ SY1070 )
= SY1069 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(923,plain,
! [SV116: $i] :
( ( ! [SY1071: $i,SY1072: $i,SY1073: $i,SY1074: $i] :
( ( SV116 = SY1071 )
| ~ ( c_Type_Otyping @ SY1072 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1073 ) @ SY1074 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1071 )
| ~ ( c_Type_Otyping @ SY1072 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1073 ) @ SY1074 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(924,plain,
! [SV117: $i] :
( ( ! [SY1075: $i,SY1076: $i,SY1077: $i] :
( ( c_Type_Otyping @ SV117 @ SY1075 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1076 @ SV117 @ SY1075 @ SY1077 ) ) @ SY1076 ) )
| ~ ( c_Type_Otyping @ SV117 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1075 ) @ SY1077 ) @ SY1076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(925,plain,
! [SV118: $i] :
( ( ! [SY1078: $i,SY1079: $i,SY1080: $i] :
( ( c_Type_Otype_Otype__case @ SV118 @ SY1078 @ ( c_Type_Otype_OAtom @ SY1079 ) @ SY1080 )
= ( hAPP @ SV118 @ SY1079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(926,plain,
! [SV119: $i] :
( ( ( c_List_Olist_ONil @ SV119 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV119 ) @ ( c_List_Olist_ONil @ SV119 ) @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(927,plain,
! [SV120: $i] :
( ( ! [SY1081: $i,SY1082: $i] :
( ( c_List_Olist_OCons @ SV120 @ SY1081 @ SY1082 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1082 ) @ ( c_List_Olist_OCons @ SV120 @ SY1081 @ SY1082 ) @ SY1082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(928,plain,
! [SV121: $i] :
( ( ! [SY1083: $i,SY1084: $i,SY1085: $i] :
( ~ ( hBOOL @ ( hAPP @ SV121 @ ( c_Type_Otype_Otype__case @ SY1083 @ SY1084 @ ( c_Type_Otype_OAtom @ SY1085 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV121 @ ( hAPP @ SY1083 @ SY1085 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(929,plain,
! [SV122: $i] :
( ( ! [SY1086: $i,SY1087: $i,SY1088: $i] :
( ~ ( hBOOL @ ( hAPP @ SV122 @ ( c_Type_Otype_Otype__case @ SY1086 @ SY1087 @ ( c_Type_Otype_OAtom @ SY1088 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV122 @ ( hAPP @ SY1086 @ SY1088 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(930,plain,
! [SV123: $i] :
( ( ! [SY1089: $i,SY1090: $i,SY1091: $i] :
( ( c_List_Olist_OCons @ SV123 @ ( c_List_Oappend @ SY1089 @ SY1090 @ SY1091 ) @ SY1091 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV123 @ SY1089 @ SY1091 ) @ SY1090 @ SY1091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(931,plain,
! [SV124: $i] :
( ( ! [SY1092: $i,SY1093: $i,SY1094: $i] :
( ( c_List_Olist_OCons @ SV124 @ ( c_List_Oappend @ SY1092 @ SY1093 @ SY1094 ) @ SY1094 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV124 @ SY1092 @ SY1094 ) @ SY1093 @ SY1094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(932,plain,
! [SV125: $i] :
( ( ! [SY1095: $i,SY1096: $i,SY1097: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV125 @ SY1095 @ SY1096 ) @ SY1097 @ SY1096 )
= ( c_List_Olist_OCons @ SV125 @ ( c_List_Oappend @ SY1095 @ SY1097 @ SY1096 ) @ SY1096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(933,plain,
! [SV126: $i] :
( ( ! [SY1098: $i,SY1099: $i,SY1100: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV126 @ SY1098 @ SY1099 ) @ SY1100 @ SY1099 )
= ( c_List_Olist_OCons @ SV126 @ ( c_List_Oappend @ SY1098 @ SY1100 @ SY1099 ) @ SY1099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(934,plain,
! [SV127: $i] :
( ( ! [SY1101: $i] : ( c_Type_Otyping @ SV127 @ ( c_Lambda_OdB_OVar @ SY1101 ) @ ( hAPP @ SV127 @ SY1101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(935,plain,
! [SV128: $i] :
( ( ! [SY1102: $i] :
( ( hBOOL @ ( hAPP @ SV128 @ SY1102 ) )
| ~ ( hBOOL @ ( hAPP @ SV128 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(936,plain,
! [SV129: $i] :
( ( ! [SY1103: $i] :
( ( c_List_Oappend @ SV129 @ ( c_List_Olist_ONil @ SY1103 ) @ SY1103 )
= SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(937,plain,
! [SV130: $i] :
( ( ! [SY1104: $i] :
( SV130
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1104 ) @ SV130 @ SY1104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(938,plain,
! [SV131: $i] :
( ( ! [SY1105: $i] :
( SV131
= ( c_List_Oappend @ SV131 @ ( c_List_Olist_ONil @ SY1105 ) @ SY1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(939,plain,
! [SV132: $i] :
( ( ! [SY1106: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV132 ) @ SY1106 @ SV132 )
= SY1106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(940,plain,
! [SV133: $i] :
( ( ! [SY1107: $i] :
( SV133
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1107 ) @ SV133 @ SY1107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(941,plain,
! [SV134: $i] :
( ( ! [SY1108: $i,SY1109: $i] :
( ( ( hAPP @ SV134 @ SY1108 )
= SY1109 )
| ~ ( c_Type_Otyping @ SV134 @ ( c_Lambda_OdB_OVar @ SY1108 ) @ SY1109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(942,plain,
! [SV135: $i] :
( ( ! [SY1110: $i,SY1111: $i,SY1112: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV135 @ SY1110 @ SY1111 @ SY1112 ) @ SY1110 )
= SY1111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(943,plain,
! [SV136: $i] :
( ( ! [SY1113: $i,SY1114: $i,SY1115: $i] :
( ( c_Type_Otype_Otype__rec @ SV136 @ SY1113 @ ( c_Type_Otype_OAtom @ SY1114 ) @ SY1115 )
= ( hAPP @ SV136 @ SY1114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(944,plain,
! [SV137: $i] :
( ( ! [SY1116: $i,SY1117: $i,SY1118: $i,SY1119: $i] :
( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1116 ) @ SY1117 ) @ SY1118 )
| ~ ( c_Type_Otyping @ SV137 @ SY1117 @ SY1119 )
| ~ ( c_Type_Otyping @ SV137 @ SY1116 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1119 ) @ SY1118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(945,plain,
! [SV138: $i] :
( ( ! [SY1120: $i,SY1121: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV138 ) @ ( c_List_Olist_OCons @ SY1120 @ SY1121 @ SV138 ) @ SV138 )
= ( c_List_Olist_OCons @ SY1120 @ SY1121 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(946,plain,
! [SV139: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV139 ) @ ( c_List_Olist_ONil @ SV139 ) @ SV139 )
= ( c_List_Olist_ONil @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(947,plain,
! [SV140: $i] :
( ( ! [SY1122: $i,SY1123: $i,SY1124: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV140 @ SY1122 @ SY1123 ) @ SY1124 @ SY1123 )
= ( c_List_Oappend @ SV140 @ ( c_List_Oappend @ SY1122 @ SY1124 @ SY1123 ) @ SY1123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(948,plain,
! [SV141: $i] :
( ( ! [SY1125: $i,SY1126: $i,SY1127: $i] :
( ( c_List_Oappend @ SV141 @ ( c_List_Oappend @ SY1125 @ SY1126 @ SY1127 ) @ SY1127 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV141 @ SY1125 @ SY1127 ) @ SY1126 @ SY1127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(949,plain,
! [SV142: $i] :
( ( ! [SY1128: $i,SY1129: $i,SY1130: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV142 @ SY1128 @ SY1129 ) @ SY1130 @ SY1129 )
= ( c_List_Oappend @ SV142 @ ( c_List_Oappend @ SY1128 @ SY1130 @ SY1129 ) @ SY1129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(950,plain,
! [SV143: $i] :
( ( ! [SY1131: $i,SY1132: $i,SY1133: $i] :
( ( c_List_Oappend @ SV143 @ ( c_List_Oappend @ SY1131 @ SY1132 @ SY1133 ) @ SY1133 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV143 @ SY1131 @ SY1133 ) @ SY1132 @ SY1133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(951,plain,
! [SV144: $i] :
( ( ! [SY1134: $i,SY1135: $i,SY1136: $i,SY1137: $i,SY1138: $i] :
( ( c_List_Ofoldr @ SV144 @ ( c_List_Olist_OCons @ SY1134 @ SY1135 @ SY1136 ) @ SY1137 @ SY1136 @ SY1138 )
= ( hAPP @ ( hAPP @ SV144 @ SY1134 ) @ ( c_List_Ofoldr @ SV144 @ SY1135 @ SY1137 @ SY1136 @ SY1138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(952,plain,
! [SV145: $i] :
( ( ! [SY1139: $i,SY1140: $i,SY1141: $i,SY1142: $i,SY1143: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Oappend @ SY1139 @ SY1140 @ SY1141 ) @ SY1142 @ SY1141 @ SY1143 )
= ( c_List_Ofoldr @ SV145 @ SY1139 @ ( c_List_Ofoldr @ SV145 @ SY1140 @ SY1142 @ SY1141 @ SY1143 ) @ SY1141 @ SY1143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(953,plain,
! [SV146: $i] :
( ( ! [SY1144: $i,SY1145: $i,SY1146: $i] :
( ( c_List_Ofoldr @ SV146 @ ( c_List_Olist_ONil @ SY1144 ) @ SY1145 @ SY1144 @ SY1146 )
= SY1145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(954,plain,
! [SV147: $i] :
( ( ! [SY1147: $i,SY1148: $i,SY1149: $i,SY1150: $i] :
( ( c_Type_Otype_Otype__rec @ SV147 @ SY1147 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1148 ) @ SY1149 ) @ SY1150 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SY1147 @ SY1148 ) @ SY1149 ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SY1147 @ SY1148 @ SY1150 ) ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SY1147 @ SY1149 @ SY1150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(955,plain,
! [SV148: $i] :
( ( ! [SY1151: $i,SY1152: $i,SY1153: $i,SY1154: $i] :
( ( c_Type_Otype_Otype__case @ SV148 @ SY1151 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1152 ) @ SY1153 ) @ SY1154 )
= ( hAPP @ ( hAPP @ SY1151 @ SY1152 ) @ SY1153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(956,plain,
! [SV149: $i] :
( ( ! [SY1155: $i,SY1156: $i,SY1157: $i,SY1158: $i] :
( ~ ( hBOOL @ ( hAPP @ SV149 @ ( c_Type_Otype_Otype__case @ SY1155 @ SY1156 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1157 ) @ SY1158 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV149 @ ( hAPP @ ( hAPP @ SY1156 @ SY1157 ) @ SY1158 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(957,plain,
! [SV150: $i] :
( ( ! [SY1159: $i,SY1160: $i,SY1161: $i,SY1162: $i] :
( ~ ( hBOOL @ ( hAPP @ SV150 @ ( c_Type_Otype_Otype__case @ SY1159 @ SY1160 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1161 ) @ SY1162 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ ( hAPP @ ( hAPP @ SY1160 @ SY1161 ) @ SY1162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(958,plain,
! [SV151: $i] :
( ( ! [SY1163: $i] : ( c_fequal @ SV151 @ SV151 @ SY1163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(959,plain,
! [SV152: $i] :
( ( ! [SY1164: $i,SY1165: $i] :
( ( SV152 = SY1164 )
| ~ ( c_fequal @ SV152 @ SY1164 @ SY1165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(960,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(961,plain,
! [SV153: $i] :
( ( ! [SY1166: $i,SY1167: $i,SY1168: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV153 ) @ SY1166 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1167 ) @ SY1168 ) )
| ( SY1166 = SY1168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(962,plain,
! [SV154: $i] :
( ( ! [SY1169: $i,SY1170: $i,SY1171: $i] :
( ( ( c_List_Orev @ SV154 @ SY1169 )
!= ( c_List_Olist_OCons @ SY1170 @ SY1171 @ SY1169 ) )
| ( SV154
= ( c_List_Oappend @ ( c_List_Orev @ SY1171 @ SY1169 ) @ ( c_List_Olist_OCons @ SY1170 @ ( c_List_Olist_ONil @ SY1169 ) @ SY1169 ) @ SY1169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(963,plain,
! [SV155: $i] :
( ( ! [SY1172: $i,SY1173: $i,SY1174: $i,SY1175: $i] :
( ( ( c_List_Oappend @ SV155 @ SY1172 @ SY1173 )
!= ( c_List_Olist_OCons @ SY1174 @ SY1175 @ SY1173 ) )
| ( SV155
= ( c_List_Olist_OCons @ SY1174 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1174 @ SY1175 @ SV155 @ SY1172 @ SY1173 ) @ SY1173 ) )
| ( SV155
= ( c_List_Olist_ONil @ SY1173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(964,plain,
! [SV156: $i] :
( ( ! [SY1176: $i,SY1177: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SY1176 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1177 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SY1176 )
= SY1177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(965,plain,
! [SV157: $i] :
( ( ! [SY1178: $i,SY1179: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV157 ) @ SY1178 )
!= ( c_Lambda_OdB_OAbs @ SY1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(966,plain,
! [SV158: $i] :
( ( ! [SY1180: $i,SY1181: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV158 ) @ SY1180 )
!= ( c_Lambda_OdB_OVar @ SY1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(967,plain,
! [SV159: $i] :
( ( ! [SY1182: $i,SY1183: $i] :
( SV159
!= ( c_List_Olist_OCons @ SY1182 @ SV159 @ SY1183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(968,plain,
! [SV160: $i] :
( ( ! [SY1184: $i,SY1185: $i,SY1186: $i,SY1187: $i] :
( ( ( c_List_Olist_OCons @ SV160 @ SY1184 @ SY1185 )
!= ( c_List_Oappend @ SY1186 @ SY1187 @ SY1185 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SY1184 @ SY1186 @ SY1187 @ SY1185 ) @ SY1185 )
= SY1186 )
| ( SY1186
= ( c_List_Olist_ONil @ SY1185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(969,plain,
! [SV161: $i] :
( ( ! [SY1188: $i,SY1189: $i,SY1190: $i,SY1191: $i] :
( ( SV161
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ SY1188 @ SV161 @ SY1189 ) @ ( c_List_Olist_OCons @ SY1190 @ SY1191 @ SY1189 ) @ SY1189 ) )
| ( ( c_List_OdropWhile @ SY1188 @ SV161 @ SY1189 )
= ( c_List_Olist_OCons @ SY1190 @ SY1191 @ SY1189 ) )
| ( hBOOL @ ( hAPP @ SY1188 @ SY1190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(970,plain,
! [SV162: $i] :
( ( ! [SY1192: $i] :
( ( ( c_Lambda_OdB_OVar @ SV162 )
!= ( c_Lambda_OdB_OVar @ SY1192 ) )
| ( SV162 = SY1192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(971,plain,
! [SV163: $i] :
( ( ! [SY1193: $i,SY1194: $i] :
( ( SV163
!= ( c_List_Oappend @ SY1193 @ SV163 @ SY1194 ) )
| ( SY1193
= ( c_List_Olist_ONil @ SY1194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(972,plain,
! [SV164: $i] :
( ( ! [SY1195: $i,SY1196: $i,SY1197: $i,SY1198: $i] :
( ( ( c_List_Oappend @ SV164 @ ( c_List_Olist_OCons @ SY1195 @ ( c_List_Olist_ONil @ SY1196 ) @ SY1196 ) @ SY1196 )
!= ( c_List_Oappend @ SY1197 @ ( c_List_Olist_OCons @ SY1198 @ ( c_List_Olist_ONil @ SY1196 ) @ SY1196 ) @ SY1196 ) )
| ( SV164 = SY1197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(973,plain,
! [SV165: $i] :
( ( ! [SY1199: $i,SY1200: $i] :
( ( ( c_Lambda_OdB_OVar @ SV165 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1199 @ SY1200 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1200
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(974,plain,
! [SV166: $i] :
( ( ! [SY1201: $i,SY1202: $i] :
( ( ( c_List_Orev @ SV166 @ SY1201 )
!= ( c_List_Olist_OCons @ SY1202 @ ( c_List_Olist_ONil @ SY1201 ) @ SY1201 ) )
| ( SV166
= ( c_List_Olist_OCons @ SY1202 @ ( c_List_Olist_ONil @ SY1201 ) @ SY1201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(975,plain,
! [SV167: $i] :
( ( ! [SY1203: $i,SY1204: $i,SY1205: $i] :
( ( ( c_List_Oappend @ SV167 @ SY1203 @ SY1204 )
!= ( c_List_Oappend @ SV167 @ SY1205 @ SY1204 ) )
| ( SY1203 = SY1205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(976,plain,
! [SV168: $i] :
( ( ! [SY1206: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV168 )
!= ( c_Lambda_OdB_OAbs @ SY1206 ) )
| ( SV168 = SY1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(977,plain,
! [SV169: $i] :
( ( ! [SY1207: $i,SY1208: $i,SY1209: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV169 ) ) @ SY1207 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1208 ) @ SY1209 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(978,plain,
! [SV170: $i] :
( ( ! [SY1210: $i,SY1211: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV170 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1210 @ SY1211 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV170 )
= SY1210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(979,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 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(980,plain,
! [SV171: $i] :
( ( ! [SY1212: $i] :
( ( ( c_Type_Otype_OAtom @ SV171 )
!= ( c_Type_Otype_OAtom @ SY1212 ) )
| ( SV171 = SY1212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(981,plain,
! [SV172: $i] :
( ( ! [SY1213: $i,SY1214: $i] :
( ( ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SY1213 ) @ SY1213 )
!= ( c_List_Orev @ SY1214 @ SY1213 ) )
| ( SY1214
= ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SY1213 ) @ SY1213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(982,plain,
! [SV173: $i] :
( ( ! [SY1215: $i,SY1216: $i,SY1217: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SY1215 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1216 ) @ SY1217 ) )
| ( SV173 = SY1216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(983,plain,
! [SV174: $i] :
( ( ! [SY1218: $i,SY1219: $i] :
( ( c_Type_Otype_OAtom @ SV174 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1218 ) @ SY1219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(984,plain,
! [SV175: $i] :
( ( ! [SY1220: $i,SY1221: $i,SY1222: $i,SY1223: $i] :
( ( ( c_List_Olist_OCons @ SV175 @ SY1220 @ SY1221 )
!= ( c_List_Oappend @ SY1222 @ SY1223 @ SY1221 ) )
| ( ( c_List_Olist_OCons @ SV175 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV175 @ SY1220 @ SY1222 @ SY1223 @ SY1221 ) @ SY1221 )
= SY1222 )
| ( ( c_List_Olist_OCons @ SV175 @ SY1220 @ SY1221 )
= SY1223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(985,plain,
! [SV176: $i] :
( ( ! [SY1224: $i] :
( ( c_Lambda_OdB_OAbs @ SV176 )
!= ( c_Lambda_OdB_OVar @ SY1224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(986,plain,
! [SV177: $i] :
( ( ! [SY1225: $i,SY1226: $i,SY1227: $i,SY1228: $i,SY1229: $i,SY1230: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SY1225 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1226 @ SY1227 @ SY1228 ) ) )
| ~ ( c_Type_Otyping @ SY1229 @ SY1227 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1227 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1229 @ SY1228 @ SV177 @ tc_Type_Otype ) @ SY1226 @ SY1230 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(987,plain,
! [SV178: $i] :
( ( ! [SY1231: $i,SY1232: $i,SY1233: $i,SY1234: $i] :
( ( ( c_List_Oappend @ SV178 @ SY1231 @ SY1232 )
!= ( c_List_Olist_OCons @ SY1233 @ SY1234 @ SY1232 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1233 @ SY1234 @ SV178 @ SY1231 @ SY1232 ) @ SY1231 @ SY1232 )
= SY1234 )
| ( SY1231
= ( c_List_Olist_OCons @ SY1233 @ SY1234 @ SY1232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(988,plain,
! [SV179: $i] :
( ( ! [SY1235: $i,SY1236: $i,SY1237: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV179 ) @ SY1235 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1236 ) @ SY1237 ) )
| ( SV179 = SY1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(989,plain,
! [SV180: $i] :
( ( ! [SY1238: $i,SY1239: $i,SY1240: $i] :
( ( ( c_List_Oappend @ SV180 @ SY1238 @ SY1239 )
!= ( c_List_Oappend @ SY1240 @ SY1238 @ SY1239 ) )
| ( SV180 = SY1240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(990,plain,
! [SV181: $i] :
( ( ! [SY1241: $i,SY1242: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV181 @ SY1241 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1242 @ SY1241 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV181 = SY1242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(991,plain,
! [SV182: $i] :
( ( ! [SY1243: $i,SY1244: $i,SY1245: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SY1243 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1244 ) @ SY1245 ) )
| ( SY1243 = SY1245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(992,plain,
! [SV183: $i] :
( ( ! [SY1246: $i,SY1247: $i] :
( ( SV183
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SY1246 ) @ SY1247 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SY1246 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SY1246 ) @ ( c_List_Oappend @ SY1247 @ ( c_List_Olist_OCons @ SY1246 @ ( 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)],[763]) ).
thf(993,plain,
! [SV184: $i] :
( ( ! [SY1248: $i,SY1249: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV184 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1248 @ SY1249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1249
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(994,plain,
! [SV185: $i] :
( ( ! [SY1250: $i,SY1251: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV185 ) @ SY1250 )
!= ( c_Type_Otype_OAtom @ SY1251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(995,plain,
! [SV186: $i] :
( ( ! [SY1252: $i,SY1253: $i] :
( ( ( c_List_Oappend @ SV186 @ SY1252 @ SY1253 )
!= SY1252 )
| ( SV186
= ( c_List_Olist_ONil @ SY1253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(996,plain,
! [SV187: $i] :
( ( ! [SY1254: $i,SY1255: $i,SY1256: $i,SY1257: $i] :
( ( ( c_List_OdropWhile @ SV187 @ SY1254 @ SY1255 )
!= ( c_List_Olist_OCons @ SY1256 @ SY1257 @ SY1255 ) )
| ( SY1254
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV187 @ SY1254 @ SY1255 ) @ ( c_List_Olist_OCons @ SY1256 @ SY1257 @ SY1255 ) @ SY1255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(997,plain,
! [SV188: $i] :
( ( ! [SY1258: $i,SY1259: $i] :
( ( c_List_Olist_ONil @ SV188 )
!= ( c_List_Olist_OCons @ SY1258 @ SY1259 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(998,plain,
! [SV189: $i] :
( ( ! [SY1260: $i,SY1261: $i,SY1262: $i,SY1263: $i] :
( ( ( c_List_Olist_OCons @ SV189 @ SY1260 @ SY1261 )
!= ( c_List_Olist_OCons @ SY1262 @ SY1263 @ SY1261 ) )
| ( SY1260 = SY1263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(999,plain,
! [SV190: $i] :
( ( ! [SY1264: $i,SY1265: $i] :
( ( ( c_List_Oreplicate @ SV190 @ SY1264 @ SY1265 )
!= ( c_List_Olist_ONil @ SY1265 ) )
| ( SV190
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1000,plain,
! [SV191: $i] :
( ( ! [SY1266: $i,SY1267: $i,SY1268: $i,SY1269: $i,SY1270: $i,SY1271: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SY1266 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1267 @ SY1268 @ SY1269 ) ) )
| ~ ( c_Type_Otyping @ SY1270 @ SY1268 @ SY1266 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1268 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1270 @ SY1269 @ SY1266 @ tc_Type_Otype ) @ SY1267 @ SY1271 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1001,plain,
! [SV192: $i] :
( ( ! [SY1272: $i,SY1273: $i] :
( ( ( c_List_Olist_ONil @ SV192 )
!= ( c_List_Oreplicate @ SY1272 @ SY1273 @ SV192 ) )
| ( SY1272
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1002,plain,
! [SV193: $i] :
( ( ! [SY1274: $i,SY1275: $i,SY1276: $i,SY1277: $i] :
( ( ( c_List_Oreplicate @ SV193 @ SY1274 @ SY1275 )
!= ( c_List_Oreplicate @ SY1276 @ SY1277 @ SY1275 ) )
| ( SV193 = SY1276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1003,plain,
! [SV194: $i] :
( ( ! [SY1278: $i,SY1279: $i,SY1280: $i,SY1281: $i] :
( ( ( c_List_Oreplicate @ SV194 @ SY1278 @ SY1279 )
!= ( c_List_Oreplicate @ SY1280 @ SY1281 @ SY1279 ) )
| ( SY1278 = SY1281 )
| ( SV194
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1004,plain,
! [SV195: $i] :
( ( ! [SY1282: $i,SY1283: $i,SY1284: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV195 ) @ SY1282 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1283 ) @ SY1284 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1282 = SY1284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1005,plain,
! [SV196: $i] :
( ( ! [SY1285: $i,SY1286: $i] :
( ( c_List_Olist_OCons @ SV196 @ SY1285 @ SY1286 )
!= SY1285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1006,plain,
! [SV197: $i] :
( ( ! [SY1287: $i,SY1288: $i,SY1289: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV197 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1287 ) @ SY1288 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SY1289 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SY1288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1007,plain,
! [SV198: $i] :
( ( ! [SY1290: $i,SY1291: $i] :
( ( ( c_List_Olist_ONil @ SV198 )
!= ( c_List_Oappend @ SY1290 @ SY1291 @ SV198 ) )
| ( SY1291
= ( c_List_Olist_ONil @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1008,plain,
! [SV199: $i] :
( ( ! [SY1292: $i] :
( ( ( c_List_Orotate1 @ SV199 @ SY1292 )
!= ( c_List_Olist_ONil @ SY1292 ) )
| ( SV199
= ( c_List_Olist_ONil @ SY1292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1009,plain,
! [SV200: $i] :
( ( ! [SY1293: $i,SY1294: $i] :
( ( ( c_List_Oappend @ SV200 @ SY1293 @ SY1294 )
!= SV200 )
| ( SY1293
= ( c_List_Olist_ONil @ SY1294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1010,plain,
! [SV201: $i] :
( ( ! [SY1295: $i,SY1296: $i] :
( ( SV201
!= ( c_List_Oappend @ SV201 @ SY1295 @ SY1296 ) )
| ( SY1295
= ( c_List_Olist_ONil @ SY1296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1011,plain,
! [SV202: $i] :
( ( ! [SY1297: $i,SY1298: $i,SY1299: $i,SY1300: $i] :
( ( ( c_List_Oappend @ SV202 @ SY1297 @ SY1298 )
!= ( c_List_Olist_OCons @ SY1299 @ SY1300 @ SY1298 ) )
| ( SV202
= ( c_List_Olist_OCons @ SY1299 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1299 @ SY1300 @ SV202 @ SY1297 @ SY1298 ) @ SY1298 ) )
| ( SY1297
= ( c_List_Olist_OCons @ SY1299 @ SY1300 @ SY1298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1012,plain,
! [SV203: $i] :
( ( ! [SY1301: $i,SY1302: $i,SY1303: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV203 ) @ SY1301 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1302 ) @ SY1303 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1013,plain,
! [SV204: $i] :
( ( ! [SY1304: $i,SY1305: $i] :
( ( ( c_List_Oappend @ SV204 @ SY1304 @ SY1305 )
!= ( c_List_Olist_ONil @ SY1305 ) )
| ( SV204
= ( c_List_Olist_ONil @ SY1305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1014,plain,
! [SV205: $i] :
( ( ! [SY1306: $i,SY1307: $i,SY1308: $i,SY1309: $i] :
( ( ( c_List_Olist_OCons @ SV205 @ SY1306 @ SY1307 )
!= ( c_List_Oappend @ SY1308 @ SY1309 @ SY1307 ) )
| ( SY1306
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV205 @ SY1306 @ SY1308 @ SY1309 @ SY1307 ) @ SY1309 @ SY1307 ) )
| ( SY1308
= ( c_List_Olist_ONil @ SY1307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1015,plain,
! [SV206: $i] :
( ( ! [SY1310: $i,SY1311: $i,SY1312: $i,SY1313: $i] :
( ( ( c_List_Olist_OCons @ SV206 @ SY1310 @ SY1311 )
!= ( c_List_Olist_OCons @ SY1312 @ SY1313 @ SY1311 ) )
| ( SV206 = SY1312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1016,plain,
! [SV207: $i] :
( ( ! [SY1314: $i,SY1315: $i,SY1316: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV207 ) @ SY1314 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1315 ) @ SY1316 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV207 = SY1315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1017,plain,
! [SV208: $i] :
( ( ! [SY1317: $i,SY1318: $i,SY1319: $i,SY1320: $i] :
( ( ( c_List_Oappend @ SV208 @ ( c_List_Olist_OCons @ SY1317 @ ( c_List_Olist_ONil @ SY1318 ) @ SY1318 ) @ SY1318 )
!= ( c_List_Oappend @ SY1319 @ ( c_List_Olist_OCons @ SY1320 @ ( c_List_Olist_ONil @ SY1318 ) @ SY1318 ) @ SY1318 ) )
| ( SY1317 = SY1320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1018,plain,
! [SV209: $i] :
( ( ! [SY1321: $i] :
( ( c_Lambda_OdB_OVar @ SV209 )
!= ( c_Lambda_OdB_OAbs @ SY1321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1019,plain,
! [SV210: $i] :
( ( ! [SY1322: $i,SY1323: $i,SY1324: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV210 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1322 ) @ SY1323 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SY1324 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SY1322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1020,plain,
! [SV211: $i] :
( ( ! [SY1325: $i,SY1326: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV211 @ SY1325 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1326 ) )
| ( SY1325
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1021,plain,
! [SV212: $i] :
( ( ! [SY1327: $i,SY1328: $i] :
( ( c_Lambda_OdB_OVar @ SV212 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1327 ) @ SY1328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1022,plain,
! [SV213: $i] :
( ( ! [SY1329: $i,SY1330: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SY1329 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1330 ) )
| ( SV213
= ( c_Lambda_OdB_OAbs @ SY1330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1023,plain,
! [SV214: $i] :
( ( ! [SY1331: $i,SY1332: $i,SY1333: $i,SY1334: $i] :
( ( ( c_List_OdropWhile @ SV214 @ SY1331 @ SY1332 )
!= ( c_List_Olist_OCons @ SY1333 @ SY1334 @ SY1332 ) )
| ~ ( hBOOL @ ( hAPP @ SV214 @ SY1333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1024,plain,
! [SV215: $i] :
( ( ! [SY1335: $i,SY1336: $i,SY1337: $i,SY1338: $i] :
( ( ( c_List_Oappend @ SV215 @ SY1335 @ SY1336 )
!= ( c_List_Olist_OCons @ SY1337 @ SY1338 @ SY1336 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1337 @ SY1338 @ SV215 @ SY1335 @ SY1336 ) @ SY1335 @ SY1336 )
= SY1338 )
| ( SV215
= ( c_List_Olist_ONil @ SY1336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1025,plain,
! [SV216: $i] :
( ( ! [SY1339: $i,SY1340: $i,SY1341: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV216 ) @ SY1339 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1340 ) @ SY1341 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV216 = SY1340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1026,plain,
! [SV217: $i] :
( ( ! [SY1342: $i,SY1343: $i] :
( ( c_List_Olist_OCons @ SV217 @ SY1342 @ SY1343 )
!= ( c_List_Olist_ONil @ SY1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1027,plain,
! [SV218: $i] :
( ( ! [SY1344: $i,SY1345: $i] :
( ( c_Lambda_OdB_OAbs @ SV218 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1344 ) @ SY1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1028,plain,
! [SV219: $i] :
( ( ! [SY1346: $i,SY1347: $i] :
( ( ( c_List_Orev @ SV219 @ SY1346 )
!= ( c_List_Orev @ SY1347 @ SY1346 ) )
| ( SV219 = SY1347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1029,plain,
! [SV220: $i] :
( ( ! [SY1348: $i,SY1349: $i] :
( ( ( c_List_Oappend @ SV220 @ SY1348 @ SY1349 )
!= ( c_List_Olist_ONil @ SY1349 ) )
| ( SY1348
= ( c_List_Olist_ONil @ SY1349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1030,plain,
! [SV221: $i] :
( ( ! [SY1350: $i] :
( ( ( c_List_Orev @ SV221 @ SY1350 )
!= ( c_List_Olist_ONil @ SY1350 ) )
| ( SV221
= ( c_List_Olist_ONil @ SY1350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1031,plain,
! [SV222: $i] :
( ( ! [SY1351: $i,SY1352: $i,SY1353: $i,SY1354: $i] :
( ( ( c_List_Olist_OCons @ SV222 @ SY1351 @ SY1352 )
!= ( c_List_Oappend @ SY1353 @ SY1354 @ SY1352 ) )
| ( SY1351
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV222 @ SY1351 @ SY1353 @ SY1354 @ SY1352 ) @ SY1354 @ SY1352 ) )
| ( ( c_List_Olist_OCons @ SV222 @ SY1351 @ SY1352 )
= SY1354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1032,plain,
! [SV223: $i] :
( ( ! [SY1355: $i,SY1356: $i] :
( ( ( c_List_Olist_ONil @ SV223 )
!= ( c_List_Oappend @ SY1355 @ SY1356 @ SV223 ) )
| ( SY1355
= ( c_List_Olist_ONil @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1033,plain,
! [SV224: $i] :
( ( ! [SY1357: $i,SY1358: $i] :
( ( ( c_Lambda_OdB_OVar @ SV224 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1357 @ SY1358 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV224 )
= SY1357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1034,plain,
! [SV225: $i] :
( ( ! [SY1359: $i,SY1360: $i] :
( ( c_List_Olist_OCons @ SV225 @ SY1359 @ SY1360 )
!= ( c_List_Olist_ONil @ SY1360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1035,plain,
! [SV226: $i] :
( ( ! [SY1361: $i] :
( ( ( c_List_Olist_ONil @ SV226 )
!= ( c_List_Orev @ SY1361 @ SV226 ) )
| ( SY1361
= ( c_List_Olist_ONil @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1036,plain,
! [SV227: $i] :
( ( ! [SY1362: $i,SY1363: $i,SY1364: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV227 ) @ SY1362 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1363 ) @ SY1364 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1362 = SY1364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1037,plain,
! [SV228: $i,SV1: $i] :
( ( ( c_List_Olist_ONil @ SV1 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV228 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1038,plain,
! [SV229: $i,SV2: $i] :
( ( ! [SY1365: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV2 @ SV229 @ SY1365 ) @ SY1365 )
= SV229 )
| ( SV2
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1039,plain,
! [SV230: $i,SV3: $i] :
( ( ! [SY1366: $i,SY1367: $i] :
( ( c_Type_Otyping @ SV3 @ SV230 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SY1366 @ SV3 @ SV230 @ SY1367 ) )
| ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SY1367 @ ( c_List_Olist_OCons @ SV230 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY1366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1040,plain,
! [SV231: $i,SV4: $i] :
( ( ! [SY1368: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV4 @ SV231 @ SY1368 ) @ SY1368 )
= SV231 )
| ( SV4
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1041,plain,
! [SV232: $i,SV5: $i] :
( ( ! [SY1369: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV5 @ SV232 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1369 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1042,plain,
! [SV233: $i,SV6: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV6 @ SV233 )
= ( c_List_Olist_ONil @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1043,plain,
! [SV8: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV8 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(1044,plain,
! [SV234: $i,SV9: $i] :
( ( ! [SY1370: $i] :
( ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV9 @ SV234 @ SY1370 ) @ SY1370 ) ) )
| ( ( c_List_OdropWhile @ SV9 @ SV234 @ SY1370 )
= ( c_List_Olist_ONil @ SY1370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1045,plain,
! [SV235: $i,SV11: $i] :
( ( ! [SY1371: $i,SY1372: $i,SY1373: $i,SY1374: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV11 @ SV235 @ SY1371 @ SY1372 ) @ SY1373 ) @ SY1374 )
= ( hAPP @ ( hAPP @ SV11 @ SY1374 ) @ SY1373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1046,plain,
! [SV236: $i,SV12: $i] :
( ( ! [SY1375: $i,SY1376: $i] :
( ( c_List_Olistsp @ SV12 @ SV236 @ SY1375 )
| ~ ( c_List_Olistsp @ SV12 @ ( c_List_Oappend @ SV236 @ SY1376 @ SY1375 ) @ SY1375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1047,plain,
! [SV237: $i,SV13: $i] :
( ( ! [SY1377: $i,SY1378: $i] :
( ( c_List_Olistsp @ SV13 @ SV237 @ SY1377 )
| ~ ( c_List_Olistsp @ SV13 @ ( c_List_Oappend @ SY1378 @ SV237 @ SY1377 ) @ SY1377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1048,plain,
! [SV238: $i,SV14: $i] :
( ( c_List_Olistsp @ SV14 @ ( c_List_Olist_ONil @ SV238 ) @ SV238 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1049,plain,
! [SV239: $i,SV15: $i] :
( ( ( c_List_OdropWhile @ SV15 @ ( c_List_Olist_ONil @ SV239 ) @ SV239 )
= ( c_List_Olist_ONil @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1050,plain,
! [SV240: $i,SV16: $i] :
( ( ! [SY1379: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV16 ) ) @ SV240 ) @ SY1379 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV16 @ SV240 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1379 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1051,plain,
! [SV241: $i,SV17: $i] :
( ( ! [SY1380: $i,SY1381: $i,SY1382: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV17 @ SV241 @ SY1380 ) @ ( c_List_Olist_OCons @ SY1381 @ SY1382 @ SY1380 ) @ SY1380 )
= ( c_List_Olist_OCons @ SV17 @ ( c_List_Olist_OCons @ SY1381 @ ( c_List_Osplice @ SV241 @ SY1382 @ SY1380 ) @ SY1380 ) @ SY1380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1052,plain,
! [SV242: $i,SV18: $i] :
( ( ! [SY1383: $i,SY1384: $i] :
( ( ( c_List_OdropWhile @ SV18 @ ( c_List_Olist_OCons @ SV242 @ SY1383 @ SY1384 ) @ SY1384 )
= ( c_List_OdropWhile @ SV18 @ SY1383 @ SY1384 ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1053,plain,
! [SV243: $i,SV19: $i] :
( ( ! [SY1385: $i,SY1386: $i] :
( ( ( c_List_OdropWhile @ SV19 @ ( c_List_Olist_OCons @ SV243 @ SY1385 @ SY1386 ) @ SY1386 )
= ( c_List_Olist_OCons @ SV243 @ SY1385 @ SY1386 ) )
| ( hBOOL @ ( hAPP @ SV19 @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1054,plain,
! [SV244: $i,SV20: $i] :
( ( ! [SY1387: $i] :
( ( c_List_Oappend @ ( c_List_OtakeWhile @ SV20 @ SV244 @ SY1387 ) @ ( c_List_OdropWhile @ SV20 @ SV244 @ SY1387 ) @ SY1387 )
= SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1055,plain,
! [SV245: $i,SV21: $i] :
( ( ! [SY1388: $i,SY1389: $i] :
( ( c_List_Olistsp @ SV21 @ ( c_List_Oappend @ SV245 @ SY1388 @ SY1389 ) @ SY1389 )
| ~ ( c_List_Olistsp @ SV21 @ SY1388 @ SY1389 )
| ~ ( c_List_Olistsp @ SV21 @ SV245 @ SY1389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1056,plain,
! [SV246: $i,SV22: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_ONil @ SV22 ) @ SV246 @ SV22 )
= SV246 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1057,plain,
! [SV247: $i,SV23: $i] :
( ( ( c_List_Osplice @ SV23 @ ( c_List_Olist_ONil @ SV247 ) @ SV247 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1058,plain,
! [SV248: $i,SV24: $i] :
( ( ! [SY1390: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV24 @ SV248 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1390 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV24 @ ( c_List_Oappend @ SV248 @ ( c_List_Olist_OCons @ SY1390 @ ( 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)],[831]) ).
thf(1059,plain,
! [SV249: $i,SV25: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV25 ) @ SV249 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV25 ) @ SV249 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1060,plain,
! [SV250: $i,SV26: $i] :
( ( ! [SY1391: $i] :
( ( ( c_List_Oappend @ SV26 @ ( c_List_Olist_OCons @ SV250 @ ( 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 @ SY1391 @ SV26 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV250 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1391 @ ( c_List_Oappend @ SV26 @ ( c_List_Olist_OCons @ SV250 @ ( 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)],[833]) ).
thf(1061,plain,
! [SV251: $i,SV27: $i] :
( ( ! [SY1392: $i,SY1393: $i] :
( ( c_Type_Otyping @ SV27 @ ( c_Lambda_OdB_OAbs @ SV251 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1392 ) @ SY1393 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV27 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1392 @ tc_Type_Otype ) @ SV251 @ SY1393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1062,plain,
! [SV252: $i,SV28: $i] :
( ( ! [SY1394: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV28 @ SV252 @ SY1394 ) @ ( c_List_Olist_ONil @ SY1394 ) @ SY1394 )
= ( c_List_Olist_OCons @ SV28 @ SV252 @ SY1394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1063,plain,
! [SV253: $i,SV29: $i] :
( ( ! [SY1395: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV29 @ SV253 @ SY1395 ) @ SY1395 )
= ( c_List_Olist_OCons @ SV29 @ ( c_List_Obutlast @ SV253 @ SY1395 ) @ SY1395 ) )
| ( SV253
= ( c_List_Olist_ONil @ SY1395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1064,plain,
! [SV254: $i,SV30: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV30 @ ( c_List_Olist_ONil @ SV254 ) @ SV254 ) @ SV254 )
= SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1065,plain,
! [SV255: $i,SV31: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV31 @ ( c_List_Olist_ONil @ SV255 ) @ SV255 ) @ SV255 )
= ( c_List_Olist_ONil @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1066,plain,
! [SV256: $i,SV32: $i] :
( ( ! [SY1396: $i,SY1397: $i] :
( ( ( c_List_OtakeWhile @ SV32 @ ( c_List_Olist_OCons @ SV256 @ SY1396 @ SY1397 ) @ SY1397 )
= ( c_List_Olist_ONil @ SY1397 ) )
| ( hBOOL @ ( hAPP @ SV32 @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1067,plain,
! [SV257: $i,SV33: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV33 @ ( c_List_Olist_ONil @ SV257 ) @ SV257 ) @ SV257 )
= ( c_List_Olist_OCons @ SV33 @ ( c_List_Olist_ONil @ SV257 ) @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1068,plain,
! [SV258: $i,SV34: $i] :
( ( ! [SY1398: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV34 @ SV258 @ SY1398 ) @ SY1398 )
= ( c_List_Olast @ SV258 @ SY1398 ) )
| ( SV258
= ( c_List_Olist_ONil @ SY1398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1069,plain,
! [SV259: $i,SV35: $i] :
( ( ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_ONil @ SV259 ) @ SV259 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_ONil @ SV259 ) @ SV259 ) @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1070,plain,
! [SV260: $i,SV36: $i] :
( ( ! [SY1399: $i,SY1400: $i,SY1401: $i,SY1402: $i,SY1403: $i] :
( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SY1399 @ SY1400 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SY1399 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1401 ) @ SY1402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
| ~ ( c_Type_Otypings @ SY1399 @ SY1402 @ SY1403 )
| ~ ( c_Type_Otyping @ SY1399 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1401 ) @ SY1402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1400 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1071,plain,
! [SV261: $i,SV37: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV37 @ SV261 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV37 @ SV261 ) @ ( c_List_Olist_ONil @ SV261 ) @ SV261 ) @ SV261 )
= SV37 )
| ( SV37
= ( c_List_Olist_ONil @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1072,plain,
! [SV262: $i,SV38: $i] :
( ( ! [SY1404: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV38 @ SV262 @ SY1404 ) @ SY1404 )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1073,plain,
! [SV263: $i,SV39: $i] :
( ( ! [SY1405: $i,SY1406: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV39 ) @ SV263 ) @ SY1405 @ SY1406 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV39 @ SY1405 @ SY1406 ) ) @ ( c_Lambda_Osubst @ SV263 @ SY1405 @ SY1406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1074,plain,
! [SV264: $i,SV41: $i] :
( ( ! [SY1407: $i,SY1408: $i] :
( ( c_Type_Otypings @ SV41 @ SV264 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1407 @ SV41 @ SY1408 @ SV264 ) )
| ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1408 ) @ SV264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1075,plain,
! [SV265: $i,SV43: $i] :
( ( ! [SY1409: $i,SY1410: $i,SY1411: $i] :
( ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_OCons @ SV265 @ SY1409 @ SY1410 ) @ ( c_List_Olist_OCons @ SV265 @ SY1411 @ SY1410 ) @ SY1410 )
| ~ ( c_ListOrder_Ostep1 @ SV43 @ SY1409 @ SY1411 @ SY1410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1076,plain,
! [SV266: $i,SV44: $i] :
( ( ! [SY1412: $i,SY1413: $i,SY1414: $i,SY1415: $i] :
( ( c_ListOrder_Ostep1 @ SV44 @ SV266 @ SY1412 @ SY1413 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SY1414 ) @ SY1415 ) )
| ~ ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SY1414 @ SV266 @ SY1413 ) @ ( c_List_Olist_OCons @ SY1415 @ SY1412 @ SY1413 ) @ SY1413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1077,plain,
! [SV267: $i,SV45: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV45 ) @ SV267 @ SV45 )
= SV267 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1078,plain,
! [SV268: $i,SV46: $i] :
( ( ( c_List_OtakeWhile @ SV46 @ ( c_List_Olist_ONil @ SV268 ) @ SV268 )
= ( c_List_Olist_ONil @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1079,plain,
! [SV269: $i,SV48: $i] :
( ( ! [SY1416: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV48 @ ( c_Lambda_OdB_OVar @ SV269 ) @ SY1416 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1080,plain,
! [SV270: $i,SV49: $i] :
( ( ! [SY1417: $i,SY1418: $i] :
( ( c_Type_Otypings @ SV49 @ SV270 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1417 @ SV49 @ SY1418 @ SV270 ) )
| ~ ( c_Type_Otyping @ SV49 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1418 @ SV270 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1081,plain,
! [SV271: $i,SV50: $i] :
( ( ! [SY1419: $i,SY1420: $i,SY1421: $i] :
( ( c_List_Ofoldr @ SV50 @ SV271 @ SY1419 @ SY1420 @ SY1421 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV50 @ SY1420 @ SY1421 @ SY1421 ) @ SY1419 @ ( c_List_Orev @ SV271 @ SY1420 ) @ SY1421 @ SY1420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1082,plain,
! [SV272: $i,SV51: $i] :
( ( ! [SY1422: $i] :
( ( c_List_Oconcat__map @ SV51 @ ( c_List_Olist_ONil @ SV272 ) @ SV272 @ SY1422 )
= ( c_List_Olist_ONil @ SY1422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1083,plain,
! [SV273: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV52 ) @ SV273 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV273 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1084,plain,
! [SV274: $i,SV53: $i] :
( ( ! [SY1423: $i,SY1424: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV53 @ SV274 @ SY1423 ) @ ( c_List_Oreplicate @ SY1424 @ SV274 @ SY1423 ) @ SY1423 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY1424 @ SV274 @ SY1423 ) @ ( c_List_Oreplicate @ SV53 @ SV274 @ SY1423 ) @ SY1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1085,plain,
! [SV275: $i,SV54: $i] :
( ( ! [SY1425: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ SV54 @ SV275 @ SY1425 ) @ SY1425 )
= SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1086,plain,
! [SV276: $i,SV55: $i] :
( ( ! [SY1426: $i,SY1427: $i,SY1428: $i,SY1429: $i] :
( ( c_ListOrder_Ostep1 @ SV55 @ SV276 @ SY1426 @ SY1427 )
| ( SY1426 = SV276 )
| ~ ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SY1428 @ SV276 @ SY1427 ) @ ( c_List_Olist_OCons @ SY1429 @ SY1426 @ SY1427 ) @ SY1427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1087,plain,
! [SV277: $i,SV56: $i] :
( ( ! [SY1430: $i,SY1431: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV56 @ SV277 @ SY1430 ) @ SY1431 @ SY1430 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY1431 @ SY1430 ) @ ( c_List_Osplice @ SV277 @ ( c_List_Otl @ SY1431 @ SY1430 ) @ SY1430 ) @ SY1430 ) @ SY1430 ) )
| ( SY1431
= ( c_List_Olist_ONil @ SY1430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1088,plain,
! [SV278: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV57 @ SV278 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1089,plain,
! [SV279: $i,SV58: $i] :
( ( ! [SY1432: $i,SY1433: $i] :
( ( c_List_Ofoldl @ SV58 @ SV279 @ ( c_List_Olist_ONil @ SY1432 ) @ SY1433 @ SY1432 )
= SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1090,plain,
! [SV280: $i,SV59: $i] :
( ( ! [SY1434: $i] :
~ ( c_ListOrder_Ostep1 @ SV59 @ SV280 @ ( c_List_Olist_ONil @ SY1434 ) @ SY1434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1091,plain,
! [SV281: $i,SV60: $i] :
( ( ! [SY1435: $i] :
~ ( c_ListOrder_Ostep1 @ SV60 @ ( c_List_Olist_ONil @ SV281 ) @ SY1435 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1092,plain,
! [SV282: $i,SV61: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Orev @ SV61 @ SV282 ) @ SV282 )
= ( c_List_Olast @ SV61 @ SV282 ) )
| ( SV61
= ( c_List_Olist_ONil @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1093,plain,
! [SV283: $i,SV63: $i] :
( ( ! [SY1436: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV63 @ SV283 @ SY1436 ) @ SY1436 )
= ( c_List_Oreplicate @ SV63 @ SV283 @ SY1436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1094,plain,
! [SV284: $i,SV64: $i] :
( ( ! [SY1437: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV64 ) @ SV284 ) @ SY1437 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV64 @ SY1437 ) ) @ ( c_Lambda_Olift @ SV284 @ SY1437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1095,plain,
! [SV285: $i,SV65: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV65 @ SV285 ) @ SV285 )
= SV65 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1096,plain,
! [SV286: $i,SV66: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV66 @ SV286 ) @ SV286 )
= SV66 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1097,plain,
! [SV287: $i,SV67: $i] :
( ( SV67
= ( c_List_Orev @ ( c_List_Orev @ SV67 @ SV287 ) @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1098,plain,
! [SV288: $i,SV68: $i] :
( ( ! [SY1438: $i,SY1439: $i,SY1440: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV288 ) @ SY1438 ) )
| ( c_ListOrder_Ostep1 @ SV68 @ ( c_List_Olist_OCons @ SV288 @ SY1439 @ SY1440 ) @ ( c_List_Olist_OCons @ SY1438 @ SY1439 @ SY1440 ) @ SY1440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1099,plain,
! [SV289: $i,SV69: $i] :
( ( ! [SY1441: $i,SY1442: $i,SY1443: $i,SY1444: $i] :
( ( SV69 = SV289 )
| ( SY1441 = SY1442 )
| ~ ( c_ListOrder_Ostep1 @ SY1443 @ ( c_List_Olist_OCons @ SV289 @ SY1442 @ SY1444 ) @ ( c_List_Olist_OCons @ SV69 @ SY1441 @ SY1444 ) @ SY1444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1100,plain,
! [SV290: $i,SV71: $i] :
( ( ( ( c_List_Olast @ ( c_List_Orev @ SV71 @ SV290 ) @ SV290 )
= ( c_List_Ohd @ SV71 @ SV290 ) )
| ( SV71
= ( c_List_Olist_ONil @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1101,plain,
! [SV291: $i,SV72: $i] :
( ( ! [SY1445: $i,SY1446: $i,SY1447: $i] :
( ( c_ListOrder_Ostep1 @ SV72 @ ( c_List_Oappend @ SV291 @ SY1445 @ SY1446 ) @ ( c_List_Oappend @ SV291 @ SY1447 @ SY1446 ) @ SY1446 )
| ~ ( c_ListOrder_Ostep1 @ SV72 @ SY1445 @ SY1447 @ SY1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1102,plain,
! [SV292: $i,SV73: $i] :
( ( ! [SY1448: $i,SY1449: $i,SY1450: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV73 @ SV292 @ SY1448 @ SY1449 )
| ( c_ListOrder_Ostep1 @ SV73 @ ( c_List_Oappend @ SV292 @ SY1450 @ SY1449 ) @ ( c_List_Oappend @ SY1448 @ SY1450 @ SY1449 ) @ SY1449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1103,plain,
! [SV293: $i,SV75: $i] :
( ( ! [SY1451: $i,SY1452: $i] :
( ( c_Type_Otypings @ SV75 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1451 @ SV75 @ SY1452 @ SV293 ) )
| ~ ( c_Type_Otyping @ SV75 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1452 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1104,plain,
! [SV294: $i,SV76: $i] :
( ( ! [SY1453: $i,SY1454: $i,SY1455: $i,SY1456: $i] :
( ( c_List_Ofoldl @ SV76 @ SV294 @ ( c_List_Olist_OCons @ SY1453 @ SY1454 @ SY1455 ) @ SY1456 @ SY1455 )
= ( c_List_Ofoldl @ SV76 @ ( hAPP @ ( hAPP @ SV76 @ SV294 ) @ SY1453 ) @ SY1454 @ SY1456 @ SY1455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1105,plain,
! [SV295: $i,SV77: $i] :
( ( ( ( c_List_Orotate1 @ SV77 @ SV295 )
= ( c_List_Oappend @ ( c_List_Otl @ SV77 @ SV295 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV77 @ SV295 ) @ ( c_List_Olist_ONil @ SV295 ) @ SV295 ) @ SV295 ) )
| ( SV77
= ( c_List_Olist_ONil @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1106,plain,
! [SV296: $i,SV78: $i] :
( ( ! [SY1457: $i,SY1458: $i,SY1459: $i,SY1460: $i] :
( ( SV78 = SV296 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1457 @ SV296 ) @ SV78 ) )
| ~ ( c_ListOrder_Ostep1 @ SY1457 @ ( c_List_Olist_OCons @ SV296 @ SY1458 @ SY1459 ) @ ( c_List_Olist_OCons @ SV78 @ SY1460 @ SY1459 ) @ SY1459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1107,plain,
! [SV297: $i,SV79: $i] :
( ( ! [SY1461: $i,SY1462: $i,SY1463: $i,SY1464: $i,SY1465: $i] :
( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY1461 @ SY1462 @ SV79 @ SV297 ) )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1463 ) @ SY1464 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1462 )
| ~ ( c_Type_Otypings @ SV79 @ SY1464 @ SY1465 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1463 ) @ SY1464 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1108,plain,
! [SV298: $i,SV80: $i] :
( ( ! [SY1466: $i,SY1467: $i] :
( ( ( c_List_OtakeWhile @ SV80 @ ( c_List_Olist_OCons @ SV298 @ SY1466 @ SY1467 ) @ SY1467 )
= ( c_List_Olist_OCons @ SV298 @ ( c_List_OtakeWhile @ SV80 @ SY1466 @ SY1467 ) @ SY1467 ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ SV298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1109,plain,
! [SV299: $i,SV81: $i] :
( ( ! [SY1468: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV81 @ SV299 ) @ SY1468 @ SV299 )
= SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1110,plain,
! [SV300: $i,SV82: $i] :
( ( ! [SY1469: $i,SY1470: $i,SY1471: $i] :
( ( c_List_Ofoldl @ SV82 @ SV300 @ SY1469 @ SY1470 @ SY1471 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV82 @ SY1470 @ SY1471 @ SY1470 ) @ ( c_List_Orev @ SY1469 @ SY1471 ) @ SV300 @ SY1471 @ SY1470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1111,plain,
! [SV301: $i,SV84: $i] :
( ( ! [SY1472: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV84 @ SV301 @ SY1472 ) @ SY1472 )
= ( c_List_Oappend @ ( c_List_Orev @ SV301 @ SY1472 ) @ ( c_List_Orev @ SV84 @ SY1472 ) @ SY1472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1112,plain,
! [SV302: $i,SV85: $i] :
( ( ! [SY1473: $i,SY1474: $i,SY1475: $i,SY1476: $i] :
( ( c_List_Ofoldl @ SV85 @ SV302 @ ( c_List_Oappend @ SY1473 @ SY1474 @ SY1475 ) @ SY1476 @ SY1475 )
= ( c_List_Ofoldl @ SV85 @ ( c_List_Ofoldl @ SV85 @ SV302 @ SY1473 @ SY1476 @ SY1475 ) @ SY1474 @ SY1476 @ SY1475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1113,plain,
! [SV303: $i,SV86: $i] :
( ( ! [SY1477: $i,SY1478: $i,SY1479: $i] :
( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SY1477 @ SY1478 @ SY1479 ) @ SY1479 ) @ SY1479 ) ) )
| ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ SY1478 @ SY1479 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV86 @ SY1477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1114,plain,
! [SV304: $i,SV87: $i] :
( ( ! [SY1480: $i,SY1481: $i,SY1482: $i] :
( ( c_List_Oconcat__map @ SV87 @ ( c_List_Olist_OCons @ SV304 @ SY1480 @ SY1481 ) @ SY1481 @ SY1482 )
= ( c_List_Oappend @ ( hAPP @ SV87 @ SV304 ) @ ( c_List_Oconcat__map @ SV87 @ SY1480 @ SY1481 @ SY1482 ) @ SY1482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1115,plain,
! [SV305: $i,SV88: $i] :
( ( ! [SY1483: $i,SY1484: $i,SY1485: $i] :
( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ ( c_List_Oappend @ SV305 @ ( c_List_Olist_OCons @ SY1483 @ SY1484 @ SY1485 ) @ SY1485 ) @ SY1485 ) ) )
| ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ SV305 @ SY1485 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV88 @ SY1483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1116,plain,
! [SV306: $i,SV89: $i] :
( ( ! [SY1486: $i,SY1487: $i,SY1488: $i] :
( ( ( c_List_OtakeWhile @ SV89 @ ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SY1486 @ SY1487 @ SY1488 ) @ SY1488 ) @ SY1488 )
= ( c_List_OtakeWhile @ SV89 @ SV306 @ SY1488 ) )
| ( hBOOL @ ( hAPP @ SV89 @ SY1486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1117,plain,
! [SV307: $i,SV90: $i] :
( ( ! [SY1489: $i,SY1490: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV90 @ SV307 @ SY1489 ) @ ( c_List_Olist_OCons @ SV307 @ SY1490 @ SY1489 ) @ SY1489 )
= ( c_List_Olist_OCons @ SV307 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV90 @ SV307 @ SY1489 ) @ SY1490 @ SY1489 ) @ SY1489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1118,plain,
! [SV308: $i,SV91: $i] :
( ( ! [SY1491: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ SV91 @ SV308 @ SY1491 ) @ SY1491 )
= ( c_List_Ohd @ SV91 @ SY1491 ) )
| ( SV91
= ( c_List_Olist_ONil @ SY1491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1119,plain,
! [SV309: $i,SV92: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV92 @ ( c_List_Olist_ONil @ SV309 ) @ SV309 ) @ SV309 )
= ( c_List_Obutlast @ SV92 @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1120,plain,
! [SV310: $i,SV93: $i] :
( ( ! [SY1492: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ SV93 @ SV310 @ SY1492 ) @ SY1492 )
= ( c_List_Oappend @ ( c_List_Otl @ SV93 @ SY1492 ) @ SV310 @ SY1492 ) )
| ( SV93
= ( c_List_Olist_ONil @ SY1492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1121,plain,
! [SV311: $i,SV94: $i] :
( ( ! [SY1493: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV94 @ SV311 @ SY1493 ) @ SY1493 )
= ( c_List_Olast @ SV311 @ SY1493 ) )
| ( SV311
= ( c_List_Olist_ONil @ SY1493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1122,plain,
! [SV312: $i,SV95: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV95 @ ( c_List_Olist_ONil @ SV312 ) @ SV312 ) @ SV312 )
= ( c_List_Olast @ SV95 @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1123,plain,
! [SV313: $i,SV96: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ SV96 ) @ SV313 @ SV96 ) @ SV96 )
= ( c_List_Ohd @ SV313 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1124,plain,
! [SV314: $i,SV97: $i] :
( ( ! [SY1494: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV97 @ SV314 @ SY1494 ) @ SY1494 )
= ( c_List_Oappend @ SV97 @ ( c_List_Obutlast @ SV314 @ SY1494 ) @ SY1494 ) )
| ( SV314
= ( c_List_Olist_ONil @ SY1494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1125,plain,
! [SV315: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV98 ) @ ( c_Lambda_OdB_OVar @ SV315 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1126,plain,
! [SV316: $i,SV99: $i] :
( ( ! [SY1495: $i,SY1496: $i] :
( ( c_Type_Otyping @ SV99 @ SV316 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1495 @ SV99 @ SY1496 @ SV316 ) )
| ~ ( c_Type_Otyping @ SV99 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1496 ) @ SV316 ) @ SY1495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1127,plain,
! [SV317: $i,SV100: $i] :
( ( ! [SY1497: $i,SY1498: $i] :
( ( c_Type_Otyping @ SV100 @ SV317 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY1497 @ SV100 @ SV317 @ SY1498 ) @ SY1497 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV317 @ SY1498 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1128,plain,
! [SV318: $i,SV101: $i] :
( ( ! [SY1499: $i,SY1500: $i,SY1501: $i] :
( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV318 @ SY1499 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1500 )
| ~ ( c_Type_Otypings @ SV101 @ SY1499 @ SY1501 )
| ~ ( c_Type_Otyping @ SV101 @ SV318 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1501 @ SY1500 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1129,plain,
! [SV319: $i,SV102: $i] :
( ( ! [SY1502: $i,SY1503: $i] :
( ( c_Type_Otyping @ SV102 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY1502 @ SV102 @ SV319 @ SY1503 ) @ SY1502 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV102 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SY1503 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1130,plain,
! [SV320: $i,SV103: $i] :
( ( ! [SY1504: $i,SY1505: $i,SY1506: $i,SY1507: $i] :
( ~ ( c_Type_Otyping @ SV103 @ SV320 @ SY1504 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SY1505 @ SY1504 @ tc_Type_Otype ) @ SY1506 @ SY1507 )
| ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SY1506 @ SV320 @ SY1505 ) @ SY1507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1131,plain,
! [SV321: $i,SV104: $i] :
( ( ! [SY1508: $i,SY1509: $i,SY1510: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV104 @ SV321 @ SY1508 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1509 @ SV321 ) @ SY1510 )
| ~ ( c_Type_Otyping @ SV104 @ SY1509 @ SY1510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1132,plain,
! [SV322: $i,SV105: $i] :
( ( ! [SY1511: $i,SY1512: $i] :
( ( c_Type_Otyping @ SV105 @ ( c_Lambda_OdB_OVar @ SV322 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY1511 @ SV105 @ SV322 @ SY1512 ) @ SY1511 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV105 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV322 ) @ SY1512 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1133,plain,
! [SV323: $i,SV106: $i] :
( ( ! [SY1513: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV106 @ SV323 @ SY1513 ) @ ( c_List_Olist_OCons @ SV323 @ ( c_List_Olist_ONil @ SY1513 ) @ SY1513 ) @ SY1513 )
= ( c_List_Olist_OCons @ SV323 @ ( c_List_Oreplicate @ SV106 @ SV323 @ SY1513 ) @ SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1134,plain,
! [SV324: $i,SV107: $i] :
( ( ! [SY1514: $i,SY1515: $i,SY1516: $i,SY1517: $i] :
( ( SV107 = SV324 )
| ( c_ListOrder_Ostep1 @ SY1514 @ SV107 @ SV324 @ SY1515 )
| ~ ( c_ListOrder_Ostep1 @ SY1514 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SY1516 @ ( c_List_Olist_ONil @ SY1515 ) @ SY1515 ) @ SY1515 ) @ ( c_List_Oappend @ SV324 @ ( c_List_Olist_OCons @ SY1517 @ ( c_List_Olist_ONil @ SY1515 ) @ SY1515 ) @ SY1515 ) @ SY1515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1135,plain,
! [SV325: $i,SV108: $i] :
( ( ! [SY1518: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV108 @ SV325 @ SY1518 ) @ SY1518 )
= ( c_List_Oappend @ SV325 @ ( c_List_Olist_OCons @ SV108 @ ( c_List_Olist_ONil @ SY1518 ) @ SY1518 ) @ SY1518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1136,plain,
! [SV326: $i,SV109: $i] :
( ( ! [SY1519: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV109 @ SV326 ) @ ( c_List_Olist_OCons @ SY1519 @ ( c_List_Olist_ONil @ SV326 ) @ SV326 ) @ SV326 ) @ SV326 )
= ( c_List_Olist_OCons @ SY1519 @ SV109 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1137,plain,
! [SV327: $i,SV110: $i] :
( ( ! [SY1520: $i,SY1521: $i,SY1522: $i,SY1523: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV327 ) @ SY1520 ) )
| ( c_ListOrder_Ostep1 @ SV110 @ SY1521 @ SY1522 @ SY1523 )
| ~ ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SY1521 @ ( c_List_Olist_OCons @ SV327 @ ( c_List_Olist_ONil @ SY1523 ) @ SY1523 ) @ SY1523 ) @ ( c_List_Oappend @ SY1522 @ ( c_List_Olist_OCons @ SY1520 @ ( c_List_Olist_ONil @ SY1523 ) @ SY1523 ) @ SY1523 ) @ SY1523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1138,plain,
! [SV328: $i,SV111: $i] :
( ( ! [SY1524: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV111 @ SV328 @ SY1524 ) @ SY1524 )
= ( c_List_Oappend @ ( c_List_Orev @ SV328 @ SY1524 ) @ ( c_List_Olist_OCons @ SV111 @ ( c_List_Olist_ONil @ SY1524 ) @ SY1524 ) @ SY1524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1139,plain,
! [SV329: $i,SV112: $i] :
( ( ! [SY1525: $i,SY1526: $i,SY1527: $i,SY1528: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SV329 ) @ SY1525 ) )
| ( SV329 = SY1525 )
| ~ ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SY1526 @ ( c_List_Olist_OCons @ SV329 @ ( c_List_Olist_ONil @ SY1527 ) @ SY1527 ) @ SY1527 ) @ ( c_List_Oappend @ SY1528 @ ( c_List_Olist_OCons @ SY1525 @ ( c_List_Olist_ONil @ SY1527 ) @ SY1527 ) @ SY1527 ) @ SY1527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1140,plain,
! [SV330: $i,SV113: $i] :
( ( ! [SY1529: $i,SY1530: $i,SY1531: $i,SY1532: $i] :
( ( SV113 = SV330 )
| ( SY1529 = SY1530 )
| ~ ( c_ListOrder_Ostep1 @ SY1531 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SY1529 @ ( c_List_Olist_ONil @ SY1532 ) @ SY1532 ) @ SY1532 ) @ ( c_List_Oappend @ SV330 @ ( c_List_Olist_OCons @ SY1530 @ ( c_List_Olist_ONil @ SY1532 ) @ SY1532 ) @ SY1532 ) @ SY1532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1141,plain,
! [SV331: $i,SV114: $i] :
( ( ! [SY1533: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV114 @ ( c_List_Olist_OCons @ SV331 @ ( c_List_Olist_ONil @ SY1533 ) @ SY1533 ) @ SY1533 ) @ SY1533 )
= SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1142,plain,
! [SV332: $i,SV115: $i] :
( ( ! [SY1534: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV115 @ ( c_List_Olist_OCons @ SV332 @ ( c_List_Olist_ONil @ SY1534 ) @ SY1534 ) @ SY1534 ) @ SY1534 )
= SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1143,plain,
! [SV333: $i,SV116: $i] :
( ( ! [SY1535: $i,SY1536: $i,SY1537: $i] :
( ( SV116 = SV333 )
| ~ ( c_Type_Otyping @ SY1535 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1536 ) @ SY1537 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV333 )
| ~ ( c_Type_Otyping @ SY1535 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1536 ) @ SY1537 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1144,plain,
! [SV334: $i,SV117: $i] :
( ( ! [SY1538: $i,SY1539: $i] :
( ( c_Type_Otyping @ SV117 @ SV334 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY1538 @ SV117 @ SV334 @ SY1539 ) ) @ SY1538 ) )
| ~ ( c_Type_Otyping @ SV117 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SY1539 ) @ SY1538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1145,plain,
! [SV335: $i,SV118: $i] :
( ( ! [SY1540: $i,SY1541: $i] :
( ( c_Type_Otype_Otype__case @ SV118 @ SV335 @ ( c_Type_Otype_OAtom @ SY1540 ) @ SY1541 )
= ( hAPP @ SV118 @ SY1540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1146,plain,
! [SV336: $i,SV120: $i] :
( ( ! [SY1542: $i] :
( ( c_List_Olist_OCons @ SV120 @ SV336 @ SY1542 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1542 ) @ ( c_List_Olist_OCons @ SV120 @ SV336 @ SY1542 ) @ SY1542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1147,plain,
! [SV337: $i,SV121: $i] :
( ( ! [SY1543: $i,SY1544: $i] :
( ~ ( hBOOL @ ( hAPP @ SV121 @ ( c_Type_Otype_Otype__case @ SV337 @ SY1543 @ ( c_Type_Otype_OAtom @ SY1544 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV121 @ ( hAPP @ SV337 @ SY1544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1148,plain,
! [SV338: $i,SV122: $i] :
( ( ! [SY1545: $i,SY1546: $i] :
( ~ ( hBOOL @ ( hAPP @ SV122 @ ( c_Type_Otype_Otype__case @ SV338 @ SY1545 @ ( c_Type_Otype_OAtom @ SY1546 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV122 @ ( hAPP @ SV338 @ SY1546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1149,plain,
! [SV339: $i,SV123: $i] :
( ( ! [SY1547: $i,SY1548: $i] :
( ( c_List_Olist_OCons @ SV123 @ ( c_List_Oappend @ SV339 @ SY1547 @ SY1548 ) @ SY1548 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV123 @ SV339 @ SY1548 ) @ SY1547 @ SY1548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1150,plain,
! [SV340: $i,SV124: $i] :
( ( ! [SY1549: $i,SY1550: $i] :
( ( c_List_Olist_OCons @ SV124 @ ( c_List_Oappend @ SV340 @ SY1549 @ SY1550 ) @ SY1550 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV124 @ SV340 @ SY1550 ) @ SY1549 @ SY1550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1151,plain,
! [SV341: $i,SV125: $i] :
( ( ! [SY1551: $i,SY1552: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV125 @ SV341 @ SY1551 ) @ SY1552 @ SY1551 )
= ( c_List_Olist_OCons @ SV125 @ ( c_List_Oappend @ SV341 @ SY1552 @ SY1551 ) @ SY1551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1152,plain,
! [SV342: $i,SV126: $i] :
( ( ! [SY1553: $i,SY1554: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV126 @ SV342 @ SY1553 ) @ SY1554 @ SY1553 )
= ( c_List_Olist_OCons @ SV126 @ ( c_List_Oappend @ SV342 @ SY1554 @ SY1553 ) @ SY1553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1153,plain,
! [SV343: $i,SV127: $i] :
( ( c_Type_Otyping @ SV127 @ ( c_Lambda_OdB_OVar @ SV343 ) @ ( hAPP @ SV127 @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1154,plain,
! [SV344: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ SV128 @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ SV128 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1155,plain,
! [SV345: $i,SV129: $i] :
( ( ( c_List_Oappend @ SV129 @ ( c_List_Olist_ONil @ SV345 ) @ SV345 )
= SV129 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1156,plain,
! [SV346: $i,SV130: $i] :
( ( SV130
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV346 ) @ SV130 @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1157,plain,
! [SV347: $i,SV131: $i] :
( ( SV131
= ( c_List_Oappend @ SV131 @ ( c_List_Olist_ONil @ SV347 ) @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1158,plain,
! [SV348: $i,SV132: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV132 ) @ SV348 @ SV132 )
= SV348 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1159,plain,
! [SV349: $i,SV133: $i] :
( ( SV133
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV349 ) @ SV133 @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1160,plain,
! [SV350: $i,SV134: $i] :
( ( ! [SY1555: $i] :
( ( ( hAPP @ SV134 @ SV350 )
= SY1555 )
| ~ ( c_Type_Otyping @ SV134 @ ( c_Lambda_OdB_OVar @ SV350 ) @ SY1555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1161,plain,
! [SV351: $i,SV135: $i] :
( ( ! [SY1556: $i,SY1557: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV135 @ SV351 @ SY1556 @ SY1557 ) @ SV351 )
= SY1556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1162,plain,
! [SV352: $i,SV136: $i] :
( ( ! [SY1558: $i,SY1559: $i] :
( ( c_Type_Otype_Otype__rec @ SV136 @ SV352 @ ( c_Type_Otype_OAtom @ SY1558 ) @ SY1559 )
= ( hAPP @ SV136 @ SY1558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1163,plain,
! [SV353: $i,SV137: $i] :
( ( ! [SY1560: $i,SY1561: $i,SY1562: $i] :
( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SY1560 ) @ SY1561 )
| ~ ( c_Type_Otyping @ SV137 @ SY1560 @ SY1562 )
| ~ ( c_Type_Otyping @ SV137 @ SV353 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1562 ) @ SY1561 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1164,plain,
! [SV354: $i,SV138: $i] :
( ( ! [SY1563: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV138 ) @ ( c_List_Olist_OCons @ SV354 @ SY1563 @ SV138 ) @ SV138 )
= ( c_List_Olist_OCons @ SV354 @ SY1563 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1165,plain,
! [SV355: $i,SV140: $i] :
( ( ! [SY1564: $i,SY1565: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV140 @ SV355 @ SY1564 ) @ SY1565 @ SY1564 )
= ( c_List_Oappend @ SV140 @ ( c_List_Oappend @ SV355 @ SY1565 @ SY1564 ) @ SY1564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1166,plain,
! [SV356: $i,SV141: $i] :
( ( ! [SY1566: $i,SY1567: $i] :
( ( c_List_Oappend @ SV141 @ ( c_List_Oappend @ SV356 @ SY1566 @ SY1567 ) @ SY1567 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV141 @ SV356 @ SY1567 ) @ SY1566 @ SY1567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1167,plain,
! [SV357: $i,SV142: $i] :
( ( ! [SY1568: $i,SY1569: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV142 @ SV357 @ SY1568 ) @ SY1569 @ SY1568 )
= ( c_List_Oappend @ SV142 @ ( c_List_Oappend @ SV357 @ SY1569 @ SY1568 ) @ SY1568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1168,plain,
! [SV358: $i,SV143: $i] :
( ( ! [SY1570: $i,SY1571: $i] :
( ( c_List_Oappend @ SV143 @ ( c_List_Oappend @ SV358 @ SY1570 @ SY1571 ) @ SY1571 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV143 @ SV358 @ SY1571 ) @ SY1570 @ SY1571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1169,plain,
! [SV359: $i,SV144: $i] :
( ( ! [SY1572: $i,SY1573: $i,SY1574: $i,SY1575: $i] :
( ( c_List_Ofoldr @ SV144 @ ( c_List_Olist_OCons @ SV359 @ SY1572 @ SY1573 ) @ SY1574 @ SY1573 @ SY1575 )
= ( hAPP @ ( hAPP @ SV144 @ SV359 ) @ ( c_List_Ofoldr @ SV144 @ SY1572 @ SY1574 @ SY1573 @ SY1575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1170,plain,
! [SV360: $i,SV145: $i] :
( ( ! [SY1576: $i,SY1577: $i,SY1578: $i,SY1579: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Oappend @ SV360 @ SY1576 @ SY1577 ) @ SY1578 @ SY1577 @ SY1579 )
= ( c_List_Ofoldr @ SV145 @ SV360 @ ( c_List_Ofoldr @ SV145 @ SY1576 @ SY1578 @ SY1577 @ SY1579 ) @ SY1577 @ SY1579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1171,plain,
! [SV361: $i,SV146: $i] :
( ( ! [SY1580: $i,SY1581: $i] :
( ( c_List_Ofoldr @ SV146 @ ( c_List_Olist_ONil @ SV361 ) @ SY1580 @ SV361 @ SY1581 )
= SY1580 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1172,plain,
! [SV362: $i,SV147: $i] :
( ( ! [SY1582: $i,SY1583: $i,SY1584: $i] :
( ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1582 ) @ SY1583 ) @ SY1584 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV362 @ SY1582 ) @ SY1583 ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ SY1582 @ SY1584 ) ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ SY1583 @ SY1584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1173,plain,
! [SV363: $i,SV148: $i] :
( ( ! [SY1585: $i,SY1586: $i,SY1587: $i] :
( ( c_Type_Otype_Otype__case @ SV148 @ SV363 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1585 ) @ SY1586 ) @ SY1587 )
= ( hAPP @ ( hAPP @ SV363 @ SY1585 ) @ SY1586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1174,plain,
! [SV364: $i,SV149: $i] :
( ( ! [SY1588: $i,SY1589: $i,SY1590: $i] :
( ~ ( hBOOL @ ( hAPP @ SV149 @ ( c_Type_Otype_Otype__case @ SV364 @ SY1588 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1589 ) @ SY1590 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV149 @ ( hAPP @ ( hAPP @ SY1588 @ SY1589 ) @ SY1590 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1175,plain,
! [SV365: $i,SV150: $i] :
( ( ! [SY1591: $i,SY1592: $i,SY1593: $i] :
( ~ ( hBOOL @ ( hAPP @ SV150 @ ( c_Type_Otype_Otype__case @ SV365 @ SY1591 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1592 ) @ SY1593 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ ( hAPP @ ( hAPP @ SY1591 @ SY1592 ) @ SY1593 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1176,plain,
! [SV366: $i,SV151: $i] :
( ( c_fequal @ SV151 @ SV151 @ SV366 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1177,plain,
! [SV367: $i,SV152: $i] :
( ( ! [SY1594: $i] :
( ( SV152 = SV367 )
| ~ ( c_fequal @ SV152 @ SV367 @ SY1594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1178,plain,
! [SV368: $i,SV153: $i] :
( ( ! [SY1595: $i,SY1596: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV153 ) @ SV368 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1595 ) @ SY1596 ) )
| ( SV368 = SY1596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1179,plain,
! [SV369: $i,SV154: $i] :
( ( ! [SY1597: $i,SY1598: $i] :
( ( ( c_List_Orev @ SV154 @ SV369 )
!= ( c_List_Olist_OCons @ SY1597 @ SY1598 @ SV369 ) )
| ( SV154
= ( c_List_Oappend @ ( c_List_Orev @ SY1598 @ SV369 ) @ ( c_List_Olist_OCons @ SY1597 @ ( c_List_Olist_ONil @ SV369 ) @ SV369 ) @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1180,plain,
! [SV370: $i,SV155: $i] :
( ( ! [SY1599: $i,SY1600: $i,SY1601: $i] :
( ( ( c_List_Oappend @ SV155 @ SV370 @ SY1599 )
!= ( c_List_Olist_OCons @ SY1600 @ SY1601 @ SY1599 ) )
| ( SV155
= ( c_List_Olist_OCons @ SY1600 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1600 @ SY1601 @ SV155 @ SV370 @ SY1599 ) @ SY1599 ) )
| ( SV155
= ( c_List_Olist_ONil @ SY1599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1181,plain,
! [SV371: $i,SV156: $i] :
( ( ! [SY1602: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SV371 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1602 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SV371 )
= SY1602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1182,plain,
! [SV372: $i,SV157: $i] :
( ( ! [SY1603: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV157 ) @ SV372 )
!= ( c_Lambda_OdB_OAbs @ SY1603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1183,plain,
! [SV373: $i,SV158: $i] :
( ( ! [SY1604: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV158 ) @ SV373 )
!= ( c_Lambda_OdB_OVar @ SY1604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1184,plain,
! [SV374: $i,SV159: $i] :
( ( ! [SY1605: $i] :
( SV159
!= ( c_List_Olist_OCons @ SV374 @ SV159 @ SY1605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1185,plain,
! [SV375: $i,SV160: $i] :
( ( ! [SY1606: $i,SY1607: $i,SY1608: $i] :
( ( ( c_List_Olist_OCons @ SV160 @ SV375 @ SY1606 )
!= ( c_List_Oappend @ SY1607 @ SY1608 @ SY1606 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV375 @ SY1607 @ SY1608 @ SY1606 ) @ SY1606 )
= SY1607 )
| ( SY1607
= ( c_List_Olist_ONil @ SY1606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1186,plain,
! [SV376: $i,SV161: $i] :
( ( ! [SY1609: $i,SY1610: $i,SY1611: $i] :
( ( SV161
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV376 @ SV161 @ SY1609 ) @ ( c_List_Olist_OCons @ SY1610 @ SY1611 @ SY1609 ) @ SY1609 ) )
| ( ( c_List_OdropWhile @ SV376 @ SV161 @ SY1609 )
= ( c_List_Olist_OCons @ SY1610 @ SY1611 @ SY1609 ) )
| ( hBOOL @ ( hAPP @ SV376 @ SY1610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1187,plain,
! [SV377: $i,SV162: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV162 )
!= ( c_Lambda_OdB_OVar @ SV377 ) )
| ( SV162 = SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1188,plain,
! [SV378: $i,SV163: $i] :
( ( ! [SY1612: $i] :
( ( SV163
!= ( c_List_Oappend @ SV378 @ SV163 @ SY1612 ) )
| ( SV378
= ( c_List_Olist_ONil @ SY1612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1189,plain,
! [SV379: $i,SV164: $i] :
( ( ! [SY1613: $i,SY1614: $i,SY1615: $i] :
( ( ( c_List_Oappend @ SV164 @ ( c_List_Olist_OCons @ SV379 @ ( c_List_Olist_ONil @ SY1613 ) @ SY1613 ) @ SY1613 )
!= ( c_List_Oappend @ SY1614 @ ( c_List_Olist_OCons @ SY1615 @ ( c_List_Olist_ONil @ SY1613 ) @ SY1613 ) @ SY1613 ) )
| ( SV164 = SY1614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1190,plain,
! [SV380: $i,SV165: $i] :
( ( ! [SY1616: $i] :
( ( ( c_Lambda_OdB_OVar @ SV165 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV380 @ SY1616 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1616
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1191,plain,
! [SV381: $i,SV166: $i] :
( ( ! [SY1617: $i] :
( ( ( c_List_Orev @ SV166 @ SV381 )
!= ( c_List_Olist_OCons @ SY1617 @ ( c_List_Olist_ONil @ SV381 ) @ SV381 ) )
| ( SV166
= ( c_List_Olist_OCons @ SY1617 @ ( c_List_Olist_ONil @ SV381 ) @ SV381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1192,plain,
! [SV382: $i,SV167: $i] :
( ( ! [SY1618: $i,SY1619: $i] :
( ( ( c_List_Oappend @ SV167 @ SV382 @ SY1618 )
!= ( c_List_Oappend @ SV167 @ SY1619 @ SY1618 ) )
| ( SV382 = SY1619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1193,plain,
! [SV383: $i,SV168: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV168 )
!= ( c_Lambda_OdB_OAbs @ SV383 ) )
| ( SV168 = SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1194,plain,
! [SV384: $i,SV169: $i] :
( ( ! [SY1620: $i,SY1621: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV169 ) ) @ SV384 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1620 ) @ SY1621 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1195,plain,
! [SV385: $i,SV170: $i] :
( ( ! [SY1622: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV170 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV385 @ SY1622 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV170 )
= SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1196,plain,
! [SV386: $i,SV171: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV171 )
!= ( c_Type_Otype_OAtom @ SV386 ) )
| ( SV171 = SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1197,plain,
! [SV387: $i,SV172: $i] :
( ( ! [SY1623: $i] :
( ( ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SV387 ) @ SV387 )
!= ( c_List_Orev @ SY1623 @ SV387 ) )
| ( SY1623
= ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SV387 ) @ SV387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1198,plain,
! [SV388: $i,SV173: $i] :
( ( ! [SY1624: $i,SY1625: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SV388 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1624 ) @ SY1625 ) )
| ( SV173 = SY1624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1199,plain,
! [SV389: $i,SV174: $i] :
( ( ! [SY1626: $i] :
( ( c_Type_Otype_OAtom @ SV174 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV389 ) @ SY1626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1200,plain,
! [SV390: $i,SV175: $i] :
( ( ! [SY1627: $i,SY1628: $i,SY1629: $i] :
( ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SY1627 )
!= ( c_List_Oappend @ SY1628 @ SY1629 @ SY1627 ) )
| ( ( c_List_Olist_OCons @ SV175 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV175 @ SV390 @ SY1628 @ SY1629 @ SY1627 ) @ SY1627 )
= SY1628 )
| ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SY1627 )
= SY1629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1201,plain,
! [SV391: $i,SV176: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV176 )
!= ( c_Lambda_OdB_OVar @ SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1202,plain,
! [SV392: $i,SV177: $i] :
( ( ! [SY1630: $i,SY1631: $i,SY1632: $i,SY1633: $i,SY1634: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1630 @ SY1631 @ SY1632 ) ) )
| ~ ( c_Type_Otyping @ SY1633 @ SY1631 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1631 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1633 @ SY1632 @ SV177 @ tc_Type_Otype ) @ SY1630 @ SY1634 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1203,plain,
! [SV393: $i,SV178: $i] :
( ( ! [SY1635: $i,SY1636: $i,SY1637: $i] :
( ( ( c_List_Oappend @ SV178 @ SV393 @ SY1635 )
!= ( c_List_Olist_OCons @ SY1636 @ SY1637 @ SY1635 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1636 @ SY1637 @ SV178 @ SV393 @ SY1635 ) @ SV393 @ SY1635 )
= SY1637 )
| ( SV393
= ( c_List_Olist_OCons @ SY1636 @ SY1637 @ SY1635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1204,plain,
! [SV394: $i,SV179: $i] :
( ( ! [SY1638: $i,SY1639: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV179 ) @ SV394 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1638 ) @ SY1639 ) )
| ( SV179 = SY1638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1205,plain,
! [SV395: $i,SV180: $i] :
( ( ! [SY1640: $i,SY1641: $i] :
( ( ( c_List_Oappend @ SV180 @ SV395 @ SY1640 )
!= ( c_List_Oappend @ SY1641 @ SV395 @ SY1640 ) )
| ( SV180 = SY1641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1206,plain,
! [SV396: $i,SV181: $i] :
( ( ! [SY1642: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV181 @ SV396 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1642 @ SV396 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV181 = SY1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1207,plain,
! [SV397: $i,SV182: $i] :
( ( ! [SY1643: $i,SY1644: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV397 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1643 ) @ SY1644 ) )
| ( SV397 = SY1644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1208,plain,
! [SV398: $i,SV183: $i] :
( ( ! [SY1645: $i] :
( ( SV183
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 ) @ SY1645 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 ) @ ( c_List_Oappend @ SY1645 @ ( c_List_Olist_OCons @ SV398 @ ( 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)],[992]) ).
thf(1209,plain,
! [SV399: $i,SV184: $i] :
( ( ! [SY1646: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV184 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV399 @ SY1646 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1646
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1210,plain,
! [SV400: $i,SV185: $i] :
( ( ! [SY1647: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV185 ) @ SV400 )
!= ( c_Type_Otype_OAtom @ SY1647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1211,plain,
! [SV401: $i,SV186: $i] :
( ( ! [SY1648: $i] :
( ( ( c_List_Oappend @ SV186 @ SV401 @ SY1648 )
!= SV401 )
| ( SV186
= ( c_List_Olist_ONil @ SY1648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1212,plain,
! [SV402: $i,SV187: $i] :
( ( ! [SY1649: $i,SY1650: $i,SY1651: $i] :
( ( ( c_List_OdropWhile @ SV187 @ SV402 @ SY1649 )
!= ( c_List_Olist_OCons @ SY1650 @ SY1651 @ SY1649 ) )
| ( SV402
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV187 @ SV402 @ SY1649 ) @ ( c_List_Olist_OCons @ SY1650 @ SY1651 @ SY1649 ) @ SY1649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1213,plain,
! [SV403: $i,SV188: $i] :
( ( ! [SY1652: $i] :
( ( c_List_Olist_ONil @ SV188 )
!= ( c_List_Olist_OCons @ SV403 @ SY1652 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1214,plain,
! [SV404: $i,SV189: $i] :
( ( ! [SY1653: $i,SY1654: $i,SY1655: $i] :
( ( ( c_List_Olist_OCons @ SV189 @ SV404 @ SY1653 )
!= ( c_List_Olist_OCons @ SY1654 @ SY1655 @ SY1653 ) )
| ( SV404 = SY1655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1215,plain,
! [SV405: $i,SV190: $i] :
( ( ! [SY1656: $i] :
( ( ( c_List_Oreplicate @ SV190 @ SV405 @ SY1656 )
!= ( c_List_Olist_ONil @ SY1656 ) )
| ( SV190
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1216,plain,
! [SV406: $i,SV191: $i] :
( ( ! [SY1657: $i,SY1658: $i,SY1659: $i,SY1660: $i,SY1661: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY1657 @ SY1658 @ SY1659 ) ) )
| ~ ( c_Type_Otyping @ SY1660 @ SY1658 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1658 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1660 @ SY1659 @ SV406 @ tc_Type_Otype ) @ SY1657 @ SY1661 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1217,plain,
! [SV407: $i,SV192: $i] :
( ( ! [SY1662: $i] :
( ( ( c_List_Olist_ONil @ SV192 )
!= ( c_List_Oreplicate @ SV407 @ SY1662 @ SV192 ) )
| ( SV407
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1218,plain,
! [SV408: $i,SV193: $i] :
( ( ! [SY1663: $i,SY1664: $i,SY1665: $i] :
( ( ( c_List_Oreplicate @ SV193 @ SV408 @ SY1663 )
!= ( c_List_Oreplicate @ SY1664 @ SY1665 @ SY1663 ) )
| ( SV193 = SY1664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1219,plain,
! [SV409: $i,SV194: $i] :
( ( ! [SY1666: $i,SY1667: $i,SY1668: $i] :
( ( ( c_List_Oreplicate @ SV194 @ SV409 @ SY1666 )
!= ( c_List_Oreplicate @ SY1667 @ SY1668 @ SY1666 ) )
| ( SV409 = SY1668 )
| ( SV194
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1220,plain,
! [SV410: $i,SV195: $i] :
( ( ! [SY1669: $i,SY1670: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV195 ) @ SV410 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1669 ) @ SY1670 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV410 = SY1670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1221,plain,
! [SV411: $i,SV196: $i] :
( ( ! [SY1671: $i] :
( ( c_List_Olist_OCons @ SV196 @ SV411 @ SY1671 )
!= SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1222,plain,
! [SV412: $i,SV197: $i] :
( ( ! [SY1672: $i,SY1673: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV197 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV412 ) @ SY1672 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SY1673 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SY1672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1223,plain,
! [SV413: $i,SV198: $i] :
( ( ! [SY1674: $i] :
( ( ( c_List_Olist_ONil @ SV198 )
!= ( c_List_Oappend @ SV413 @ SY1674 @ SV198 ) )
| ( SY1674
= ( c_List_Olist_ONil @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1224,plain,
! [SV414: $i,SV199: $i] :
( ( ( ( c_List_Orotate1 @ SV199 @ SV414 )
!= ( c_List_Olist_ONil @ SV414 ) )
| ( SV199
= ( c_List_Olist_ONil @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1225,plain,
! [SV415: $i,SV200: $i] :
( ( ! [SY1675: $i] :
( ( ( c_List_Oappend @ SV200 @ SV415 @ SY1675 )
!= SV200 )
| ( SV415
= ( c_List_Olist_ONil @ SY1675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1226,plain,
! [SV416: $i,SV201: $i] :
( ( ! [SY1676: $i] :
( ( SV201
!= ( c_List_Oappend @ SV201 @ SV416 @ SY1676 ) )
| ( SV416
= ( c_List_Olist_ONil @ SY1676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1227,plain,
! [SV417: $i,SV202: $i] :
( ( ! [SY1677: $i,SY1678: $i,SY1679: $i] :
( ( ( c_List_Oappend @ SV202 @ SV417 @ SY1677 )
!= ( c_List_Olist_OCons @ SY1678 @ SY1679 @ SY1677 ) )
| ( SV202
= ( c_List_Olist_OCons @ SY1678 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1678 @ SY1679 @ SV202 @ SV417 @ SY1677 ) @ SY1677 ) )
| ( SV417
= ( c_List_Olist_OCons @ SY1678 @ SY1679 @ SY1677 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1228,plain,
! [SV418: $i,SV203: $i] :
( ( ! [SY1680: $i,SY1681: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV203 ) @ SV418 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1680 ) @ SY1681 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1229,plain,
! [SV419: $i,SV204: $i] :
( ( ! [SY1682: $i] :
( ( ( c_List_Oappend @ SV204 @ SV419 @ SY1682 )
!= ( c_List_Olist_ONil @ SY1682 ) )
| ( SV204
= ( c_List_Olist_ONil @ SY1682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1230,plain,
! [SV420: $i,SV205: $i] :
( ( ! [SY1683: $i,SY1684: $i,SY1685: $i] :
( ( ( c_List_Olist_OCons @ SV205 @ SV420 @ SY1683 )
!= ( c_List_Oappend @ SY1684 @ SY1685 @ SY1683 ) )
| ( SV420
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV205 @ SV420 @ SY1684 @ SY1685 @ SY1683 ) @ SY1685 @ SY1683 ) )
| ( SY1684
= ( c_List_Olist_ONil @ SY1683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1231,plain,
! [SV421: $i,SV206: $i] :
( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ( ( c_List_Olist_OCons @ SV206 @ SV421 @ SY1686 )
!= ( c_List_Olist_OCons @ SY1687 @ SY1688 @ SY1686 ) )
| ( SV206 = SY1687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1232,plain,
! [SV422: $i,SV207: $i] :
( ( ! [SY1689: $i,SY1690: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV207 ) @ SV422 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1689 ) @ SY1690 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV207 = SY1689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1233,plain,
! [SV423: $i,SV208: $i] :
( ( ! [SY1691: $i,SY1692: $i,SY1693: $i] :
( ( ( c_List_Oappend @ SV208 @ ( c_List_Olist_OCons @ SV423 @ ( c_List_Olist_ONil @ SY1691 ) @ SY1691 ) @ SY1691 )
!= ( c_List_Oappend @ SY1692 @ ( c_List_Olist_OCons @ SY1693 @ ( c_List_Olist_ONil @ SY1691 ) @ SY1691 ) @ SY1691 ) )
| ( SV423 = SY1693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1234,plain,
! [SV424: $i,SV209: $i] :
( ( ( c_Lambda_OdB_OVar @ SV209 )
!= ( c_Lambda_OdB_OAbs @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1235,plain,
! [SV425: $i,SV210: $i] :
( ( ! [SY1694: $i,SY1695: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV210 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV425 ) @ SY1694 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SY1695 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1236,plain,
! [SV426: $i,SV211: $i] :
( ( ! [SY1696: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV211 @ SV426 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1696 ) )
| ( SV426
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1237,plain,
! [SV427: $i,SV212: $i] :
( ( ! [SY1697: $i] :
( ( c_Lambda_OdB_OVar @ SV212 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV427 ) @ SY1697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1238,plain,
! [SV428: $i,SV213: $i] :
( ( ! [SY1698: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV428 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1698 ) )
| ( SV213
= ( c_Lambda_OdB_OAbs @ SY1698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1239,plain,
! [SV429: $i,SV214: $i] :
( ( ! [SY1699: $i,SY1700: $i,SY1701: $i] :
( ( ( c_List_OdropWhile @ SV214 @ SV429 @ SY1699 )
!= ( c_List_Olist_OCons @ SY1700 @ SY1701 @ SY1699 ) )
| ~ ( hBOOL @ ( hAPP @ SV214 @ SY1700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1240,plain,
! [SV430: $i,SV215: $i] :
( ( ! [SY1702: $i,SY1703: $i,SY1704: $i] :
( ( ( c_List_Oappend @ SV215 @ SV430 @ SY1702 )
!= ( c_List_Olist_OCons @ SY1703 @ SY1704 @ SY1702 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1703 @ SY1704 @ SV215 @ SV430 @ SY1702 ) @ SV430 @ SY1702 )
= SY1704 )
| ( SV215
= ( c_List_Olist_ONil @ SY1702 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1241,plain,
! [SV431: $i,SV216: $i] :
( ( ! [SY1705: $i,SY1706: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV216 ) @ SV431 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1705 ) @ SY1706 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV216 = SY1705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1242,plain,
! [SV432: $i,SV217: $i] :
( ( ! [SY1707: $i] :
( ( c_List_Olist_OCons @ SV217 @ SV432 @ SY1707 )
!= ( c_List_Olist_ONil @ SY1707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1243,plain,
! [SV433: $i,SV218: $i] :
( ( ! [SY1708: $i] :
( ( c_Lambda_OdB_OAbs @ SV218 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV433 ) @ SY1708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1244,plain,
! [SV434: $i,SV219: $i] :
( ( ! [SY1709: $i] :
( ( ( c_List_Orev @ SV219 @ SV434 )
!= ( c_List_Orev @ SY1709 @ SV434 ) )
| ( SV219 = SY1709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1245,plain,
! [SV435: $i,SV220: $i] :
( ( ! [SY1710: $i] :
( ( ( c_List_Oappend @ SV220 @ SV435 @ SY1710 )
!= ( c_List_Olist_ONil @ SY1710 ) )
| ( SV435
= ( c_List_Olist_ONil @ SY1710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1246,plain,
! [SV436: $i,SV221: $i] :
( ( ( ( c_List_Orev @ SV221 @ SV436 )
!= ( c_List_Olist_ONil @ SV436 ) )
| ( SV221
= ( c_List_Olist_ONil @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1247,plain,
! [SV437: $i,SV222: $i] :
( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SY1711 )
!= ( c_List_Oappend @ SY1712 @ SY1713 @ SY1711 ) )
| ( SV437
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV222 @ SV437 @ SY1712 @ SY1713 @ SY1711 ) @ SY1713 @ SY1711 ) )
| ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SY1711 )
= SY1713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1248,plain,
! [SV438: $i,SV223: $i] :
( ( ! [SY1714: $i] :
( ( ( c_List_Olist_ONil @ SV223 )
!= ( c_List_Oappend @ SV438 @ SY1714 @ SV223 ) )
| ( SV438
= ( c_List_Olist_ONil @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1249,plain,
! [SV439: $i,SV224: $i] :
( ( ! [SY1715: $i] :
( ( ( c_Lambda_OdB_OVar @ SV224 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV439 @ SY1715 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV224 )
= SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1250,plain,
! [SV440: $i,SV225: $i] :
( ( ! [SY1716: $i] :
( ( c_List_Olist_OCons @ SV225 @ SV440 @ SY1716 )
!= ( c_List_Olist_ONil @ SY1716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1251,plain,
! [SV441: $i,SV226: $i] :
( ( ( ( c_List_Olist_ONil @ SV226 )
!= ( c_List_Orev @ SV441 @ SV226 ) )
| ( SV441
= ( c_List_Olist_ONil @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1252,plain,
! [SV442: $i,SV227: $i] :
( ( ! [SY1717: $i,SY1718: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV227 ) @ SV442 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1717 ) @ SY1718 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV442 = SY1718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1253,plain,
! [SV443: $i,SV229: $i,SV2: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV2 @ SV229 @ SV443 ) @ SV443 )
= SV229 )
| ( SV2
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1254,plain,
! [SV444: $i,SV230: $i,SV3: $i] :
( ( ! [SY1719: $i] :
( ( c_Type_Otyping @ SV3 @ SV230 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV444 @ SV3 @ SV230 @ SY1719 ) )
| ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SY1719 @ ( c_List_Olist_OCons @ SV230 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1255,plain,
! [SV445: $i,SV231: $i,SV4: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV4 @ SV231 @ SV445 ) @ SV445 )
= SV231 )
| ( SV4
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1256,plain,
! [SV446: $i,SV232: $i,SV5: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV5 @ SV232 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV446 @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1257,plain,
! [SV8: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV8 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1258,plain,
! [SV447: $i,SV234: $i,SV9: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV9 @ SV234 @ SV447 ) @ SV447 ) ) )
| ( ( c_List_OdropWhile @ SV9 @ SV234 @ SV447 )
= ( c_List_Olist_ONil @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1259,plain,
! [SV448: $i,SV235: $i,SV11: $i] :
( ( ! [SY1720: $i,SY1721: $i,SY1722: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV11 @ SV235 @ SV448 @ SY1720 ) @ SY1721 ) @ SY1722 )
= ( hAPP @ ( hAPP @ SV11 @ SY1722 ) @ SY1721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1260,plain,
! [SV449: $i,SV236: $i,SV12: $i] :
( ( ! [SY1723: $i] :
( ( c_List_Olistsp @ SV12 @ SV236 @ SV449 )
| ~ ( c_List_Olistsp @ SV12 @ ( c_List_Oappend @ SV236 @ SY1723 @ SV449 ) @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1261,plain,
! [SV450: $i,SV237: $i,SV13: $i] :
( ( ! [SY1724: $i] :
( ( c_List_Olistsp @ SV13 @ SV237 @ SV450 )
| ~ ( c_List_Olistsp @ SV13 @ ( c_List_Oappend @ SY1724 @ SV237 @ SV450 ) @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1262,plain,
! [SV451: $i,SV240: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV16 ) ) @ SV240 ) @ SV451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV16 @ SV240 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1263,plain,
! [SV452: $i,SV241: $i,SV17: $i] :
( ( ! [SY1725: $i,SY1726: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV17 @ SV241 @ SV452 ) @ ( c_List_Olist_OCons @ SY1725 @ SY1726 @ SV452 ) @ SV452 )
= ( c_List_Olist_OCons @ SV17 @ ( c_List_Olist_OCons @ SY1725 @ ( c_List_Osplice @ SV241 @ SY1726 @ SV452 ) @ SV452 ) @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1264,plain,
! [SV453: $i,SV242: $i,SV18: $i] :
( ( ! [SY1727: $i] :
( ( ( c_List_OdropWhile @ SV18 @ ( c_List_Olist_OCons @ SV242 @ SV453 @ SY1727 ) @ SY1727 )
= ( c_List_OdropWhile @ SV18 @ SV453 @ SY1727 ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1265,plain,
! [SV454: $i,SV243: $i,SV19: $i] :
( ( ! [SY1728: $i] :
( ( ( c_List_OdropWhile @ SV19 @ ( c_List_Olist_OCons @ SV243 @ SV454 @ SY1728 ) @ SY1728 )
= ( c_List_Olist_OCons @ SV243 @ SV454 @ SY1728 ) )
| ( hBOOL @ ( hAPP @ SV19 @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1266,plain,
! [SV455: $i,SV244: $i,SV20: $i] :
( ( ( c_List_Oappend @ ( c_List_OtakeWhile @ SV20 @ SV244 @ SV455 ) @ ( c_List_OdropWhile @ SV20 @ SV244 @ SV455 ) @ SV455 )
= SV244 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1267,plain,
! [SV456: $i,SV245: $i,SV21: $i] :
( ( ! [SY1729: $i] :
( ( c_List_Olistsp @ SV21 @ ( c_List_Oappend @ SV245 @ SV456 @ SY1729 ) @ SY1729 )
| ~ ( c_List_Olistsp @ SV21 @ SV456 @ SY1729 )
| ~ ( c_List_Olistsp @ SV21 @ SV245 @ SY1729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1268,plain,
! [SV457: $i,SV248: $i,SV24: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV24 @ SV248 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV457 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV24 @ ( c_List_Oappend @ SV248 @ ( c_List_Olist_OCons @ SV457 @ ( 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)],[1058]) ).
thf(1269,plain,
! [SV458: $i,SV250: $i,SV26: $i] :
( ( ( ( c_List_Oappend @ SV26 @ ( c_List_Olist_OCons @ SV250 @ ( 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 @ SV458 @ SV26 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV250 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV458 @ ( c_List_Oappend @ SV26 @ ( c_List_Olist_OCons @ SV250 @ ( 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)],[1060]) ).
thf(1270,plain,
! [SV459: $i,SV251: $i,SV27: $i] :
( ( ! [SY1730: $i] :
( ( c_Type_Otyping @ SV27 @ ( c_Lambda_OdB_OAbs @ SV251 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV459 ) @ SY1730 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV27 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV459 @ tc_Type_Otype ) @ SV251 @ SY1730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1271,plain,
! [SV460: $i,SV252: $i,SV28: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV28 @ SV252 @ SV460 ) @ ( c_List_Olist_ONil @ SV460 ) @ SV460 )
= ( c_List_Olist_OCons @ SV28 @ SV252 @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1272,plain,
! [SV461: $i,SV253: $i,SV29: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV29 @ SV253 @ SV461 ) @ SV461 )
= ( c_List_Olist_OCons @ SV29 @ ( c_List_Obutlast @ SV253 @ SV461 ) @ SV461 ) )
| ( SV253
= ( c_List_Olist_ONil @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1273,plain,
! [SV462: $i,SV256: $i,SV32: $i] :
( ( ! [SY1731: $i] :
( ( ( c_List_OtakeWhile @ SV32 @ ( c_List_Olist_OCons @ SV256 @ SV462 @ SY1731 ) @ SY1731 )
= ( c_List_Olist_ONil @ SY1731 ) )
| ( hBOOL @ ( hAPP @ SV32 @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1274,plain,
! [SV463: $i,SV258: $i,SV34: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV34 @ SV258 @ SV463 ) @ SV463 )
= ( c_List_Olast @ SV258 @ SV463 ) )
| ( SV258
= ( c_List_Olist_ONil @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1275,plain,
! [SV464: $i,SV260: $i,SV36: $i] :
( ( ! [SY1732: $i,SY1733: $i,SY1734: $i,SY1735: $i] :
( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SY1732 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1733 ) @ SY1734 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
| ~ ( c_Type_Otypings @ SV464 @ SY1734 @ SY1735 )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1733 ) @ SY1734 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1732 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1276,plain,
! [SV261: $i,SV37: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV37 @ SV261 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV37 @ SV261 ) @ ( c_List_Olist_ONil @ SV261 ) @ SV261 ) @ SV261 )
= SV37 )
= $true )
| ( ( SV37
= ( c_List_Olist_ONil @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1277,plain,
! [SV465: $i,SV262: $i,SV38: $i] :
( ( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV38 @ SV262 @ SV465 ) @ SV465 )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1278,plain,
! [SV466: $i,SV263: $i,SV39: $i] :
( ( ! [SY1736: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV39 ) @ SV263 ) @ SV466 @ SY1736 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV39 @ SV466 @ SY1736 ) ) @ ( c_Lambda_Osubst @ SV263 @ SV466 @ SY1736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1279,plain,
! [SV467: $i,SV264: $i,SV41: $i] :
( ( ! [SY1737: $i] :
( ( c_Type_Otypings @ SV41 @ SV264 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV467 @ SV41 @ SY1737 @ SV264 ) )
| ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1737 ) @ SV264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1280,plain,
! [SV468: $i,SV265: $i,SV43: $i] :
( ( ! [SY1738: $i,SY1739: $i] :
( ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_OCons @ SV265 @ SV468 @ SY1738 ) @ ( c_List_Olist_OCons @ SV265 @ SY1739 @ SY1738 ) @ SY1738 )
| ~ ( c_ListOrder_Ostep1 @ SV43 @ SV468 @ SY1739 @ SY1738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1281,plain,
! [SV469: $i,SV266: $i,SV44: $i] :
( ( ! [SY1740: $i,SY1741: $i,SY1742: $i] :
( ( c_ListOrder_Ostep1 @ SV44 @ SV266 @ SV469 @ SY1740 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SY1741 ) @ SY1742 ) )
| ~ ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SY1741 @ SV266 @ SY1740 ) @ ( c_List_Olist_OCons @ SY1742 @ SV469 @ SY1740 ) @ SY1740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1282,plain,
! [SV470: $i,SV269: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV48 @ ( c_Lambda_OdB_OVar @ SV269 ) @ SV470 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1283,plain,
! [SV471: $i,SV270: $i,SV49: $i] :
( ( ! [SY1743: $i] :
( ( c_Type_Otypings @ SV49 @ SV270 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV471 @ SV49 @ SY1743 @ SV270 ) )
| ~ ( c_Type_Otyping @ SV49 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1743 @ SV270 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1284,plain,
! [SV472: $i,SV271: $i,SV50: $i] :
( ( ! [SY1744: $i,SY1745: $i] :
( ( c_List_Ofoldr @ SV50 @ SV271 @ SV472 @ SY1744 @ SY1745 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV50 @ SY1744 @ SY1745 @ SY1745 ) @ SV472 @ ( c_List_Orev @ SV271 @ SY1744 ) @ SY1745 @ SY1744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1285,plain,
! [SV473: $i,SV272: $i,SV51: $i] :
( ( ( c_List_Oconcat__map @ SV51 @ ( c_List_Olist_ONil @ SV272 ) @ SV272 @ SV473 )
= ( c_List_Olist_ONil @ SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1286,plain,
! [SV273: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV52 ) @ SV273 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV273 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1287,plain,
! [SV474: $i,SV274: $i,SV53: $i] :
( ( ! [SY1746: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV53 @ SV274 @ SV474 ) @ ( c_List_Oreplicate @ SY1746 @ SV274 @ SV474 ) @ SV474 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY1746 @ SV274 @ SV474 ) @ ( c_List_Oreplicate @ SV53 @ SV274 @ SV474 ) @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1288,plain,
! [SV475: $i,SV275: $i,SV54: $i] :
( ( ( c_List_Otl @ ( c_List_Olist_OCons @ SV54 @ SV275 @ SV475 ) @ SV475 )
= SV275 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1289,plain,
! [SV476: $i,SV276: $i,SV55: $i] :
( ( ! [SY1747: $i,SY1748: $i,SY1749: $i] :
( ( c_ListOrder_Ostep1 @ SV55 @ SV276 @ SV476 @ SY1747 )
| ( SV476 = SV276 )
| ~ ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SY1748 @ SV276 @ SY1747 ) @ ( c_List_Olist_OCons @ SY1749 @ SV476 @ SY1747 ) @ SY1747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1290,plain,
! [SV477: $i,SV277: $i,SV56: $i] :
( ( ! [SY1750: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV56 @ SV277 @ SV477 ) @ SY1750 @ SV477 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY1750 @ SV477 ) @ ( c_List_Osplice @ SV277 @ ( c_List_Otl @ SY1750 @ SV477 ) @ SV477 ) @ SV477 ) @ SV477 ) )
| ( SY1750
= ( c_List_Olist_ONil @ SV477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1291,plain,
! [SV278: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV57 @ SV278 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1292,plain,
! [SV478: $i,SV279: $i,SV58: $i] :
( ( ! [SY1751: $i] :
( ( c_List_Ofoldl @ SV58 @ SV279 @ ( c_List_Olist_ONil @ SV478 ) @ SY1751 @ SV478 )
= SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1293,plain,
! [SV479: $i,SV280: $i,SV59: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV59 @ SV280 @ ( c_List_Olist_ONil @ SV479 ) @ SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1294,plain,
! [SV480: $i,SV281: $i,SV60: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV60 @ ( c_List_Olist_ONil @ SV281 ) @ SV480 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1295,plain,
! [SV282: $i,SV61: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Orev @ SV61 @ SV282 ) @ SV282 )
= ( c_List_Olast @ SV61 @ SV282 ) )
= $true )
| ( ( SV61
= ( c_List_Olist_ONil @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1296,plain,
! [SV481: $i,SV283: $i,SV63: $i] :
( ( ( c_List_Orev @ ( c_List_Oreplicate @ SV63 @ SV283 @ SV481 ) @ SV481 )
= ( c_List_Oreplicate @ SV63 @ SV283 @ SV481 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1297,plain,
! [SV482: $i,SV284: $i,SV64: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV64 ) @ SV284 ) @ SV482 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV64 @ SV482 ) ) @ ( c_Lambda_Olift @ SV284 @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1298,plain,
! [SV483: $i,SV288: $i,SV68: $i] :
( ( ! [SY1752: $i,SY1753: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV288 ) @ SV483 ) )
| ( c_ListOrder_Ostep1 @ SV68 @ ( c_List_Olist_OCons @ SV288 @ SY1752 @ SY1753 ) @ ( c_List_Olist_OCons @ SV483 @ SY1752 @ SY1753 ) @ SY1753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1299,plain,
! [SV484: $i,SV289: $i,SV69: $i] :
( ( ! [SY1754: $i,SY1755: $i,SY1756: $i] :
( ( SV69 = SV289 )
| ( SV484 = SY1754 )
| ~ ( c_ListOrder_Ostep1 @ SY1755 @ ( c_List_Olist_OCons @ SV289 @ SY1754 @ SY1756 ) @ ( c_List_Olist_OCons @ SV69 @ SV484 @ SY1756 ) @ SY1756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1300,plain,
! [SV290: $i,SV71: $i] :
( ( ( ( c_List_Olast @ ( c_List_Orev @ SV71 @ SV290 ) @ SV290 )
= ( c_List_Ohd @ SV71 @ SV290 ) )
= $true )
| ( ( SV71
= ( c_List_Olist_ONil @ SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1301,plain,
! [SV485: $i,SV291: $i,SV72: $i] :
( ( ! [SY1757: $i,SY1758: $i] :
( ( c_ListOrder_Ostep1 @ SV72 @ ( c_List_Oappend @ SV291 @ SV485 @ SY1757 ) @ ( c_List_Oappend @ SV291 @ SY1758 @ SY1757 ) @ SY1757 )
| ~ ( c_ListOrder_Ostep1 @ SV72 @ SV485 @ SY1758 @ SY1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1302,plain,
! [SV486: $i,SV292: $i,SV73: $i] :
( ( ! [SY1759: $i,SY1760: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV73 @ SV292 @ SV486 @ SY1759 )
| ( c_ListOrder_Ostep1 @ SV73 @ ( c_List_Oappend @ SV292 @ SY1760 @ SY1759 ) @ ( c_List_Oappend @ SV486 @ SY1760 @ SY1759 ) @ SY1759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1303,plain,
! [SV487: $i,SV293: $i,SV75: $i] :
( ( ! [SY1761: $i] :
( ( c_Type_Otypings @ SV75 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV487 @ SV75 @ SY1761 @ SV293 ) )
| ~ ( c_Type_Otyping @ SV75 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1761 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1304,plain,
! [SV488: $i,SV294: $i,SV76: $i] :
( ( ! [SY1762: $i,SY1763: $i,SY1764: $i] :
( ( c_List_Ofoldl @ SV76 @ SV294 @ ( c_List_Olist_OCons @ SV488 @ SY1762 @ SY1763 ) @ SY1764 @ SY1763 )
= ( c_List_Ofoldl @ SV76 @ ( hAPP @ ( hAPP @ SV76 @ SV294 ) @ SV488 ) @ SY1762 @ SY1764 @ SY1763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1305,plain,
! [SV295: $i,SV77: $i] :
( ( ( ( c_List_Orotate1 @ SV77 @ SV295 )
= ( c_List_Oappend @ ( c_List_Otl @ SV77 @ SV295 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV77 @ SV295 ) @ ( c_List_Olist_ONil @ SV295 ) @ SV295 ) @ SV295 ) )
= $true )
| ( ( SV77
= ( c_List_Olist_ONil @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1306,plain,
! [SV489: $i,SV296: $i,SV78: $i] :
( ( ! [SY1765: $i,SY1766: $i,SY1767: $i] :
( ( SV78 = SV296 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV489 @ SV296 ) @ SV78 ) )
| ~ ( c_ListOrder_Ostep1 @ SV489 @ ( c_List_Olist_OCons @ SV296 @ SY1765 @ SY1766 ) @ ( c_List_Olist_OCons @ SV78 @ SY1767 @ SY1766 ) @ SY1766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1307,plain,
! [SV490: $i,SV297: $i,SV79: $i] :
( ( ! [SY1768: $i,SY1769: $i,SY1770: $i,SY1771: $i] :
( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SY1768 @ SV79 @ SV297 ) )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1769 ) @ SY1770 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1768 )
| ~ ( c_Type_Otypings @ SV79 @ SY1770 @ SY1771 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1769 ) @ SY1770 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1308,plain,
! [SV491: $i,SV298: $i,SV80: $i] :
( ( ! [SY1772: $i] :
( ( ( c_List_OtakeWhile @ SV80 @ ( c_List_Olist_OCons @ SV298 @ SV491 @ SY1772 ) @ SY1772 )
= ( c_List_Olist_OCons @ SV298 @ ( c_List_OtakeWhile @ SV80 @ SV491 @ SY1772 ) @ SY1772 ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ SV298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1309,plain,
! [SV492: $i,SV299: $i,SV81: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV81 @ SV299 ) @ SV492 @ SV299 )
= SV81 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1310,plain,
! [SV493: $i,SV300: $i,SV82: $i] :
( ( ! [SY1773: $i,SY1774: $i] :
( ( c_List_Ofoldl @ SV82 @ SV300 @ SV493 @ SY1773 @ SY1774 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV82 @ SY1773 @ SY1774 @ SY1773 ) @ ( c_List_Orev @ SV493 @ SY1774 ) @ SV300 @ SY1774 @ SY1773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1311,plain,
! [SV494: $i,SV301: $i,SV84: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ SV84 @ SV301 @ SV494 ) @ SV494 )
= ( c_List_Oappend @ ( c_List_Orev @ SV301 @ SV494 ) @ ( c_List_Orev @ SV84 @ SV494 ) @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1312,plain,
! [SV495: $i,SV302: $i,SV85: $i] :
( ( ! [SY1775: $i,SY1776: $i,SY1777: $i] :
( ( c_List_Ofoldl @ SV85 @ SV302 @ ( c_List_Oappend @ SV495 @ SY1775 @ SY1776 ) @ SY1777 @ SY1776 )
= ( c_List_Ofoldl @ SV85 @ ( c_List_Ofoldl @ SV85 @ SV302 @ SV495 @ SY1777 @ SY1776 ) @ SY1775 @ SY1777 @ SY1776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1313,plain,
! [SV496: $i,SV303: $i,SV86: $i] :
( ( ! [SY1778: $i,SY1779: $i] :
( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV496 @ SY1778 @ SY1779 ) @ SY1779 ) @ SY1779 ) ) )
| ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ SY1778 @ SY1779 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV86 @ SV496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1314,plain,
! [SV497: $i,SV304: $i,SV87: $i] :
( ( ! [SY1780: $i,SY1781: $i] :
( ( c_List_Oconcat__map @ SV87 @ ( c_List_Olist_OCons @ SV304 @ SV497 @ SY1780 ) @ SY1780 @ SY1781 )
= ( c_List_Oappend @ ( hAPP @ SV87 @ SV304 ) @ ( c_List_Oconcat__map @ SV87 @ SV497 @ SY1780 @ SY1781 ) @ SY1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1315,plain,
! [SV498: $i,SV305: $i,SV88: $i] :
( ( ! [SY1782: $i,SY1783: $i] :
( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ ( c_List_Oappend @ SV305 @ ( c_List_Olist_OCons @ SV498 @ SY1782 @ SY1783 ) @ SY1783 ) @ SY1783 ) ) )
| ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ SV305 @ SY1783 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV88 @ SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1316,plain,
! [SV499: $i,SV306: $i,SV89: $i] :
( ( ! [SY1784: $i,SY1785: $i] :
( ( ( c_List_OtakeWhile @ SV89 @ ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV499 @ SY1784 @ SY1785 ) @ SY1785 ) @ SY1785 )
= ( c_List_OtakeWhile @ SV89 @ SV306 @ SY1785 ) )
| ( hBOOL @ ( hAPP @ SV89 @ SV499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1317,plain,
! [SV500: $i,SV307: $i,SV90: $i] :
( ( ! [SY1786: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV90 @ SV307 @ SV500 ) @ ( c_List_Olist_OCons @ SV307 @ SY1786 @ SV500 ) @ SV500 )
= ( c_List_Olist_OCons @ SV307 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV90 @ SV307 @ SV500 ) @ SY1786 @ SV500 ) @ SV500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1318,plain,
! [SV501: $i,SV308: $i,SV91: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oappend @ SV91 @ SV308 @ SV501 ) @ SV501 )
= ( c_List_Ohd @ SV91 @ SV501 ) )
| ( SV91
= ( c_List_Olist_ONil @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1319,plain,
! [SV502: $i,SV310: $i,SV93: $i] :
( ( ( ( c_List_Otl @ ( c_List_Oappend @ SV93 @ SV310 @ SV502 ) @ SV502 )
= ( c_List_Oappend @ ( c_List_Otl @ SV93 @ SV502 ) @ SV310 @ SV502 ) )
| ( SV93
= ( c_List_Olist_ONil @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1320,plain,
! [SV503: $i,SV311: $i,SV94: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV94 @ SV311 @ SV503 ) @ SV503 )
= ( c_List_Olast @ SV311 @ SV503 ) )
| ( SV311
= ( c_List_Olist_ONil @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1321,plain,
! [SV504: $i,SV314: $i,SV97: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV97 @ SV314 @ SV504 ) @ SV504 )
= ( c_List_Oappend @ SV97 @ ( c_List_Obutlast @ SV314 @ SV504 ) @ SV504 ) )
| ( SV314
= ( c_List_Olist_ONil @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1322,plain,
! [SV315: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV98 ) @ ( c_Lambda_OdB_OVar @ SV315 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1323,plain,
! [SV505: $i,SV316: $i,SV99: $i] :
( ( ! [SY1787: $i] :
( ( c_Type_Otyping @ SV99 @ SV316 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV505 @ SV99 @ SY1787 @ SV316 ) )
| ~ ( c_Type_Otyping @ SV99 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1787 ) @ SV316 ) @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1324,plain,
! [SV506: $i,SV317: $i,SV100: $i] :
( ( ! [SY1788: $i] :
( ( c_Type_Otyping @ SV100 @ SV317 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV506 @ SV100 @ SV317 @ SY1788 ) @ SV506 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV317 @ SY1788 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1325,plain,
! [SV507: $i,SV318: $i,SV101: $i] :
( ( ! [SY1789: $i,SY1790: $i] :
( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV318 @ SV507 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY1789 )
| ~ ( c_Type_Otypings @ SV101 @ SV507 @ SY1790 )
| ~ ( c_Type_Otyping @ SV101 @ SV318 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1790 @ SY1789 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1326,plain,
! [SV508: $i,SV319: $i,SV102: $i] :
( ( ! [SY1791: $i] :
( ( c_Type_Otyping @ SV102 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV508 @ SV102 @ SV319 @ SY1791 ) @ SV508 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV102 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SY1791 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1327,plain,
! [SV509: $i,SV320: $i,SV103: $i] :
( ( ! [SY1792: $i,SY1793: $i,SY1794: $i] :
( ~ ( c_Type_Otyping @ SV103 @ SV320 @ SV509 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SY1792 @ SV509 @ tc_Type_Otype ) @ SY1793 @ SY1794 )
| ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SY1793 @ SV320 @ SY1792 ) @ SY1794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1328,plain,
! [SV510: $i,SV321: $i,SV104: $i] :
( ( ! [SY1795: $i,SY1796: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV104 @ SV321 @ SV510 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1795 @ SV321 ) @ SY1796 )
| ~ ( c_Type_Otyping @ SV104 @ SY1795 @ SY1796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1329,plain,
! [SV511: $i,SV322: $i,SV105: $i] :
( ( ! [SY1797: $i] :
( ( c_Type_Otyping @ SV105 @ ( c_Lambda_OdB_OVar @ SV322 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV511 @ SV105 @ SV322 @ SY1797 ) @ SV511 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV105 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV322 ) @ SY1797 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1330,plain,
! [SV512: $i,SV323: $i,SV106: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV106 @ SV323 @ SV512 ) @ ( c_List_Olist_OCons @ SV323 @ ( c_List_Olist_ONil @ SV512 ) @ SV512 ) @ SV512 )
= ( c_List_Olist_OCons @ SV323 @ ( c_List_Oreplicate @ SV106 @ SV323 @ SV512 ) @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1331,plain,
! [SV513: $i,SV324: $i,SV107: $i] :
( ( ! [SY1798: $i,SY1799: $i,SY1800: $i] :
( ( SV107 = SV324 )
| ( c_ListOrder_Ostep1 @ SV513 @ SV107 @ SV324 @ SY1798 )
| ~ ( c_ListOrder_Ostep1 @ SV513 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SY1799 @ ( c_List_Olist_ONil @ SY1798 ) @ SY1798 ) @ SY1798 ) @ ( c_List_Oappend @ SV324 @ ( c_List_Olist_OCons @ SY1800 @ ( c_List_Olist_ONil @ SY1798 ) @ SY1798 ) @ SY1798 ) @ SY1798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1332,plain,
! [SV514: $i,SV325: $i,SV108: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV108 @ SV325 @ SV514 ) @ SV514 )
= ( c_List_Oappend @ SV325 @ ( c_List_Olist_OCons @ SV108 @ ( c_List_Olist_ONil @ SV514 ) @ SV514 ) @ SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1333,plain,
! [SV515: $i,SV326: $i,SV109: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV109 @ SV326 ) @ ( c_List_Olist_OCons @ SV515 @ ( c_List_Olist_ONil @ SV326 ) @ SV326 ) @ SV326 ) @ SV326 )
= ( c_List_Olist_OCons @ SV515 @ SV109 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1334,plain,
! [SV516: $i,SV327: $i,SV110: $i] :
( ( ! [SY1801: $i,SY1802: $i,SY1803: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV327 ) @ SV516 ) )
| ( c_ListOrder_Ostep1 @ SV110 @ SY1801 @ SY1802 @ SY1803 )
| ~ ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SY1801 @ ( c_List_Olist_OCons @ SV327 @ ( c_List_Olist_ONil @ SY1803 ) @ SY1803 ) @ SY1803 ) @ ( c_List_Oappend @ SY1802 @ ( c_List_Olist_OCons @ SV516 @ ( c_List_Olist_ONil @ SY1803 ) @ SY1803 ) @ SY1803 ) @ SY1803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1335,plain,
! [SV517: $i,SV328: $i,SV111: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV111 @ SV328 @ SV517 ) @ SV517 )
= ( c_List_Oappend @ ( c_List_Orev @ SV328 @ SV517 ) @ ( c_List_Olist_OCons @ SV111 @ ( c_List_Olist_ONil @ SV517 ) @ SV517 ) @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1336,plain,
! [SV518: $i,SV329: $i,SV112: $i] :
( ( ! [SY1804: $i,SY1805: $i,SY1806: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SV329 ) @ SV518 ) )
| ( SV329 = SV518 )
| ~ ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SY1804 @ ( c_List_Olist_OCons @ SV329 @ ( c_List_Olist_ONil @ SY1805 ) @ SY1805 ) @ SY1805 ) @ ( c_List_Oappend @ SY1806 @ ( c_List_Olist_OCons @ SV518 @ ( c_List_Olist_ONil @ SY1805 ) @ SY1805 ) @ SY1805 ) @ SY1805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1337,plain,
! [SV519: $i,SV330: $i,SV113: $i] :
( ( ! [SY1807: $i,SY1808: $i,SY1809: $i] :
( ( SV113 = SV330 )
| ( SV519 = SY1807 )
| ~ ( c_ListOrder_Ostep1 @ SY1808 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SV519 @ ( c_List_Olist_ONil @ SY1809 ) @ SY1809 ) @ SY1809 ) @ ( c_List_Oappend @ SV330 @ ( c_List_Olist_OCons @ SY1807 @ ( c_List_Olist_ONil @ SY1809 ) @ SY1809 ) @ SY1809 ) @ SY1809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1338,plain,
! [SV520: $i,SV331: $i,SV114: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV114 @ ( c_List_Olist_OCons @ SV331 @ ( c_List_Olist_ONil @ SV520 ) @ SV520 ) @ SV520 ) @ SV520 )
= SV114 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1339,plain,
! [SV521: $i,SV332: $i,SV115: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV115 @ ( c_List_Olist_OCons @ SV332 @ ( c_List_Olist_ONil @ SV521 ) @ SV521 ) @ SV521 ) @ SV521 )
= SV332 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1340,plain,
! [SV522: $i,SV333: $i,SV116: $i] :
( ( ! [SY1810: $i,SY1811: $i] :
( ( SV116 = SV333 )
| ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1810 ) @ SY1811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV333 )
| ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1810 ) @ SY1811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1341,plain,
! [SV523: $i,SV334: $i,SV117: $i] :
( ( ! [SY1812: $i] :
( ( c_Type_Otyping @ SV117 @ SV334 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV523 @ SV117 @ SV334 @ SY1812 ) ) @ SV523 ) )
| ~ ( c_Type_Otyping @ SV117 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SY1812 ) @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1342,plain,
! [SV524: $i,SV335: $i,SV118: $i] :
( ( ! [SY1813: $i] :
( ( c_Type_Otype_Otype__case @ SV118 @ SV335 @ ( c_Type_Otype_OAtom @ SV524 ) @ SY1813 )
= ( hAPP @ SV118 @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1343,plain,
! [SV525: $i,SV336: $i,SV120: $i] :
( ( ( c_List_Olist_OCons @ SV120 @ SV336 @ SV525 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV525 ) @ ( c_List_Olist_OCons @ SV120 @ SV336 @ SV525 ) @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1344,plain,
! [SV526: $i,SV337: $i,SV121: $i] :
( ( ! [SY1814: $i] :
( ~ ( hBOOL @ ( hAPP @ SV121 @ ( c_Type_Otype_Otype__case @ SV337 @ SV526 @ ( c_Type_Otype_OAtom @ SY1814 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV121 @ ( hAPP @ SV337 @ SY1814 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1345,plain,
! [SV527: $i,SV338: $i,SV122: $i] :
( ( ! [SY1815: $i] :
( ~ ( hBOOL @ ( hAPP @ SV122 @ ( c_Type_Otype_Otype__case @ SV338 @ SV527 @ ( c_Type_Otype_OAtom @ SY1815 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV122 @ ( hAPP @ SV338 @ SY1815 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1346,plain,
! [SV528: $i,SV339: $i,SV123: $i] :
( ( ! [SY1816: $i] :
( ( c_List_Olist_OCons @ SV123 @ ( c_List_Oappend @ SV339 @ SV528 @ SY1816 ) @ SY1816 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV123 @ SV339 @ SY1816 ) @ SV528 @ SY1816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1347,plain,
! [SV529: $i,SV340: $i,SV124: $i] :
( ( ! [SY1817: $i] :
( ( c_List_Olist_OCons @ SV124 @ ( c_List_Oappend @ SV340 @ SV529 @ SY1817 ) @ SY1817 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV124 @ SV340 @ SY1817 ) @ SV529 @ SY1817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1348,plain,
! [SV530: $i,SV341: $i,SV125: $i] :
( ( ! [SY1818: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV125 @ SV341 @ SV530 ) @ SY1818 @ SV530 )
= ( c_List_Olist_OCons @ SV125 @ ( c_List_Oappend @ SV341 @ SY1818 @ SV530 ) @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1349,plain,
! [SV531: $i,SV342: $i,SV126: $i] :
( ( ! [SY1819: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV126 @ SV342 @ SV531 ) @ SY1819 @ SV531 )
= ( c_List_Olist_OCons @ SV126 @ ( c_List_Oappend @ SV342 @ SY1819 @ SV531 ) @ SV531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1350,plain,
! [SV344: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ SV128 @ SV344 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV128 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1351,plain,
! [SV532: $i,SV350: $i,SV134: $i] :
( ( ( ( hAPP @ SV134 @ SV350 )
= SV532 )
| ~ ( c_Type_Otyping @ SV134 @ ( c_Lambda_OdB_OVar @ SV350 ) @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1352,plain,
! [SV533: $i,SV351: $i,SV135: $i] :
( ( ! [SY1820: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV135 @ SV351 @ SV533 @ SY1820 ) @ SV351 )
= SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1353,plain,
! [SV534: $i,SV352: $i,SV136: $i] :
( ( ! [SY1821: $i] :
( ( c_Type_Otype_Otype__rec @ SV136 @ SV352 @ ( c_Type_Otype_OAtom @ SV534 ) @ SY1821 )
= ( hAPP @ SV136 @ SV534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1354,plain,
! [SV535: $i,SV353: $i,SV137: $i] :
( ( ! [SY1822: $i,SY1823: $i] :
( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV535 ) @ SY1822 )
| ~ ( c_Type_Otyping @ SV137 @ SV535 @ SY1823 )
| ~ ( c_Type_Otyping @ SV137 @ SV353 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1823 ) @ SY1822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1355,plain,
! [SV536: $i,SV354: $i,SV138: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV138 ) @ ( c_List_Olist_OCons @ SV354 @ SV536 @ SV138 ) @ SV138 )
= ( c_List_Olist_OCons @ SV354 @ SV536 @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1356,plain,
! [SV537: $i,SV355: $i,SV140: $i] :
( ( ! [SY1824: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV140 @ SV355 @ SV537 ) @ SY1824 @ SV537 )
= ( c_List_Oappend @ SV140 @ ( c_List_Oappend @ SV355 @ SY1824 @ SV537 ) @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1357,plain,
! [SV538: $i,SV356: $i,SV141: $i] :
( ( ! [SY1825: $i] :
( ( c_List_Oappend @ SV141 @ ( c_List_Oappend @ SV356 @ SV538 @ SY1825 ) @ SY1825 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV141 @ SV356 @ SY1825 ) @ SV538 @ SY1825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1358,plain,
! [SV539: $i,SV357: $i,SV142: $i] :
( ( ! [SY1826: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV142 @ SV357 @ SV539 ) @ SY1826 @ SV539 )
= ( c_List_Oappend @ SV142 @ ( c_List_Oappend @ SV357 @ SY1826 @ SV539 ) @ SV539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1359,plain,
! [SV540: $i,SV358: $i,SV143: $i] :
( ( ! [SY1827: $i] :
( ( c_List_Oappend @ SV143 @ ( c_List_Oappend @ SV358 @ SV540 @ SY1827 ) @ SY1827 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV143 @ SV358 @ SY1827 ) @ SV540 @ SY1827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1360,plain,
! [SV541: $i,SV359: $i,SV144: $i] :
( ( ! [SY1828: $i,SY1829: $i,SY1830: $i] :
( ( c_List_Ofoldr @ SV144 @ ( c_List_Olist_OCons @ SV359 @ SV541 @ SY1828 ) @ SY1829 @ SY1828 @ SY1830 )
= ( hAPP @ ( hAPP @ SV144 @ SV359 ) @ ( c_List_Ofoldr @ SV144 @ SV541 @ SY1829 @ SY1828 @ SY1830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1361,plain,
! [SV542: $i,SV360: $i,SV145: $i] :
( ( ! [SY1831: $i,SY1832: $i,SY1833: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Oappend @ SV360 @ SV542 @ SY1831 ) @ SY1832 @ SY1831 @ SY1833 )
= ( c_List_Ofoldr @ SV145 @ SV360 @ ( c_List_Ofoldr @ SV145 @ SV542 @ SY1832 @ SY1831 @ SY1833 ) @ SY1831 @ SY1833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1362,plain,
! [SV543: $i,SV361: $i,SV146: $i] :
( ( ! [SY1834: $i] :
( ( c_List_Ofoldr @ SV146 @ ( c_List_Olist_ONil @ SV361 ) @ SV543 @ SV361 @ SY1834 )
= SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1363,plain,
! [SV544: $i,SV362: $i,SV147: $i] :
( ( ! [SY1835: $i,SY1836: $i] :
( ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV544 ) @ SY1835 ) @ SY1836 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV362 @ SV544 ) @ SY1835 ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ SV544 @ SY1836 ) ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ SY1835 @ SY1836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1364,plain,
! [SV545: $i,SV363: $i,SV148: $i] :
( ( ! [SY1837: $i,SY1838: $i] :
( ( c_Type_Otype_Otype__case @ SV148 @ SV363 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV545 ) @ SY1837 ) @ SY1838 )
= ( hAPP @ ( hAPP @ SV363 @ SV545 ) @ SY1837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1365,plain,
! [SV546: $i,SV364: $i,SV149: $i] :
( ( ! [SY1839: $i,SY1840: $i] :
( ~ ( hBOOL @ ( hAPP @ SV149 @ ( c_Type_Otype_Otype__case @ SV364 @ SV546 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1839 ) @ SY1840 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV149 @ ( hAPP @ ( hAPP @ SV546 @ SY1839 ) @ SY1840 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1366,plain,
! [SV547: $i,SV365: $i,SV150: $i] :
( ( ! [SY1841: $i,SY1842: $i] :
( ~ ( hBOOL @ ( hAPP @ SV150 @ ( c_Type_Otype_Otype__case @ SV365 @ SV547 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1841 ) @ SY1842 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ ( hAPP @ ( hAPP @ SV547 @ SY1841 ) @ SY1842 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1367,plain,
! [SV548: $i,SV367: $i,SV152: $i] :
( ( ( SV152 = SV367 )
| ~ ( c_fequal @ SV152 @ SV367 @ SV548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1368,plain,
! [SV549: $i,SV368: $i,SV153: $i] :
( ( ! [SY1843: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV153 ) @ SV368 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV549 ) @ SY1843 ) )
| ( SV368 = SY1843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1369,plain,
! [SV550: $i,SV369: $i,SV154: $i] :
( ( ! [SY1844: $i] :
( ( ( c_List_Orev @ SV154 @ SV369 )
!= ( c_List_Olist_OCons @ SV550 @ SY1844 @ SV369 ) )
| ( SV154
= ( c_List_Oappend @ ( c_List_Orev @ SY1844 @ SV369 ) @ ( c_List_Olist_OCons @ SV550 @ ( c_List_Olist_ONil @ SV369 ) @ SV369 ) @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1370,plain,
! [SV551: $i,SV370: $i,SV155: $i] :
( ( ! [SY1845: $i,SY1846: $i] :
( ( ( c_List_Oappend @ SV155 @ SV370 @ SV551 )
!= ( c_List_Olist_OCons @ SY1845 @ SY1846 @ SV551 ) )
| ( SV155
= ( c_List_Olist_OCons @ SY1845 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1845 @ SY1846 @ SV155 @ SV370 @ SV551 ) @ SV551 ) )
| ( SV155
= ( c_List_Olist_ONil @ SV551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1371,plain,
! [SV552: $i,SV371: $i,SV156: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SV371 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV552 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SV371 )
= SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1372,plain,
! [SV553: $i,SV372: $i,SV157: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV157 ) @ SV372 )
!= ( c_Lambda_OdB_OAbs @ SV553 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1373,plain,
! [SV554: $i,SV373: $i,SV158: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV158 ) @ SV373 )
!= ( c_Lambda_OdB_OVar @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1374,plain,
! [SV555: $i,SV374: $i,SV159: $i] :
( ( SV159
!= ( c_List_Olist_OCons @ SV374 @ SV159 @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1375,plain,
! [SV556: $i,SV375: $i,SV160: $i] :
( ( ! [SY1847: $i,SY1848: $i] :
( ( ( c_List_Olist_OCons @ SV160 @ SV375 @ SV556 )
!= ( c_List_Oappend @ SY1847 @ SY1848 @ SV556 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV375 @ SY1847 @ SY1848 @ SV556 ) @ SV556 )
= SY1847 )
| ( SY1847
= ( c_List_Olist_ONil @ SV556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1376,plain,
! [SV557: $i,SV376: $i,SV161: $i] :
( ( ! [SY1849: $i,SY1850: $i] :
( ( SV161
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV376 @ SV161 @ SV557 ) @ ( c_List_Olist_OCons @ SY1849 @ SY1850 @ SV557 ) @ SV557 ) )
| ( ( c_List_OdropWhile @ SV376 @ SV161 @ SV557 )
= ( c_List_Olist_OCons @ SY1849 @ SY1850 @ SV557 ) )
| ( hBOOL @ ( hAPP @ SV376 @ SY1849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1377,plain,
! [SV377: $i,SV162: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV162 )
!= ( c_Lambda_OdB_OVar @ SV377 ) )
= $true )
| ( ( SV162 = SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1378,plain,
! [SV558: $i,SV378: $i,SV163: $i] :
( ( ( SV163
!= ( c_List_Oappend @ SV378 @ SV163 @ SV558 ) )
| ( SV378
= ( c_List_Olist_ONil @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1379,plain,
! [SV559: $i,SV379: $i,SV164: $i] :
( ( ! [SY1851: $i,SY1852: $i] :
( ( ( c_List_Oappend @ SV164 @ ( c_List_Olist_OCons @ SV379 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 )
!= ( c_List_Oappend @ SY1851 @ ( c_List_Olist_OCons @ SY1852 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 ) )
| ( SV164 = SY1851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1380,plain,
! [SV560: $i,SV380: $i,SV165: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV165 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV380 @ SV560 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV560
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1381,plain,
! [SV561: $i,SV381: $i,SV166: $i] :
( ( ( ( c_List_Orev @ SV166 @ SV381 )
!= ( c_List_Olist_OCons @ SV561 @ ( c_List_Olist_ONil @ SV381 ) @ SV381 ) )
| ( SV166
= ( c_List_Olist_OCons @ SV561 @ ( c_List_Olist_ONil @ SV381 ) @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1382,plain,
! [SV562: $i,SV382: $i,SV167: $i] :
( ( ! [SY1853: $i] :
( ( ( c_List_Oappend @ SV167 @ SV382 @ SV562 )
!= ( c_List_Oappend @ SV167 @ SY1853 @ SV562 ) )
| ( SV382 = SY1853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1383,plain,
! [SV383: $i,SV168: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV168 )
!= ( c_Lambda_OdB_OAbs @ SV383 ) )
= $true )
| ( ( SV168 = SV383 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1384,plain,
! [SV563: $i,SV384: $i,SV169: $i] :
( ( ! [SY1854: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV169 ) ) @ SV384 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV563 ) @ SY1854 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1385,plain,
! [SV564: $i,SV385: $i,SV170: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV170 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV385 @ SV564 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV170 )
= SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1386,plain,
! [SV386: $i,SV171: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV171 )
!= ( c_Type_Otype_OAtom @ SV386 ) )
= $true )
| ( ( SV171 = SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1387,plain,
! [SV565: $i,SV387: $i,SV172: $i] :
( ( ( ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SV387 ) @ SV387 )
!= ( c_List_Orev @ SV565 @ SV387 ) )
| ( SV565
= ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SV387 ) @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1388,plain,
! [SV566: $i,SV388: $i,SV173: $i] :
( ( ! [SY1855: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SV388 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV566 ) @ SY1855 ) )
| ( SV173 = SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1389,plain,
! [SV567: $i,SV389: $i,SV174: $i] :
( ( ( c_Type_Otype_OAtom @ SV174 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV389 ) @ SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1390,plain,
! [SV568: $i,SV390: $i,SV175: $i] :
( ( ! [SY1856: $i,SY1857: $i] :
( ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
!= ( c_List_Oappend @ SY1856 @ SY1857 @ SV568 ) )
| ( ( c_List_Olist_OCons @ SV175 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV175 @ SV390 @ SY1856 @ SY1857 @ SV568 ) @ SV568 )
= SY1856 )
| ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
= SY1857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1391,plain,
! [SV391: $i,SV176: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV176 )
= ( c_Lambda_OdB_OVar @ SV391 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1392,plain,
! [SV569: $i,SV392: $i,SV177: $i] :
( ( ! [SY1858: $i,SY1859: $i,SY1860: $i,SY1861: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SY1858 @ SY1859 ) ) )
| ~ ( c_Type_Otyping @ SY1860 @ SY1858 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1858 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1860 @ SY1859 @ SV177 @ tc_Type_Otype ) @ SV569 @ SY1861 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1393,plain,
! [SV570: $i,SV393: $i,SV178: $i] :
( ( ! [SY1862: $i,SY1863: $i] :
( ( ( c_List_Oappend @ SV178 @ SV393 @ SV570 )
!= ( c_List_Olist_OCons @ SY1862 @ SY1863 @ SV570 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1862 @ SY1863 @ SV178 @ SV393 @ SV570 ) @ SV393 @ SV570 )
= SY1863 )
| ( SV393
= ( c_List_Olist_OCons @ SY1862 @ SY1863 @ SV570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1394,plain,
! [SV571: $i,SV394: $i,SV179: $i] :
( ( ! [SY1864: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV179 ) @ SV394 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV571 ) @ SY1864 ) )
| ( SV179 = SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1395,plain,
! [SV572: $i,SV395: $i,SV180: $i] :
( ( ! [SY1865: $i] :
( ( ( c_List_Oappend @ SV180 @ SV395 @ SV572 )
!= ( c_List_Oappend @ SY1865 @ SV395 @ SV572 ) )
| ( SV180 = SY1865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1396,plain,
! [SV573: $i,SV396: $i,SV181: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV181 @ SV396 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV573 @ SV396 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV181 = SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1397,plain,
! [SV574: $i,SV397: $i,SV182: $i] :
( ( ! [SY1866: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV397 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV574 ) @ SY1866 ) )
| ( SV397 = SY1866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1398,plain,
! [SV575: $i,SV398: $i,SV183: $i] :
( ( ( SV183
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 ) @ SV575 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 ) @ ( c_List_Oappend @ SV575 @ ( c_List_Olist_OCons @ SV398 @ ( 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)],[1208]) ).
thf(1399,plain,
! [SV576: $i,SV399: $i,SV184: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV184 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV399 @ SV576 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV576
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1400,plain,
! [SV577: $i,SV400: $i,SV185: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV185 ) @ SV400 )
!= ( c_Type_Otype_OAtom @ SV577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1401,plain,
! [SV578: $i,SV401: $i,SV186: $i] :
( ( ( ( c_List_Oappend @ SV186 @ SV401 @ SV578 )
!= SV401 )
| ( SV186
= ( c_List_Olist_ONil @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1402,plain,
! [SV579: $i,SV402: $i,SV187: $i] :
( ( ! [SY1867: $i,SY1868: $i] :
( ( ( c_List_OdropWhile @ SV187 @ SV402 @ SV579 )
!= ( c_List_Olist_OCons @ SY1867 @ SY1868 @ SV579 ) )
| ( SV402
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV187 @ SV402 @ SV579 ) @ ( c_List_Olist_OCons @ SY1867 @ SY1868 @ SV579 ) @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1403,plain,
! [SV580: $i,SV403: $i,SV188: $i] :
( ( ( c_List_Olist_ONil @ SV188 )
!= ( c_List_Olist_OCons @ SV403 @ SV580 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1404,plain,
! [SV581: $i,SV404: $i,SV189: $i] :
( ( ! [SY1869: $i,SY1870: $i] :
( ( ( c_List_Olist_OCons @ SV189 @ SV404 @ SV581 )
!= ( c_List_Olist_OCons @ SY1869 @ SY1870 @ SV581 ) )
| ( SV404 = SY1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1405,plain,
! [SV582: $i,SV405: $i,SV190: $i] :
( ( ( ( c_List_Oreplicate @ SV190 @ SV405 @ SV582 )
!= ( c_List_Olist_ONil @ SV582 ) )
| ( SV190
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1406,plain,
! [SV583: $i,SV406: $i,SV191: $i] :
( ( ! [SY1871: $i,SY1872: $i,SY1873: $i,SY1874: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SY1871 @ SY1872 ) ) )
| ~ ( c_Type_Otyping @ SY1873 @ SY1871 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1871 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1873 @ SY1872 @ SV406 @ tc_Type_Otype ) @ SV583 @ SY1874 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1407,plain,
! [SV584: $i,SV407: $i,SV192: $i] :
( ( ( ( c_List_Olist_ONil @ SV192 )
!= ( c_List_Oreplicate @ SV407 @ SV584 @ SV192 ) )
| ( SV407
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1408,plain,
! [SV585: $i,SV408: $i,SV193: $i] :
( ( ! [SY1875: $i,SY1876: $i] :
( ( ( c_List_Oreplicate @ SV193 @ SV408 @ SV585 )
!= ( c_List_Oreplicate @ SY1875 @ SY1876 @ SV585 ) )
| ( SV193 = SY1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1409,plain,
! [SV586: $i,SV409: $i,SV194: $i] :
( ( ! [SY1877: $i,SY1878: $i] :
( ( ( c_List_Oreplicate @ SV194 @ SV409 @ SV586 )
!= ( c_List_Oreplicate @ SY1877 @ SY1878 @ SV586 ) )
| ( SV409 = SY1878 )
| ( SV194
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1410,plain,
! [SV587: $i,SV410: $i,SV195: $i] :
( ( ! [SY1879: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV195 ) @ SV410 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV587 ) @ SY1879 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV410 = SY1879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1411,plain,
! [SV588: $i,SV411: $i,SV196: $i] :
( ( ( c_List_Olist_OCons @ SV196 @ SV411 @ SV588 )
!= SV411 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1412,plain,
! [SV589: $i,SV412: $i,SV197: $i] :
( ( ! [SY1880: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV197 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV412 ) @ SV589 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SY1880 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SV589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1413,plain,
! [SV590: $i,SV413: $i,SV198: $i] :
( ( ( ( c_List_Olist_ONil @ SV198 )
!= ( c_List_Oappend @ SV413 @ SV590 @ SV198 ) )
| ( SV590
= ( c_List_Olist_ONil @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1414,plain,
! [SV414: $i,SV199: $i] :
( ( ( ( c_List_Orotate1 @ SV199 @ SV414 )
!= ( c_List_Olist_ONil @ SV414 ) )
= $true )
| ( ( SV199
= ( c_List_Olist_ONil @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1415,plain,
! [SV591: $i,SV415: $i,SV200: $i] :
( ( ( ( c_List_Oappend @ SV200 @ SV415 @ SV591 )
!= SV200 )
| ( SV415
= ( c_List_Olist_ONil @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1416,plain,
! [SV592: $i,SV416: $i,SV201: $i] :
( ( ( SV201
!= ( c_List_Oappend @ SV201 @ SV416 @ SV592 ) )
| ( SV416
= ( c_List_Olist_ONil @ SV592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1417,plain,
! [SV593: $i,SV417: $i,SV202: $i] :
( ( ! [SY1881: $i,SY1882: $i] :
( ( ( c_List_Oappend @ SV202 @ SV417 @ SV593 )
!= ( c_List_Olist_OCons @ SY1881 @ SY1882 @ SV593 ) )
| ( SV202
= ( c_List_Olist_OCons @ SY1881 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1881 @ SY1882 @ SV202 @ SV417 @ SV593 ) @ SV593 ) )
| ( SV417
= ( c_List_Olist_OCons @ SY1881 @ SY1882 @ SV593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1418,plain,
! [SV594: $i,SV418: $i,SV203: $i] :
( ( ! [SY1883: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV203 ) @ SV418 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV594 ) @ SY1883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1419,plain,
! [SV595: $i,SV419: $i,SV204: $i] :
( ( ( ( c_List_Oappend @ SV204 @ SV419 @ SV595 )
!= ( c_List_Olist_ONil @ SV595 ) )
| ( SV204
= ( c_List_Olist_ONil @ SV595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1420,plain,
! [SV596: $i,SV420: $i,SV205: $i] :
( ( ! [SY1884: $i,SY1885: $i] :
( ( ( c_List_Olist_OCons @ SV205 @ SV420 @ SV596 )
!= ( c_List_Oappend @ SY1884 @ SY1885 @ SV596 ) )
| ( SV420
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV205 @ SV420 @ SY1884 @ SY1885 @ SV596 ) @ SY1885 @ SV596 ) )
| ( SY1884
= ( c_List_Olist_ONil @ SV596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1421,plain,
! [SV597: $i,SV421: $i,SV206: $i] :
( ( ! [SY1886: $i,SY1887: $i] :
( ( ( c_List_Olist_OCons @ SV206 @ SV421 @ SV597 )
!= ( c_List_Olist_OCons @ SY1886 @ SY1887 @ SV597 ) )
| ( SV206 = SY1886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1422,plain,
! [SV598: $i,SV422: $i,SV207: $i] :
( ( ! [SY1888: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV207 ) @ SV422 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV598 ) @ SY1888 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV207 = SV598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1423,plain,
! [SV599: $i,SV423: $i,SV208: $i] :
( ( ! [SY1889: $i,SY1890: $i] :
( ( ( c_List_Oappend @ SV208 @ ( c_List_Olist_OCons @ SV423 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 )
!= ( c_List_Oappend @ SY1889 @ ( c_List_Olist_OCons @ SY1890 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 ) )
| ( SV423 = SY1890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1424,plain,
! [SV424: $i,SV209: $i] :
( ( ( c_Lambda_OdB_OVar @ SV209 )
= ( c_Lambda_OdB_OAbs @ SV424 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1425,plain,
! [SV600: $i,SV425: $i,SV210: $i] :
( ( ! [SY1891: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV210 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV425 ) @ SV600 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SY1891 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1426,plain,
! [SV601: $i,SV426: $i,SV211: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV211 @ SV426 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV601 ) )
| ( SV426
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1427,plain,
! [SV602: $i,SV427: $i,SV212: $i] :
( ( ( c_Lambda_OdB_OVar @ SV212 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV427 ) @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1428,plain,
! [SV603: $i,SV428: $i,SV213: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV428 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV603 ) )
| ( SV213
= ( c_Lambda_OdB_OAbs @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1429,plain,
! [SV604: $i,SV429: $i,SV214: $i] :
( ( ! [SY1892: $i,SY1893: $i] :
( ( ( c_List_OdropWhile @ SV214 @ SV429 @ SV604 )
!= ( c_List_Olist_OCons @ SY1892 @ SY1893 @ SV604 ) )
| ~ ( hBOOL @ ( hAPP @ SV214 @ SY1892 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1430,plain,
! [SV605: $i,SV430: $i,SV215: $i] :
( ( ! [SY1894: $i,SY1895: $i] :
( ( ( c_List_Oappend @ SV215 @ SV430 @ SV605 )
!= ( c_List_Olist_OCons @ SY1894 @ SY1895 @ SV605 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1894 @ SY1895 @ SV215 @ SV430 @ SV605 ) @ SV430 @ SV605 )
= SY1895 )
| ( SV215
= ( c_List_Olist_ONil @ SV605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1431,plain,
! [SV606: $i,SV431: $i,SV216: $i] :
( ( ! [SY1896: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV216 ) @ SV431 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV606 ) @ SY1896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV216 = SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1432,plain,
! [SV607: $i,SV432: $i,SV217: $i] :
( ( ( c_List_Olist_OCons @ SV217 @ SV432 @ SV607 )
!= ( c_List_Olist_ONil @ SV607 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1433,plain,
! [SV608: $i,SV433: $i,SV218: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV218 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV433 ) @ SV608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1434,plain,
! [SV609: $i,SV434: $i,SV219: $i] :
( ( ( ( c_List_Orev @ SV219 @ SV434 )
!= ( c_List_Orev @ SV609 @ SV434 ) )
| ( SV219 = SV609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1435,plain,
! [SV610: $i,SV435: $i,SV220: $i] :
( ( ( ( c_List_Oappend @ SV220 @ SV435 @ SV610 )
!= ( c_List_Olist_ONil @ SV610 ) )
| ( SV435
= ( c_List_Olist_ONil @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1436,plain,
! [SV436: $i,SV221: $i] :
( ( ( ( c_List_Orev @ SV221 @ SV436 )
!= ( c_List_Olist_ONil @ SV436 ) )
= $true )
| ( ( SV221
= ( c_List_Olist_ONil @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1437,plain,
! [SV611: $i,SV437: $i,SV222: $i] :
( ( ! [SY1897: $i,SY1898: $i] :
( ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
!= ( c_List_Oappend @ SY1897 @ SY1898 @ SV611 ) )
| ( SV437
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV222 @ SV437 @ SY1897 @ SY1898 @ SV611 ) @ SY1898 @ SV611 ) )
| ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
= SY1898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1438,plain,
! [SV612: $i,SV438: $i,SV223: $i] :
( ( ( ( c_List_Olist_ONil @ SV223 )
!= ( c_List_Oappend @ SV438 @ SV612 @ SV223 ) )
| ( SV438
= ( c_List_Olist_ONil @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1439,plain,
! [SV613: $i,SV439: $i,SV224: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV224 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV439 @ SV613 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV224 )
= SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1440,plain,
! [SV614: $i,SV440: $i,SV225: $i] :
( ( ( c_List_Olist_OCons @ SV225 @ SV440 @ SV614 )
!= ( c_List_Olist_ONil @ SV614 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1441,plain,
! [SV441: $i,SV226: $i] :
( ( ( ( c_List_Olist_ONil @ SV226 )
!= ( c_List_Orev @ SV441 @ SV226 ) )
= $true )
| ( ( SV441
= ( c_List_Olist_ONil @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1442,plain,
! [SV615: $i,SV442: $i,SV227: $i] :
( ( ! [SY1899: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV227 ) @ SV442 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV615 ) @ SY1899 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV442 = SY1899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1443,plain,
! [SV443: $i,SV229: $i,SV2: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV2 @ SV229 @ SV443 ) @ SV443 )
= SV229 )
= $true )
| ( ( SV2
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1444,plain,
! [SV616: $i,SV444: $i,SV230: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ SV230 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV444 @ SV3 @ SV230 @ SV616 ) )
| ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SV616 @ ( c_List_Olist_OCons @ SV230 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1445,plain,
! [SV445: $i,SV231: $i,SV4: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV4 @ SV231 @ SV445 ) @ SV445 )
= SV231 )
= $true )
| ( ( SV4
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1446,plain,
! [SV447: $i,SV234: $i,SV9: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV9 @ SV234 @ SV447 ) @ SV447 ) ) ) )
= $true )
| ( ( ( c_List_OdropWhile @ SV9 @ SV234 @ SV447 )
= ( c_List_Olist_ONil @ SV447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1447,plain,
! [SV617: $i,SV448: $i,SV235: $i,SV11: $i] :
( ( ! [SY1900: $i,SY1901: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV11 @ SV235 @ SV448 @ SV617 ) @ SY1900 ) @ SY1901 )
= ( hAPP @ ( hAPP @ SV11 @ SY1901 ) @ SY1900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1448,plain,
! [SV618: $i,SV449: $i,SV236: $i,SV12: $i] :
( ( ( c_List_Olistsp @ SV12 @ SV236 @ SV449 )
| ~ ( c_List_Olistsp @ SV12 @ ( c_List_Oappend @ SV236 @ SV618 @ SV449 ) @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1449,plain,
! [SV619: $i,SV450: $i,SV237: $i,SV13: $i] :
( ( ( c_List_Olistsp @ SV13 @ SV237 @ SV450 )
| ~ ( c_List_Olistsp @ SV13 @ ( c_List_Oappend @ SV619 @ SV237 @ SV450 ) @ SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1450,plain,
! [SV451: $i,SV240: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV16 ) ) @ SV240 ) @ SV451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV16 @ SV240 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1451,plain,
! [SV620: $i,SV452: $i,SV241: $i,SV17: $i] :
( ( ! [SY1902: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV17 @ SV241 @ SV452 ) @ ( c_List_Olist_OCons @ SV620 @ SY1902 @ SV452 ) @ SV452 )
= ( c_List_Olist_OCons @ SV17 @ ( c_List_Olist_OCons @ SV620 @ ( c_List_Osplice @ SV241 @ SY1902 @ SV452 ) @ SV452 ) @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1452,plain,
! [SV621: $i,SV453: $i,SV242: $i,SV18: $i] :
( ( ( ( c_List_OdropWhile @ SV18 @ ( c_List_Olist_OCons @ SV242 @ SV453 @ SV621 ) @ SV621 )
= ( c_List_OdropWhile @ SV18 @ SV453 @ SV621 ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1453,plain,
! [SV622: $i,SV454: $i,SV243: $i,SV19: $i] :
( ( ( ( c_List_OdropWhile @ SV19 @ ( c_List_Olist_OCons @ SV243 @ SV454 @ SV622 ) @ SV622 )
= ( c_List_Olist_OCons @ SV243 @ SV454 @ SV622 ) )
| ( hBOOL @ ( hAPP @ SV19 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1454,plain,
! [SV623: $i,SV456: $i,SV245: $i,SV21: $i] :
( ( ( c_List_Olistsp @ SV21 @ ( c_List_Oappend @ SV245 @ SV456 @ SV623 ) @ SV623 )
| ~ ( c_List_Olistsp @ SV21 @ SV456 @ SV623 )
| ~ ( c_List_Olistsp @ SV21 @ SV245 @ SV623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1455,plain,
! [SV458: $i,SV250: $i,SV26: $i] :
( ( ( ( c_List_Oappend @ SV26 @ ( c_List_Olist_OCons @ SV250 @ ( 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 @ SV458 @ SV26 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV250 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV458 @ ( c_List_Oappend @ SV26 @ ( c_List_Olist_OCons @ SV250 @ ( 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)],[1269]) ).
thf(1456,plain,
! [SV624: $i,SV459: $i,SV251: $i,SV27: $i] :
( ( ( c_Type_Otyping @ SV27 @ ( c_Lambda_OdB_OAbs @ SV251 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV459 ) @ SV624 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV27 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV459 @ tc_Type_Otype ) @ SV251 @ SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1457,plain,
! [SV461: $i,SV253: $i,SV29: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV29 @ SV253 @ SV461 ) @ SV461 )
= ( c_List_Olist_OCons @ SV29 @ ( c_List_Obutlast @ SV253 @ SV461 ) @ SV461 ) )
= $true )
| ( ( SV253
= ( c_List_Olist_ONil @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1458,plain,
! [SV625: $i,SV462: $i,SV256: $i,SV32: $i] :
( ( ( ( c_List_OtakeWhile @ SV32 @ ( c_List_Olist_OCons @ SV256 @ SV462 @ SV625 ) @ SV625 )
= ( c_List_Olist_ONil @ SV625 ) )
| ( hBOOL @ ( hAPP @ SV32 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1459,plain,
! [SV463: $i,SV258: $i,SV34: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV34 @ SV258 @ SV463 ) @ SV463 )
= ( c_List_Olast @ SV258 @ SV463 ) )
= $true )
| ( ( SV258
= ( c_List_Olist_ONil @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1460,plain,
! [SV626: $i,SV464: $i,SV260: $i,SV36: $i] :
( ( ! [SY1903: $i,SY1904: $i,SY1905: $i] :
( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1903 ) @ SY1904 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
| ~ ( c_Type_Otypings @ SV464 @ SY1904 @ SY1905 )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1903 ) @ SY1904 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1461,plain,
! [SV627: $i,SV466: $i,SV263: $i,SV39: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV39 ) @ SV263 ) @ SV466 @ SV627 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV39 @ SV466 @ SV627 ) ) @ ( c_Lambda_Osubst @ SV263 @ SV466 @ SV627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1462,plain,
! [SV628: $i,SV467: $i,SV264: $i,SV41: $i] :
( ( ( c_Type_Otypings @ SV41 @ SV264 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV467 @ SV41 @ SV628 @ SV264 ) )
| ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV628 ) @ SV264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1463,plain,
! [SV629: $i,SV468: $i,SV265: $i,SV43: $i] :
( ( ! [SY1906: $i] :
( ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_OCons @ SV265 @ SV468 @ SV629 ) @ ( c_List_Olist_OCons @ SV265 @ SY1906 @ SV629 ) @ SV629 )
| ~ ( c_ListOrder_Ostep1 @ SV43 @ SV468 @ SY1906 @ SV629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1464,plain,
! [SV630: $i,SV469: $i,SV266: $i,SV44: $i] :
( ( ! [SY1907: $i,SY1908: $i] :
( ( c_ListOrder_Ostep1 @ SV44 @ SV266 @ SV469 @ SV630 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SY1907 ) @ SY1908 ) )
| ~ ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SY1907 @ SV266 @ SV630 ) @ ( c_List_Olist_OCons @ SY1908 @ SV469 @ SV630 ) @ SV630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1465,plain,
! [SV470: $i,SV269: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV48 @ ( c_Lambda_OdB_OVar @ SV269 ) @ SV470 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1466,plain,
! [SV631: $i,SV471: $i,SV270: $i,SV49: $i] :
( ( ( c_Type_Otypings @ SV49 @ SV270 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV471 @ SV49 @ SV631 @ SV270 ) )
| ~ ( c_Type_Otyping @ SV49 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV631 @ SV270 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1467,plain,
! [SV632: $i,SV472: $i,SV271: $i,SV50: $i] :
( ( ! [SY1909: $i] :
( ( c_List_Ofoldr @ SV50 @ SV271 @ SV472 @ SV632 @ SY1909 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV50 @ SV632 @ SY1909 @ SY1909 ) @ SV472 @ ( c_List_Orev @ SV271 @ SV632 ) @ SY1909 @ SV632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1468,plain,
! [SV52: $i,SV273: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV273 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV52 ) @ SV273 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1469,plain,
! [SV633: $i,SV474: $i,SV274: $i,SV53: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV53 @ SV274 @ SV474 ) @ ( c_List_Oreplicate @ SV633 @ SV274 @ SV474 ) @ SV474 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV633 @ SV274 @ SV474 ) @ ( c_List_Oreplicate @ SV53 @ SV274 @ SV474 ) @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1470,plain,
! [SV634: $i,SV476: $i,SV276: $i,SV55: $i] :
( ( ! [SY1910: $i,SY1911: $i] :
( ( c_ListOrder_Ostep1 @ SV55 @ SV276 @ SV476 @ SV634 )
| ( SV476 = SV276 )
| ~ ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SY1910 @ SV276 @ SV634 ) @ ( c_List_Olist_OCons @ SY1911 @ SV476 @ SV634 ) @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1471,plain,
! [SV635: $i,SV477: $i,SV277: $i,SV56: $i] :
( ( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV56 @ SV277 @ SV477 ) @ SV635 @ SV477 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV635 @ SV477 ) @ ( c_List_Osplice @ SV277 @ ( c_List_Otl @ SV635 @ SV477 ) @ SV477 ) @ SV477 ) @ SV477 ) )
| ( SV635
= ( c_List_Olist_ONil @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1472,plain,
! [SV278: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV57 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV57 @ SV278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1473,plain,
! [SV636: $i,SV478: $i,SV279: $i,SV58: $i] :
( ( ( c_List_Ofoldl @ SV58 @ SV279 @ ( c_List_Olist_ONil @ SV478 ) @ SV636 @ SV478 )
= SV279 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1474,plain,
! [SV479: $i,SV280: $i,SV59: $i] :
( ( c_ListOrder_Ostep1 @ SV59 @ SV280 @ ( c_List_Olist_ONil @ SV479 ) @ SV479 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1475,plain,
! [SV480: $i,SV281: $i,SV60: $i] :
( ( c_ListOrder_Ostep1 @ SV60 @ ( c_List_Olist_ONil @ SV281 ) @ SV480 @ SV281 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1476,plain,
! [SV637: $i,SV483: $i,SV288: $i,SV68: $i] :
( ( ! [SY1912: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV288 ) @ SV483 ) )
| ( c_ListOrder_Ostep1 @ SV68 @ ( c_List_Olist_OCons @ SV288 @ SV637 @ SY1912 ) @ ( c_List_Olist_OCons @ SV483 @ SV637 @ SY1912 ) @ SY1912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1477,plain,
! [SV638: $i,SV484: $i,SV289: $i,SV69: $i] :
( ( ! [SY1913: $i,SY1914: $i] :
( ( SV69 = SV289 )
| ( SV484 = SV638 )
| ~ ( c_ListOrder_Ostep1 @ SY1913 @ ( c_List_Olist_OCons @ SV289 @ SV638 @ SY1914 ) @ ( c_List_Olist_OCons @ SV69 @ SV484 @ SY1914 ) @ SY1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1478,plain,
! [SV639: $i,SV485: $i,SV291: $i,SV72: $i] :
( ( ! [SY1915: $i] :
( ( c_ListOrder_Ostep1 @ SV72 @ ( c_List_Oappend @ SV291 @ SV485 @ SV639 ) @ ( c_List_Oappend @ SV291 @ SY1915 @ SV639 ) @ SV639 )
| ~ ( c_ListOrder_Ostep1 @ SV72 @ SV485 @ SY1915 @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1479,plain,
! [SV640: $i,SV486: $i,SV292: $i,SV73: $i] :
( ( ! [SY1916: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV73 @ SV292 @ SV486 @ SV640 )
| ( c_ListOrder_Ostep1 @ SV73 @ ( c_List_Oappend @ SV292 @ SY1916 @ SV640 ) @ ( c_List_Oappend @ SV486 @ SY1916 @ SV640 ) @ SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1480,plain,
! [SV641: $i,SV487: $i,SV293: $i,SV75: $i] :
( ( ( c_Type_Otypings @ SV75 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV487 @ SV75 @ SV641 @ SV293 ) )
| ~ ( c_Type_Otyping @ SV75 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV641 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1481,plain,
! [SV642: $i,SV488: $i,SV294: $i,SV76: $i] :
( ( ! [SY1917: $i,SY1918: $i] :
( ( c_List_Ofoldl @ SV76 @ SV294 @ ( c_List_Olist_OCons @ SV488 @ SV642 @ SY1917 ) @ SY1918 @ SY1917 )
= ( c_List_Ofoldl @ SV76 @ ( hAPP @ ( hAPP @ SV76 @ SV294 ) @ SV488 ) @ SV642 @ SY1918 @ SY1917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1482,plain,
! [SV643: $i,SV489: $i,SV296: $i,SV78: $i] :
( ( ! [SY1919: $i,SY1920: $i] :
( ( SV78 = SV296 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV489 @ SV296 ) @ SV78 ) )
| ~ ( c_ListOrder_Ostep1 @ SV489 @ ( c_List_Olist_OCons @ SV296 @ SV643 @ SY1919 ) @ ( c_List_Olist_OCons @ SV78 @ SY1920 @ SY1919 ) @ SY1919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1483,plain,
! [SV644: $i,SV490: $i,SV297: $i,SV79: $i] :
( ( ! [SY1921: $i,SY1922: $i,SY1923: $i] :
( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1921 ) @ SY1922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
| ~ ( c_Type_Otypings @ SV79 @ SY1922 @ SY1923 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1921 ) @ SY1922 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1484,plain,
! [SV645: $i,SV491: $i,SV298: $i,SV80: $i] :
( ( ( ( c_List_OtakeWhile @ SV80 @ ( c_List_Olist_OCons @ SV298 @ SV491 @ SV645 ) @ SV645 )
= ( c_List_Olist_OCons @ SV298 @ ( c_List_OtakeWhile @ SV80 @ SV491 @ SV645 ) @ SV645 ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1485,plain,
! [SV646: $i,SV493: $i,SV300: $i,SV82: $i] :
( ( ! [SY1924: $i] :
( ( c_List_Ofoldl @ SV82 @ SV300 @ SV493 @ SV646 @ SY1924 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV82 @ SV646 @ SY1924 @ SV646 ) @ ( c_List_Orev @ SV493 @ SY1924 ) @ SV300 @ SY1924 @ SV646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1486,plain,
! [SV647: $i,SV495: $i,SV302: $i,SV85: $i] :
( ( ! [SY1925: $i,SY1926: $i] :
( ( c_List_Ofoldl @ SV85 @ SV302 @ ( c_List_Oappend @ SV495 @ SV647 @ SY1925 ) @ SY1926 @ SY1925 )
= ( c_List_Ofoldl @ SV85 @ ( c_List_Ofoldl @ SV85 @ SV302 @ SV495 @ SY1926 @ SY1925 ) @ SV647 @ SY1926 @ SY1925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1487,plain,
! [SV648: $i,SV496: $i,SV303: $i,SV86: $i] :
( ( ! [SY1927: $i] :
( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV496 @ SV648 @ SY1927 ) @ SY1927 ) @ SY1927 ) ) )
| ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ SV648 @ SY1927 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV86 @ SV496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1488,plain,
! [SV649: $i,SV497: $i,SV304: $i,SV87: $i] :
( ( ! [SY1928: $i] :
( ( c_List_Oconcat__map @ SV87 @ ( c_List_Olist_OCons @ SV304 @ SV497 @ SV649 ) @ SV649 @ SY1928 )
= ( c_List_Oappend @ ( hAPP @ SV87 @ SV304 ) @ ( c_List_Oconcat__map @ SV87 @ SV497 @ SV649 @ SY1928 ) @ SY1928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1489,plain,
! [SV650: $i,SV498: $i,SV305: $i,SV88: $i] :
( ( ! [SY1929: $i] :
( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ ( c_List_Oappend @ SV305 @ ( c_List_Olist_OCons @ SV498 @ SV650 @ SY1929 ) @ SY1929 ) @ SY1929 ) ) )
| ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ SV305 @ SY1929 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV88 @ SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1490,plain,
! [SV651: $i,SV499: $i,SV306: $i,SV89: $i] :
( ( ! [SY1930: $i] :
( ( ( c_List_OtakeWhile @ SV89 @ ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV499 @ SV651 @ SY1930 ) @ SY1930 ) @ SY1930 )
= ( c_List_OtakeWhile @ SV89 @ SV306 @ SY1930 ) )
| ( hBOOL @ ( hAPP @ SV89 @ SV499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1491,plain,
! [SV652: $i,SV500: $i,SV307: $i,SV90: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV90 @ SV307 @ SV500 ) @ ( c_List_Olist_OCons @ SV307 @ SV652 @ SV500 ) @ SV500 )
= ( c_List_Olist_OCons @ SV307 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV90 @ SV307 @ SV500 ) @ SV652 @ SV500 ) @ SV500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1492,plain,
! [SV501: $i,SV308: $i,SV91: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oappend @ SV91 @ SV308 @ SV501 ) @ SV501 )
= ( c_List_Ohd @ SV91 @ SV501 ) )
= $true )
| ( ( SV91
= ( c_List_Olist_ONil @ SV501 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1493,plain,
! [SV502: $i,SV310: $i,SV93: $i] :
( ( ( ( c_List_Otl @ ( c_List_Oappend @ SV93 @ SV310 @ SV502 ) @ SV502 )
= ( c_List_Oappend @ ( c_List_Otl @ SV93 @ SV502 ) @ SV310 @ SV502 ) )
= $true )
| ( ( SV93
= ( c_List_Olist_ONil @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1494,plain,
! [SV503: $i,SV311: $i,SV94: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV94 @ SV311 @ SV503 ) @ SV503 )
= ( c_List_Olast @ SV311 @ SV503 ) )
= $true )
| ( ( SV311
= ( c_List_Olist_ONil @ SV503 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1495,plain,
! [SV504: $i,SV314: $i,SV97: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV97 @ SV314 @ SV504 ) @ SV504 )
= ( c_List_Oappend @ SV97 @ ( c_List_Obutlast @ SV314 @ SV504 ) @ SV504 ) )
= $true )
| ( ( SV314
= ( c_List_Olist_ONil @ SV504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1496,plain,
! [SV315: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV98 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV98 ) @ ( c_Lambda_OdB_OVar @ SV315 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1497,plain,
! [SV653: $i,SV505: $i,SV316: $i,SV99: $i] :
( ( ( c_Type_Otyping @ SV99 @ SV316 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV505 @ SV99 @ SV653 @ SV316 ) )
| ~ ( c_Type_Otyping @ SV99 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV653 ) @ SV316 ) @ SV505 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1498,plain,
! [SV654: $i,SV506: $i,SV317: $i,SV100: $i] :
( ( ( c_Type_Otyping @ SV100 @ SV317 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV506 @ SV100 @ SV317 @ SV654 ) @ SV506 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV317 @ SV654 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1499,plain,
! [SV655: $i,SV507: $i,SV318: $i,SV101: $i] :
( ( ! [SY1931: $i] :
( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV318 @ SV507 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV655 )
| ~ ( c_Type_Otypings @ SV101 @ SV507 @ SY1931 )
| ~ ( c_Type_Otyping @ SV101 @ SV318 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY1931 @ SV655 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1500,plain,
! [SV656: $i,SV508: $i,SV319: $i,SV102: $i] :
( ( ( c_Type_Otyping @ SV102 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV508 @ SV102 @ SV319 @ SV656 ) @ SV508 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV102 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1501,plain,
! [SV657: $i,SV509: $i,SV320: $i,SV103: $i] :
( ( ! [SY1932: $i,SY1933: $i] :
( ~ ( c_Type_Otyping @ SV103 @ SV320 @ SV509 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SV657 @ SV509 @ tc_Type_Otype ) @ SY1932 @ SY1933 )
| ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SY1932 @ SV320 @ SV657 ) @ SY1933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1502,plain,
! [SV658: $i,SV510: $i,SV321: $i,SV104: $i] :
( ( ! [SY1934: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV104 @ SV321 @ SV510 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV658 @ SV321 ) @ SY1934 )
| ~ ( c_Type_Otyping @ SV104 @ SV658 @ SY1934 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1503,plain,
! [SV659: $i,SV511: $i,SV322: $i,SV105: $i] :
( ( ( c_Type_Otyping @ SV105 @ ( c_Lambda_OdB_OVar @ SV322 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV511 @ SV105 @ SV322 @ SV659 ) @ SV511 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV105 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV322 ) @ SV659 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1504,plain,
! [SV660: $i,SV513: $i,SV324: $i,SV107: $i] :
( ( ! [SY1935: $i,SY1936: $i] :
( ( SV107 = SV324 )
| ( c_ListOrder_Ostep1 @ SV513 @ SV107 @ SV324 @ SV660 )
| ~ ( c_ListOrder_Ostep1 @ SV513 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SY1935 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ ( c_List_Oappend @ SV324 @ ( c_List_Olist_OCons @ SY1936 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ SV660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1505,plain,
! [SV661: $i,SV516: $i,SV327: $i,SV110: $i] :
( ( ! [SY1937: $i,SY1938: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV327 ) @ SV516 ) )
| ( c_ListOrder_Ostep1 @ SV110 @ SV661 @ SY1937 @ SY1938 )
| ~ ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SV661 @ ( c_List_Olist_OCons @ SV327 @ ( c_List_Olist_ONil @ SY1938 ) @ SY1938 ) @ SY1938 ) @ ( c_List_Oappend @ SY1937 @ ( c_List_Olist_OCons @ SV516 @ ( c_List_Olist_ONil @ SY1938 ) @ SY1938 ) @ SY1938 ) @ SY1938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1506,plain,
! [SV662: $i,SV518: $i,SV329: $i,SV112: $i] :
( ( ! [SY1939: $i,SY1940: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SV329 ) @ SV518 ) )
| ( SV329 = SV518 )
| ~ ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SV662 @ ( c_List_Olist_OCons @ SV329 @ ( c_List_Olist_ONil @ SY1939 ) @ SY1939 ) @ SY1939 ) @ ( c_List_Oappend @ SY1940 @ ( c_List_Olist_OCons @ SV518 @ ( c_List_Olist_ONil @ SY1939 ) @ SY1939 ) @ SY1939 ) @ SY1939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1507,plain,
! [SV663: $i,SV519: $i,SV330: $i,SV113: $i] :
( ( ! [SY1941: $i,SY1942: $i] :
( ( SV113 = SV330 )
| ( SV519 = SV663 )
| ~ ( c_ListOrder_Ostep1 @ SY1941 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SV519 @ ( c_List_Olist_ONil @ SY1942 ) @ SY1942 ) @ SY1942 ) @ ( c_List_Oappend @ SV330 @ ( c_List_Olist_OCons @ SV663 @ ( c_List_Olist_ONil @ SY1942 ) @ SY1942 ) @ SY1942 ) @ SY1942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1508,plain,
! [SV664: $i,SV522: $i,SV333: $i,SV116: $i] :
( ( ! [SY1943: $i] :
( ( SV116 = SV333 )
| ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SY1943 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV333 )
| ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SY1943 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1509,plain,
! [SV665: $i,SV523: $i,SV334: $i,SV117: $i] :
( ( ( c_Type_Otyping @ SV117 @ SV334 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV523 @ SV117 @ SV334 @ SV665 ) ) @ SV523 ) )
| ~ ( c_Type_Otyping @ SV117 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SV665 ) @ SV523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1510,plain,
! [SV666: $i,SV524: $i,SV335: $i,SV118: $i] :
( ( ( c_Type_Otype_Otype__case @ SV118 @ SV335 @ ( c_Type_Otype_OAtom @ SV524 ) @ SV666 )
= ( hAPP @ SV118 @ SV524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1511,plain,
! [SV667: $i,SV526: $i,SV337: $i,SV121: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV121 @ ( c_Type_Otype_Otype__case @ SV337 @ SV526 @ ( c_Type_Otype_OAtom @ SV667 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV121 @ ( hAPP @ SV337 @ SV667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1512,plain,
! [SV668: $i,SV527: $i,SV338: $i,SV122: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV122 @ ( c_Type_Otype_Otype__case @ SV338 @ SV527 @ ( c_Type_Otype_OAtom @ SV668 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV122 @ ( hAPP @ SV338 @ SV668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1513,plain,
! [SV669: $i,SV528: $i,SV339: $i,SV123: $i] :
( ( ( c_List_Olist_OCons @ SV123 @ ( c_List_Oappend @ SV339 @ SV528 @ SV669 ) @ SV669 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV123 @ SV339 @ SV669 ) @ SV528 @ SV669 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1514,plain,
! [SV670: $i,SV529: $i,SV340: $i,SV124: $i] :
( ( ( c_List_Olist_OCons @ SV124 @ ( c_List_Oappend @ SV340 @ SV529 @ SV670 ) @ SV670 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV124 @ SV340 @ SV670 ) @ SV529 @ SV670 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1515,plain,
! [SV671: $i,SV530: $i,SV341: $i,SV125: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV125 @ SV341 @ SV530 ) @ SV671 @ SV530 )
= ( c_List_Olist_OCons @ SV125 @ ( c_List_Oappend @ SV341 @ SV671 @ SV530 ) @ SV530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1516,plain,
! [SV672: $i,SV531: $i,SV342: $i,SV126: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV126 @ SV342 @ SV531 ) @ SV672 @ SV531 )
= ( c_List_Olist_OCons @ SV126 @ ( c_List_Oappend @ SV342 @ SV672 @ SV531 ) @ SV531 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1517,plain,
! [SV344: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ SV128 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV128 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV128 @ SV344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1518,plain,
! [SV532: $i,SV350: $i,SV134: $i] :
( ( ( ( hAPP @ SV134 @ SV350 )
= SV532 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV134 @ ( c_Lambda_OdB_OVar @ SV350 ) @ SV532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1519,plain,
! [SV673: $i,SV533: $i,SV351: $i,SV135: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV135 @ SV351 @ SV533 @ SV673 ) @ SV351 )
= SV533 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1520,plain,
! [SV674: $i,SV534: $i,SV352: $i,SV136: $i] :
( ( ( c_Type_Otype_Otype__rec @ SV136 @ SV352 @ ( c_Type_Otype_OAtom @ SV534 ) @ SV674 )
= ( hAPP @ SV136 @ SV534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1521,plain,
! [SV675: $i,SV535: $i,SV353: $i,SV137: $i] :
( ( ! [SY1944: $i] :
( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV535 ) @ SV675 )
| ~ ( c_Type_Otyping @ SV137 @ SV535 @ SY1944 )
| ~ ( c_Type_Otyping @ SV137 @ SV353 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY1944 ) @ SV675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1522,plain,
! [SV676: $i,SV537: $i,SV355: $i,SV140: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV140 @ SV355 @ SV537 ) @ SV676 @ SV537 )
= ( c_List_Oappend @ SV140 @ ( c_List_Oappend @ SV355 @ SV676 @ SV537 ) @ SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1523,plain,
! [SV677: $i,SV538: $i,SV356: $i,SV141: $i] :
( ( ( c_List_Oappend @ SV141 @ ( c_List_Oappend @ SV356 @ SV538 @ SV677 ) @ SV677 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV141 @ SV356 @ SV677 ) @ SV538 @ SV677 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1524,plain,
! [SV678: $i,SV539: $i,SV357: $i,SV142: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV142 @ SV357 @ SV539 ) @ SV678 @ SV539 )
= ( c_List_Oappend @ SV142 @ ( c_List_Oappend @ SV357 @ SV678 @ SV539 ) @ SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1525,plain,
! [SV679: $i,SV540: $i,SV358: $i,SV143: $i] :
( ( ( c_List_Oappend @ SV143 @ ( c_List_Oappend @ SV358 @ SV540 @ SV679 ) @ SV679 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV143 @ SV358 @ SV679 ) @ SV540 @ SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1526,plain,
! [SV680: $i,SV541: $i,SV359: $i,SV144: $i] :
( ( ! [SY1945: $i,SY1946: $i] :
( ( c_List_Ofoldr @ SV144 @ ( c_List_Olist_OCons @ SV359 @ SV541 @ SV680 ) @ SY1945 @ SV680 @ SY1946 )
= ( hAPP @ ( hAPP @ SV144 @ SV359 ) @ ( c_List_Ofoldr @ SV144 @ SV541 @ SY1945 @ SV680 @ SY1946 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1527,plain,
! [SV681: $i,SV542: $i,SV360: $i,SV145: $i] :
( ( ! [SY1947: $i,SY1948: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Oappend @ SV360 @ SV542 @ SV681 ) @ SY1947 @ SV681 @ SY1948 )
= ( c_List_Ofoldr @ SV145 @ SV360 @ ( c_List_Ofoldr @ SV145 @ SV542 @ SY1947 @ SV681 @ SY1948 ) @ SV681 @ SY1948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1528,plain,
! [SV682: $i,SV543: $i,SV361: $i,SV146: $i] :
( ( ( c_List_Ofoldr @ SV146 @ ( c_List_Olist_ONil @ SV361 ) @ SV543 @ SV361 @ SV682 )
= SV543 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1529,plain,
! [SV683: $i,SV544: $i,SV362: $i,SV147: $i] :
( ( ! [SY1949: $i] :
( ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV544 ) @ SV683 ) @ SY1949 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV362 @ SV544 ) @ SV683 ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ SV544 @ SY1949 ) ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ SV683 @ SY1949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1530,plain,
! [SV684: $i,SV545: $i,SV363: $i,SV148: $i] :
( ( ! [SY1950: $i] :
( ( c_Type_Otype_Otype__case @ SV148 @ SV363 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV545 ) @ SV684 ) @ SY1950 )
= ( hAPP @ ( hAPP @ SV363 @ SV545 ) @ SV684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1531,plain,
! [SV685: $i,SV546: $i,SV364: $i,SV149: $i] :
( ( ! [SY1951: $i] :
( ~ ( hBOOL @ ( hAPP @ SV149 @ ( c_Type_Otype_Otype__case @ SV364 @ SV546 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV685 ) @ SY1951 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV149 @ ( hAPP @ ( hAPP @ SV546 @ SV685 ) @ SY1951 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1532,plain,
! [SV686: $i,SV547: $i,SV365: $i,SV150: $i] :
( ( ! [SY1952: $i] :
( ~ ( hBOOL @ ( hAPP @ SV150 @ ( c_Type_Otype_Otype__case @ SV365 @ SV547 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV686 ) @ SY1952 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ ( hAPP @ ( hAPP @ SV547 @ SV686 ) @ SY1952 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1533,plain,
! [SV548: $i,SV367: $i,SV152: $i] :
( ( ( SV152 = SV367 )
= $true )
| ( ( ~ ( c_fequal @ SV152 @ SV367 @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1534,plain,
! [SV687: $i,SV549: $i,SV368: $i,SV153: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV153 ) @ SV368 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV549 ) @ SV687 ) )
| ( SV368 = SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1535,plain,
! [SV688: $i,SV550: $i,SV369: $i,SV154: $i] :
( ( ( ( c_List_Orev @ SV154 @ SV369 )
!= ( c_List_Olist_OCons @ SV550 @ SV688 @ SV369 ) )
| ( SV154
= ( c_List_Oappend @ ( c_List_Orev @ SV688 @ SV369 ) @ ( c_List_Olist_OCons @ SV550 @ ( c_List_Olist_ONil @ SV369 ) @ SV369 ) @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1536,plain,
! [SV689: $i,SV551: $i,SV370: $i,SV155: $i] :
( ( ! [SY1953: $i] :
( ( ( c_List_Oappend @ SV155 @ SV370 @ SV551 )
!= ( c_List_Olist_OCons @ SV689 @ SY1953 @ SV551 ) )
| ( SV155
= ( c_List_Olist_OCons @ SV689 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV689 @ SY1953 @ SV155 @ SV370 @ SV551 ) @ SV551 ) )
| ( SV155
= ( c_List_Olist_ONil @ SV551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1537,plain,
! [SV552: $i,SV371: $i,SV156: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SV371 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV552 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SV371 )
= SV552 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1538,plain,
! [SV553: $i,SV372: $i,SV157: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV157 ) @ SV372 )
= ( c_Lambda_OdB_OAbs @ SV553 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1539,plain,
! [SV554: $i,SV373: $i,SV158: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV158 ) @ SV373 )
= ( c_Lambda_OdB_OVar @ SV554 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1540,plain,
! [SV555: $i,SV374: $i,SV159: $i] :
( ( SV159
= ( c_List_Olist_OCons @ SV374 @ SV159 @ SV555 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1541,plain,
! [SV690: $i,SV556: $i,SV375: $i,SV160: $i] :
( ( ! [SY1954: $i] :
( ( ( c_List_Olist_OCons @ SV160 @ SV375 @ SV556 )
!= ( c_List_Oappend @ SV690 @ SY1954 @ SV556 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV375 @ SV690 @ SY1954 @ SV556 ) @ SV556 )
= SV690 )
| ( SV690
= ( c_List_Olist_ONil @ SV556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1542,plain,
! [SV691: $i,SV557: $i,SV376: $i,SV161: $i] :
( ( ! [SY1955: $i] :
( ( SV161
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV376 @ SV161 @ SV557 ) @ ( c_List_Olist_OCons @ SV691 @ SY1955 @ SV557 ) @ SV557 ) )
| ( ( c_List_OdropWhile @ SV376 @ SV161 @ SV557 )
= ( c_List_Olist_OCons @ SV691 @ SY1955 @ SV557 ) )
| ( hBOOL @ ( hAPP @ SV376 @ SV691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1543,plain,
! [SV377: $i,SV162: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV162 )
= ( c_Lambda_OdB_OVar @ SV377 ) )
= $false )
| ( ( SV162 = SV377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1544,plain,
! [SV558: $i,SV378: $i,SV163: $i] :
( ( ( SV163
!= ( c_List_Oappend @ SV378 @ SV163 @ SV558 ) )
= $true )
| ( ( SV378
= ( c_List_Olist_ONil @ SV558 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1545,plain,
! [SV692: $i,SV559: $i,SV379: $i,SV164: $i] :
( ( ! [SY1956: $i] :
( ( ( c_List_Oappend @ SV164 @ ( c_List_Olist_OCons @ SV379 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 )
!= ( c_List_Oappend @ SV692 @ ( c_List_Olist_OCons @ SY1956 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 ) )
| ( SV164 = SV692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1546,plain,
! [SV560: $i,SV380: $i,SV165: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV165 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV380 @ SV560 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV560
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1547,plain,
! [SV561: $i,SV381: $i,SV166: $i] :
( ( ( ( c_List_Orev @ SV166 @ SV381 )
!= ( c_List_Olist_OCons @ SV561 @ ( c_List_Olist_ONil @ SV381 ) @ SV381 ) )
= $true )
| ( ( SV166
= ( c_List_Olist_OCons @ SV561 @ ( c_List_Olist_ONil @ SV381 ) @ SV381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1548,plain,
! [SV693: $i,SV562: $i,SV382: $i,SV167: $i] :
( ( ( ( c_List_Oappend @ SV167 @ SV382 @ SV562 )
!= ( c_List_Oappend @ SV167 @ SV693 @ SV562 ) )
| ( SV382 = SV693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1549,plain,
! [SV383: $i,SV168: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV168 )
= ( c_Lambda_OdB_OAbs @ SV383 ) )
= $false )
| ( ( SV168 = SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1550,plain,
! [SV694: $i,SV563: $i,SV384: $i,SV169: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV169 ) ) @ SV384 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV563 ) @ SV694 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1551,plain,
! [SV564: $i,SV385: $i,SV170: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV170 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV385 @ SV564 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV170 )
= SV385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1552,plain,
! [SV386: $i,SV171: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV171 )
= ( c_Type_Otype_OAtom @ SV386 ) )
= $false )
| ( ( SV171 = SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1553,plain,
! [SV565: $i,SV387: $i,SV172: $i] :
( ( ( ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SV387 ) @ SV387 )
!= ( c_List_Orev @ SV565 @ SV387 ) )
= $true )
| ( ( SV565
= ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SV387 ) @ SV387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1554,plain,
! [SV695: $i,SV566: $i,SV388: $i,SV173: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SV388 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV566 ) @ SV695 ) )
| ( SV173 = SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1555,plain,
! [SV567: $i,SV389: $i,SV174: $i] :
( ( ( c_Type_Otype_OAtom @ SV174 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV389 ) @ SV567 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1556,plain,
! [SV696: $i,SV568: $i,SV390: $i,SV175: $i] :
( ( ! [SY1957: $i] :
( ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
!= ( c_List_Oappend @ SV696 @ SY1957 @ SV568 ) )
| ( ( c_List_Olist_OCons @ SV175 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV175 @ SV390 @ SV696 @ SY1957 @ SV568 ) @ SV568 )
= SV696 )
| ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
= SY1957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1557,plain,
! [SV697: $i,SV569: $i,SV392: $i,SV177: $i] :
( ( ! [SY1958: $i,SY1959: $i,SY1960: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SY1958 ) ) )
| ~ ( c_Type_Otyping @ SY1959 @ SV697 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1959 @ SY1958 @ SV177 @ tc_Type_Otype ) @ SV569 @ SY1960 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1558,plain,
! [SV698: $i,SV570: $i,SV393: $i,SV178: $i] :
( ( ! [SY1961: $i] :
( ( ( c_List_Oappend @ SV178 @ SV393 @ SV570 )
!= ( c_List_Olist_OCons @ SV698 @ SY1961 @ SV570 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV698 @ SY1961 @ SV178 @ SV393 @ SV570 ) @ SV393 @ SV570 )
= SY1961 )
| ( SV393
= ( c_List_Olist_OCons @ SV698 @ SY1961 @ SV570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1559,plain,
! [SV699: $i,SV571: $i,SV394: $i,SV179: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV179 ) @ SV394 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV571 ) @ SV699 ) )
| ( SV179 = SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1560,plain,
! [SV700: $i,SV572: $i,SV395: $i,SV180: $i] :
( ( ( ( c_List_Oappend @ SV180 @ SV395 @ SV572 )
!= ( c_List_Oappend @ SV700 @ SV395 @ SV572 ) )
| ( SV180 = SV700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1561,plain,
! [SV573: $i,SV396: $i,SV181: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV181 @ SV396 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV573 @ SV396 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV181 = SV573 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1562,plain,
! [SV701: $i,SV574: $i,SV397: $i,SV182: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV397 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV574 ) @ SV701 ) )
| ( SV397 = SV701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1563,plain,
! [SV575: $i,SV398: $i,SV183: $i] :
( ( ( SV183
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 ) @ SV575 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 ) @ ( c_List_Oappend @ SV575 @ ( c_List_Olist_OCons @ SV398 @ ( 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)],[1398]) ).
thf(1564,plain,
! [SV576: $i,SV399: $i,SV184: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV184 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV399 @ SV576 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV576
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1565,plain,
! [SV577: $i,SV400: $i,SV185: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV185 ) @ SV400 )
= ( c_Type_Otype_OAtom @ SV577 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1566,plain,
! [SV578: $i,SV401: $i,SV186: $i] :
( ( ( ( c_List_Oappend @ SV186 @ SV401 @ SV578 )
!= SV401 )
= $true )
| ( ( SV186
= ( c_List_Olist_ONil @ SV578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1567,plain,
! [SV702: $i,SV579: $i,SV402: $i,SV187: $i] :
( ( ! [SY1962: $i] :
( ( ( c_List_OdropWhile @ SV187 @ SV402 @ SV579 )
!= ( c_List_Olist_OCons @ SV702 @ SY1962 @ SV579 ) )
| ( SV402
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV187 @ SV402 @ SV579 ) @ ( c_List_Olist_OCons @ SV702 @ SY1962 @ SV579 ) @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1568,plain,
! [SV580: $i,SV403: $i,SV188: $i] :
( ( ( c_List_Olist_ONil @ SV188 )
= ( c_List_Olist_OCons @ SV403 @ SV580 @ SV188 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1569,plain,
! [SV703: $i,SV581: $i,SV404: $i,SV189: $i] :
( ( ! [SY1963: $i] :
( ( ( c_List_Olist_OCons @ SV189 @ SV404 @ SV581 )
!= ( c_List_Olist_OCons @ SV703 @ SY1963 @ SV581 ) )
| ( SV404 = SY1963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1570,plain,
! [SV582: $i,SV405: $i,SV190: $i] :
( ( ( ( c_List_Oreplicate @ SV190 @ SV405 @ SV582 )
!= ( c_List_Olist_ONil @ SV582 ) )
= $true )
| ( ( SV190
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1571,plain,
! [SV704: $i,SV583: $i,SV406: $i,SV191: $i] :
( ( ! [SY1964: $i,SY1965: $i,SY1966: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SY1964 ) ) )
| ~ ( c_Type_Otyping @ SY1965 @ SV704 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1965 @ SY1964 @ SV406 @ tc_Type_Otype ) @ SV583 @ SY1966 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1572,plain,
! [SV584: $i,SV407: $i,SV192: $i] :
( ( ( ( c_List_Olist_ONil @ SV192 )
!= ( c_List_Oreplicate @ SV407 @ SV584 @ SV192 ) )
= $true )
| ( ( SV407
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1573,plain,
! [SV705: $i,SV585: $i,SV408: $i,SV193: $i] :
( ( ! [SY1967: $i] :
( ( ( c_List_Oreplicate @ SV193 @ SV408 @ SV585 )
!= ( c_List_Oreplicate @ SV705 @ SY1967 @ SV585 ) )
| ( SV193 = SV705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1574,plain,
! [SV706: $i,SV586: $i,SV409: $i,SV194: $i] :
( ( ! [SY1968: $i] :
( ( ( c_List_Oreplicate @ SV194 @ SV409 @ SV586 )
!= ( c_List_Oreplicate @ SV706 @ SY1968 @ SV586 ) )
| ( SV409 = SY1968 )
| ( SV194
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1575,plain,
! [SV707: $i,SV587: $i,SV410: $i,SV195: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV195 ) @ SV410 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV587 ) @ SV707 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV410 = SV707 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1576,plain,
! [SV588: $i,SV411: $i,SV196: $i] :
( ( ( c_List_Olist_OCons @ SV196 @ SV411 @ SV588 )
= SV411 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1577,plain,
! [SV708: $i,SV589: $i,SV412: $i,SV197: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV197 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV412 ) @ SV589 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SV708 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SV589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1578,plain,
! [SV590: $i,SV413: $i,SV198: $i] :
( ( ( ( c_List_Olist_ONil @ SV198 )
!= ( c_List_Oappend @ SV413 @ SV590 @ SV198 ) )
= $true )
| ( ( SV590
= ( c_List_Olist_ONil @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1579,plain,
! [SV414: $i,SV199: $i] :
( ( ( ( c_List_Orotate1 @ SV199 @ SV414 )
= ( c_List_Olist_ONil @ SV414 ) )
= $false )
| ( ( SV199
= ( c_List_Olist_ONil @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1580,plain,
! [SV591: $i,SV415: $i,SV200: $i] :
( ( ( ( c_List_Oappend @ SV200 @ SV415 @ SV591 )
!= SV200 )
= $true )
| ( ( SV415
= ( c_List_Olist_ONil @ SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1581,plain,
! [SV592: $i,SV416: $i,SV201: $i] :
( ( ( SV201
!= ( c_List_Oappend @ SV201 @ SV416 @ SV592 ) )
= $true )
| ( ( SV416
= ( c_List_Olist_ONil @ SV592 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1582,plain,
! [SV709: $i,SV593: $i,SV417: $i,SV202: $i] :
( ( ! [SY1969: $i] :
( ( ( c_List_Oappend @ SV202 @ SV417 @ SV593 )
!= ( c_List_Olist_OCons @ SV709 @ SY1969 @ SV593 ) )
| ( SV202
= ( c_List_Olist_OCons @ SV709 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV709 @ SY1969 @ SV202 @ SV417 @ SV593 ) @ SV593 ) )
| ( SV417
= ( c_List_Olist_OCons @ SV709 @ SY1969 @ SV593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1583,plain,
! [SV710: $i,SV594: $i,SV418: $i,SV203: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV203 ) @ SV418 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV594 ) @ SV710 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1584,plain,
! [SV595: $i,SV419: $i,SV204: $i] :
( ( ( ( c_List_Oappend @ SV204 @ SV419 @ SV595 )
!= ( c_List_Olist_ONil @ SV595 ) )
= $true )
| ( ( SV204
= ( c_List_Olist_ONil @ SV595 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1585,plain,
! [SV711: $i,SV596: $i,SV420: $i,SV205: $i] :
( ( ! [SY1970: $i] :
( ( ( c_List_Olist_OCons @ SV205 @ SV420 @ SV596 )
!= ( c_List_Oappend @ SV711 @ SY1970 @ SV596 ) )
| ( SV420
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV205 @ SV420 @ SV711 @ SY1970 @ SV596 ) @ SY1970 @ SV596 ) )
| ( SV711
= ( c_List_Olist_ONil @ SV596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1586,plain,
! [SV712: $i,SV597: $i,SV421: $i,SV206: $i] :
( ( ! [SY1971: $i] :
( ( ( c_List_Olist_OCons @ SV206 @ SV421 @ SV597 )
!= ( c_List_Olist_OCons @ SV712 @ SY1971 @ SV597 ) )
| ( SV206 = SV712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1587,plain,
! [SV713: $i,SV598: $i,SV422: $i,SV207: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV207 ) @ SV422 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV598 ) @ SV713 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV207 = SV598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1588,plain,
! [SV714: $i,SV599: $i,SV423: $i,SV208: $i] :
( ( ! [SY1972: $i] :
( ( ( c_List_Oappend @ SV208 @ ( c_List_Olist_OCons @ SV423 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 )
!= ( c_List_Oappend @ SV714 @ ( c_List_Olist_OCons @ SY1972 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 ) )
| ( SV423 = SY1972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1589,plain,
! [SV715: $i,SV600: $i,SV425: $i,SV210: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV210 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV425 ) @ SV600 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SV715 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1590,plain,
! [SV601: $i,SV426: $i,SV211: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV211 @ SV426 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV601 ) )
= $true )
| ( ( SV426
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1591,plain,
! [SV602: $i,SV427: $i,SV212: $i] :
( ( ( c_Lambda_OdB_OVar @ SV212 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV427 ) @ SV602 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1592,plain,
! [SV603: $i,SV428: $i,SV213: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV428 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV603 ) )
= $true )
| ( ( SV213
= ( c_Lambda_OdB_OAbs @ SV603 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1593,plain,
! [SV716: $i,SV604: $i,SV429: $i,SV214: $i] :
( ( ! [SY1973: $i] :
( ( ( c_List_OdropWhile @ SV214 @ SV429 @ SV604 )
!= ( c_List_Olist_OCons @ SV716 @ SY1973 @ SV604 ) )
| ~ ( hBOOL @ ( hAPP @ SV214 @ SV716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1594,plain,
! [SV717: $i,SV605: $i,SV430: $i,SV215: $i] :
( ( ! [SY1974: $i] :
( ( ( c_List_Oappend @ SV215 @ SV430 @ SV605 )
!= ( c_List_Olist_OCons @ SV717 @ SY1974 @ SV605 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV717 @ SY1974 @ SV215 @ SV430 @ SV605 ) @ SV430 @ SV605 )
= SY1974 )
| ( SV215
= ( c_List_Olist_ONil @ SV605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1595,plain,
! [SV718: $i,SV606: $i,SV431: $i,SV216: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV216 ) @ SV431 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV606 ) @ SV718 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV216 = SV606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1596,plain,
! [SV607: $i,SV432: $i,SV217: $i] :
( ( ( c_List_Olist_OCons @ SV217 @ SV432 @ SV607 )
= ( c_List_Olist_ONil @ SV607 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1597,plain,
! [SV608: $i,SV433: $i,SV218: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV218 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV433 ) @ SV608 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1598,plain,
! [SV609: $i,SV434: $i,SV219: $i] :
( ( ( ( c_List_Orev @ SV219 @ SV434 )
!= ( c_List_Orev @ SV609 @ SV434 ) )
= $true )
| ( ( SV219 = SV609 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1599,plain,
! [SV610: $i,SV435: $i,SV220: $i] :
( ( ( ( c_List_Oappend @ SV220 @ SV435 @ SV610 )
!= ( c_List_Olist_ONil @ SV610 ) )
= $true )
| ( ( SV435
= ( c_List_Olist_ONil @ SV610 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1600,plain,
! [SV436: $i,SV221: $i] :
( ( ( ( c_List_Orev @ SV221 @ SV436 )
= ( c_List_Olist_ONil @ SV436 ) )
= $false )
| ( ( SV221
= ( c_List_Olist_ONil @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1601,plain,
! [SV719: $i,SV611: $i,SV437: $i,SV222: $i] :
( ( ! [SY1975: $i] :
( ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
!= ( c_List_Oappend @ SV719 @ SY1975 @ SV611 ) )
| ( SV437
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV222 @ SV437 @ SV719 @ SY1975 @ SV611 ) @ SY1975 @ SV611 ) )
| ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
= SY1975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1602,plain,
! [SV612: $i,SV438: $i,SV223: $i] :
( ( ( ( c_List_Olist_ONil @ SV223 )
!= ( c_List_Oappend @ SV438 @ SV612 @ SV223 ) )
= $true )
| ( ( SV438
= ( c_List_Olist_ONil @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1603,plain,
! [SV613: $i,SV439: $i,SV224: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV224 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV439 @ SV613 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV224 )
= SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1604,plain,
! [SV614: $i,SV440: $i,SV225: $i] :
( ( ( c_List_Olist_OCons @ SV225 @ SV440 @ SV614 )
= ( c_List_Olist_ONil @ SV614 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1605,plain,
! [SV441: $i,SV226: $i] :
( ( ( ( c_List_Olist_ONil @ SV226 )
= ( c_List_Orev @ SV441 @ SV226 ) )
= $false )
| ( ( SV441
= ( c_List_Olist_ONil @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1606,plain,
! [SV720: $i,SV615: $i,SV442: $i,SV227: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV227 ) @ SV442 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV615 ) @ SV720 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV442 = SV720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1607,plain,
! [SV616: $i,SV444: $i,SV230: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ SV230 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV444 @ SV3 @ SV230 @ SV616 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SV616 @ ( c_List_Olist_OCons @ SV230 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1608,plain,
! [SV447: $i,SV234: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV9 @ SV234 @ SV447 ) @ SV447 ) ) )
= $false )
| ( ( ( c_List_OdropWhile @ SV9 @ SV234 @ SV447 )
= ( c_List_Olist_ONil @ SV447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1609,plain,
! [SV721: $i,SV617: $i,SV448: $i,SV235: $i,SV11: $i] :
( ( ! [SY1976: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV11 @ SV235 @ SV448 @ SV617 ) @ SV721 ) @ SY1976 )
= ( hAPP @ ( hAPP @ SV11 @ SY1976 ) @ SV721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1610,plain,
! [SV618: $i,SV449: $i,SV236: $i,SV12: $i] :
( ( ( c_List_Olistsp @ SV12 @ SV236 @ SV449 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV12 @ ( c_List_Oappend @ SV236 @ SV618 @ SV449 ) @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1611,plain,
! [SV619: $i,SV450: $i,SV237: $i,SV13: $i] :
( ( ( c_List_Olistsp @ SV13 @ SV237 @ SV450 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV13 @ ( c_List_Oappend @ SV619 @ SV237 @ SV450 ) @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1612,plain,
! [SV451: $i,SV16: $i,SV240: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV16 @ SV240 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV451 @ 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 @ SV16 ) ) @ SV240 ) @ SV451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1613,plain,
! [SV722: $i,SV620: $i,SV452: $i,SV241: $i,SV17: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV17 @ SV241 @ SV452 ) @ ( c_List_Olist_OCons @ SV620 @ SV722 @ SV452 ) @ SV452 )
= ( c_List_Olist_OCons @ SV17 @ ( c_List_Olist_OCons @ SV620 @ ( c_List_Osplice @ SV241 @ SV722 @ SV452 ) @ SV452 ) @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1614,plain,
! [SV621: $i,SV453: $i,SV242: $i,SV18: $i] :
( ( ( ( c_List_OdropWhile @ SV18 @ ( c_List_Olist_OCons @ SV242 @ SV453 @ SV621 ) @ SV621 )
= ( c_List_OdropWhile @ SV18 @ SV453 @ SV621 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ SV242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1452]) ).
thf(1615,plain,
! [SV622: $i,SV454: $i,SV243: $i,SV19: $i] :
( ( ( ( c_List_OdropWhile @ SV19 @ ( c_List_Olist_OCons @ SV243 @ SV454 @ SV622 ) @ SV622 )
= ( c_List_Olist_OCons @ SV243 @ SV454 @ SV622 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV19 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1616,plain,
! [SV623: $i,SV456: $i,SV245: $i,SV21: $i] :
( ( ( c_List_Olistsp @ SV21 @ ( c_List_Oappend @ SV245 @ SV456 @ SV623 ) @ SV623 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV21 @ SV456 @ SV623 )
| ~ ( c_List_Olistsp @ SV21 @ SV245 @ SV623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1617,plain,
! [SV624: $i,SV459: $i,SV251: $i,SV27: $i] :
( ( ( c_Type_Otyping @ SV27 @ ( c_Lambda_OdB_OAbs @ SV251 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV459 ) @ SV624 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV27 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV459 @ tc_Type_Otype ) @ SV251 @ SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1618,plain,
! [SV625: $i,SV462: $i,SV256: $i,SV32: $i] :
( ( ( ( c_List_OtakeWhile @ SV32 @ ( c_List_Olist_OCons @ SV256 @ SV462 @ SV625 ) @ SV625 )
= ( c_List_Olist_ONil @ SV625 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV32 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1619,plain,
! [SV723: $i,SV626: $i,SV464: $i,SV260: $i,SV36: $i] :
( ( ! [SY1977: $i,SY1978: $i] :
( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SY1977 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
| ~ ( c_Type_Otypings @ SV464 @ SY1977 @ SY1978 )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SY1977 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1620,plain,
! [SV628: $i,SV467: $i,SV264: $i,SV41: $i] :
( ( ( c_Type_Otypings @ SV41 @ SV264 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV467 @ SV41 @ SV628 @ SV264 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV628 ) @ SV264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1621,plain,
! [SV724: $i,SV629: $i,SV468: $i,SV265: $i,SV43: $i] :
( ( ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_OCons @ SV265 @ SV468 @ SV629 ) @ ( c_List_Olist_OCons @ SV265 @ SV724 @ SV629 ) @ SV629 )
| ~ ( c_ListOrder_Ostep1 @ SV43 @ SV468 @ SV724 @ SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1622,plain,
! [SV725: $i,SV630: $i,SV469: $i,SV266: $i,SV44: $i] :
( ( ! [SY1979: $i] :
( ( c_ListOrder_Ostep1 @ SV44 @ SV266 @ SV469 @ SV630 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SV725 ) @ SY1979 ) )
| ~ ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SV725 @ SV266 @ SV630 ) @ ( c_List_Olist_OCons @ SY1979 @ SV469 @ SV630 ) @ SV630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1623,plain,
! [SV470: $i,SV269: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV48 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV48 @ ( c_Lambda_OdB_OVar @ SV269 ) @ SV470 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1624,plain,
! [SV631: $i,SV471: $i,SV270: $i,SV49: $i] :
( ( ( c_Type_Otypings @ SV49 @ SV270 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV471 @ SV49 @ SV631 @ SV270 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV49 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV631 @ SV270 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV471 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1625,plain,
! [SV726: $i,SV632: $i,SV472: $i,SV271: $i,SV50: $i] :
( ( ( c_List_Ofoldr @ SV50 @ SV271 @ SV472 @ SV632 @ SV726 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV50 @ SV632 @ SV726 @ SV726 ) @ SV472 @ ( c_List_Orev @ SV271 @ SV632 ) @ SV726 @ SV632 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1626,plain,
! [SV727: $i,SV634: $i,SV476: $i,SV276: $i,SV55: $i] :
( ( ! [SY1980: $i] :
( ( c_ListOrder_Ostep1 @ SV55 @ SV276 @ SV476 @ SV634 )
| ( SV476 = SV276 )
| ~ ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SV727 @ SV276 @ SV634 ) @ ( c_List_Olist_OCons @ SY1980 @ SV476 @ SV634 ) @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1627,plain,
! [SV635: $i,SV477: $i,SV277: $i,SV56: $i] :
( ( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV56 @ SV277 @ SV477 ) @ SV635 @ SV477 )
= ( c_List_Olist_OCons @ SV56 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV635 @ SV477 ) @ ( c_List_Osplice @ SV277 @ ( c_List_Otl @ SV635 @ SV477 ) @ SV477 ) @ SV477 ) @ SV477 ) )
= $true )
| ( ( SV635
= ( c_List_Olist_ONil @ SV477 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1628,plain,
! [SV728: $i,SV637: $i,SV483: $i,SV288: $i,SV68: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV288 ) @ SV483 ) )
| ( c_ListOrder_Ostep1 @ SV68 @ ( c_List_Olist_OCons @ SV288 @ SV637 @ SV728 ) @ ( c_List_Olist_OCons @ SV483 @ SV637 @ SV728 ) @ SV728 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1629,plain,
! [SV729: $i,SV638: $i,SV484: $i,SV289: $i,SV69: $i] :
( ( ! [SY1981: $i] :
( ( SV69 = SV289 )
| ( SV484 = SV638 )
| ~ ( c_ListOrder_Ostep1 @ SV729 @ ( c_List_Olist_OCons @ SV289 @ SV638 @ SY1981 ) @ ( c_List_Olist_OCons @ SV69 @ SV484 @ SY1981 ) @ SY1981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1630,plain,
! [SV730: $i,SV639: $i,SV485: $i,SV291: $i,SV72: $i] :
( ( ( c_ListOrder_Ostep1 @ SV72 @ ( c_List_Oappend @ SV291 @ SV485 @ SV639 ) @ ( c_List_Oappend @ SV291 @ SV730 @ SV639 ) @ SV639 )
| ~ ( c_ListOrder_Ostep1 @ SV72 @ SV485 @ SV730 @ SV639 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1631,plain,
! [SV731: $i,SV640: $i,SV486: $i,SV292: $i,SV73: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV73 @ SV292 @ SV486 @ SV640 )
| ( c_ListOrder_Ostep1 @ SV73 @ ( c_List_Oappend @ SV292 @ SV731 @ SV640 ) @ ( c_List_Oappend @ SV486 @ SV731 @ SV640 ) @ SV640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1632,plain,
! [SV641: $i,SV487: $i,SV293: $i,SV75: $i] :
( ( ( c_Type_Otypings @ SV75 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV487 @ SV75 @ SV641 @ SV293 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV75 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV641 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1633,plain,
! [SV732: $i,SV642: $i,SV488: $i,SV294: $i,SV76: $i] :
( ( ! [SY1982: $i] :
( ( c_List_Ofoldl @ SV76 @ SV294 @ ( c_List_Olist_OCons @ SV488 @ SV642 @ SV732 ) @ SY1982 @ SV732 )
= ( c_List_Ofoldl @ SV76 @ ( hAPP @ ( hAPP @ SV76 @ SV294 ) @ SV488 ) @ SV642 @ SY1982 @ SV732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1634,plain,
! [SV733: $i,SV643: $i,SV489: $i,SV296: $i,SV78: $i] :
( ( ! [SY1983: $i] :
( ( SV78 = SV296 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV489 @ SV296 ) @ SV78 ) )
| ~ ( c_ListOrder_Ostep1 @ SV489 @ ( c_List_Olist_OCons @ SV296 @ SV643 @ SV733 ) @ ( c_List_Olist_OCons @ SV78 @ SY1983 @ SV733 ) @ SV733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1635,plain,
! [SV734: $i,SV644: $i,SV490: $i,SV297: $i,SV79: $i] :
( ( ! [SY1984: $i,SY1985: $i] :
( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SY1984 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
| ~ ( c_Type_Otypings @ SV79 @ SY1984 @ SY1985 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SY1984 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1636,plain,
! [SV645: $i,SV491: $i,SV298: $i,SV80: $i] :
( ( ( ( c_List_OtakeWhile @ SV80 @ ( c_List_Olist_OCons @ SV298 @ SV491 @ SV645 ) @ SV645 )
= ( c_List_Olist_OCons @ SV298 @ ( c_List_OtakeWhile @ SV80 @ SV491 @ SV645 ) @ SV645 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV80 @ SV298 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1637,plain,
! [SV735: $i,SV646: $i,SV493: $i,SV300: $i,SV82: $i] :
( ( ( c_List_Ofoldl @ SV82 @ SV300 @ SV493 @ SV646 @ SV735 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV82 @ SV646 @ SV735 @ SV646 ) @ ( c_List_Orev @ SV493 @ SV735 ) @ SV300 @ SV735 @ SV646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1638,plain,
! [SV736: $i,SV647: $i,SV495: $i,SV302: $i,SV85: $i] :
( ( ! [SY1986: $i] :
( ( c_List_Ofoldl @ SV85 @ SV302 @ ( c_List_Oappend @ SV495 @ SV647 @ SV736 ) @ SY1986 @ SV736 )
= ( c_List_Ofoldl @ SV85 @ ( c_List_Ofoldl @ SV85 @ SV302 @ SV495 @ SY1986 @ SV736 ) @ SV647 @ SY1986 @ SV736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1639,plain,
! [SV737: $i,SV648: $i,SV496: $i,SV303: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV496 @ SV648 @ SV737 ) @ SV737 ) @ SV737 ) ) )
| ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ SV648 @ SV737 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV86 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1640,plain,
! [SV738: $i,SV649: $i,SV497: $i,SV304: $i,SV87: $i] :
( ( ( c_List_Oconcat__map @ SV87 @ ( c_List_Olist_OCons @ SV304 @ SV497 @ SV649 ) @ SV649 @ SV738 )
= ( c_List_Oappend @ ( hAPP @ SV87 @ SV304 ) @ ( c_List_Oconcat__map @ SV87 @ SV497 @ SV649 @ SV738 ) @ SV738 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1641,plain,
! [SV739: $i,SV650: $i,SV498: $i,SV305: $i,SV88: $i] :
( ( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ ( c_List_Oappend @ SV305 @ ( c_List_Olist_OCons @ SV498 @ SV650 @ SV739 ) @ SV739 ) @ SV739 ) ) )
| ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ SV305 @ SV739 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV88 @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1642,plain,
! [SV740: $i,SV651: $i,SV499: $i,SV306: $i,SV89: $i] :
( ( ( ( c_List_OtakeWhile @ SV89 @ ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV499 @ SV651 @ SV740 ) @ SV740 ) @ SV740 )
= ( c_List_OtakeWhile @ SV89 @ SV306 @ SV740 ) )
| ( hBOOL @ ( hAPP @ SV89 @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1643,plain,
! [SV653: $i,SV505: $i,SV316: $i,SV99: $i] :
( ( ( c_Type_Otyping @ SV99 @ SV316 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV505 @ SV99 @ SV653 @ SV316 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV99 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV653 ) @ SV316 ) @ SV505 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1644,plain,
! [SV654: $i,SV506: $i,SV317: $i,SV100: $i] :
( ( ( c_Type_Otyping @ SV100 @ SV317 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV506 @ SV100 @ SV317 @ SV654 ) @ SV506 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV317 @ SV654 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1645,plain,
! [SV741: $i,SV655: $i,SV507: $i,SV318: $i,SV101: $i] :
( ( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV318 @ SV507 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV655 )
| ~ ( c_Type_Otypings @ SV101 @ SV507 @ SV741 )
| ~ ( c_Type_Otyping @ SV101 @ SV318 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV741 @ SV655 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1646,plain,
! [SV656: $i,SV508: $i,SV319: $i,SV102: $i] :
( ( ( c_Type_Otyping @ SV102 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV508 @ SV102 @ SV319 @ SV656 ) @ SV508 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV102 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV508 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1647,plain,
! [SV742: $i,SV657: $i,SV509: $i,SV320: $i,SV103: $i] :
( ( ! [SY1987: $i] :
( ~ ( c_Type_Otyping @ SV103 @ SV320 @ SV509 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SV657 @ SV509 @ tc_Type_Otype ) @ SV742 @ SY1987 )
| ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SV742 @ SV320 @ SV657 ) @ SY1987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1648,plain,
! [SV743: $i,SV658: $i,SV510: $i,SV321: $i,SV104: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV104 @ SV321 @ SV510 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV658 @ SV321 ) @ SV743 )
| ~ ( c_Type_Otyping @ SV104 @ SV658 @ SV743 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1649,plain,
! [SV659: $i,SV511: $i,SV322: $i,SV105: $i] :
( ( ( c_Type_Otyping @ SV105 @ ( c_Lambda_OdB_OVar @ SV322 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV511 @ SV105 @ SV322 @ SV659 ) @ SV511 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV105 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV322 ) @ SV659 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1650,plain,
! [SV744: $i,SV660: $i,SV513: $i,SV324: $i,SV107: $i] :
( ( ! [SY1988: $i] :
( ( SV107 = SV324 )
| ( c_ListOrder_Ostep1 @ SV513 @ SV107 @ SV324 @ SV660 )
| ~ ( c_ListOrder_Ostep1 @ SV513 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ ( c_List_Oappend @ SV324 @ ( c_List_Olist_OCons @ SY1988 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ SV660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1651,plain,
! [SV745: $i,SV661: $i,SV516: $i,SV327: $i,SV110: $i] :
( ( ! [SY1989: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV327 ) @ SV516 ) )
| ( c_ListOrder_Ostep1 @ SV110 @ SV661 @ SV745 @ SY1989 )
| ~ ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SV661 @ ( c_List_Olist_OCons @ SV327 @ ( c_List_Olist_ONil @ SY1989 ) @ SY1989 ) @ SY1989 ) @ ( c_List_Oappend @ SV745 @ ( c_List_Olist_OCons @ SV516 @ ( c_List_Olist_ONil @ SY1989 ) @ SY1989 ) @ SY1989 ) @ SY1989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1652,plain,
! [SV746: $i,SV662: $i,SV518: $i,SV329: $i,SV112: $i] :
( ( ! [SY1990: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SV329 ) @ SV518 ) )
| ( SV329 = SV518 )
| ~ ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SV662 @ ( c_List_Olist_OCons @ SV329 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ ( c_List_Oappend @ SY1990 @ ( c_List_Olist_OCons @ SV518 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ SV746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1653,plain,
! [SV747: $i,SV663: $i,SV519: $i,SV330: $i,SV113: $i] :
( ( ! [SY1991: $i] :
( ( SV113 = SV330 )
| ( SV519 = SV663 )
| ~ ( c_ListOrder_Ostep1 @ SV747 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SV519 @ ( c_List_Olist_ONil @ SY1991 ) @ SY1991 ) @ SY1991 ) @ ( c_List_Oappend @ SV330 @ ( c_List_Olist_OCons @ SV663 @ ( c_List_Olist_ONil @ SY1991 ) @ SY1991 ) @ SY1991 ) @ SY1991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1654,plain,
! [SV748: $i,SV664: $i,SV522: $i,SV333: $i,SV116: $i] :
( ( ( SV116 = SV333 )
| ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV333 )
| ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1655,plain,
! [SV665: $i,SV523: $i,SV334: $i,SV117: $i] :
( ( ( c_Type_Otyping @ SV117 @ SV334 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV523 @ SV117 @ SV334 @ SV665 ) ) @ SV523 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV117 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SV665 ) @ SV523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1656,plain,
! [SV667: $i,SV526: $i,SV337: $i,SV121: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV121 @ ( c_Type_Otype_Otype__case @ SV337 @ SV526 @ ( c_Type_Otype_OAtom @ SV667 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV121 @ ( hAPP @ SV337 @ SV667 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1657,plain,
! [SV668: $i,SV527: $i,SV338: $i,SV122: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV122 @ ( c_Type_Otype_Otype__case @ SV338 @ SV527 @ ( c_Type_Otype_OAtom @ SV668 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV122 @ ( hAPP @ SV338 @ SV668 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1658,plain,
! [SV532: $i,SV350: $i,SV134: $i] :
( ( ( c_Type_Otyping @ SV134 @ ( c_Lambda_OdB_OVar @ SV350 ) @ SV532 )
= $false )
| ( ( ( hAPP @ SV134 @ SV350 )
= SV532 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1659,plain,
! [SV749: $i,SV675: $i,SV535: $i,SV353: $i,SV137: $i] :
( ( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV535 ) @ SV675 )
| ~ ( c_Type_Otyping @ SV137 @ SV535 @ SV749 )
| ~ ( c_Type_Otyping @ SV137 @ SV353 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV749 ) @ SV675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1660,plain,
! [SV750: $i,SV680: $i,SV541: $i,SV359: $i,SV144: $i] :
( ( ! [SY1992: $i] :
( ( c_List_Ofoldr @ SV144 @ ( c_List_Olist_OCons @ SV359 @ SV541 @ SV680 ) @ SV750 @ SV680 @ SY1992 )
= ( hAPP @ ( hAPP @ SV144 @ SV359 ) @ ( c_List_Ofoldr @ SV144 @ SV541 @ SV750 @ SV680 @ SY1992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1661,plain,
! [SV751: $i,SV681: $i,SV542: $i,SV360: $i,SV145: $i] :
( ( ! [SY1993: $i] :
( ( c_List_Ofoldr @ SV145 @ ( c_List_Oappend @ SV360 @ SV542 @ SV681 ) @ SV751 @ SV681 @ SY1993 )
= ( c_List_Ofoldr @ SV145 @ SV360 @ ( c_List_Ofoldr @ SV145 @ SV542 @ SV751 @ SV681 @ SY1993 ) @ SV681 @ SY1993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1662,plain,
! [SV752: $i,SV683: $i,SV544: $i,SV362: $i,SV147: $i] :
( ( ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV544 ) @ SV683 ) @ SV752 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV362 @ SV544 ) @ SV683 ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ SV544 @ SV752 ) ) @ ( c_Type_Otype_Otype__rec @ SV147 @ SV362 @ SV683 @ SV752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1663,plain,
! [SV753: $i,SV684: $i,SV545: $i,SV363: $i,SV148: $i] :
( ( ( c_Type_Otype_Otype__case @ SV148 @ SV363 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV545 ) @ SV684 ) @ SV753 )
= ( hAPP @ ( hAPP @ SV363 @ SV545 ) @ SV684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1664,plain,
! [SV754: $i,SV685: $i,SV546: $i,SV364: $i,SV149: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV149 @ ( c_Type_Otype_Otype__case @ SV364 @ SV546 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV685 ) @ SV754 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV149 @ ( hAPP @ ( hAPP @ SV546 @ SV685 ) @ SV754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1665,plain,
! [SV755: $i,SV686: $i,SV547: $i,SV365: $i,SV150: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( c_Type_Otype_Otype__case @ SV365 @ SV547 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV686 ) @ SV755 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV150 @ ( hAPP @ ( hAPP @ SV547 @ SV686 ) @ SV755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1666,plain,
! [SV548: $i,SV367: $i,SV152: $i] :
( ( ( c_fequal @ SV152 @ SV367 @ SV548 )
= $false )
| ( ( SV152 = SV367 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1667,plain,
! [SV687: $i,SV549: $i,SV368: $i,SV153: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV153 ) @ SV368 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV549 ) @ SV687 ) )
= $true )
| ( ( SV368 = SV687 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1668,plain,
! [SV688: $i,SV550: $i,SV369: $i,SV154: $i] :
( ( ( ( c_List_Orev @ SV154 @ SV369 )
!= ( c_List_Olist_OCons @ SV550 @ SV688 @ SV369 ) )
= $true )
| ( ( SV154
= ( c_List_Oappend @ ( c_List_Orev @ SV688 @ SV369 ) @ ( c_List_Olist_OCons @ SV550 @ ( c_List_Olist_ONil @ SV369 ) @ SV369 ) @ SV369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1669,plain,
! [SV756: $i,SV689: $i,SV551: $i,SV370: $i,SV155: $i] :
( ( ( ( c_List_Oappend @ SV155 @ SV370 @ SV551 )
!= ( c_List_Olist_OCons @ SV689 @ SV756 @ SV551 ) )
| ( SV155
= ( c_List_Olist_OCons @ SV689 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV689 @ SV756 @ SV155 @ SV370 @ SV551 ) @ SV551 ) )
| ( SV155
= ( c_List_Olist_ONil @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1670,plain,
! [SV552: $i,SV371: $i,SV156: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SV371 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV552 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV156 ) @ SV371 )
= SV552 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1671,plain,
! [SV757: $i,SV690: $i,SV556: $i,SV375: $i,SV160: $i] :
( ( ( ( c_List_Olist_OCons @ SV160 @ SV375 @ SV556 )
!= ( c_List_Oappend @ SV690 @ SV757 @ SV556 ) )
| ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV375 @ SV690 @ SV757 @ SV556 ) @ SV556 )
= SV690 )
| ( SV690
= ( c_List_Olist_ONil @ SV556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1672,plain,
! [SV758: $i,SV691: $i,SV557: $i,SV376: $i,SV161: $i] :
( ( ( SV161
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV376 @ SV161 @ SV557 ) @ ( c_List_Olist_OCons @ SV691 @ SV758 @ SV557 ) @ SV557 ) )
| ( ( c_List_OdropWhile @ SV376 @ SV161 @ SV557 )
= ( c_List_Olist_OCons @ SV691 @ SV758 @ SV557 ) )
| ( hBOOL @ ( hAPP @ SV376 @ SV691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1673,plain,
! [SV558: $i,SV378: $i,SV163: $i] :
( ( ( SV163
= ( c_List_Oappend @ SV378 @ SV163 @ SV558 ) )
= $false )
| ( ( SV378
= ( c_List_Olist_ONil @ SV558 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1674,plain,
! [SV759: $i,SV692: $i,SV559: $i,SV379: $i,SV164: $i] :
( ( ( ( c_List_Oappend @ SV164 @ ( c_List_Olist_OCons @ SV379 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 )
!= ( c_List_Oappend @ SV692 @ ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 ) )
| ( SV164 = SV692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1675,plain,
! [SV560: $i,SV380: $i,SV165: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV165 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV380 @ SV560 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV560
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1676,plain,
! [SV561: $i,SV381: $i,SV166: $i] :
( ( ( ( c_List_Orev @ SV166 @ SV381 )
= ( c_List_Olist_OCons @ SV561 @ ( c_List_Olist_ONil @ SV381 ) @ SV381 ) )
= $false )
| ( ( SV166
= ( c_List_Olist_OCons @ SV561 @ ( c_List_Olist_ONil @ SV381 ) @ SV381 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1677,plain,
! [SV693: $i,SV562: $i,SV382: $i,SV167: $i] :
( ( ( ( c_List_Oappend @ SV167 @ SV382 @ SV562 )
!= ( c_List_Oappend @ SV167 @ SV693 @ SV562 ) )
= $true )
| ( ( SV382 = SV693 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1678,plain,
! [SV694: $i,SV563: $i,SV384: $i,SV169: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV169 ) ) @ SV384 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV563 ) @ SV694 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1679,plain,
! [SV564: $i,SV385: $i,SV170: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV170 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV385 @ SV564 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV170 )
= SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1680,plain,
! [SV565: $i,SV387: $i,SV172: $i] :
( ( ( ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SV387 ) @ SV387 )
= ( c_List_Orev @ SV565 @ SV387 ) )
= $false )
| ( ( SV565
= ( c_List_Olist_OCons @ SV172 @ ( c_List_Olist_ONil @ SV387 ) @ SV387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1681,plain,
! [SV695: $i,SV566: $i,SV388: $i,SV173: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SV388 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV566 ) @ SV695 ) )
= $true )
| ( ( SV173 = SV566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1682,plain,
! [SV760: $i,SV696: $i,SV568: $i,SV390: $i,SV175: $i] :
( ( ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
!= ( c_List_Oappend @ SV696 @ SV760 @ SV568 ) )
| ( ( c_List_Olist_OCons @ SV175 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV175 @ SV390 @ SV696 @ SV760 @ SV568 ) @ SV568 )
= SV696 )
| ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
= SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1683,plain,
! [SV761: $i,SV697: $i,SV569: $i,SV392: $i,SV177: $i] :
( ( ! [SY1994: $i,SY1995: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
| ~ ( c_Type_Otyping @ SY1994 @ SV697 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1994 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SY1995 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1684,plain,
! [SV762: $i,SV698: $i,SV570: $i,SV393: $i,SV178: $i] :
( ( ( ( c_List_Oappend @ SV178 @ SV393 @ SV570 )
!= ( c_List_Olist_OCons @ SV698 @ SV762 @ SV570 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV698 @ SV762 @ SV178 @ SV393 @ SV570 ) @ SV393 @ SV570 )
= SV762 )
| ( SV393
= ( c_List_Olist_OCons @ SV698 @ SV762 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1685,plain,
! [SV699: $i,SV571: $i,SV394: $i,SV179: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV179 ) @ SV394 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV571 ) @ SV699 ) )
= $true )
| ( ( SV179 = SV571 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1686,plain,
! [SV700: $i,SV572: $i,SV395: $i,SV180: $i] :
( ( ( ( c_List_Oappend @ SV180 @ SV395 @ SV572 )
!= ( c_List_Oappend @ SV700 @ SV395 @ SV572 ) )
= $true )
| ( ( SV180 = SV700 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1687,plain,
! [SV573: $i,SV396: $i,SV181: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV181 @ SV396 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV573 @ SV396 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV181 = SV573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1688,plain,
! [SV701: $i,SV574: $i,SV397: $i,SV182: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV397 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV574 ) @ SV701 ) )
= $true )
| ( ( SV397 = SV701 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1689,plain,
! [SV575: $i,SV398: $i,SV183: $i] :
( ( ( SV183
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 ) @ SV575 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV183 ) @ SV398 ) @ ( c_List_Oappend @ SV575 @ ( c_List_Olist_OCons @ SV398 @ ( 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)],[1563]) ).
thf(1690,plain,
! [SV576: $i,SV399: $i,SV184: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV184 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV399 @ SV576 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV576
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1691,plain,
! [SV578: $i,SV401: $i,SV186: $i] :
( ( ( ( c_List_Oappend @ SV186 @ SV401 @ SV578 )
= SV401 )
= $false )
| ( ( SV186
= ( c_List_Olist_ONil @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1692,plain,
! [SV763: $i,SV702: $i,SV579: $i,SV402: $i,SV187: $i] :
( ( ( ( c_List_OdropWhile @ SV187 @ SV402 @ SV579 )
!= ( c_List_Olist_OCons @ SV702 @ SV763 @ SV579 ) )
| ( SV402
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV187 @ SV402 @ SV579 ) @ ( c_List_Olist_OCons @ SV702 @ SV763 @ SV579 ) @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1693,plain,
! [SV764: $i,SV703: $i,SV581: $i,SV404: $i,SV189: $i] :
( ( ( ( c_List_Olist_OCons @ SV189 @ SV404 @ SV581 )
!= ( c_List_Olist_OCons @ SV703 @ SV764 @ SV581 ) )
| ( SV404 = SV764 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1694,plain,
! [SV582: $i,SV405: $i,SV190: $i] :
( ( ( ( c_List_Oreplicate @ SV190 @ SV405 @ SV582 )
= ( c_List_Olist_ONil @ SV582 ) )
= $false )
| ( ( SV190
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1695,plain,
! [SV765: $i,SV704: $i,SV583: $i,SV406: $i,SV191: $i] :
( ( ! [SY1996: $i,SY1997: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
| ~ ( c_Type_Otyping @ SY1996 @ SV704 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1996 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SY1997 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1696,plain,
! [SV584: $i,SV407: $i,SV192: $i] :
( ( ( ( c_List_Olist_ONil @ SV192 )
= ( c_List_Oreplicate @ SV407 @ SV584 @ SV192 ) )
= $false )
| ( ( SV407
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1697,plain,
! [SV766: $i,SV705: $i,SV585: $i,SV408: $i,SV193: $i] :
( ( ( ( c_List_Oreplicate @ SV193 @ SV408 @ SV585 )
!= ( c_List_Oreplicate @ SV705 @ SV766 @ SV585 ) )
| ( SV193 = SV705 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1698,plain,
! [SV767: $i,SV706: $i,SV586: $i,SV409: $i,SV194: $i] :
( ( ( ( c_List_Oreplicate @ SV194 @ SV409 @ SV586 )
!= ( c_List_Oreplicate @ SV706 @ SV767 @ SV586 ) )
| ( SV409 = SV767 )
| ( SV194
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1699,plain,
! [SV707: $i,SV587: $i,SV410: $i,SV195: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV195 ) @ SV410 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV587 ) @ SV707 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV410 = SV707 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1700,plain,
! [SV708: $i,SV589: $i,SV412: $i,SV197: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV197 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV412 ) @ SV589 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV197 @ SV708 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SV589 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1701,plain,
! [SV590: $i,SV413: $i,SV198: $i] :
( ( ( ( c_List_Olist_ONil @ SV198 )
= ( c_List_Oappend @ SV413 @ SV590 @ SV198 ) )
= $false )
| ( ( SV590
= ( c_List_Olist_ONil @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1702,plain,
! [SV591: $i,SV415: $i,SV200: $i] :
( ( ( ( c_List_Oappend @ SV200 @ SV415 @ SV591 )
= SV200 )
= $false )
| ( ( SV415
= ( c_List_Olist_ONil @ SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1703,plain,
! [SV592: $i,SV416: $i,SV201: $i] :
( ( ( SV201
= ( c_List_Oappend @ SV201 @ SV416 @ SV592 ) )
= $false )
| ( ( SV416
= ( c_List_Olist_ONil @ SV592 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1704,plain,
! [SV768: $i,SV709: $i,SV593: $i,SV417: $i,SV202: $i] :
( ( ( ( c_List_Oappend @ SV202 @ SV417 @ SV593 )
!= ( c_List_Olist_OCons @ SV709 @ SV768 @ SV593 ) )
| ( SV202
= ( c_List_Olist_OCons @ SV709 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV709 @ SV768 @ SV202 @ SV417 @ SV593 ) @ SV593 ) )
| ( SV417
= ( c_List_Olist_OCons @ SV709 @ SV768 @ SV593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1705,plain,
! [SV710: $i,SV594: $i,SV418: $i,SV203: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV203 ) @ SV418 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV594 ) @ SV710 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1706,plain,
! [SV595: $i,SV419: $i,SV204: $i] :
( ( ( ( c_List_Oappend @ SV204 @ SV419 @ SV595 )
= ( c_List_Olist_ONil @ SV595 ) )
= $false )
| ( ( SV204
= ( c_List_Olist_ONil @ SV595 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1707,plain,
! [SV769: $i,SV711: $i,SV596: $i,SV420: $i,SV205: $i] :
( ( ( ( c_List_Olist_OCons @ SV205 @ SV420 @ SV596 )
!= ( c_List_Oappend @ SV711 @ SV769 @ SV596 ) )
| ( SV420
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV205 @ SV420 @ SV711 @ SV769 @ SV596 ) @ SV769 @ SV596 ) )
| ( SV711
= ( c_List_Olist_ONil @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1708,plain,
! [SV770: $i,SV712: $i,SV597: $i,SV421: $i,SV206: $i] :
( ( ( ( c_List_Olist_OCons @ SV206 @ SV421 @ SV597 )
!= ( c_List_Olist_OCons @ SV712 @ SV770 @ SV597 ) )
| ( SV206 = SV712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1709,plain,
! [SV713: $i,SV598: $i,SV422: $i,SV207: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV207 ) @ SV422 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV598 ) @ SV713 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV207 = SV598 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1710,plain,
! [SV771: $i,SV714: $i,SV599: $i,SV423: $i,SV208: $i] :
( ( ( ( c_List_Oappend @ SV208 @ ( c_List_Olist_OCons @ SV423 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 )
!= ( c_List_Oappend @ SV714 @ ( c_List_Olist_OCons @ SV771 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 ) )
| ( SV423 = SV771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1711,plain,
! [SV715: $i,SV600: $i,SV425: $i,SV210: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV210 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV425 ) @ SV600 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV210 @ SV715 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SV425 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1712,plain,
! [SV601: $i,SV426: $i,SV211: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV211 @ SV426 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV601 ) )
= $false )
| ( ( SV426
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1713,plain,
! [SV603: $i,SV428: $i,SV213: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV213 @ SV428 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV603 ) )
= $false )
| ( ( SV213
= ( c_Lambda_OdB_OAbs @ SV603 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1714,plain,
! [SV772: $i,SV716: $i,SV604: $i,SV429: $i,SV214: $i] :
( ( ( ( c_List_OdropWhile @ SV214 @ SV429 @ SV604 )
!= ( c_List_Olist_OCons @ SV716 @ SV772 @ SV604 ) )
| ~ ( hBOOL @ ( hAPP @ SV214 @ SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1715,plain,
! [SV773: $i,SV717: $i,SV605: $i,SV430: $i,SV215: $i] :
( ( ( ( c_List_Oappend @ SV215 @ SV430 @ SV605 )
!= ( c_List_Olist_OCons @ SV717 @ SV773 @ SV605 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV717 @ SV773 @ SV215 @ SV430 @ SV605 ) @ SV430 @ SV605 )
= SV773 )
| ( SV215
= ( c_List_Olist_ONil @ SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1716,plain,
! [SV718: $i,SV606: $i,SV431: $i,SV216: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV216 ) @ SV431 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV606 ) @ SV718 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV216 = SV606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1717,plain,
! [SV609: $i,SV434: $i,SV219: $i] :
( ( ( ( c_List_Orev @ SV219 @ SV434 )
= ( c_List_Orev @ SV609 @ SV434 ) )
= $false )
| ( ( SV219 = SV609 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1718,plain,
! [SV610: $i,SV435: $i,SV220: $i] :
( ( ( ( c_List_Oappend @ SV220 @ SV435 @ SV610 )
= ( c_List_Olist_ONil @ SV610 ) )
= $false )
| ( ( SV435
= ( c_List_Olist_ONil @ SV610 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1719,plain,
! [SV774: $i,SV719: $i,SV611: $i,SV437: $i,SV222: $i] :
( ( ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
!= ( c_List_Oappend @ SV719 @ SV774 @ SV611 ) )
| ( SV437
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV222 @ SV437 @ SV719 @ SV774 @ SV611 ) @ SV774 @ SV611 ) )
| ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
= SV774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1720,plain,
! [SV612: $i,SV438: $i,SV223: $i] :
( ( ( ( c_List_Olist_ONil @ SV223 )
= ( c_List_Oappend @ SV438 @ SV612 @ SV223 ) )
= $false )
| ( ( SV438
= ( c_List_Olist_ONil @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1721,plain,
! [SV613: $i,SV439: $i,SV224: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV224 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV439 @ SV613 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV224 )
= SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1722,plain,
! [SV720: $i,SV615: $i,SV442: $i,SV227: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV227 ) @ SV442 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV615 ) @ SV720 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV442 = SV720 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1723,plain,
! [SV444: $i,SV230: $i,SV616: $i,SV3: $i] :
( ( ( c_Type_Otypings @ SV3 @ ( c_List_Oappend @ SV616 @ ( c_List_Olist_OCons @ SV230 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV444 )
= $false )
| ( ( c_Type_Otyping @ SV3 @ SV230 @ ( c_Type_Osko__Type__Xtypes__snocE__1__2 @ SV444 @ SV3 @ SV230 @ SV616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1724,plain,
! [SV775: $i,SV721: $i,SV617: $i,SV448: $i,SV235: $i,SV11: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV11 @ SV235 @ SV448 @ SV617 ) @ SV721 ) @ SV775 )
= ( hAPP @ ( hAPP @ SV11 @ SV775 ) @ SV721 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1725,plain,
! [SV449: $i,SV618: $i,SV236: $i,SV12: $i] :
( ( ( c_List_Olistsp @ SV12 @ ( c_List_Oappend @ SV236 @ SV618 @ SV449 ) @ SV449 )
= $false )
| ( ( c_List_Olistsp @ SV12 @ SV236 @ SV449 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1726,plain,
! [SV450: $i,SV237: $i,SV619: $i,SV13: $i] :
( ( ( c_List_Olistsp @ SV13 @ ( c_List_Oappend @ SV619 @ SV237 @ SV450 ) @ SV450 )
= $false )
| ( ( c_List_Olistsp @ SV13 @ SV237 @ SV450 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1727,plain,
! [SV451: $i,SV16: $i,SV240: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV16 @ SV240 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV451 @ 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 @ SV16 ) ) @ SV240 ) @ SV451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1728,plain,
! [SV621: $i,SV453: $i,SV242: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ SV242 ) )
= $false )
| ( ( ( c_List_OdropWhile @ SV18 @ ( c_List_Olist_OCons @ SV242 @ SV453 @ SV621 ) @ SV621 )
= ( c_List_OdropWhile @ SV18 @ SV453 @ SV621 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1729,plain,
! [SV245: $i,SV623: $i,SV456: $i,SV21: $i] :
( ( ( ~ ( c_List_Olistsp @ SV21 @ SV456 @ SV623 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV21 @ SV245 @ SV623 ) )
= $true )
| ( ( c_List_Olistsp @ SV21 @ ( c_List_Oappend @ SV245 @ SV456 @ SV623 ) @ SV623 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1730,plain,
! [SV624: $i,SV251: $i,SV459: $i,SV27: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV27 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV459 @ tc_Type_Otype ) @ SV251 @ SV624 )
= $false )
| ( ( c_Type_Otyping @ SV27 @ ( c_Lambda_OdB_OAbs @ SV251 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV459 ) @ SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1731,plain,
! [SV776: $i,SV723: $i,SV626: $i,SV464: $i,SV260: $i,SV36: $i] :
( ( ! [SY1998: $i] :
( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
| ~ ( c_Type_Otypings @ SV464 @ SV776 @ SY1998 )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1732,plain,
! [SV467: $i,SV264: $i,SV628: $i,SV41: $i] :
( ( ( c_Type_Otyping @ SV41 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV628 ) @ SV264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV467 )
= $false )
| ( ( c_Type_Otypings @ SV41 @ SV264 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV467 @ SV41 @ SV628 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1733,plain,
! [SV724: $i,SV629: $i,SV468: $i,SV265: $i,SV43: $i] :
( ( ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_OCons @ SV265 @ SV468 @ SV629 ) @ ( c_List_Olist_OCons @ SV265 @ SV724 @ SV629 ) @ SV629 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV43 @ SV468 @ SV724 @ SV629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1734,plain,
! [SV777: $i,SV725: $i,SV630: $i,SV469: $i,SV266: $i,SV44: $i] :
( ( ( c_ListOrder_Ostep1 @ SV44 @ SV266 @ SV469 @ SV630 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SV725 ) @ SV777 ) )
| ~ ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SV725 @ SV266 @ SV630 ) @ ( c_List_Olist_OCons @ SV777 @ SV469 @ SV630 ) @ SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1735,plain,
! [SV471: $i,SV270: $i,SV631: $i,SV49: $i] :
( ( ( c_Type_Otyping @ SV49 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV631 @ SV270 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV471 )
= $false )
| ( ( c_Type_Otypings @ SV49 @ SV270 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV471 @ SV49 @ SV631 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1736,plain,
! [SV778: $i,SV727: $i,SV634: $i,SV476: $i,SV276: $i,SV55: $i] :
( ( ( c_ListOrder_Ostep1 @ SV55 @ SV276 @ SV476 @ SV634 )
| ( SV476 = SV276 )
| ~ ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SV727 @ SV276 @ SV634 ) @ ( c_List_Olist_OCons @ SV778 @ SV476 @ SV634 ) @ SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1737,plain,
! [SV728: $i,SV637: $i,SV483: $i,SV288: $i,SV68: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV288 ) @ SV483 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV68 @ ( c_List_Olist_OCons @ SV288 @ SV637 @ SV728 ) @ ( c_List_Olist_OCons @ SV483 @ SV637 @ SV728 ) @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1738,plain,
! [SV779: $i,SV729: $i,SV638: $i,SV484: $i,SV289: $i,SV69: $i] :
( ( ( SV69 = SV289 )
| ( SV484 = SV638 )
| ~ ( c_ListOrder_Ostep1 @ SV729 @ ( c_List_Olist_OCons @ SV289 @ SV638 @ SV779 ) @ ( c_List_Olist_OCons @ SV69 @ SV484 @ SV779 ) @ SV779 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1739,plain,
! [SV730: $i,SV639: $i,SV485: $i,SV291: $i,SV72: $i] :
( ( ( c_ListOrder_Ostep1 @ SV72 @ ( c_List_Oappend @ SV291 @ SV485 @ SV639 ) @ ( c_List_Oappend @ SV291 @ SV730 @ SV639 ) @ SV639 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV72 @ SV485 @ SV730 @ SV639 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1740,plain,
! [SV731: $i,SV640: $i,SV486: $i,SV292: $i,SV73: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV73 @ SV292 @ SV486 @ SV640 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV73 @ ( c_List_Oappend @ SV292 @ SV731 @ SV640 ) @ ( c_List_Oappend @ SV486 @ SV731 @ SV640 ) @ SV640 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1741,plain,
! [SV487: $i,SV293: $i,SV641: $i,SV75: $i] :
( ( ( c_Type_Otyping @ SV75 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV641 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV487 )
= $false )
| ( ( c_Type_Otypings @ SV75 @ SV293 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV487 @ SV75 @ SV641 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1742,plain,
! [SV780: $i,SV732: $i,SV642: $i,SV488: $i,SV294: $i,SV76: $i] :
( ( ( c_List_Ofoldl @ SV76 @ SV294 @ ( c_List_Olist_OCons @ SV488 @ SV642 @ SV732 ) @ SV780 @ SV732 )
= ( c_List_Ofoldl @ SV76 @ ( hAPP @ ( hAPP @ SV76 @ SV294 ) @ SV488 ) @ SV642 @ SV780 @ SV732 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1743,plain,
! [SV781: $i,SV733: $i,SV643: $i,SV489: $i,SV296: $i,SV78: $i] :
( ( ( SV78 = SV296 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV489 @ SV296 ) @ SV78 ) )
| ~ ( c_ListOrder_Ostep1 @ SV489 @ ( c_List_Olist_OCons @ SV296 @ SV643 @ SV733 ) @ ( c_List_Olist_OCons @ SV78 @ SV781 @ SV733 ) @ SV733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1744,plain,
! [SV782: $i,SV734: $i,SV644: $i,SV490: $i,SV297: $i,SV79: $i] :
( ( ! [SY1999: $i] :
( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
| ~ ( c_Type_Otypings @ SV79 @ SV782 @ SY1999 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1745,plain,
! [SV645: $i,SV491: $i,SV298: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ SV80 @ SV298 ) )
= $false )
| ( ( ( c_List_OtakeWhile @ SV80 @ ( c_List_Olist_OCons @ SV298 @ SV491 @ SV645 ) @ SV645 )
= ( c_List_Olist_OCons @ SV298 @ ( c_List_OtakeWhile @ SV80 @ SV491 @ SV645 ) @ SV645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1746,plain,
! [SV783: $i,SV736: $i,SV647: $i,SV495: $i,SV302: $i,SV85: $i] :
( ( ( c_List_Ofoldl @ SV85 @ SV302 @ ( c_List_Oappend @ SV495 @ SV647 @ SV736 ) @ SV783 @ SV736 )
= ( c_List_Ofoldl @ SV85 @ ( c_List_Ofoldl @ SV85 @ SV302 @ SV495 @ SV783 @ SV736 ) @ SV647 @ SV783 @ SV736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1747,plain,
! [SV737: $i,SV648: $i,SV496: $i,SV303: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV496 @ SV648 @ SV737 ) @ SV737 ) @ SV737 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ SV648 @ SV737 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV86 @ SV496 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1748,plain,
! [SV739: $i,SV650: $i,SV498: $i,SV305: $i,SV88: $i] :
( ( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ ( c_List_Oappend @ SV305 @ ( c_List_Olist_OCons @ SV498 @ SV650 @ SV739 ) @ SV739 ) @ SV739 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ SV305 @ SV739 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV88 @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1749,plain,
! [SV740: $i,SV651: $i,SV499: $i,SV306: $i,SV89: $i] :
( ( ( ( c_List_OtakeWhile @ SV89 @ ( c_List_Oappend @ SV306 @ ( c_List_Olist_OCons @ SV499 @ SV651 @ SV740 ) @ SV740 ) @ SV740 )
= ( c_List_OtakeWhile @ SV89 @ SV306 @ SV740 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV89 @ SV499 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1750,plain,
! [SV505: $i,SV316: $i,SV653: $i,SV99: $i] :
( ( ( c_Type_Otyping @ SV99 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV653 ) @ SV316 ) @ SV505 )
= $false )
| ( ( c_Type_Otyping @ SV99 @ SV316 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV505 @ SV99 @ SV653 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1751,plain,
! [SV506: $i,SV654: $i,SV317: $i,SV100: $i] :
( ( ( c_Type_Otyping @ SV100 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV317 @ SV654 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV506 )
= $false )
| ( ( c_Type_Otyping @ SV100 @ SV317 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV506 @ SV100 @ SV317 @ SV654 ) @ SV506 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1752,plain,
! [SV741: $i,SV655: $i,SV507: $i,SV318: $i,SV101: $i] :
( ( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV318 @ SV507 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV655 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV101 @ SV507 @ SV741 )
| ~ ( c_Type_Otyping @ SV101 @ SV318 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV741 @ SV655 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1753,plain,
! [SV508: $i,SV656: $i,SV319: $i,SV102: $i] :
( ( ( c_Type_Otyping @ SV102 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV319 @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV508 )
= $false )
| ( ( c_Type_Otyping @ SV102 @ SV319 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV508 @ SV102 @ SV319 @ SV656 ) @ SV508 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1754,plain,
! [SV784: $i,SV742: $i,SV657: $i,SV509: $i,SV320: $i,SV103: $i] :
( ( ~ ( c_Type_Otyping @ SV103 @ SV320 @ SV509 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SV657 @ SV509 @ tc_Type_Otype ) @ SV742 @ SV784 )
| ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SV742 @ SV320 @ SV657 ) @ SV784 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1755,plain,
! [SV743: $i,SV658: $i,SV510: $i,SV321: $i,SV104: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV104 @ SV321 @ SV510 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV658 @ SV321 ) @ SV743 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV104 @ SV658 @ SV743 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1756,plain,
! [SV511: $i,SV659: $i,SV322: $i,SV105: $i] :
( ( ( c_Type_Otyping @ SV105 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV322 ) @ SV659 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV511 )
= $false )
| ( ( c_Type_Otyping @ SV105 @ ( c_Lambda_OdB_OVar @ SV322 ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV511 @ SV105 @ SV322 @ SV659 ) @ SV511 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1757,plain,
! [SV785: $i,SV744: $i,SV660: $i,SV513: $i,SV324: $i,SV107: $i] :
( ( ( SV107 = SV324 )
| ( c_ListOrder_Ostep1 @ SV513 @ SV107 @ SV324 @ SV660 )
| ~ ( c_ListOrder_Ostep1 @ SV513 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ ( c_List_Oappend @ SV324 @ ( c_List_Olist_OCons @ SV785 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ SV660 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1758,plain,
! [SV786: $i,SV745: $i,SV661: $i,SV516: $i,SV327: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV327 ) @ SV516 ) )
| ( c_ListOrder_Ostep1 @ SV110 @ SV661 @ SV745 @ SV786 )
| ~ ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SV661 @ ( c_List_Olist_OCons @ SV327 @ ( c_List_Olist_ONil @ SV786 ) @ SV786 ) @ SV786 ) @ ( c_List_Oappend @ SV745 @ ( c_List_Olist_OCons @ SV516 @ ( c_List_Olist_ONil @ SV786 ) @ SV786 ) @ SV786 ) @ SV786 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1759,plain,
! [SV787: $i,SV746: $i,SV662: $i,SV518: $i,SV329: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SV329 ) @ SV518 ) )
| ( SV329 = SV518 )
| ~ ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SV662 @ ( c_List_Olist_OCons @ SV329 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ ( c_List_Oappend @ SV787 @ ( c_List_Olist_OCons @ SV518 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ SV746 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1760,plain,
! [SV788: $i,SV747: $i,SV663: $i,SV519: $i,SV330: $i,SV113: $i] :
( ( ( SV113 = SV330 )
| ( SV519 = SV663 )
| ~ ( c_ListOrder_Ostep1 @ SV747 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SV519 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ ( c_List_Oappend @ SV330 @ ( c_List_Olist_OCons @ SV663 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ SV788 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1761,plain,
! [SV748: $i,SV664: $i,SV522: $i,SV333: $i,SV116: $i] :
( ( ( SV116 = SV333 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV333 )
| ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1762,plain,
! [SV523: $i,SV665: $i,SV334: $i,SV117: $i] :
( ( ( c_Type_Otyping @ SV117 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV334 ) @ SV665 ) @ SV523 )
= $false )
| ( ( c_Type_Otyping @ SV117 @ SV334 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV523 @ SV117 @ SV334 @ SV665 ) ) @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1763,plain,
! [SV667: $i,SV526: $i,SV337: $i,SV121: $i] :
( ( ( hBOOL @ ( hAPP @ SV121 @ ( c_Type_Otype_Otype__case @ SV337 @ SV526 @ ( c_Type_Otype_OAtom @ SV667 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV121 @ ( hAPP @ SV337 @ SV667 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1764,plain,
! [SV668: $i,SV527: $i,SV338: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ SV122 @ ( c_Type_Otype_Otype__case @ SV338 @ SV527 @ ( c_Type_Otype_OAtom @ SV668 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV122 @ ( hAPP @ SV338 @ SV668 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1765,plain,
! [SV749: $i,SV675: $i,SV535: $i,SV353: $i,SV137: $i] :
( ( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV535 ) @ SV675 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV137 @ SV535 @ SV749 )
| ~ ( c_Type_Otyping @ SV137 @ SV353 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV749 ) @ SV675 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1766,plain,
! [SV789: $i,SV750: $i,SV680: $i,SV541: $i,SV359: $i,SV144: $i] :
( ( ( c_List_Ofoldr @ SV144 @ ( c_List_Olist_OCons @ SV359 @ SV541 @ SV680 ) @ SV750 @ SV680 @ SV789 )
= ( hAPP @ ( hAPP @ SV144 @ SV359 ) @ ( c_List_Ofoldr @ SV144 @ SV541 @ SV750 @ SV680 @ SV789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1767,plain,
! [SV790: $i,SV751: $i,SV681: $i,SV542: $i,SV360: $i,SV145: $i] :
( ( ( c_List_Ofoldr @ SV145 @ ( c_List_Oappend @ SV360 @ SV542 @ SV681 ) @ SV751 @ SV681 @ SV790 )
= ( c_List_Ofoldr @ SV145 @ SV360 @ ( c_List_Ofoldr @ SV145 @ SV542 @ SV751 @ SV681 @ SV790 ) @ SV681 @ SV790 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1768,plain,
! [SV754: $i,SV685: $i,SV546: $i,SV364: $i,SV149: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV149 @ ( c_Type_Otype_Otype__case @ SV364 @ SV546 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV685 ) @ SV754 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV149 @ ( hAPP @ ( hAPP @ SV546 @ SV685 ) @ SV754 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(1769,plain,
! [SV755: $i,SV686: $i,SV547: $i,SV365: $i,SV150: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV150 @ ( c_Type_Otype_Otype__case @ SV365 @ SV547 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV686 ) @ SV755 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV150 @ ( hAPP @ ( hAPP @ SV547 @ SV686 ) @ SV755 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1770,plain,
! [SV687: $i,SV549: $i,SV368: $i,SV153: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV153 ) @ SV368 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV549 ) @ SV687 ) )
= $false )
| ( ( SV368 = SV687 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1771,plain,
! [SV688: $i,SV550: $i,SV369: $i,SV154: $i] :
( ( ( ( c_List_Orev @ SV154 @ SV369 )
= ( c_List_Olist_OCons @ SV550 @ SV688 @ SV369 ) )
= $false )
| ( ( SV154
= ( c_List_Oappend @ ( c_List_Orev @ SV688 @ SV369 ) @ ( c_List_Olist_OCons @ SV550 @ ( c_List_Olist_ONil @ SV369 ) @ SV369 ) @ SV369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1772,plain,
! [SV756: $i,SV689: $i,SV551: $i,SV370: $i,SV155: $i] :
( ( ( ( c_List_Oappend @ SV155 @ SV370 @ SV551 )
!= ( c_List_Olist_OCons @ SV689 @ SV756 @ SV551 ) )
= $true )
| ( ( ( SV155
= ( c_List_Olist_OCons @ SV689 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV689 @ SV756 @ SV155 @ SV370 @ SV551 ) @ SV551 ) )
| ( SV155
= ( c_List_Olist_ONil @ SV551 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1773,plain,
! [SV757: $i,SV690: $i,SV556: $i,SV375: $i,SV160: $i] :
( ( ( ( c_List_Olist_OCons @ SV160 @ SV375 @ SV556 )
!= ( c_List_Oappend @ SV690 @ SV757 @ SV556 ) )
= $true )
| ( ( ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV375 @ SV690 @ SV757 @ SV556 ) @ SV556 )
= SV690 )
| ( SV690
= ( c_List_Olist_ONil @ SV556 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1774,plain,
! [SV758: $i,SV691: $i,SV557: $i,SV376: $i,SV161: $i] :
( ( ( SV161
!= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV376 @ SV161 @ SV557 ) @ ( c_List_Olist_OCons @ SV691 @ SV758 @ SV557 ) @ SV557 ) )
= $true )
| ( ( ( ( c_List_OdropWhile @ SV376 @ SV161 @ SV557 )
= ( c_List_Olist_OCons @ SV691 @ SV758 @ SV557 ) )
| ( hBOOL @ ( hAPP @ SV376 @ SV691 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1775,plain,
! [SV759: $i,SV692: $i,SV559: $i,SV379: $i,SV164: $i] :
( ( ( ( c_List_Oappend @ SV164 @ ( c_List_Olist_OCons @ SV379 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 )
!= ( c_List_Oappend @ SV692 @ ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 ) )
= $true )
| ( ( SV164 = SV692 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1776,plain,
! [SV693: $i,SV562: $i,SV382: $i,SV167: $i] :
( ( ( ( c_List_Oappend @ SV167 @ SV382 @ SV562 )
= ( c_List_Oappend @ SV167 @ SV693 @ SV562 ) )
= $false )
| ( ( SV382 = SV693 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1777,plain,
! [SV695: $i,SV566: $i,SV388: $i,SV173: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV173 ) @ SV388 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV566 ) @ SV695 ) )
= $false )
| ( ( SV173 = SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1681]) ).
thf(1778,plain,
! [SV760: $i,SV696: $i,SV568: $i,SV390: $i,SV175: $i] :
( ( ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
!= ( c_List_Oappend @ SV696 @ SV760 @ SV568 ) )
= $true )
| ( ( ( ( c_List_Olist_OCons @ SV175 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV175 @ SV390 @ SV696 @ SV760 @ SV568 ) @ SV568 )
= SV696 )
| ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
= SV760 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1779,plain,
! [SV791: $i,SV761: $i,SV697: $i,SV569: $i,SV392: $i,SV177: $i] :
( ( ! [SY2000: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
| ~ ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SY2000 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1780,plain,
! [SV762: $i,SV698: $i,SV570: $i,SV393: $i,SV178: $i] :
( ( ( ( c_List_Oappend @ SV178 @ SV393 @ SV570 )
!= ( c_List_Olist_OCons @ SV698 @ SV762 @ SV570 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV698 @ SV762 @ SV178 @ SV393 @ SV570 ) @ SV393 @ SV570 )
= SV762 )
| ( SV393
= ( c_List_Olist_OCons @ SV698 @ SV762 @ SV570 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1781,plain,
! [SV699: $i,SV571: $i,SV394: $i,SV179: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV179 ) @ SV394 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV571 ) @ SV699 ) )
= $false )
| ( ( SV179 = SV571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1782,plain,
! [SV700: $i,SV572: $i,SV395: $i,SV180: $i] :
( ( ( ( c_List_Oappend @ SV180 @ SV395 @ SV572 )
= ( c_List_Oappend @ SV700 @ SV395 @ SV572 ) )
= $false )
| ( ( SV180 = SV700 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1783,plain,
! [SV701: $i,SV574: $i,SV397: $i,SV182: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV397 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV574 ) @ SV701 ) )
= $false )
| ( ( SV397 = SV701 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1784,plain,
! [SV763: $i,SV702: $i,SV579: $i,SV402: $i,SV187: $i] :
( ( ( ( c_List_OdropWhile @ SV187 @ SV402 @ SV579 )
!= ( c_List_Olist_OCons @ SV702 @ SV763 @ SV579 ) )
= $true )
| ( ( SV402
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV187 @ SV402 @ SV579 ) @ ( c_List_Olist_OCons @ SV702 @ SV763 @ SV579 ) @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1785,plain,
! [SV764: $i,SV703: $i,SV581: $i,SV404: $i,SV189: $i] :
( ( ( ( c_List_Olist_OCons @ SV189 @ SV404 @ SV581 )
!= ( c_List_Olist_OCons @ SV703 @ SV764 @ SV581 ) )
= $true )
| ( ( SV404 = SV764 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1786,plain,
! [SV792: $i,SV765: $i,SV704: $i,SV583: $i,SV406: $i,SV191: $i] :
( ( ! [SY2001: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
| ~ ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SY2001 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1787,plain,
! [SV766: $i,SV705: $i,SV585: $i,SV408: $i,SV193: $i] :
( ( ( ( c_List_Oreplicate @ SV193 @ SV408 @ SV585 )
!= ( c_List_Oreplicate @ SV705 @ SV766 @ SV585 ) )
= $true )
| ( ( SV193 = SV705 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1788,plain,
! [SV767: $i,SV706: $i,SV586: $i,SV409: $i,SV194: $i] :
( ( ( ( c_List_Oreplicate @ SV194 @ SV409 @ SV586 )
!= ( c_List_Oreplicate @ SV706 @ SV767 @ SV586 ) )
= $true )
| ( ( ( SV409 = SV767 )
| ( SV194
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1789,plain,
! [SV707: $i,SV587: $i,SV410: $i,SV195: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV195 ) @ SV410 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV587 ) @ SV707 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV410 = SV707 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1790,plain,
! [SV708: $i,SV589: $i,SV412: $i,SV197: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV197 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV412 ) @ SV589 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV197 @ SV708 ) )
| ( hBOOL @ ( hAPP @ SV197 @ SV589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1791,plain,
! [SV768: $i,SV709: $i,SV593: $i,SV417: $i,SV202: $i] :
( ( ( ( c_List_Oappend @ SV202 @ SV417 @ SV593 )
!= ( c_List_Olist_OCons @ SV709 @ SV768 @ SV593 ) )
= $true )
| ( ( ( SV202
= ( c_List_Olist_OCons @ SV709 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV709 @ SV768 @ SV202 @ SV417 @ SV593 ) @ SV593 ) )
| ( SV417
= ( c_List_Olist_OCons @ SV709 @ SV768 @ SV593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1792,plain,
! [SV769: $i,SV711: $i,SV596: $i,SV420: $i,SV205: $i] :
( ( ( ( c_List_Olist_OCons @ SV205 @ SV420 @ SV596 )
!= ( c_List_Oappend @ SV711 @ SV769 @ SV596 ) )
= $true )
| ( ( ( SV420
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV205 @ SV420 @ SV711 @ SV769 @ SV596 ) @ SV769 @ SV596 ) )
| ( SV711
= ( c_List_Olist_ONil @ SV596 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1793,plain,
! [SV770: $i,SV712: $i,SV597: $i,SV421: $i,SV206: $i] :
( ( ( ( c_List_Olist_OCons @ SV206 @ SV421 @ SV597 )
!= ( c_List_Olist_OCons @ SV712 @ SV770 @ SV597 ) )
= $true )
| ( ( SV206 = SV712 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1794,plain,
! [SV713: $i,SV598: $i,SV422: $i,SV207: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV207 ) @ SV422 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV598 ) @ SV713 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV207 = SV598 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1795,plain,
! [SV771: $i,SV714: $i,SV599: $i,SV423: $i,SV208: $i] :
( ( ( ( c_List_Oappend @ SV208 @ ( c_List_Olist_OCons @ SV423 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 )
!= ( c_List_Oappend @ SV714 @ ( c_List_Olist_OCons @ SV771 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 ) )
= $true )
| ( ( SV423 = SV771 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1796,plain,
! [SV715: $i,SV600: $i,SV425: $i,SV210: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV210 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV425 ) @ SV600 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV210 @ SV715 ) )
| ( hBOOL @ ( hAPP @ SV210 @ SV425 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1797,plain,
! [SV772: $i,SV716: $i,SV604: $i,SV429: $i,SV214: $i] :
( ( ( ( c_List_OdropWhile @ SV214 @ SV429 @ SV604 )
!= ( c_List_Olist_OCons @ SV716 @ SV772 @ SV604 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV214 @ SV716 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(1798,plain,
! [SV773: $i,SV717: $i,SV605: $i,SV430: $i,SV215: $i] :
( ( ( ( c_List_Oappend @ SV215 @ SV430 @ SV605 )
!= ( c_List_Olist_OCons @ SV717 @ SV773 @ SV605 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV717 @ SV773 @ SV215 @ SV430 @ SV605 ) @ SV430 @ SV605 )
= SV773 )
| ( SV215
= ( c_List_Olist_ONil @ SV605 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(1799,plain,
! [SV718: $i,SV606: $i,SV431: $i,SV216: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV216 ) @ SV431 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV606 ) @ SV718 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV216 = SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1800,plain,
! [SV774: $i,SV719: $i,SV611: $i,SV437: $i,SV222: $i] :
( ( ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
!= ( c_List_Oappend @ SV719 @ SV774 @ SV611 ) )
= $true )
| ( ( ( SV437
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV222 @ SV437 @ SV719 @ SV774 @ SV611 ) @ SV774 @ SV611 ) )
| ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
= SV774 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1801,plain,
! [SV720: $i,SV615: $i,SV442: $i,SV227: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV227 ) @ SV442 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV615 ) @ SV720 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV442 = SV720 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1802,plain,
! [SV451: $i,SV240: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV16 @ SV240 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV240 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV16 ) ) @ SV240 ) @ SV451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1803,plain,
! [SV245: $i,SV623: $i,SV456: $i,SV21: $i] :
( ( ( c_List_Olistsp @ SV21 @ SV456 @ SV623 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV21 @ SV245 @ SV623 ) )
= $true )
| ( ( c_List_Olistsp @ SV21 @ ( c_List_Oappend @ SV245 @ SV456 @ SV623 ) @ SV623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1804,plain,
! [SV793: $i,SV776: $i,SV723: $i,SV626: $i,SV464: $i,SV260: $i,SV36: $i] :
( ( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
| ~ ( c_Type_Otypings @ SV464 @ SV776 @ SV793 )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1805,plain,
! [SV265: $i,SV629: $i,SV724: $i,SV468: $i,SV43: $i] :
( ( ( c_ListOrder_Ostep1 @ SV43 @ SV468 @ SV724 @ SV629 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV43 @ ( c_List_Olist_OCons @ SV265 @ SV468 @ SV629 ) @ ( c_List_Olist_OCons @ SV265 @ SV724 @ SV629 ) @ SV629 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1806,plain,
! [SV777: $i,SV725: $i,SV630: $i,SV469: $i,SV266: $i,SV44: $i] :
( ( ( c_ListOrder_Ostep1 @ SV44 @ SV266 @ SV469 @ SV630 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SV725 ) @ SV777 ) )
| ~ ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SV725 @ SV266 @ SV630 ) @ ( c_List_Olist_OCons @ SV777 @ SV469 @ SV630 ) @ SV630 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1807,plain,
! [SV778: $i,SV727: $i,SV634: $i,SV476: $i,SV276: $i,SV55: $i] :
( ( ( c_ListOrder_Ostep1 @ SV55 @ SV276 @ SV476 @ SV634 )
= $true )
| ( ( ( SV476 = SV276 )
| ~ ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SV727 @ SV276 @ SV634 ) @ ( c_List_Olist_OCons @ SV778 @ SV476 @ SV634 ) @ SV634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1808,plain,
! [SV728: $i,SV637: $i,SV483: $i,SV288: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV288 ) @ SV483 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV68 @ ( c_List_Olist_OCons @ SV288 @ SV637 @ SV728 ) @ ( c_List_Olist_OCons @ SV483 @ SV637 @ SV728 ) @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1809,plain,
! [SV779: $i,SV729: $i,SV638: $i,SV484: $i,SV289: $i,SV69: $i] :
( ( ( SV69 = SV289 )
= $true )
| ( ( ( SV484 = SV638 )
| ~ ( c_ListOrder_Ostep1 @ SV729 @ ( c_List_Olist_OCons @ SV289 @ SV638 @ SV779 ) @ ( c_List_Olist_OCons @ SV69 @ SV484 @ SV779 ) @ SV779 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1810,plain,
! [SV291: $i,SV639: $i,SV730: $i,SV485: $i,SV72: $i] :
( ( ( c_ListOrder_Ostep1 @ SV72 @ SV485 @ SV730 @ SV639 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV72 @ ( c_List_Oappend @ SV291 @ SV485 @ SV639 ) @ ( c_List_Oappend @ SV291 @ SV730 @ SV639 ) @ SV639 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1811,plain,
! [SV731: $i,SV640: $i,SV486: $i,SV292: $i,SV73: $i] :
( ( ( c_ListOrder_Ostep1 @ SV73 @ SV292 @ SV486 @ SV640 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV73 @ ( c_List_Oappend @ SV292 @ SV731 @ SV640 ) @ ( c_List_Oappend @ SV486 @ SV731 @ SV640 ) @ SV640 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1812,plain,
! [SV781: $i,SV733: $i,SV643: $i,SV489: $i,SV296: $i,SV78: $i] :
( ( ( SV78 = SV296 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV489 @ SV296 ) @ SV78 ) )
| ~ ( c_ListOrder_Ostep1 @ SV489 @ ( c_List_Olist_OCons @ SV296 @ SV643 @ SV733 ) @ ( c_List_Olist_OCons @ SV78 @ SV781 @ SV733 ) @ SV733 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1743]) ).
thf(1813,plain,
! [SV794: $i,SV782: $i,SV734: $i,SV644: $i,SV490: $i,SV297: $i,SV79: $i] :
( ( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
| ~ ( c_Type_Otypings @ SV79 @ SV782 @ SV794 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1814,plain,
! [SV303: $i,SV496: $i,SV737: $i,SV648: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ SV648 @ SV737 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV86 @ SV496 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV496 @ SV648 @ SV737 ) @ SV737 ) @ SV737 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(1815,plain,
! [SV650: $i,SV498: $i,SV739: $i,SV305: $i,SV88: $i] :
( ( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ SV305 @ SV739 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV88 @ SV498 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ ( c_List_Oappend @ SV305 @ ( c_List_Olist_OCons @ SV498 @ SV650 @ SV739 ) @ SV739 ) @ SV739 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1816,plain,
! [SV655: $i,SV318: $i,SV741: $i,SV507: $i,SV101: $i] :
( ( ( ~ ( c_Type_Otypings @ SV101 @ SV507 @ SV741 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV101 @ SV318 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV741 @ SV655 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV318 @ SV507 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV655 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1817,plain,
! [SV784: $i,SV742: $i,SV657: $i,SV509: $i,SV320: $i,SV103: $i] :
( ( ( ~ ( c_Type_Otyping @ SV103 @ SV320 @ SV509 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SV657 @ SV509 @ tc_Type_Otype ) @ SV742 @ SV784 )
| ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SV742 @ SV320 @ SV657 ) @ SV784 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1818,plain,
! [SV510: $i,SV321: $i,SV743: $i,SV658: $i,SV104: $i] :
( ( ( c_Type_Otyping @ SV104 @ SV658 @ SV743 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV104 @ SV321 @ SV510 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV658 @ SV321 ) @ SV743 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1819,plain,
! [SV785: $i,SV744: $i,SV660: $i,SV513: $i,SV324: $i,SV107: $i] :
( ( ( SV107 = SV324 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV513 @ SV107 @ SV324 @ SV660 )
| ~ ( c_ListOrder_Ostep1 @ SV513 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ ( c_List_Oappend @ SV324 @ ( c_List_Olist_OCons @ SV785 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ SV660 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(1820,plain,
! [SV786: $i,SV745: $i,SV661: $i,SV516: $i,SV327: $i,SV110: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV327 ) @ SV516 ) )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV110 @ SV661 @ SV745 @ SV786 )
| ~ ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SV661 @ ( c_List_Olist_OCons @ SV327 @ ( c_List_Olist_ONil @ SV786 ) @ SV786 ) @ SV786 ) @ ( c_List_Oappend @ SV745 @ ( c_List_Olist_OCons @ SV516 @ ( c_List_Olist_ONil @ SV786 ) @ SV786 ) @ SV786 ) @ SV786 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1758]) ).
thf(1821,plain,
! [SV787: $i,SV746: $i,SV662: $i,SV518: $i,SV329: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SV329 ) @ SV518 ) )
= $true )
| ( ( ( SV329 = SV518 )
| ~ ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SV662 @ ( c_List_Olist_OCons @ SV329 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ ( c_List_Oappend @ SV787 @ ( c_List_Olist_OCons @ SV518 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ SV746 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1822,plain,
! [SV788: $i,SV747: $i,SV663: $i,SV519: $i,SV330: $i,SV113: $i] :
( ( ( SV113 = SV330 )
= $true )
| ( ( ( SV519 = SV663 )
| ~ ( c_ListOrder_Ostep1 @ SV747 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SV519 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ ( c_List_Oappend @ SV330 @ ( c_List_Olist_OCons @ SV663 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ SV788 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1823,plain,
! [SV116: $i,SV333: $i,SV748: $i,SV664: $i,SV522: $i] :
( ( ( ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV333 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 ) )
= $true )
| ( ( SV116 = SV333 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(1824,plain,
! [SV675: $i,SV353: $i,SV749: $i,SV535: $i,SV137: $i] :
( ( ( ~ ( c_Type_Otyping @ SV137 @ SV535 @ SV749 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV137 @ SV353 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV749 ) @ SV675 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV535 ) @ SV675 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1825,plain,
! [SV754: $i,SV685: $i,SV546: $i,SV364: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ SV149 @ ( c_Type_Otype_Otype__case @ SV364 @ SV546 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV685 ) @ SV754 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV149 @ ( hAPP @ ( hAPP @ SV546 @ SV685 ) @ SV754 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1826,plain,
! [SV755: $i,SV686: $i,SV547: $i,SV365: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP @ SV150 @ ( c_Type_Otype_Otype__case @ SV365 @ SV547 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV686 ) @ SV755 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV150 @ ( hAPP @ ( hAPP @ SV547 @ SV686 ) @ SV755 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1827,plain,
! [SV756: $i,SV689: $i,SV551: $i,SV370: $i,SV155: $i] :
( ( ( ( c_List_Oappend @ SV155 @ SV370 @ SV551 )
= ( c_List_Olist_OCons @ SV689 @ SV756 @ SV551 ) )
= $false )
| ( ( ( SV155
= ( c_List_Olist_OCons @ SV689 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV689 @ SV756 @ SV155 @ SV370 @ SV551 ) @ SV551 ) )
| ( SV155
= ( c_List_Olist_ONil @ SV551 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1828,plain,
! [SV757: $i,SV690: $i,SV556: $i,SV375: $i,SV160: $i] :
( ( ( ( c_List_Olist_OCons @ SV160 @ SV375 @ SV556 )
= ( c_List_Oappend @ SV690 @ SV757 @ SV556 ) )
= $false )
| ( ( ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV375 @ SV690 @ SV757 @ SV556 ) @ SV556 )
= SV690 )
| ( SV690
= ( c_List_Olist_ONil @ SV556 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1829,plain,
! [SV758: $i,SV691: $i,SV557: $i,SV376: $i,SV161: $i] :
( ( ( SV161
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV376 @ SV161 @ SV557 ) @ ( c_List_Olist_OCons @ SV691 @ SV758 @ SV557 ) @ SV557 ) )
= $false )
| ( ( ( ( c_List_OdropWhile @ SV376 @ SV161 @ SV557 )
= ( c_List_Olist_OCons @ SV691 @ SV758 @ SV557 ) )
| ( hBOOL @ ( hAPP @ SV376 @ SV691 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1830,plain,
! [SV759: $i,SV692: $i,SV559: $i,SV379: $i,SV164: $i] :
( ( ( ( c_List_Oappend @ SV164 @ ( c_List_Olist_OCons @ SV379 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 )
= ( c_List_Oappend @ SV692 @ ( c_List_Olist_OCons @ SV759 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 ) @ SV559 ) )
= $false )
| ( ( SV164 = SV692 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1831,plain,
! [SV760: $i,SV696: $i,SV568: $i,SV390: $i,SV175: $i] :
( ( ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
= ( c_List_Oappend @ SV696 @ SV760 @ SV568 ) )
= $false )
| ( ( ( ( c_List_Olist_OCons @ SV175 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV175 @ SV390 @ SV696 @ SV760 @ SV568 ) @ SV568 )
= SV696 )
| ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
= SV760 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1832,plain,
! [SV795: $i,SV791: $i,SV761: $i,SV697: $i,SV569: $i,SV392: $i,SV177: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
| ~ ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(1833,plain,
! [SV762: $i,SV698: $i,SV570: $i,SV393: $i,SV178: $i] :
( ( ( ( c_List_Oappend @ SV178 @ SV393 @ SV570 )
= ( c_List_Olist_OCons @ SV698 @ SV762 @ SV570 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV698 @ SV762 @ SV178 @ SV393 @ SV570 ) @ SV393 @ SV570 )
= SV762 )
| ( SV393
= ( c_List_Olist_OCons @ SV698 @ SV762 @ SV570 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1834,plain,
! [SV763: $i,SV702: $i,SV579: $i,SV402: $i,SV187: $i] :
( ( ( ( c_List_OdropWhile @ SV187 @ SV402 @ SV579 )
= ( c_List_Olist_OCons @ SV702 @ SV763 @ SV579 ) )
= $false )
| ( ( SV402
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV187 @ SV402 @ SV579 ) @ ( c_List_Olist_OCons @ SV702 @ SV763 @ SV579 ) @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1835,plain,
! [SV764: $i,SV703: $i,SV581: $i,SV404: $i,SV189: $i] :
( ( ( ( c_List_Olist_OCons @ SV189 @ SV404 @ SV581 )
= ( c_List_Olist_OCons @ SV703 @ SV764 @ SV581 ) )
= $false )
| ( ( SV404 = SV764 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1836,plain,
! [SV796: $i,SV792: $i,SV765: $i,SV704: $i,SV583: $i,SV406: $i,SV191: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
| ~ ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(1837,plain,
! [SV766: $i,SV705: $i,SV585: $i,SV408: $i,SV193: $i] :
( ( ( ( c_List_Oreplicate @ SV193 @ SV408 @ SV585 )
= ( c_List_Oreplicate @ SV705 @ SV766 @ SV585 ) )
= $false )
| ( ( SV193 = SV705 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1838,plain,
! [SV767: $i,SV706: $i,SV586: $i,SV409: $i,SV194: $i] :
( ( ( ( c_List_Oreplicate @ SV194 @ SV409 @ SV586 )
= ( c_List_Oreplicate @ SV706 @ SV767 @ SV586 ) )
= $false )
| ( ( ( SV409 = SV767 )
| ( SV194
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1839,plain,
! [SV412: $i,SV589: $i,SV708: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ SV197 @ SV708 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV197 @ SV589 ) )
= $true )
| ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV197 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV412 ) @ SV589 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1840,plain,
! [SV768: $i,SV709: $i,SV593: $i,SV417: $i,SV202: $i] :
( ( ( ( c_List_Oappend @ SV202 @ SV417 @ SV593 )
= ( c_List_Olist_OCons @ SV709 @ SV768 @ SV593 ) )
= $false )
| ( ( ( SV202
= ( c_List_Olist_OCons @ SV709 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV709 @ SV768 @ SV202 @ SV417 @ SV593 ) @ SV593 ) )
| ( SV417
= ( c_List_Olist_OCons @ SV709 @ SV768 @ SV593 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1841,plain,
! [SV769: $i,SV711: $i,SV596: $i,SV420: $i,SV205: $i] :
( ( ( ( c_List_Olist_OCons @ SV205 @ SV420 @ SV596 )
= ( c_List_Oappend @ SV711 @ SV769 @ SV596 ) )
= $false )
| ( ( ( SV420
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV205 @ SV420 @ SV711 @ SV769 @ SV596 ) @ SV769 @ SV596 ) )
| ( SV711
= ( c_List_Olist_ONil @ SV596 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1842,plain,
! [SV770: $i,SV712: $i,SV597: $i,SV421: $i,SV206: $i] :
( ( ( ( c_List_Olist_OCons @ SV206 @ SV421 @ SV597 )
= ( c_List_Olist_OCons @ SV712 @ SV770 @ SV597 ) )
= $false )
| ( ( SV206 = SV712 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1843,plain,
! [SV771: $i,SV714: $i,SV599: $i,SV423: $i,SV208: $i] :
( ( ( ( c_List_Oappend @ SV208 @ ( c_List_Olist_OCons @ SV423 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 )
= ( c_List_Oappend @ SV714 @ ( c_List_Olist_OCons @ SV771 @ ( c_List_Olist_ONil @ SV599 ) @ SV599 ) @ SV599 ) )
= $false )
| ( ( SV423 = SV771 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1844,plain,
! [SV600: $i,SV425: $i,SV715: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ SV210 @ SV715 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV210 @ SV425 ) )
= $true )
| ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV210 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV425 ) @ SV600 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1845,plain,
! [SV772: $i,SV716: $i,SV604: $i,SV429: $i,SV214: $i] :
( ( ( ( c_List_OdropWhile @ SV214 @ SV429 @ SV604 )
= ( c_List_Olist_OCons @ SV716 @ SV772 @ SV604 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV214 @ SV716 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1846,plain,
! [SV773: $i,SV717: $i,SV605: $i,SV430: $i,SV215: $i] :
( ( ( ( c_List_Oappend @ SV215 @ SV430 @ SV605 )
= ( c_List_Olist_OCons @ SV717 @ SV773 @ SV605 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV717 @ SV773 @ SV215 @ SV430 @ SV605 ) @ SV430 @ SV605 )
= SV773 )
| ( SV215
= ( c_List_Olist_ONil @ SV605 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1847,plain,
! [SV774: $i,SV719: $i,SV611: $i,SV437: $i,SV222: $i] :
( ( ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
= ( c_List_Oappend @ SV719 @ SV774 @ SV611 ) )
= $false )
| ( ( ( SV437
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV222 @ SV437 @ SV719 @ SV774 @ SV611 ) @ SV774 @ SV611 ) )
| ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
= SV774 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1848,plain,
! [SV456: $i,SV623: $i,SV245: $i,SV21: $i] :
( ( ( c_List_Olistsp @ SV21 @ SV245 @ SV623 )
= $false )
| ( ( c_List_Olistsp @ SV21 @ SV456 @ SV623 )
= $false )
| ( ( c_List_Olistsp @ SV21 @ ( c_List_Oappend @ SV245 @ SV456 @ SV623 ) @ SV623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1849,plain,
! [SV793: $i,SV776: $i,SV723: $i,SV626: $i,SV464: $i,SV260: $i,SV36: $i] :
( ( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
| ~ ( c_Type_Otypings @ SV464 @ SV776 @ SV793 )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1850,plain,
! [SV469: $i,SV630: $i,SV266: $i,SV777: $i,SV725: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SV725 ) @ SV777 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SV725 @ SV266 @ SV630 ) @ ( c_List_Olist_OCons @ SV777 @ SV469 @ SV630 ) @ SV630 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV44 @ SV266 @ SV469 @ SV630 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(1851,plain,
! [SV778: $i,SV634: $i,SV727: $i,SV55: $i,SV276: $i,SV476: $i] :
( ( ( SV476 = SV276 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SV727 @ SV276 @ SV634 ) @ ( c_List_Olist_OCons @ SV778 @ SV476 @ SV634 ) @ SV634 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV55 @ SV276 @ SV476 @ SV634 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1852,plain,
! [SV69: $i,SV779: $i,SV289: $i,SV729: $i,SV638: $i,SV484: $i] :
( ( ( SV484 = SV638 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV729 @ ( c_List_Olist_OCons @ SV289 @ SV638 @ SV779 ) @ ( c_List_Olist_OCons @ SV69 @ SV484 @ SV779 ) @ SV779 ) )
= $true )
| ( ( SV69 = SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1853,plain,
! [SV781: $i,SV733: $i,SV643: $i,SV78: $i,SV296: $i,SV489: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV489 @ SV296 ) @ SV78 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV489 @ ( c_List_Olist_OCons @ SV296 @ SV643 @ SV733 ) @ ( c_List_Olist_OCons @ SV78 @ SV781 @ SV733 ) @ SV733 ) )
= $true )
| ( ( SV78 = SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(1854,plain,
! [SV794: $i,SV782: $i,SV734: $i,SV644: $i,SV490: $i,SV297: $i,SV79: $i] :
( ( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
| ~ ( c_Type_Otypings @ SV79 @ SV782 @ SV794 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1855,plain,
! [SV303: $i,SV737: $i,SV648: $i,SV496: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ SV86 @ SV496 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ SV648 @ SV737 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV86 @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 @ SV86 @ ( c_List_Oappend @ SV303 @ ( c_List_Olist_OCons @ SV496 @ SV648 @ SV737 ) @ SV737 ) @ SV737 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1856,plain,
! [SV650: $i,SV739: $i,SV305: $i,SV498: $i,SV88: $i] :
( ( ( hBOOL @ ( hAPP @ SV88 @ SV498 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ SV305 @ SV739 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV88 @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 @ SV88 @ ( c_List_Oappend @ SV305 @ ( c_List_Olist_OCons @ SV498 @ SV650 @ SV739 ) @ SV739 ) @ SV739 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1857,plain,
! [SV655: $i,SV318: $i,SV741: $i,SV507: $i,SV101: $i] :
( ( ( c_Type_Otypings @ SV101 @ SV507 @ SV741 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV101 @ SV318 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV741 @ SV655 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV318 @ SV507 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV655 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1858,plain,
! [SV784: $i,SV742: $i,SV657: $i,SV509: $i,SV320: $i,SV103: $i] :
( ( ( c_Type_Otyping @ SV103 @ SV320 @ SV509 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SV657 @ SV509 @ tc_Type_Otype ) @ SV742 @ SV784 )
| ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SV742 @ SV320 @ SV657 ) @ SV784 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1859,plain,
! [SV785: $i,SV744: $i,SV660: $i,SV324: $i,SV107: $i,SV513: $i] :
( ( ( c_ListOrder_Ostep1 @ SV513 @ SV107 @ SV324 @ SV660 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV513 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ ( c_List_Oappend @ SV324 @ ( c_List_Olist_OCons @ SV785 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ SV660 ) )
= $true )
| ( ( SV107 = SV324 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(1860,plain,
! [SV516: $i,SV327: $i,SV786: $i,SV745: $i,SV661: $i,SV110: $i] :
( ( ( c_ListOrder_Ostep1 @ SV110 @ SV661 @ SV745 @ SV786 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SV661 @ ( c_List_Olist_OCons @ SV327 @ ( c_List_Olist_ONil @ SV786 ) @ SV786 ) @ SV786 ) @ ( c_List_Oappend @ SV745 @ ( c_List_Olist_OCons @ SV516 @ ( c_List_Olist_ONil @ SV786 ) @ SV786 ) @ SV786 ) @ SV786 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV327 ) @ SV516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1861,plain,
! [SV787: $i,SV746: $i,SV662: $i,SV112: $i,SV518: $i,SV329: $i] :
( ( ( SV329 = SV518 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SV662 @ ( c_List_Olist_OCons @ SV329 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ ( c_List_Oappend @ SV787 @ ( c_List_Olist_OCons @ SV518 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ SV746 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SV329 ) @ SV518 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1862,plain,
! [SV330: $i,SV788: $i,SV113: $i,SV747: $i,SV663: $i,SV519: $i] :
( ( ( SV519 = SV663 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV747 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SV519 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ ( c_List_Oappend @ SV330 @ ( c_List_Olist_OCons @ SV663 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ SV788 ) )
= $true )
| ( ( SV113 = SV330 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(1863,plain,
! [SV116: $i,SV333: $i,SV748: $i,SV664: $i,SV522: $i] :
( ( ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV333 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 ) )
= $true )
| ( ( SV116 = SV333 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1864,plain,
! [SV675: $i,SV353: $i,SV749: $i,SV535: $i,SV137: $i] :
( ( ( c_Type_Otyping @ SV137 @ SV535 @ SV749 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV137 @ SV353 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV749 ) @ SV675 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV535 ) @ SV675 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1865,plain,
! [SV551: $i,SV370: $i,SV756: $i,SV689: $i,SV155: $i] :
( ( ( SV155
= ( c_List_Olist_OCons @ SV689 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV689 @ SV756 @ SV155 @ SV370 @ SV551 ) @ SV551 ) )
= $true )
| ( ( SV155
= ( c_List_Olist_ONil @ SV551 ) )
= $true )
| ( ( ( c_List_Oappend @ SV155 @ SV370 @ SV551 )
= ( c_List_Olist_OCons @ SV689 @ SV756 @ SV551 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(1866,plain,
! [SV556: $i,SV757: $i,SV690: $i,SV375: $i,SV160: $i] :
( ( ( ( c_List_Olist_OCons @ SV160 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV160 @ SV375 @ SV690 @ SV757 @ SV556 ) @ SV556 )
= SV690 )
= $true )
| ( ( SV690
= ( c_List_Olist_ONil @ SV556 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV160 @ SV375 @ SV556 )
= ( c_List_Oappend @ SV690 @ SV757 @ SV556 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1867,plain,
! [SV758: $i,SV691: $i,SV557: $i,SV161: $i,SV376: $i] :
( ( ( ( c_List_OdropWhile @ SV376 @ SV161 @ SV557 )
= ( c_List_Olist_OCons @ SV691 @ SV758 @ SV557 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV376 @ SV691 ) )
= $true )
| ( ( SV161
= ( c_List_Oappend @ ( c_List_OtakeWhile @ SV376 @ SV161 @ SV557 ) @ ( c_List_Olist_OCons @ SV691 @ SV758 @ SV557 ) @ SV557 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1868,plain,
! [SV568: $i,SV760: $i,SV696: $i,SV390: $i,SV175: $i] :
( ( ( ( c_List_Olist_OCons @ SV175 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV175 @ SV390 @ SV696 @ SV760 @ SV568 ) @ SV568 )
= SV696 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
= SV760 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV175 @ SV390 @ SV568 )
= ( c_List_Oappend @ SV696 @ SV760 @ SV568 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(1869,plain,
! [SV795: $i,SV791: $i,SV761: $i,SV697: $i,SV569: $i,SV392: $i,SV177: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
| ~ ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(1870,plain,
! [SV570: $i,SV393: $i,SV178: $i,SV762: $i,SV698: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV698 @ SV762 @ SV178 @ SV393 @ SV570 ) @ SV393 @ SV570 )
= SV762 )
= $true )
| ( ( SV393
= ( c_List_Olist_OCons @ SV698 @ SV762 @ SV570 ) )
= $true )
| ( ( ( c_List_Oappend @ SV178 @ SV393 @ SV570 )
= ( c_List_Olist_OCons @ SV698 @ SV762 @ SV570 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1871,plain,
! [SV796: $i,SV792: $i,SV765: $i,SV704: $i,SV583: $i,SV406: $i,SV191: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
| ~ ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(1872,plain,
! [SV706: $i,SV586: $i,SV194: $i,SV767: $i,SV409: $i] :
( ( ( SV409 = SV767 )
= $true )
| ( ( SV194
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Oreplicate @ SV194 @ SV409 @ SV586 )
= ( c_List_Oreplicate @ SV706 @ SV767 @ SV586 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(1873,plain,
! [SV593: $i,SV417: $i,SV768: $i,SV709: $i,SV202: $i] :
( ( ( SV202
= ( c_List_Olist_OCons @ SV709 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV709 @ SV768 @ SV202 @ SV417 @ SV593 ) @ SV593 ) )
= $true )
| ( ( SV417
= ( c_List_Olist_OCons @ SV709 @ SV768 @ SV593 ) )
= $true )
| ( ( ( c_List_Oappend @ SV202 @ SV417 @ SV593 )
= ( c_List_Olist_OCons @ SV709 @ SV768 @ SV593 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(1874,plain,
! [SV596: $i,SV769: $i,SV711: $i,SV205: $i,SV420: $i] :
( ( ( SV420
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV205 @ SV420 @ SV711 @ SV769 @ SV596 ) @ SV769 @ SV596 ) )
= $true )
| ( ( SV711
= ( c_List_Olist_ONil @ SV596 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV205 @ SV420 @ SV596 )
= ( c_List_Oappend @ SV711 @ SV769 @ SV596 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(1875,plain,
! [SV772: $i,SV604: $i,SV429: $i,SV716: $i,SV214: $i] :
( ( ( hBOOL @ ( hAPP @ SV214 @ SV716 ) )
= $false )
| ( ( ( c_List_OdropWhile @ SV214 @ SV429 @ SV604 )
= ( c_List_Olist_OCons @ SV716 @ SV772 @ SV604 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1876,plain,
! [SV605: $i,SV430: $i,SV215: $i,SV773: $i,SV717: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV717 @ SV773 @ SV215 @ SV430 @ SV605 ) @ SV430 @ SV605 )
= SV773 )
= $true )
| ( ( SV215
= ( c_List_Olist_ONil @ SV605 ) )
= $true )
| ( ( ( c_List_Oappend @ SV215 @ SV430 @ SV605 )
= ( c_List_Olist_OCons @ SV717 @ SV773 @ SV605 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1877,plain,
! [SV611: $i,SV774: $i,SV719: $i,SV222: $i,SV437: $i] :
( ( ( SV437
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV222 @ SV437 @ SV719 @ SV774 @ SV611 ) @ SV774 @ SV611 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
= SV774 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV222 @ SV437 @ SV611 )
= ( c_List_Oappend @ SV719 @ SV774 @ SV611 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(1878,plain,
! [SV260: $i,SV626: $i,SV793: $i,SV36: $i,SV776: $i,SV723: $i,SV464: $i] :
( ( ( ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV464 @ SV776 @ SV793 )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) )
= $true )
| ( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(1879,plain,
! [SV469: $i,SV777: $i,SV630: $i,SV266: $i,SV725: $i,SV44: $i] :
( ( ( c_ListOrder_Ostep1 @ SV44 @ ( c_List_Olist_OCons @ SV725 @ SV266 @ SV630 ) @ ( c_List_Olist_OCons @ SV777 @ SV469 @ SV630 ) @ SV630 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV44 @ SV725 ) @ SV777 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV44 @ SV266 @ SV469 @ SV630 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1880,plain,
! [SV476: $i,SV778: $i,SV634: $i,SV276: $i,SV727: $i,SV55: $i] :
( ( ( c_ListOrder_Ostep1 @ SV55 @ ( c_List_Olist_OCons @ SV727 @ SV276 @ SV634 ) @ ( c_List_Olist_OCons @ SV778 @ SV476 @ SV634 ) @ SV634 )
= $false )
| ( ( SV476 = SV276 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV55 @ SV276 @ SV476 @ SV634 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1881,plain,
! [SV484: $i,SV69: $i,SV779: $i,SV638: $i,SV289: $i,SV729: $i] :
( ( ( c_ListOrder_Ostep1 @ SV729 @ ( c_List_Olist_OCons @ SV289 @ SV638 @ SV779 ) @ ( c_List_Olist_OCons @ SV69 @ SV484 @ SV779 ) @ SV779 )
= $false )
| ( ( SV484 = SV638 )
= $true )
| ( ( SV69 = SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1882,plain,
! [SV781: $i,SV78: $i,SV733: $i,SV643: $i,SV296: $i,SV489: $i] :
( ( ( c_ListOrder_Ostep1 @ SV489 @ ( c_List_Olist_OCons @ SV296 @ SV643 @ SV733 ) @ ( c_List_Olist_OCons @ SV78 @ SV781 @ SV733 ) @ SV733 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV489 @ SV296 ) @ SV78 ) )
= $true )
| ( ( SV78 = SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1883,plain,
! [SV490: $i,SV297: $i,SV794: $i,SV644: $i,SV782: $i,SV734: $i,SV79: $i] :
( ( ( ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV79 @ SV782 @ SV794 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) )
= $true )
| ( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(1884,plain,
! [SV507: $i,SV655: $i,SV741: $i,SV318: $i,SV101: $i] :
( ( ( c_Type_Otyping @ SV101 @ SV318 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV741 @ SV655 @ tc_Type_Otype @ tc_Type_Otype ) )
= $false )
| ( ( c_Type_Otypings @ SV101 @ SV507 @ SV741 )
= $false )
| ( ( c_Type_Otyping @ SV101 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV318 @ SV507 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV655 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1885,plain,
! [SV320: $i,SV784: $i,SV742: $i,SV509: $i,SV657: $i,SV103: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SV657 @ SV509 @ tc_Type_Otype ) @ SV742 @ SV784 ) )
= $true )
| ( ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SV742 @ SV320 @ SV657 ) @ SV784 )
= $true )
| ( ( c_Type_Otyping @ SV103 @ SV320 @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(1886,plain,
! [SV785: $i,SV324: $i,SV660: $i,SV744: $i,SV107: $i,SV513: $i] :
( ( ( c_ListOrder_Ostep1 @ SV513 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV744 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ ( c_List_Oappend @ SV324 @ ( c_List_Olist_OCons @ SV785 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) @ SV660 ) @ SV660 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV513 @ SV107 @ SV324 @ SV660 )
= $true )
| ( ( SV107 = SV324 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1887,plain,
! [SV516: $i,SV745: $i,SV786: $i,SV327: $i,SV661: $i,SV110: $i] :
( ( ( c_ListOrder_Ostep1 @ SV110 @ ( c_List_Oappend @ SV661 @ ( c_List_Olist_OCons @ SV327 @ ( c_List_Olist_ONil @ SV786 ) @ SV786 ) @ SV786 ) @ ( c_List_Oappend @ SV745 @ ( c_List_Olist_OCons @ SV516 @ ( c_List_Olist_ONil @ SV786 ) @ SV786 ) @ SV786 ) @ SV786 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV110 @ SV661 @ SV745 @ SV786 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV110 @ SV327 ) @ SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1888,plain,
! [SV518: $i,SV787: $i,SV746: $i,SV329: $i,SV662: $i,SV112: $i] :
( ( ( c_ListOrder_Ostep1 @ SV112 @ ( c_List_Oappend @ SV662 @ ( c_List_Olist_OCons @ SV329 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ ( c_List_Oappend @ SV787 @ ( c_List_Olist_OCons @ SV518 @ ( c_List_Olist_ONil @ SV746 ) @ SV746 ) @ SV746 ) @ SV746 )
= $false )
| ( ( SV329 = SV518 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV112 @ SV329 ) @ SV518 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1889,plain,
! [SV663: $i,SV330: $i,SV788: $i,SV519: $i,SV113: $i,SV747: $i] :
( ( ( c_ListOrder_Ostep1 @ SV747 @ ( c_List_Oappend @ SV113 @ ( c_List_Olist_OCons @ SV519 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ ( c_List_Oappend @ SV330 @ ( c_List_Olist_OCons @ SV663 @ ( c_List_Olist_ONil @ SV788 ) @ SV788 ) @ SV788 ) @ SV788 )
= $false )
| ( ( SV519 = SV663 )
= $true )
| ( ( SV113 = SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1890,plain,
! [SV333: $i,SV116: $i,SV748: $i,SV664: $i,SV522: $i] :
( ( ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV116 )
= $false )
| ( ( c_Type_Otyping @ SV522 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV664 ) @ SV748 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV333 )
= $false )
| ( ( SV116 = SV333 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(1891,plain,
! [SV535: $i,SV675: $i,SV749: $i,SV353: $i,SV137: $i] :
( ( ( c_Type_Otyping @ SV137 @ SV353 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV749 ) @ SV675 ) )
= $false )
| ( ( c_Type_Otyping @ SV137 @ SV535 @ SV749 )
= $false )
| ( ( c_Type_Otyping @ SV137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV535 ) @ SV675 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1892,plain,
! [SV795: $i,SV791: $i,SV761: $i,SV697: $i,SV569: $i,SV392: $i,SV177: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
| ~ ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1893,plain,
! [SV796: $i,SV792: $i,SV765: $i,SV704: $i,SV583: $i,SV406: $i,SV191: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
| ~ ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1894,plain,
! [SV260: $i,SV626: $i,SV793: $i,SV36: $i,SV776: $i,SV723: $i,SV464: $i] :
( ( ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV464 @ SV776 @ SV793 )
| ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) )
= $true )
| ( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1895,plain,
! [SV490: $i,SV297: $i,SV794: $i,SV644: $i,SV782: $i,SV734: $i,SV79: $i] :
( ( ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV79 @ SV782 @ SV794 )
| ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) )
= $true )
| ( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1896,plain,
! [SV320: $i,SV784: $i,SV742: $i,SV509: $i,SV657: $i,SV103: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV103 @ SV657 @ SV509 @ tc_Type_Otype ) @ SV742 @ SV784 )
= $false )
| ( ( c_Type_Otyping @ SV103 @ ( c_Lambda_Osubst @ SV742 @ SV320 @ SV657 ) @ SV784 )
= $true )
| ( ( c_Type_Otyping @ SV103 @ SV320 @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1897,plain,
! [SV392: $i,SV795: $i,SV177: $i,SV791: $i,SV761: $i,SV697: $i,SV569: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(1898,plain,
! [SV191: $i,SV796: $i,SV406: $i,SV792: $i,SV765: $i,SV704: $i,SV583: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(1899,plain,
! [SV36: $i,SV260: $i,SV626: $i,SV723: $i,SV793: $i,SV776: $i,SV464: $i] :
( ( ( ~ ( c_Type_Otypings @ SV464 @ SV776 @ SV793 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) )
= $true )
| ( ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
= $false )
| ( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(1900,plain,
! [SV644: $i,SV490: $i,SV297: $i,SV734: $i,SV794: $i,SV782: $i,SV79: $i] :
( ( ( ~ ( c_Type_Otypings @ SV79 @ SV782 @ SV794 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) )
= $true )
| ( ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
= $false )
| ( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(1901,plain,
! [SV392: $i,SV795: $i,SV569: $i,SV761: $i,SV177: $i,SV697: $i,SV791: $i] :
( ( ( ~ ( c_Type_Otyping @ SV791 @ SV697 @ SV177 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(1902,plain,
! [SV191: $i,SV796: $i,SV583: $i,SV765: $i,SV406: $i,SV704: $i,SV792: $i] :
( ( ( ~ ( c_Type_Otyping @ SV792 @ SV704 @ SV406 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(1903,plain,
! [SV36: $i,SV260: $i,SV626: $i,SV723: $i,SV793: $i,SV776: $i,SV464: $i] :
( ( ( c_Type_Otypings @ SV464 @ SV776 @ SV793 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 ) )
= $true )
| ( ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
= $false )
| ( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(1904,plain,
! [SV644: $i,SV490: $i,SV297: $i,SV734: $i,SV794: $i,SV782: $i,SV79: $i] :
( ( ( c_Type_Otypings @ SV79 @ SV782 @ SV794 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 ) )
= $true )
| ( ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
= $false )
| ( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(1905,plain,
! [SV392: $i,SV795: $i,SV569: $i,SV761: $i,SV177: $i,SV697: $i,SV791: $i] :
( ( ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1906,plain,
! [SV191: $i,SV796: $i,SV583: $i,SV765: $i,SV406: $i,SV704: $i,SV792: $i] :
( ( ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1907,plain,
! [SV36: $i,SV793: $i,SV260: $i,SV626: $i,SV776: $i,SV723: $i,SV464: $i] :
( ( ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV260 )
= $false )
| ( ( c_Type_Otypings @ SV464 @ SV776 @ SV793 )
= $false )
| ( ( c_Type_Otyping @ SV464 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV723 ) @ SV776 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV36 )
= $false )
| ( ( SV36
= ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV260 @ SV36 @ SV464 @ SV626 ) @ SV260 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(1908,plain,
! [SV644: $i,SV794: $i,SV490: $i,SV297: $i,SV782: $i,SV734: $i,SV79: $i] :
( ( ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV490 )
= $false )
| ( ( c_Type_Otypings @ SV79 @ SV782 @ SV794 )
= $false )
| ( ( c_Type_Otyping @ SV79 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV734 ) @ SV782 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV644 )
= $false )
| ( ( c_Type_Otypings @ SV79 @ SV297 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV490 @ SV644 @ SV79 @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1909,plain,
! [SV392: $i,SV795: $i,SV569: $i,SV177: $i,SV761: $i,SV791: $i,SV697: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(1910,plain,
! [SV191: $i,SV796: $i,SV583: $i,SV406: $i,SV765: $i,SV792: $i,SV704: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(1911,plain,
! [SV392: $i,SV795: $i,SV569: $i,SV177: $i,SV761: $i,SV791: $i,SV697: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(1912,plain,
! [SV191: $i,SV796: $i,SV583: $i,SV406: $i,SV765: $i,SV792: $i,SV704: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1913,plain,
! [SV392: $i,SV697: $i,SV795: $i,SV569: $i,SV177: $i,SV761: $i,SV791: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
= $false )
| ( ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1914,plain,
! [SV191: $i,SV704: $i,SV796: $i,SV583: $i,SV406: $i,SV765: $i,SV792: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
= $false )
| ( ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(1915,plain,
! [SV392: $i,SV697: $i,SV795: $i,SV569: $i,SV177: $i,SV761: $i,SV791: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
= $false )
| ( ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1916,plain,
! [SV191: $i,SV704: $i,SV796: $i,SV583: $i,SV406: $i,SV765: $i,SV792: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
= $false )
| ( ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1917,plain,
! [SV392: $i,SV697: $i,SV795: $i,SV177: $i,SV761: $i,SV791: $i,SV569: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV569 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV791 @ SV761 @ SV177 @ tc_Type_Otype ) @ SV569 @ SV795 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV697 ) )
= $false )
| ( ( c_Type_Otyping @ SV791 @ SV697 @ SV177 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV569 @ SV697 @ SV761 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV177 ) @ SV392 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(1918,plain,
! [SV191: $i,SV704: $i,SV796: $i,SV406: $i,SV765: $i,SV792: $i,SV583: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV583 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV792 @ SV765 @ SV406 @ tc_Type_Otype ) @ SV583 @ SV796 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV704 ) )
= $false )
| ( ( c_Type_Otyping @ SV792 @ SV704 @ SV406 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV583 @ SV704 @ SV765 ) ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV191 ) @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1919,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[494,1918,1917,1908,1907,1896,1891,1890,1889,1888,1887,1886,1884,1882,1881,1880,1879,1877,1876,1875,1874,1873,1872,1870,1868,1867,1866,1865,1856,1855,1848,1844,1843,1842,1839,1837,1835,1834,1830,1826,1825,1818,1811,1810,1808,1805,1802,1801,1799,1794,1789,1783,1782,1781,1777,1776,1771,1770,1767,1766,1764,1763,1762,1756,1753,1751,1750,1749,1746,1745,1742,1741,1735,1732,1730,1728,1726,1725,1724,1723,1721,1720,1718,1717,1713,1712,1706,1705,1703,1702,1701,1696,1694,1691,1690,1689,1687,1680,1679,1678,1676,1675,1673,1670,1666,1663,1662,1658,1640,1637,1627,1625,1623,1618,1615,1613,1608,1605,1604,1600,1597,1596,1591,1579,1576,1568,1565,1555,1552,1549,1543,1540,1539,1538,1528,1525,1524,1523,1522,1520,1519,1517,1516,1515,1514,1513,1510,1496,1495,1494,1493,1492,1491,1475,1474,1473,1472,1469,1468,1461,1459,1457,1455,1445,1443,1424,1391,1355,1343,1339,1338,1335,1333,1332,1330,1311,1309,1305,1300,1297,1296,1295,1288,1285,1277,1276,1271,1268,1266,1257,1256,1176,1159,1158,1157,1156,1155,1153,1123,1122,1119,1097,1096,1095,1078,1077,1069,1067,1065,1064,1059,1057,1056,1049,1048,1042,1037,979,960,946,926,890,881,877,869,854,849,847,817,814,728,727,720,719,691,684,658,657,656,604,601,550,510]) ).
thf(1920,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1919]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL788-1 : 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
% 0.11/0.16 % Computer : n005.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Oct 6 12:34:00 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.78/4.17 .
% 23.78/4.17
% 23.78/4.17 No.of.Axioms: 242
% 23.78/4.17
% 23.78/4.17 Length.of.Defs: 0
% 23.78/4.17
% 23.78/4.17 Contains.Choice.Funs: false
% 23.78/4.17 ..................................................................................
% 23.78/4.17
% 23.78/4.17 ********************************
% 23.78/4.17 * All subproblems solved! *
% 23.78/4.17 ********************************
% 23.78/4.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:242,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1919,loop_count:0,foatp_calls:1,translation:fof_full)
% 23.78/4.17
% 23.78/4.17 %**** Beginning of derivation protocol ****
% 23.78/4.17 % SZS output start CNFRefutation
% See solution above
% 23.78/4.19
% 23.78/4.19 %**** End of derivation protocol ****
% 23.78/4.19 %**** no. of clauses in derivation: 1920 ****
% 23.78/4.19 %**** clause counter: 1919 ****
% 23.78/4.19
% 23.78/4.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:242,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1919,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------