%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL771-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:30:24 AM UTC 2026
% Result : Unsatisfiable 45.24s 7.97s
% Output : CNFRefutation 45.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 429
% Syntax : Number of formulae : 3470 (2430 unt; 0 typ; 0 def)
% Number of atoms : 15232 (7194 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 44099 (2543 ~;3548 |; 0 &;38008 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 99 ( 96 usr; 12 con; 0-5 aty)
% Number of variables : 11790 ( 0 ^;11790 !; 0 ?;11790 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
thf(tp_c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
thf(tp_c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tp_c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
thf(tp_c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(tp_c_Lambda_OdB_OdB__case,type,
c_Lambda_OdB_OdB__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Lambda_OdB_OdB__rec,type,
c_Lambda_OdB_OdB__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Lambda_Olift,type,
c_Lambda_Olift: $i > $i > $i ).
thf(tp_c_Lambda_Oliftn,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(tp_c_Lambda_Osubstn,type,
c_Lambda_Osubstn: $i > $i > $i > $i ).
thf(tp_c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(tp_c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(tp_c_List_Obutlast,type,
c_List_Obutlast: $i > $i > $i ).
thf(tp_c_List_Ofilter,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(tp_c_List_Ofiltermap,type,
c_List_Ofiltermap: $i > $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_Olast,type,
c_List_Olast: $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osorted,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olist_Olist__case,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_Olist__rec,type,
c_List_Olist_Olist__rec: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist__ex,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(tp_c_List_Olist__update,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olistrelp,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(tp_c_List_Omap,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(tp_c_List_Onull,type,
c_List_Onull: $i > $i > $o ).
thf(tp_c_List_Oremdups,type,
c_List_Oremdups: $i > $i > $i ).
thf(tp_c_List_Oremove1,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i > $i ).
thf(tp_c_List_Orotate,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(tp_c_List_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__XCons__eq__filter__iff__1__3,type,
c_List_Osko__List__XCons__eq__filter__iff__1__3: $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__Xfilter__eq__Cons__iff__1__3,type,
c_List_Osko__List__Xfilter__eq__Cons__iff__1__3: $i > $i > $i > $i ).
thf(tp_c_List_Osko__List__Xin__listsp__conv__set__1__1,type,
c_List_Osko__List__Xin__listsp__conv__set__1__1: $i > $i > $i > $i ).
thf(tp_c_List_Osublist,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(tp_c_Map_Omap__upds,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i > $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
thf(tp_class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $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_t_b,type,
t_b: $i ).
thf(tp_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_List_Olist,type,
tc_List_Olist: $i > $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_i,type,
v_i: $i ).
thf(tp_v_rs,type,
v_rs: $i ).
thf(tp_v_sko__List__Xconcat__Xinduct__1,type,
v_sko__List__Xconcat__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xconcat__Xinduct__2,type,
v_sko__List__Xconcat__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xdistinct__Xinduct__1,type,
v_sko__List__Xdistinct__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xdistinct__Xinduct__2,type,
v_sko__List__Xdistinct__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__XdropWhile__Xinduct__1,type,
v_sko__List__XdropWhile__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__XdropWhile__Xinduct__2,type,
v_sko__List__XdropWhile__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xlist__Xinduct__1,type,
v_sko__List__Xlist__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xlist__Xinduct__2,type,
v_sko__List__Xlist__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xlistset__Xinduct__1,type,
v_sko__List__Xlistset__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xlistset__Xinduct__2,type,
v_sko__List__Xlistset__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xlistsp__Xcases__1,type,
v_sko__List__Xlistsp__Xcases__1: $i > $i > $i ).
thf(tp_v_sko__List__Xlistsp__Xcases__2,type,
v_sko__List__Xlistsp__Xcases__2: $i > $i > $i ).
thf(tp_v_sko__List__Xlistsp__Xinduct__1,type,
v_sko__List__Xlistsp__Xinduct__1: $i > $i > $i ).
thf(tp_v_sko__List__Xlistsp__Xinduct__2,type,
v_sko__List__Xlistsp__Xinduct__2: $i > $i > $i ).
thf(tp_v_sko__List__Xlistsp__Xinducts__1,type,
v_sko__List__Xlistsp__Xinducts__1: $i > $i > $i ).
thf(tp_v_sko__List__Xlistsp__Xinducts__2,type,
v_sko__List__Xlistsp__Xinducts__2: $i > $i > $i ).
thf(tp_v_sko__List__Xmap__Xinduct__1,type,
v_sko__List__Xmap__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xmap__Xinduct__2,type,
v_sko__List__Xmap__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xremove1__Xinduct__1,type,
v_sko__List__Xremove1__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xremove1__Xinduct__2,type,
v_sko__List__Xremove1__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xtake__Xinduct__1,type,
v_sko__List__Xtake__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xtake__Xinduct__2,type,
v_sko__List__Xtake__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xzip__Xinduct__1,type,
v_sko__List__Xzip__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xzip__Xinduct__2,type,
v_sko__List__Xzip__Xinduct__2: $i > $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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(4,axiom,
! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(6,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(8,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(9,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(10,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(11,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(12,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(13,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(14,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(15,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(16,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(17,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(18,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(20,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(21,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(22,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(23,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(24,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(25,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(26,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(27,axiom,
! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(28,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(29,axiom,
! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(30,axiom,
! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(31,axiom,
! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(32,axiom,
! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(33,axiom,
! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_1) ).
thf(34,axiom,
! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_1) ).
thf(35,axiom,
! [V_A: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xcases__1 @ V_A @ V_a ) ) )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_1) ).
thf(36,axiom,
! [V_A: $i,V_a: $i] :
( ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xcases__2 @ V_A @ V_a ) @ t_a )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_2) ).
thf(37,axiom,
! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_2) ).
thf(38,axiom,
! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xinduct__1 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_0) ).
thf(39,axiom,
! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_2) ).
thf(40,axiom,
! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xinducts__1 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_0) ).
thf(41,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(42,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(43,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(44,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(45,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(48,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_l: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_l @ T_a )
| ~ ( c_List_Olistsp @ V_B @ V_l @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__infI_0) ).
thf(49,axiom,
! [V_A: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_A @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ V_A @ V_xs @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(51,axiom,
! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(52,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(53,axiom,
! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(54,axiom,
! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(55,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(56,axiom,
! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(57,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
thf(58,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(59,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(60,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
thf(61,axiom,
! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(62,axiom,
! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(63,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
thf(64,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xd: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_xd ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
thf(65,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(66,axiom,
! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(67,axiom,
! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(68,axiom,
! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(69,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(70,axiom,
! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(71,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(72,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(73,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(74,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB1 @ T_a ) ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB2 @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
thf(75,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
thf(76,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(77,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
thf(78,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_xb ) @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xb ) @ V_xc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
thf(79,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(80,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(81,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(82,axiom,
! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(83,axiom,
! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(84,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xmap__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).
thf(85,axiom,
! [V_r: $i,T_a: $i] : ( c_List_Olistrelp @ V_r @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(87,axiom,
! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(88,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).
thf(89,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(91,axiom,
! [V_f1: $i,V_f2: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_f1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).
thf(92,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xremove1__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).
thf(93,axiom,
! [V_m: $i,T_a: $i,V_bs: $i,T_b: $i] :
( ( c_Map_Omap__upds @ V_m @ ( c_List_Olist_ONil @ T_a ) @ V_bs @ T_a @ T_b )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).
thf(94,axiom,
! [V_m: $i,V_as: $i,T_b: $i,T_a: $i] :
( ( c_Map_Omap__upds @ V_m @ V_as @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).
thf(95,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xdistinct__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).
thf(96,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(99,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xconcat__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).
thf(100,axiom,
! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(101,axiom,
! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(102,axiom,
! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(103,axiom,
! [V_P: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(104,axiom,
! [T_a: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oremdups @ V_x @ T_a ) )
| ( V_x
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(105,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofiltermap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).
thf(106,axiom,
! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(107,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xtake__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take_Oinduct_0) ).
thf(108,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XdropWhile__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_0) ).
thf(109,axiom,
! [V_f1: $i,V_f2: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_f1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Orecs_I1_J_0) ).
thf(110,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistset__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listset_Oinduct_0) ).
thf(111,axiom,
! [T_a: $i,V_A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sublist__nil_0) ).
thf(112,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(113,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xzip__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zip_Oinduct_0) ).
thf(114,axiom,
! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(115,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_f1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_0) ).
thf(116,axiom,
! [T_a: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_0) ).
thf(117,axiom,
! [V_P: $i,T_a: $i] :
~ ( c_List_Olist__ex @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I1_J_0) ).
thf(118,axiom,
! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ V_a @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(123,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(124,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_xa @ V_xb @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).
thf(125,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_a: $i,V_list: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osplit_1) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(128,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__filter_0) ).
thf(129,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(130,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ofilter @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(131,axiom,
! [T_a: $i,V_l: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ V_l @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(132,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(133,axiom,
! [T_a: $i,V_ys: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_ys @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(134,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(135,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(138,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(139,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(141,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_xa ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).
thf(142,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_dB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(144,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(145,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(146,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(147,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
thf(148,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ ( hAPP @ V_f3 @ V_dB ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(151,axiom,
! [V_f1: $i,V_f2: $i,V_a: $i,V_list: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) @ ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ V_list @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Orecs_I2_J_0) ).
thf(152,axiom,
! [V_x: $i,V_P: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oremove1 @ V_x @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(153,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(154,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(155,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(156,axiom,
! [V_a: $i,V_A: $i] :
( ( V_a
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ V_A @ V_a ) @ ( v_sko__List__Xlistsp__Xcases__2 @ V_A @ V_a ) @ t_a ) )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Ocases_0) ).
thf(157,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(158,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(159,axiom,
! [V_x: $i,V_y: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ ( c_List_Oremove1 @ V_x @ V_xs @ T_a ) @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(160,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(161,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(162,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(163,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(164,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(165,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(166,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(167,axiom,
! [V_r: $i,V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Olistrelp @ V_r @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistrelp @ V_r @ V_xs @ V_ys @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).
thf(168,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Olist__ex @ V_P @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).
thf(169,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__ex @ V_P @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(171,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(173,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(174,axiom,
! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(175,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(176,axiom,
! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orotate @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__map_0) ).
thf(177,axiom,
! [V_P: $i,V_ys: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Ofilter @ V_P @ V_ys @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(180,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__map_0) ).
thf(181,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(182,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ V_f3 @ V_dB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(184,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ofilter @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(185,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__filter_0) ).
thf(186,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_P: $i,V_ys: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Ofilter @ V_P @ V_ys @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(191,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(192,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(193,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(194,axiom,
! [T_a: $i,V_y: $i,V_zs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(195,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(198,axiom,
! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(199,axiom,
! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(200,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(201,axiom,
! [V_f1: $i,V_f2: $i,V_a: $i,V_list: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).
thf(202,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(205,axiom,
! [T_a: $i,V_xs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(207,axiom,
! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ V_A @ V_P ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinduct_3) ).
thf(208,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(209,axiom,
! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ V_A @ V_P ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_Oinducts_3) ).
thf(210,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(214,axiom,
! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__update_0) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr_0) ).
thf(217,axiom,
! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(218,axiom,
! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(219,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(220,axiom,
! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) @ V_k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
thf(221,axiom,
! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_1) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(234,axiom,
! [V_P: $i,V_x: $i,V_xa: $i,T_a: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ V_P @ V_xa @ T_a ) ) )
| ( ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xb @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__eq__Cons__iff_5) ).
thf(235,axiom,
! [V_P: $i,V_x: $i,V_xa: $i,T_a: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ V_P @ V_xa @ T_a ) ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xb @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filter__iff_5) ).
thf(236,axiom,
! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(237,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(238,axiom,
! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(239,axiom,
! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(240,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ V_P ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).
thf(241,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ V_P ) @ ( v_sko__List__Xremove1__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).
thf(242,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlistset__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listset_Oinduct_1) ).
thf(243,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ V_P ) @ ( v_sko__List__Xzip__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zip_Oinduct_1) ).
thf(244,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ V_P ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_1) ).
thf(245,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlist__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).
thf(246,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ V_P ) @ ( v_sko__List__Xmap__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Oinduct_1) ).
thf(247,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ V_P ) @ ( v_sko__List__Xtake__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take_Oinduct_1) ).
thf(248,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ V_P ) @ ( v_sko__List__Xconcat__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_concat_Oinduct_1) ).
thf(249,axiom,
! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(250,axiom,
! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(251,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(257,axiom,
! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(258,axiom,
! [T_a: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(259,axiom,
! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(261,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(266,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(267,axiom,
! [V_x: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_x
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(268,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/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(270,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/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(272,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(273,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(274,axiom,
! [V_xs: $i,T_a: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_List_Onull @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_1) ).
thf(275,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(277,axiom,
! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ ( c_List_Ofilter @ V_P @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(279,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/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(280,axiom,
! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(281,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(282,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(283,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(284,axiom,
! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(285,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i,T_b: $i,V_m: $i,V_zs: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) )
| ( ( c_Map_Omap__upds @ V_m @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_b ) @ T_a @ T_b )
= ( c_Map_Omap__upds @ V_m @ V_xs @ V_ys @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).
thf(286,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i,T_b: $i,V_m: $i,V_zs: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) )
| ( ( c_Map_Omap__upds @ V_m @ ( c_List_Oappend @ V_xs @ V_zs @ T_a ) @ V_ys @ T_a @ T_b )
= ( c_Map_Omap__upds @ V_m @ V_xs @ V_ys @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).
thf(287,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(288,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(289,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(290,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(291,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(292,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(293,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
thf(294,axiom,
! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(295,axiom,
! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(296,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(297,axiom,
! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(298,axiom,
! [V_P: $i,V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ofilter @ V_P @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_1) ).
thf(299,axiom,
! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(300,axiom,
! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(301,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(302,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(303,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/sandbox/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(304,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/sandbox/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(310,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(314,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/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(315,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/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(316,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(317,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/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).
thf(318,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/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_5) ).
thf(320,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/sandbox/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(321,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(322,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(323,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(324,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(325,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(326,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(327,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Orotate @ V_n @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
thf(328,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(329,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(330,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(331,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(332,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(333,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(334,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(335,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(337,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(338,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(339,axiom,
! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(340,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(342,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(343,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(344,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(345,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(346,axiom,
! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(347,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(348,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(349,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(350,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(351,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/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(352,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(353,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(354,axiom,
! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(355,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(356,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(357,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(358,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(359,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(360,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(361,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(362,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(363,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(364,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(365,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/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(366,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate_0) ).
thf(367,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append1_0) ).
thf(368,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_0) ).
thf(369,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(370,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(371,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(372,axiom,
! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(373,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
thf(374,axiom,
! [V_P: $i,V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ofilter @ V_P @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_0) ).
thf(375,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(376,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(377,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(378,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(379,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/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(380,axiom,
! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__replicate_0) ).
thf(381,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__map_0) ).
thf(382,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
!= V_xs )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__eq_1) ).
thf(383,axiom,
! [T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(384,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/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(385,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(386,axiom,
! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(387,axiom,
! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(388,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(389,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(390,axiom,
! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(391,axiom,
! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).
thf(392,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(394,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(395,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(396,axiom,
! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(397,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(398,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/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(399,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/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(400,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/sandbox/benchmark/theBenchmark.p',cls_last__replicate_0) ).
thf(401,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Orotate1 @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__Suc_0) ).
thf(402,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(403,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
thf(404,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(405,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(406,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(407,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(408,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(409,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(410,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(411,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(412,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
thf(413,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/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(414,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/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(415,axiom,
! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
thf(416,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(417,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(419,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/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(420,axiom,
! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(421,axiom,
! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(422,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(423,axiom,
! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(424,axiom,
! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(425,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) )
| ( ( c_List_Oremdups @ V_xs @ T_a )
= V_xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).
thf(426,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(427,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[426]) ).
thf(428,negated_conjecture,
~ ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(429,negated_conjecture,
c_List_Olistsp @ ( c_COMBB @ c_InductTermi_OIT @ ( hAPP @ ( c_COMBC @ c_Lambda_OdB_OApp @ tc_Lambda_OdB @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OVar @ v_i ) ) @ tc_Lambda_OdB @ tc_bool @ tc_Lambda_OdB ) @ v_rs @ tc_Lambda_OdB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(430,negated_conjecture,
c_List_Olistsp @ c_InductTermi_OIT @ v_rs @ tc_Lambda_OdB,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(431,plain,
$false = $false,
inference(unfold_def,[status(thm)],[427]) ).
thf(432,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(433,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(434,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(435,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(436,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(437,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(438,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(439,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(440,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(441,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(442,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(443,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(444,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(445,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(446,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(447,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(448,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(449,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)],[18]) ).
thf(450,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)],[19]) ).
thf(451,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(452,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)],[21]) ).
thf(453,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(454,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)],[23]) ).
thf(455,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)],[24]) ).
thf(456,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)],[25]) ).
thf(457,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)],[26]) ).
thf(458,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)],[27]) ).
thf(459,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)],[28]) ).
thf(460,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)],[29]) ).
thf(461,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)],[30]) ).
thf(462,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)],[31]) ).
thf(463,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)],[32]) ).
thf(464,plain,
( ( ! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(465,plain,
( ( ! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(466,plain,
( ( ! [V_A: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xcases__1 @ V_A @ V_a ) ) )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(467,plain,
( ( ! [V_A: $i,V_a: $i] :
( ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xcases__2 @ V_A @ V_a ) @ t_a )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(468,plain,
( ( ! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(469,plain,
( ( ! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xinduct__1 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(470,plain,
( ( ! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(471,plain,
( ( ! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xinducts__1 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(472,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)],[41]) ).
thf(473,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)],[42]) ).
thf(474,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)],[43]) ).
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)],[44]) ).
thf(476,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)],[45]) ).
thf(477,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)],[46]) ).
thf(478,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)],[47]) ).
thf(479,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_l: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_l @ T_a )
| ~ ( c_List_Olistsp @ V_B @ V_l @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(480,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_A @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ V_A @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(481,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)],[50]) ).
thf(482,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)],[51]) ).
thf(483,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)],[52]) ).
thf(484,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(485,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)],[54]) ).
thf(486,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)],[55]) ).
thf(487,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)],[56]) ).
thf(488,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(489,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)],[58]) ).
thf(490,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(491,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(492,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(493,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)],[62]) ).
thf(494,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(495,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xd: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_xd ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xd ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(496,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)],[65]) ).
thf(497,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)],[66]) ).
thf(498,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)],[67]) ).
thf(499,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)],[68]) ).
thf(500,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(501,plain,
( ( ! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(502,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(503,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(504,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)],[73]) ).
thf(505,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB1 @ T_a ) ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB2 @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(506,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(507,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)],[76]) ).
thf(508,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(509,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_xb ) @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xb ) @ V_xc ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(510,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)],[79]) ).
thf(511,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)],[80]) ).
thf(512,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)],[81]) ).
thf(513,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(514,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)],[83]) ).
thf(515,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xmap__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(516,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_List_Olistrelp @ V_r @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(517,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)],[86]) ).
thf(518,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(519,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(520,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(521,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)],[90]) ).
thf(522,plain,
( ( ! [V_f1: $i,V_f2: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_f1 ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(523,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xremove1__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(524,plain,
( ( ! [V_m: $i,T_a: $i,V_bs: $i,T_b: $i] :
( ( c_Map_Omap__upds @ V_m @ ( c_List_Olist_ONil @ T_a ) @ V_bs @ T_a @ T_b )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(525,plain,
( ( ! [V_m: $i,V_as: $i,T_b: $i,T_a: $i] :
( ( c_Map_Omap__upds @ V_m @ V_as @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(526,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xdistinct__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(527,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(528,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)],[97]) ).
thf(529,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)],[98]) ).
thf(530,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xconcat__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(531,plain,
( ( ! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(532,plain,
( ( ! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(533,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(534,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(535,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oremdups @ V_x @ T_a ) )
| ( V_x
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(536,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofiltermap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(537,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(538,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xtake__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(539,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XdropWhile__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(540,plain,
( ( ! [V_f1: $i,V_f2: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_f1 ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(541,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistset__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(542,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(543,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(544,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xzip__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(545,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)],[114]) ).
thf(546,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_f1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(547,plain,
( ( ! [T_a: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(548,plain,
( ( ! [V_P: $i,T_a: $i] :
~ ( c_List_Olist__ex @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(549,plain,
( ( ! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ V_a @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(550,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)],[119]) ).
thf(551,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)],[120]) ).
thf(552,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)],[121]) ).
thf(553,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)],[122]) ).
thf(554,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(555,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_xa @ V_xb @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(556,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_a: $i,V_list: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(557,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)],[126]) ).
thf(558,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)],[127]) ).
thf(559,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(560,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(561,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ofilter @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(562,plain,
( ( ! [T_a: $i,V_l: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ V_l @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(563,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(564,plain,
( ( ! [T_a: $i,V_ys: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_ys @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(565,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(566,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(567,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)],[136]) ).
thf(568,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)],[137]) ).
thf(569,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(570,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(571,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)],[140]) ).
thf(572,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_xa ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(573,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_dB ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(574,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)],[143]) ).
thf(575,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(576,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(577,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(578,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(579,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ ( hAPP @ V_f3 @ V_dB ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(580,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)],[149]) ).
thf(581,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)],[150]) ).
thf(582,plain,
( ( ! [V_f1: $i,V_f2: $i,V_a: $i,V_list: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) @ ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ V_list @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(583,plain,
( ( ! [V_x: $i,V_P: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oremove1 @ V_x @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(584,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)],[153]) ).
thf(585,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)],[154]) ).
thf(586,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)],[155]) ).
thf(587,plain,
( ( ! [V_a: $i,V_A: $i] :
( ( V_a
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ V_A @ V_a ) @ ( v_sko__List__Xlistsp__Xcases__2 @ V_A @ V_a ) @ t_a ) )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(588,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(589,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(590,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ ( c_List_Oremove1 @ V_x @ V_xs @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(591,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)],[160]) ).
thf(592,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(593,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(594,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(595,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(596,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(597,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(598,plain,
( ( ! [V_r: $i,V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Olistrelp @ V_r @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistrelp @ V_r @ V_xs @ V_ys @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(599,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Olist__ex @ V_P @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(600,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__ex @ V_P @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(601,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)],[170]) ).
thf(602,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(603,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)],[172]) ).
thf(604,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)],[173]) ).
thf(605,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)],[174]) ).
thf(606,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)],[175]) ).
thf(607,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orotate @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(608,plain,
( ( ! [V_P: $i,V_ys: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( ( c_List_Ofilter @ V_P @ V_ys @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(609,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)],[178]) ).
thf(610,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)],[179]) ).
thf(611,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(612,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(613,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ V_f3 @ V_dB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(614,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)],[183]) ).
thf(615,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ofilter @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(616,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(617,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_P: $i,V_ys: $i] :
( ( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Ofilter @ V_P @ V_ys @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(618,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)],[187]) ).
thf(619,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)],[188]) ).
thf(620,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)],[189]) ).
thf(621,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)],[190]) ).
thf(622,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(623,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(624,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(625,plain,
( ( ! [T_a: $i,V_y: $i,V_zs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(626,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)],[195]) ).
thf(627,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(628,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(629,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(630,plain,
( ( ! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(631,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(632,plain,
( ( ! [V_f1: $i,V_f2: $i,V_a: $i,V_list: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(633,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(634,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)],[203]) ).
thf(635,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)],[204]) ).
thf(636,plain,
( ( ! [T_a: $i,V_xs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(637,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)],[206]) ).
thf(638,plain,
( ( ! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ V_A @ V_P ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(639,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)],[208]) ).
thf(640,plain,
( ( ! [V_P: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ V_A @ V_P ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(641,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(642,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)],[211]) ).
thf(643,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)],[212]) ).
thf(644,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)],[213]) ).
thf(645,plain,
( ( ! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(646,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)],[215]) ).
thf(647,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)],[216]) ).
thf(648,plain,
( ( ! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(649,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(650,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(651,plain,
( ( ! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) @ V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(652,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(653,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)],[222]) ).
thf(654,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)],[223]) ).
thf(655,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)],[224]) ).
thf(656,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)],[225]) ).
thf(657,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)],[226]) ).
thf(658,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)],[227]) ).
thf(659,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)],[228]) ).
thf(660,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)],[229]) ).
thf(661,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)],[230]) ).
thf(662,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)],[231]) ).
thf(663,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)],[232]) ).
thf(664,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)],[233]) ).
thf(665,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i,T_a: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ V_P @ V_xa @ T_a ) ) )
| ( ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xb @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(666,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i,T_a: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ V_P @ V_xa @ T_a ) ) )
| ( ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xb @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(667,plain,
( ( ! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(668,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(669,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(670,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(671,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ V_P ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(672,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ V_P ) @ ( v_sko__List__Xremove1__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(673,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlistset__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(674,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ V_P ) @ ( v_sko__List__Xzip__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(675,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ V_P ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(676,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlist__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(677,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ V_P ) @ ( v_sko__List__Xmap__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(678,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ V_P ) @ ( v_sko__List__Xtake__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(679,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ V_P ) @ ( v_sko__List__Xconcat__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(680,plain,
( ( ! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(681,plain,
( ( ! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(682,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)],[251]) ).
thf(683,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)],[252]) ).
thf(684,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)],[253]) ).
thf(685,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)],[254]) ).
thf(686,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)],[255]) ).
thf(687,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)],[256]) ).
thf(688,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(689,plain,
( ( ! [T_a: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(690,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)],[259]) ).
thf(691,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)],[260]) ).
thf(692,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)],[261]) ).
thf(693,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)],[262]) ).
thf(694,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)],[263]) ).
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(unfold_def,[status(thm)],[264]) ).
thf(696,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)],[265]) ).
thf(697,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(698,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_x
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(699,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)],[268]) ).
thf(700,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)],[269]) ).
thf(701,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)],[270]) ).
thf(702,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)],[271]) ).
thf(703,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(704,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)],[273]) ).
thf(705,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_List_Onull @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(706,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
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(unfold_def,[status(thm)],[276]) ).
thf(708,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ ( c_List_Ofilter @ V_P @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(709,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)],[278]) ).
thf(710,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)],[279]) ).
thf(711,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(712,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(713,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(714,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(715,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(716,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i,T_b: $i,V_m: $i,V_zs: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) )
| ( ( c_Map_Omap__upds @ V_m @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_b ) @ T_a @ T_b )
= ( c_Map_Omap__upds @ V_m @ V_xs @ V_ys @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(717,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i,T_b: $i,V_m: $i,V_zs: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) )
| ( ( c_Map_Omap__upds @ V_m @ ( c_List_Oappend @ V_xs @ V_zs @ T_a ) @ V_ys @ T_a @ T_b )
= ( c_Map_Omap__upds @ V_m @ V_xs @ V_ys @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(718,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(719,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(720,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(721,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(722,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(723,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(724,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(725,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(726,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(727,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(728,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(729,plain,
( ( ! [V_P: $i,V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ofilter @ V_P @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(730,plain,
( ( ! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(731,plain,
( ( ! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(732,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(733,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(734,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)],[303]) ).
thf(735,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)],[304]) ).
thf(736,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)],[305]) ).
thf(737,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)],[306]) ).
thf(738,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)],[307]) ).
thf(739,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)],[308]) ).
thf(740,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)],[309]) ).
thf(741,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)],[310]) ).
thf(742,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)],[311]) ).
thf(743,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)],[312]) ).
thf(744,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)],[313]) ).
thf(745,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)],[314]) ).
thf(746,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)],[315]) ).
thf(747,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(748,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)],[317]) ).
thf(749,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)],[318]) ).
thf(750,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)],[319]) ).
thf(751,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)],[320]) ).
thf(752,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(753,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(754,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(755,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(756,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(757,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(758,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Orotate @ V_n @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(759,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(760,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(761,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(762,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)],[331]) ).
thf(763,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)],[332]) ).
thf(764,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(765,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(766,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(767,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)],[336]) ).
thf(768,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(769,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(770,plain,
( ( ! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(771,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(772,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)],[341]) ).
thf(773,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(774,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(775,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(776,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(777,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(778,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(779,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(780,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(781,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(782,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)],[351]) ).
thf(783,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(784,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(785,plain,
( ( ! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(786,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(787,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(788,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(789,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)],[358]) ).
thf(790,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(791,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(792,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(793,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(794,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(795,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(796,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)],[365]) ).
thf(797,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(798,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(799,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(800,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(801,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(802,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(803,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(804,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(805,plain,
( ( ! [V_P: $i,V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ofilter @ V_P @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(806,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(807,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(808,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(809,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(810,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)],[379]) ).
thf(811,plain,
( ( ! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(812,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(813,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
!= V_xs )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(814,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)],[383]) ).
thf(815,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)],[384]) ).
thf(816,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)],[385]) ).
thf(817,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)],[386]) ).
thf(818,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)],[387]) ).
thf(819,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(820,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(821,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(822,plain,
( ( ! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(823,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(824,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)],[393]) ).
thf(825,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(826,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(827,plain,
( ( ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(828,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(829,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)],[398]) ).
thf(830,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)],[399]) ).
thf(831,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)],[400]) ).
thf(832,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Orotate1 @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(833,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)],[402]) ).
thf(834,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(835,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(836,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(837,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(838,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(839,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(840,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(841,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(842,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(843,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(844,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)],[413]) ).
thf(845,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)],[414]) ).
thf(846,plain,
( ( ! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(847,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(848,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)],[417]) ).
thf(849,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)],[418]) ).
thf(850,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)],[419]) ).
thf(851,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(852,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(853,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(854,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(855,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(856,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) )
| ( ( c_List_Oremdups @ V_xs @ T_a )
= V_xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(857,plain,
( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(858,plain,
( ( c_List_Olistsp @ ( c_COMBB @ c_InductTermi_OIT @ ( hAPP @ ( c_COMBC @ c_Lambda_OdB_OApp @ tc_Lambda_OdB @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OVar @ v_i ) ) @ tc_Lambda_OdB @ tc_bool @ tc_Lambda_OdB ) @ v_rs @ tc_Lambda_OdB )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(859,plain,
( ( c_List_Olistsp @ c_InductTermi_OIT @ v_rs @ tc_Lambda_OdB )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(860,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[431]) ).
thf(861,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[432]) ).
thf(862,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(extcnf_combined,[status(esa)],[449]) ).
thf(863,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(extcnf_combined,[status(esa)],[454]) ).
thf(864,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(extcnf_combined,[status(esa)],[455]) ).
thf(865,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(extcnf_combined,[status(esa)],[456]) ).
thf(866,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(extcnf_combined,[status(esa)],[457]) ).
thf(867,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(extcnf_combined,[status(esa)],[459]) ).
thf(868,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(extcnf_combined,[status(esa)],[461]) ).
thf(869,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(extcnf_combined,[status(esa)],[462]) ).
thf(870,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[464]) ).
thf(871,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[465]) ).
thf(872,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[468]) ).
thf(873,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xinduct__1 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[469]) ).
thf(874,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[470]) ).
thf(875,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xinducts__1 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[471]) ).
thf(876,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(extcnf_combined,[status(esa)],[472]) ).
thf(877,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(extcnf_combined,[status(esa)],[473]) ).
thf(878,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(extcnf_combined,[status(esa)],[474]) ).
thf(879,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(extcnf_combined,[status(esa)],[476]) ).
thf(880,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ! [V_ys: $i] :
~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[477]) ).
thf(881,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ! [V_xs: $i] :
~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[478]) ).
thf(882,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(extcnf_combined,[status(esa)],[483]) ).
thf(883,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[484]) ).
thf(884,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(extcnf_combined,[status(esa)],[486]) ).
thf(885,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[490]) ).
thf(886,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[496]) ).
thf(887,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(extcnf_combined,[status(esa)],[497]) ).
thf(888,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(extcnf_combined,[status(esa)],[498]) ).
thf(889,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i] :
( ( V_T = V_U )
| ! [V_i: $i,V_ts: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[499]) ).
thf(890,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(extcnf_combined,[status(esa)],[504]) ).
thf(891,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(extcnf_combined,[status(esa)],[510]) ).
thf(892,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(extcnf_combined,[status(esa)],[511]) ).
thf(893,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[513]) ).
thf(894,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xmap__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[515]) ).
thf(895,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[519]) ).
thf(896,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(extcnf_combined,[status(esa)],[521]) ).
thf(897,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xremove1__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[523]) ).
thf(898,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xdistinct__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[526]) ).
thf(899,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(extcnf_combined,[status(esa)],[528]) ).
thf(900,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(extcnf_combined,[status(esa)],[529]) ).
thf(901,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xconcat__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[530]) ).
thf(902,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oremdups @ V_x @ T_a ) )
| ( V_x
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[535]) ).
thf(903,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xtake__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[538]) ).
thf(904,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XdropWhile__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[539]) ).
thf(905,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistset__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[541]) ).
thf(906,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xzip__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[544]) ).
thf(907,plain,
( ( ! [V_P: $i,V_f1: $i] :
( ! [V_f2: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_f1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[546]) ).
thf(908,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_a: $i,V_xs: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ V_a @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[549]) ).
thf(909,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(extcnf_combined,[status(esa)],[557]) ).
thf(910,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(extcnf_combined,[status(esa)],[558]) ).
thf(911,plain,
( ( ! [V_P: $i,V_x: $i] :
( ! [V_xs: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[561]) ).
thf(912,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_l: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ V_l @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_l @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[562]) ).
thf(913,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i] :
( ! [V_x_H: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[563]) ).
thf(914,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_ys: $i] :
( ( c_List_Olinorder__class_Osorted @ V_ys @ T_a )
| ! [V_xs: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[564]) ).
thf(915,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_xs: $i] :
( ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ! [V_ys: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[565]) ).
thf(916,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[566]) ).
thf(917,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(extcnf_combined,[status(esa)],[567]) ).
thf(918,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(extcnf_combined,[status(esa)],[568]) ).
thf(919,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[570]) ).
thf(920,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[576]) ).
thf(921,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[577]) ).
thf(922,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(extcnf_combined,[status(esa)],[581]) ).
thf(923,plain,
( ( ! [V_x: $i,V_P: $i] :
( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[583]) ).
thf(924,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(extcnf_combined,[status(esa)],[584]) ).
thf(925,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(extcnf_combined,[status(esa)],[585]) ).
thf(926,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(extcnf_combined,[status(esa)],[586]) ).
thf(927,plain,
( ( ! [V_x: $i,V_y: $i] :
( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ ( c_List_Oremove1 @ V_x @ V_xs @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[590]) ).
thf(928,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(extcnf_combined,[status(esa)],[591]) ).
thf(929,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[594]) ).
thf(930,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[595]) ).
thf(931,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[596]) ).
thf(932,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[597]) ).
thf(933,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__ex @ V_P @ V_xs @ T_a )
| ! [V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[599]) ).
thf(934,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(extcnf_combined,[status(esa)],[601]) ).
thf(935,plain,
( ( ! [V_P: $i,V_x: $i] :
( ! [V_xs: $i,T_a: $i] : ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[602]) ).
thf(936,plain,
( ( ! [V_P: $i,V_ys: $i,T_a: $i,V_x: $i] :
( ! [V_xs: $i] :
( ( c_List_Ofilter @ V_P @ V_ys @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[608]) ).
thf(937,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(extcnf_combined,[status(esa)],[609]) ).
thf(938,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(extcnf_combined,[status(esa)],[610]) ).
thf(939,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(extcnf_combined,[status(esa)],[614]) ).
thf(940,plain,
( ( ! [V_P: $i,V_x: $i] :
( ! [V_xs: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[615]) ).
thf(941,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_P: $i] :
( ! [V_ys: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Ofilter @ V_P @ V_ys @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[617]) ).
thf(942,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(extcnf_combined,[status(esa)],[621]) ).
thf(943,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[623]) ).
thf(944,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[624]) ).
thf(945,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_zs: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ! [V_x: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[625]) ).
thf(946,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(extcnf_combined,[status(esa)],[626]) ).
thf(947,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_xs: $i] :
( ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ! [V_x: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[636]) ).
thf(948,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ V_A @ V_P ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[638]) ).
thf(949,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ V_A @ V_P ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[640]) ).
thf(950,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(extcnf_combined,[status(esa)],[642]) ).
thf(951,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[643]) ).
thf(952,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[648]) ).
thf(953,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[652]) ).
thf(954,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( 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(extcnf_combined,[status(esa)],[654]) ).
thf(955,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [V_xs: $i,T_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[656]) ).
thf(956,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(extcnf_combined,[status(esa)],[657]) ).
thf(957,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(extcnf_combined,[status(esa)],[658]) ).
thf(958,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ! [T_a: $i,V_xs: $i] :
~ ( 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(extcnf_combined,[status(esa)],[659]) ).
thf(959,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ! [V_r: $i,T_a: $i] :
~ ( 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(extcnf_combined,[status(esa)],[660]) ).
thf(960,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(extcnf_combined,[status(esa)],[663]) ).
thf(961,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(extcnf_combined,[status(esa)],[664]) ).
thf(962,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
( ! [V_xb: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xb @ T_a ) @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ V_P @ V_xa @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[665]) ).
thf(963,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
( ! [V_xb: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xb @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ V_P @ V_xa @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[666]) ).
thf(964,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ V_P ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[671]) ).
thf(965,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ V_P ) @ ( v_sko__List__Xremove1__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[672]) ).
thf(966,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlistset__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[673]) ).
thf(967,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ V_P ) @ ( v_sko__List__Xzip__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[674]) ).
thf(968,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ V_P ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[675]) ).
thf(969,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlist__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[676]) ).
thf(970,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ V_P ) @ ( v_sko__List__Xmap__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[677]) ).
thf(971,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ V_P ) @ ( v_sko__List__Xtake__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[678]) ).
thf(972,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ V_P ) @ ( v_sko__List__Xconcat__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[679]) ).
thf(973,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[688]) ).
thf(974,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(extcnf_combined,[status(esa)],[691]) ).
thf(975,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(extcnf_combined,[status(esa)],[692]) ).
thf(976,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(extcnf_combined,[status(esa)],[693]) ).
thf(977,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(extcnf_combined,[status(esa)],[694]) ).
thf(978,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(extcnf_combined,[status(esa)],[695]) ).
thf(979,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(extcnf_combined,[status(esa)],[696]) ).
thf(980,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[697]) ).
thf(981,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_x
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[698]) ).
thf(982,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(extcnf_combined,[status(esa)],[699]) ).
thf(983,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(extcnf_combined,[status(esa)],[700]) ).
thf(984,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(extcnf_combined,[status(esa)],[701]) ).
thf(985,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(extcnf_combined,[status(esa)],[702]) ).
thf(986,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i] :
( ! [T_a: $i] :
( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[706]) ).
thf(987,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] : ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[712]) ).
thf(988,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_B: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[713]) ).
thf(989,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) )
| ! [V_m: $i,V_zs: $i] :
( ( c_Map_Omap__upds @ V_m @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_b ) @ T_a @ T_b )
= ( c_Map_Omap__upds @ V_m @ V_xs @ V_ys @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[716]) ).
thf(990,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) )
| ! [V_m: $i,V_zs: $i] :
( ( c_Map_Omap__upds @ V_m @ ( c_List_Oappend @ V_xs @ V_zs @ T_a ) @ V_ys @ T_a @ T_b )
= ( c_Map_Omap__upds @ V_m @ V_xs @ V_ys @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[717]) ).
thf(991,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[719]) ).
thf(992,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[722]) ).
thf(993,plain,
( ( ! [V_P: $i,V_n: $i,V_x: $i] :
( ! [T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[729]) ).
thf(994,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(extcnf_combined,[status(esa)],[739]) ).
thf(995,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(extcnf_combined,[status(esa)],[740]) ).
thf(996,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(extcnf_combined,[status(esa)],[741]) ).
thf(997,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(extcnf_combined,[status(esa)],[742]) ).
thf(998,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[747]) ).
thf(999,plain,
( ( ! [V_x: $i,V_s: $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 ) )
| ! [V_t: $i] :
( ( 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(extcnf_combined,[status(esa)],[748]) ).
thf(1000,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(extcnf_combined,[status(esa)],[750]) ).
thf(1001,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[752]) ).
thf(1002,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[753]) ).
thf(1003,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[754]) ).
thf(1004,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[755]) ).
thf(1005,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[756]) ).
thf(1006,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[757]) ).
thf(1007,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[763]) ).
thf(1008,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[764]) ).
thf(1009,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(extcnf_combined,[status(esa)],[765]) ).
thf(1010,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[766]) ).
thf(1011,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(extcnf_combined,[status(esa)],[767]) ).
thf(1012,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[771]) ).
thf(1013,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(extcnf_combined,[status(esa)],[772]) ).
thf(1014,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ! [V_j: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[773]) ).
thf(1015,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[776]) ).
thf(1016,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[777]) ).
thf(1017,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[778]) ).
thf(1018,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[779]) ).
thf(1019,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[780]) ).
thf(1020,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[781]) ).
thf(1021,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[783]) ).
thf(1022,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[784]) ).
thf(1023,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[786]) ).
thf(1024,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[787]) ).
thf(1025,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[788]) ).
thf(1026,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ! [V_y: $i,V_x: $i] :
~ ( 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(extcnf_combined,[status(esa)],[789]) ).
thf(1027,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[790]) ).
thf(1028,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[791]) ).
thf(1029,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[792]) ).
thf(1030,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i] :
( ! [V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[798]) ).
thf(1031,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ! [V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[799]) ).
thf(1032,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[804]) ).
thf(1033,plain,
( ( ! [V_P: $i,V_n: $i,V_x: $i] :
( ! [T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[805]) ).
thf(1034,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[808]) ).
thf(1035,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[809]) ).
thf(1036,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
!= V_xs )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[813]) ).
thf(1037,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(extcnf_combined,[status(esa)],[815]) ).
thf(1038,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(extcnf_combined,[status(esa)],[824]) ).
thf(1039,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(extcnf_combined,[status(esa)],[831]) ).
thf(1040,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [T_a: $i,V_xs: $i] :
~ ( 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(extcnf_combined,[status(esa)],[833]) ).
thf(1041,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[834]) ).
thf(1042,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[841]) ).
thf(1043,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[842]) ).
thf(1044,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_x: $i] : ( 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(extcnf_combined,[status(esa)],[844]) ).
thf(1045,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ! [V_r: $i,T_a: $i] :
~ ( 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(extcnf_combined,[status(esa)],[848]) ).
thf(1046,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ! [V_x: $i,T_a: $i] : ( 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(extcnf_combined,[status(esa)],[849]) ).
thf(1047,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(extcnf_combined,[status(esa)],[850]) ).
thf(1048,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[853]) ).
thf(1049,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[854]) ).
thf(1050,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[855]) ).
thf(1051,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) )
| ( ( c_List_Oremdups @ V_xs @ T_a )
= V_xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[856]) ).
thf(1052,plain,
( ( c_List_Olistsp @ c_InductTermi_OIT @ v_rs @ tc_Lambda_OdB )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(1053,plain,
( ( c_List_Olistsp @ ( c_COMBB @ c_InductTermi_OIT @ ( hAPP @ ( c_COMBC @ c_Lambda_OdB_OApp @ tc_Lambda_OdB @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OVar @ v_i ) ) @ tc_Lambda_OdB @ tc_bool @ tc_Lambda_OdB ) @ v_rs @ tc_Lambda_OdB )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1054,plain,
( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1055,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) )
| ( ( c_List_Oremdups @ V_xs @ T_a )
= V_xs ) ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(1056,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(1057,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1049]) ).
thf(1058,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(1059,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1060,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1061,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)],[1047]) ).
thf(1062,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ! [V_x: $i,T_a: $i] : ( 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)],[1046]) ).
thf(1063,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ! [V_r: $i,T_a: $i] :
~ ( 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)],[1045]) ).
thf(1064,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1065,plain,
( ( ! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1066,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)],[845]) ).
thf(1067,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_x: $i] : ( 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)],[1044]) ).
thf(1068,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1069,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1043]) ).
thf(1070,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(1071,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(1072,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(1073,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(1074,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(1075,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1076,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(1077,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(1078,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [T_a: $i,V_xs: $i] :
~ ( 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)],[1040]) ).
thf(1079,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Orotate1 @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(1080,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)],[1039]) ).
thf(1081,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)],[830]) ).
thf(1082,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)],[829]) ).
thf(1083,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(1084,plain,
( ( ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(1085,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1086,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1087,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)],[1038]) ).
thf(1088,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1089,plain,
( ( ! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(1090,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1091,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(1092,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(1093,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)],[818]) ).
thf(1094,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)],[817]) ).
thf(1095,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)],[816]) ).
thf(1096,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)],[1037]) ).
thf(1097,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)],[814]) ).
thf(1098,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
!= V_xs )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1036]) ).
thf(1099,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1100,plain,
( ( ! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(1101,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)],[810]) ).
thf(1102,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(1103,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(1104,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1105,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1106,plain,
( ( ! [V_P: $i,V_n: $i,V_x: $i] :
( ! [T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(1107,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(1108,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(1109,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(1110,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(1111,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(1112,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ! [V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(1113,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i] :
( ! [V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1114,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(1115,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)],[796]) ).
thf(1116,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(1117,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1118,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1119,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1120,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1121,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1122,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ! [V_y: $i,V_x: $i] :
~ ( 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)],[1026]) ).
thf(1123,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(1124,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(1125,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(1126,plain,
( ( ! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1127,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(1128,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1021]) ).
thf(1129,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)],[782]) ).
thf(1130,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1020]) ).
thf(1131,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1019]) ).
thf(1132,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(1133,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(1134,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(1135,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(1136,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(1137,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1138,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ! [V_j: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(1139,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)],[1013]) ).
thf(1140,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(1141,plain,
( ( ! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1142,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1143,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1144,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)],[1011]) ).
thf(1145,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(1146,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1147,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(1148,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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)],[1007]) ).
thf(1149,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)],[762]) ).
thf(1150,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(1151,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1152,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1153,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Orotate @ V_n @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1154,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(1155,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(1156,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(1157,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(1158,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(1159,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(1160,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)],[751]) ).
thf(1161,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)],[1000]) ).
thf(1162,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)],[749]) ).
thf(1163,plain,
( ( ! [V_x: $i,V_s: $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 ) )
| ! [V_t: $i] :
( ( 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)],[999]) ).
thf(1164,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(1165,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)],[746]) ).
thf(1166,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)],[745]) ).
thf(1167,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)],[744]) ).
thf(1168,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)],[743]) ).
thf(1169,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)],[997]) ).
thf(1170,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)],[996]) ).
thf(1171,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)],[995]) ).
thf(1172,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)],[994]) ).
thf(1173,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)],[738]) ).
thf(1174,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)],[737]) ).
thf(1175,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)],[736]) ).
thf(1176,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)],[735]) ).
thf(1177,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)],[734]) ).
thf(1178,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(1179,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(1180,plain,
( ( ! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(1181,plain,
( ( ! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1182,plain,
( ( ! [V_P: $i,V_n: $i,V_x: $i] :
( ! [T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(1183,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(1184,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1185,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1186,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(1187,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1188,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1189,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(1190,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(1191,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(1192,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[991]) ).
thf(1193,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(1194,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) )
| ! [V_m: $i,V_zs: $i] :
( ( c_Map_Omap__upds @ V_m @ ( c_List_Oappend @ V_xs @ V_zs @ T_a ) @ V_ys @ T_a @ T_b )
= ( c_Map_Omap__upds @ V_m @ V_xs @ V_ys @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[990]) ).
thf(1195,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) )
| ! [V_m: $i,V_zs: $i] :
( ( c_Map_Omap__upds @ V_m @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_b ) @ T_a @ T_b )
= ( c_Map_Omap__upds @ V_m @ V_xs @ V_ys @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[989]) ).
thf(1196,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(1197,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(1198,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_B: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[988]) ).
thf(1199,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] : ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[987]) ).
thf(1200,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(1201,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)],[710]) ).
thf(1202,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)],[709]) ).
thf(1203,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ ( c_List_Ofilter @ V_P @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(1204,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)],[707]) ).
thf(1205,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i] :
( ! [T_a: $i] :
( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[986]) ).
thf(1206,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_List_Onull @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(1207,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)],[704]) ).
thf(1208,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(1209,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)],[985]) ).
thf(1210,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)],[984]) ).
thf(1211,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)],[983]) ).
thf(1212,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)],[982]) ).
thf(1213,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_x
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(1214,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(1215,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)],[979]) ).
thf(1216,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)],[978]) ).
thf(1217,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)],[977]) ).
thf(1218,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)],[976]) ).
thf(1219,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)],[975]) ).
thf(1220,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)],[974]) ).
thf(1221,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)],[690]) ).
thf(1222,plain,
( ( ! [T_a: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(1223,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(1224,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)],[687]) ).
thf(1225,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)],[686]) ).
thf(1226,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)],[685]) ).
thf(1227,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)],[684]) ).
thf(1228,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)],[683]) ).
thf(1229,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)],[682]) ).
thf(1230,plain,
( ( ! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1231,plain,
( ( ! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(1232,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ V_P ) @ ( v_sko__List__Xconcat__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[972]) ).
thf(1233,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ V_P ) @ ( v_sko__List__Xtake__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(1234,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ V_P ) @ ( v_sko__List__Xmap__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(1235,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlist__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(1236,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ V_P ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(1237,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ V_P ) @ ( v_sko__List__Xzip__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(1238,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlistset__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(1239,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ V_P ) @ ( v_sko__List__Xremove1__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(1240,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ V_P ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(1241,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(1242,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(1243,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(1244,plain,
( ( ! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(1245,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
( ! [V_xb: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xb @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ V_P @ V_xa @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(1246,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
( ! [V_xb: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xb @ T_a ) @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ V_P @ V_xa @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(1247,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)],[961]) ).
thf(1248,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)],[960]) ).
thf(1249,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)],[662]) ).
thf(1250,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)],[661]) ).
thf(1251,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ! [V_r: $i,T_a: $i] :
~ ( 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)],[959]) ).
thf(1252,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ! [T_a: $i,V_xs: $i] :
~ ( 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)],[958]) ).
thf(1253,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)],[957]) ).
thf(1254,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)],[956]) ).
thf(1255,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [V_xs: $i,T_a: $i] :
( ( 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)],[955]) ).
thf(1256,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)],[655]) ).
thf(1257,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( 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)],[954]) ).
thf(1258,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)],[653]) ).
thf(1259,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(1260,plain,
( ( ! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(1261,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(1262,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(1263,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(1264,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)],[647]) ).
thf(1265,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)],[646]) ).
thf(1266,plain,
( ( ! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(1267,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)],[644]) ).
thf(1268,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)],[951]) ).
thf(1269,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)],[950]) ).
thf(1270,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(1271,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ V_A @ V_P ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(1272,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)],[639]) ).
thf(1273,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ V_A @ V_P ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1274,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)],[637]) ).
thf(1275,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_xs: $i] :
( ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ! [V_x: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(1276,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)],[635]) ).
thf(1277,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)],[634]) ).
thf(1278,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(1279,plain,
( ( ! [V_f1: $i,V_f2: $i,V_a: $i,V_list: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(1280,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(1281,plain,
( ( ! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(1282,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(1283,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)],[628]) ).
thf(1284,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)],[627]) ).
thf(1285,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)],[946]) ).
thf(1286,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_zs: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ! [V_x: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(1287,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1288,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(1289,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(1290,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)],[942]) ).
thf(1291,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)],[620]) ).
thf(1292,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)],[619]) ).
thf(1293,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)],[618]) ).
thf(1294,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_P: $i] :
( ! [V_ys: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
!= ( c_List_Ofilter @ V_P @ V_ys @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(1295,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(1296,plain,
( ( ! [V_P: $i,V_x: $i] :
( ! [V_xs: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(1297,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)],[939]) ).
thf(1298,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ V_f3 @ V_dB ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(1299,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(1300,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(1301,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)],[938]) ).
thf(1302,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)],[937]) ).
thf(1303,plain,
( ( ! [V_P: $i,V_ys: $i,T_a: $i,V_x: $i] :
( ! [V_xs: $i] :
( ( c_List_Ofilter @ V_P @ V_ys @ T_a )
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(1304,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orotate @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(1305,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)],[606]) ).
thf(1306,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)],[605]) ).
thf(1307,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)],[604]) ).
thf(1308,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)],[603]) ).
thf(1309,plain,
( ( ! [V_P: $i,V_x: $i] :
( ! [V_xs: $i,T_a: $i] : ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(1310,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)],[934]) ).
thf(1311,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__ex @ V_P @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(1312,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__ex @ V_P @ V_xs @ T_a )
| ! [V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_List_Olist__ex @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(1313,plain,
( ( ! [V_r: $i,V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Olistrelp @ V_r @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistrelp @ V_r @ V_xs @ V_ys @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(1314,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(1315,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(1316,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(1317,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(1318,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(1319,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(1320,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)],[928]) ).
thf(1321,plain,
( ( ! [V_x: $i,V_y: $i] :
( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ ( c_List_Oremove1 @ V_x @ V_xs @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(1322,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(1323,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(1324,plain,
( ( ! [V_a: $i,V_A: $i] :
( ( V_a
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ V_A @ V_a ) @ ( v_sko__List__Xlistsp__Xcases__2 @ V_A @ V_a ) @ t_a ) )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(1325,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)],[926]) ).
thf(1326,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)],[925]) ).
thf(1327,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)],[924]) ).
thf(1328,plain,
( ( ! [V_x: $i,V_P: $i] :
( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(1329,plain,
( ( ! [V_f1: $i,V_f2: $i,V_a: $i,V_list: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) @ ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ V_list @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(1330,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)],[922]) ).
thf(1331,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)],[580]) ).
thf(1332,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ ( hAPP @ V_f3 @ V_dB ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(1333,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(1334,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(1335,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(1336,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(1337,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)],[574]) ).
thf(1338,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_dB ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(1339,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(1340,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)],[571]) ).
thf(1341,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(1342,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(1343,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)],[918]) ).
thf(1344,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)],[917]) ).
thf(1345,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1346,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_xs: $i] :
( ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ! [V_ys: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(1347,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_ys: $i] :
( ( c_List_Olinorder__class_Osorted @ V_ys @ T_a )
| ! [V_xs: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(1348,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i] :
( ! [V_x_H: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(1349,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_l: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ V_l @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_l @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(1350,plain,
( ( ! [V_P: $i,V_x: $i] :
( ! [V_xs: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(1351,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(1352,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
= ( c_List_Ofilter @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(1353,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)],[910]) ).
thf(1354,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)],[909]) ).
thf(1355,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_a: $i,V_list: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_a @ V_list @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_a ) @ V_list ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(1356,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_OCons @ V_xa @ V_xb @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(1357,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(1358,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)],[553]) ).
thf(1359,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)],[552]) ).
thf(1360,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)],[551]) ).
thf(1361,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)],[550]) ).
thf(1362,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_a: $i,V_xs: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ V_a @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(1363,plain,
( ( ! [V_P: $i,T_a: $i] :
~ ( c_List_Olist__ex @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(1364,plain,
( ( ! [T_a: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(1365,plain,
( ( ! [V_P: $i,V_f1: $i] :
( ! [V_f2: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_f1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(1366,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)],[545]) ).
thf(1367,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xzip__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1368,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(1369,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(1370,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistset__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(1371,plain,
( ( ! [V_f1: $i,V_f2: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__rec @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_f1 ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(1372,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XdropWhile__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1373,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xtake__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(1374,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(1375,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofiltermap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1376,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oremdups @ V_x @ T_a ) )
| ( V_x
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1377,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_Ofilter @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(1378,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1379,plain,
( ( ! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1380,plain,
( ( ! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(1381,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xconcat__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(1382,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)],[900]) ).
thf(1383,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)],[899]) ).
thf(1384,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oremove1 @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1385,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xdistinct__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(1386,plain,
( ( ! [V_m: $i,V_as: $i,T_b: $i,T_a: $i] :
( ( c_Map_Omap__upds @ V_m @ V_as @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(1387,plain,
( ( ! [V_m: $i,T_a: $i,V_bs: $i,T_b: $i] :
( ( c_Map_Omap__upds @ V_m @ ( c_List_Olist_ONil @ T_a ) @ V_bs @ T_a @ T_b )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(1388,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xremove1__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(1389,plain,
( ( ! [V_f1: $i,V_f2: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_Olist__case @ V_f1 @ V_f2 @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_f1 ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(1390,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)],[896]) ).
thf(1391,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Orotate @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(1392,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(1393,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(1394,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)],[517]) ).
thf(1395,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_List_Olistrelp @ V_r @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(1396,plain,
( ( ! [V_P: $i] :
( ! [V_list: $i] : ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xmap__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1397,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)],[514]) ).
thf(1398,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(1399,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)],[512]) ).
thf(1400,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)],[892]) ).
thf(1401,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)],[891]) ).
thf(1402,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_xb ) @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xb ) @ V_xc ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(1403,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(1404,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)],[507]) ).
thf(1405,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(1406,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB1 @ T_a ) ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB2 @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(1407,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)],[890]) ).
thf(1408,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(1409,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(1410,plain,
( ( ! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(1411,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(1412,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i] :
( ( V_T = V_U )
| ! [V_i: $i,V_ts: $i] :
( ~ ( 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)],[889]) ).
thf(1413,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)],[888]) ).
thf(1414,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)],[887]) ).
thf(1415,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)],[886]) ).
thf(1416,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xd: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_xd ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xd ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(1417,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(1418,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)],[493]) ).
thf(1419,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(1420,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(1421,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)],[885]) ).
thf(1422,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)],[489]) ).
thf(1423,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(1424,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)],[487]) ).
thf(1425,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)],[884]) ).
thf(1426,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)],[485]) ).
thf(1427,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(1428,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)],[882]) ).
thf(1429,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)],[482]) ).
thf(1430,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)],[481]) ).
thf(1431,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_A @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ V_A @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(1432,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_l: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_l @ T_a )
| ~ ( c_List_Olistsp @ V_B @ V_l @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(1433,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ! [V_xs: $i] :
~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1434,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ! [V_ys: $i] :
~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(1435,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)],[879]) ).
thf(1436,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(1437,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)],[878]) ).
thf(1438,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)],[877]) ).
thf(1439,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)],[876]) ).
thf(1440,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xinducts__1 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1441,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(1442,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xinduct__1 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(1443,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(1444,plain,
( ( ! [V_A: $i,V_a: $i] :
( ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xcases__2 @ V_A @ V_a ) @ t_a )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(1445,plain,
( ( ! [V_A: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( v_sko__List__Xlistsp__Xcases__1 @ V_A @ V_a ) ) )
| ( V_a
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ V_A @ V_a @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(1446,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xinducts__2 @ V_A @ V_P ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(1447,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ( c_List_Olistsp @ V_A @ ( v_sko__List__Xlistsp__Xinduct__2 @ V_A @ V_P ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ V_A @ V_x @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(1448,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)],[463]) ).
thf(1449,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)],[869]) ).
thf(1450,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)],[868]) ).
thf(1451,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)],[460]) ).
thf(1452,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)],[867]) ).
thf(1453,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)],[458]) ).
thf(1454,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)],[866]) ).
thf(1455,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)],[865]) ).
thf(1456,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)],[864]) ).
thf(1457,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)],[863]) ).
thf(1458,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(1459,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)],[452]) ).
thf(1460,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(1461,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)],[450]) ).
thf(1462,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)],[862]) ).
thf(1463,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(1464,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(1465,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(1466,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(1467,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(1468,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(1469,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(1470,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(1471,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(1472,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(1473,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(1474,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(1475,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(1476,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)],[435]) ).
thf(1477,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(1478,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(1479,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(1480,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[860]) ).
thf(1481,plain,
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1482,plain,
! [SV1: $i] :
( ( ! [SY1327: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ SV1 @ SY1327 ) @ ( tc_List_Olist @ SY1327 ) )
!= ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SY1327 ) ) )
| ( ( c_List_Oremdups @ SV1 @ SY1327 )
= SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1483,plain,
! [SV2: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1484,plain,
! [SV3: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1485,plain,
! [SV4: $i] :
( ( ! [SY1328: $i,SY1329: $i,SY1330: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SY1328 ) @ SY1329 ) @ SY1330 ) )
| ! [SY1331: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SY1328 ) @ SY1331 ) @ SY1330 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SY1328 ) @ SY1329 ) @ SY1331 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1486,plain,
! [SV5: $i] :
( ( ! [SY1332: $i,SY1333: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV5 @ SY1332 ) @ SY1333 ) @ SY1333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1487,plain,
! [SV6: $i] :
( ( ! [SY1334: $i,SY1335: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV6 @ SY1334 ) @ SY1335 ) @ SY1335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1488,plain,
! [SV7: $i] :
( ( ! [SY1336: $i,SY1337: $i,SY1338: $i] :
( ! [SY1339: $i] :
( ( c_List_Oreplicate @ SV7 @ SY1336 @ SY1337 )
!= ( c_List_Oreplicate @ SY1338 @ SY1339 @ SY1337 ) )
| ( SV7 = SY1338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1489,plain,
! [SV8: $i] :
( ( ! [SY1340: $i,SY1341: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV8 @ SY1340 ) @ SY1341 ) )
| ! [SY1342: $i,SY1343: $i] : ( c_ListOrder_Ostep1 @ SV8 @ ( c_List_Olist_OCons @ SY1340 @ SY1342 @ SY1343 ) @ ( c_List_Olist_OCons @ SY1341 @ SY1342 @ SY1343 ) @ SY1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1490,plain,
! [SV9: $i] :
( ( ! [SY1344: $i,SY1345: $i,SY1346: $i] :
( ( SV9 = SY1344 )
| ( SY1345 = SY1346 )
| ! [SY1347: $i,SY1348: $i] :
~ ( c_ListOrder_Ostep1 @ SY1347 @ ( c_List_Olist_OCons @ SY1344 @ SY1346 @ SY1348 ) @ ( c_List_Olist_OCons @ SV9 @ SY1345 @ SY1348 ) @ SY1348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1491,plain,
! [SV10: $i] :
( ( ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1492,plain,
! [SV11: $i] :
( ( ! [SY1349: $i,SY1350: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SY1349 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SY1350 @ SV11 @ SY1349 ) @ ( tc_List_Olist @ SY1349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1493,plain,
! [SV12: $i] :
( ( ! [SY1351: $i,SY1352: $i,SY1353: $i,SY1354: $i] :
( ( c_ListOrder_Ostep1 @ SV12 @ ( c_List_Oappend @ SY1351 @ SY1352 @ SY1353 ) @ ( c_List_Oappend @ SY1351 @ SY1354 @ SY1353 ) @ SY1353 )
| ~ ( c_ListOrder_Ostep1 @ SV12 @ SY1352 @ SY1354 @ SY1353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1494,plain,
! [SV13: $i] :
( ( ! [SY1355: $i,SY1356: $i,SY1357: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV13 @ SY1355 @ SY1356 @ SY1357 )
| ! [SY1358: $i] : ( c_ListOrder_Ostep1 @ SV13 @ ( c_List_Oappend @ SY1355 @ SY1358 @ SY1357 ) @ ( c_List_Oappend @ SY1356 @ SY1358 @ SY1357 ) @ SY1357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1495,plain,
! [SV14: $i] :
( ( ! [SY1359: $i,SY1360: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV14 @ SY1359 @ SY1360 ) @ ( tc_List_Olist @ SY1360 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SY1359 @ ( tc_List_Olist @ SY1360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1496,plain,
! [SV15: $i] :
( ( ! [SY1361: $i] :
( ~ ( class_Orderings_Opreorder @ SV15 )
| ! [SY1362: $i] :
( ( c_HOL_Oord__class_Oless @ SY1361 @ SY1362 @ SV15 )
| ! [SY1363: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1363 @ SY1362 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SY1361 @ SY1363 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1497,plain,
! [SV16: $i] :
( ( ! [SY1364: $i] :
( ~ ( class_Orderings_Oorder @ SV16 )
| ! [SY1365: $i] :
( ( c_HOL_Oord__class_Oless @ SY1364 @ SY1365 @ SV16 )
| ! [SY1366: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1364 @ SY1366 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SY1366 @ SY1365 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1498,plain,
! [SV17: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV17 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1499,plain,
! [SV18: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV18 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1500,plain,
! [SV19: $i] :
( ( ! [SY1367: $i,SY1368: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV19 ) @ SY1367 @ SY1368 )
= ( c_List_Olist_OCons @ SY1367 @ ( c_List_Oreplicate @ SV19 @ SY1367 @ SY1368 ) @ SY1368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1501,plain,
! [SV20: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV20 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1502,plain,
! [SV21: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV21 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1503,plain,
! [SV22: $i] :
( ( ! [SY1369: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV22 ) @ SY1369 @ tc_nat )
| ( ( c_Suc @ SV22 )
= SY1369 )
| ~ ( c_HOL_Oord__class_Oless @ SV22 @ SY1369 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1504,plain,
! [SV23: $i] :
( ( ! [SY1370: $i] :
( ( SV23
= ( c_List_Olist_ONil @ SY1370 ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV23 @ ( tc_List_Olist @ SY1370 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1505,plain,
! [SV24: $i] :
( ( ! [SY1371: $i,SY1372: $i,SY1373: $i] :
( ( SV24 = SY1371 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1372 @ SY1371 ) @ SV24 ) )
| ! [SY1374: $i,SY1375: $i] :
~ ( c_ListOrder_Ostep1 @ SY1372 @ ( c_List_Olist_OCons @ SY1371 @ SY1373 @ SY1374 ) @ ( c_List_Olist_OCons @ SV24 @ SY1375 @ SY1374 ) @ SY1374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1506,plain,
! [SV25: $i] :
( ( ! [SY1376: $i,SY1377: $i] :
( ( c_List_Orotate @ ( c_Suc @ SV25 ) @ SY1376 @ SY1377 )
= ( c_List_Orotate1 @ ( c_List_Orotate @ SV25 @ SY1376 @ SY1377 ) @ SY1377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1507,plain,
! [SV26: $i] :
( ( ! [SY1378: $i,SY1379: $i] :
( ( c_List_Olast @ ( c_List_Oreplicate @ SV26 @ SY1378 @ SY1379 ) @ SY1379 )
= SY1378 )
| ( SV26
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1508,plain,
! [SV27: $i] :
( ( ! [SY1380: $i,SY1381: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV27 @ SY1380 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1381 @ SY1380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1509,plain,
! [SV28: $i] :
( ( ! [SY1382: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV28 @ SY1382 )
= ( c_List_Olist_ONil @ SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1510,plain,
! [SV29: $i] :
( ( ! [SY1383: $i,SY1384: $i,SY1385: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV29 @ SY1383 @ SY1384 @ SY1385 ) @ ( tc_List_Olist @ SY1385 ) )
= ( c_Nat_Osize__class_Osize @ SV29 @ ( tc_List_Olist @ SY1385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1511,plain,
! [SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV30 @ SV30 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV30 @ ( c_Suc @ SV30 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1512,plain,
! [SV31: $i] :
( ( ! [SY1386: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV31 @ SY1386 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1386 @ ( c_Suc @ SV31 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1513,plain,
! [SV32: $i] :
( ( ! [SY1387: $i] :
( ( c_HOL_Oord__class_Oless @ SV32 @ ( c_Suc @ SY1387 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1387 @ SV32 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1514,plain,
! [SV33: $i] :
( ( ! [SY1388: $i,SY1389: $i,SY1390: $i,SY1391: $i] :
( ( ( c_List_Oreplicate @ SV33 @ SY1388 @ SY1389 )
!= ( c_List_Oreplicate @ SY1390 @ SY1391 @ SY1389 ) )
| ( SY1388 = SY1391 )
| ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1515,plain,
! [SV34: $i] :
( ( ! [SY1392: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV34 @ SY1392 ) @ SY1392 )
= ( c_Transitive__Closure_Ortranclp @ SV34 @ SY1392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1516,plain,
! [SV35: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV35 ) @ ( tc_List_Olist @ SV35 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1517,plain,
! [SV36: $i] :
( ( ! [SY1393: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV36 ) @ ( c_Suc @ SY1393 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV36 @ SY1393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1518,plain,
! [SV37: $i] :
( ( ! [SY1394: $i] :
( ( c_HOL_Oord__class_Oless @ SV37 @ SY1394 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV37 ) @ ( c_Suc @ SY1394 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1519,plain,
! [SV38: $i] :
( ( ! [SY1395: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV38 ) @ ( c_Suc @ SY1395 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SY1395 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1520,plain,
! [SV39: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ SV39 ) @ SV39 )
= ( c_List_Olist_ONil @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1521,plain,
! [SV40: $i] :
( ( ! [SY1396: $i,SY1397: $i] :
~ ( c_ListOrder_Ostep1 @ SV40 @ SY1396 @ ( c_List_Olist_ONil @ SY1397 ) @ SY1397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1522,plain,
! [SV41: $i] :
( ( ! [SY1398: $i,SY1399: $i] :
~ ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Olist_ONil @ SY1398 ) @ SY1399 @ SY1398 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1523,plain,
! [SV42: $i] :
( ( ! [SY1400: $i] :
( ( ( c_List_Orotate1 @ SV42 @ SY1400 )
!= ( c_List_Olist_ONil @ SY1400 ) )
| ( SV42
= ( c_List_Olist_ONil @ SY1400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1524,plain,
! [SV43: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ SV43 ) @ SV43 )
= ( c_List_Olist_ONil @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1525,plain,
! [SV44: $i] :
( ( ! [SY1401: $i] :
( ( ( c_List_Oremdups @ SV44 @ SY1401 )
!= SV44 )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ SV44 @ SY1401 ) @ ( tc_List_Olist @ SY1401 ) )
= ( c_Nat_Osize__class_Osize @ SV44 @ ( tc_List_Olist @ SY1401 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1526,plain,
! [SV45: $i] :
( ( ! [SY1402: $i,SY1403: $i,SY1404: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV45 @ SY1402 @ SY1403 @ SY1404 ) @ ( tc_List_Olist @ SY1404 ) )
= ( c_Nat_Osize__class_Osize @ SY1402 @ ( tc_List_Olist @ SY1403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1527,plain,
! [SV46: $i] :
( ( ! [SY1405: $i,SY1406: $i,SY1407: $i,SY1408: $i] :
( ( c_List_Omap @ SV46 @ ( c_List_Oreplicate @ SY1405 @ SY1406 @ SY1407 ) @ SY1407 @ SY1408 )
= ( c_List_Oreplicate @ SY1405 @ ( hAPP @ SV46 @ SY1406 ) @ SY1408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1528,plain,
! [SV47: $i] :
( ( ! [SY1409: $i,SY1410: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV47 @ SY1409 @ SY1410 ) @ SY1410 )
= ( c_List_Oreplicate @ SV47 @ SY1409 @ SY1410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1529,plain,
! [SV48: $i] :
( ( ! [SY1411: $i] :
( ( ( c_Suc @ SV48 )
!= ( c_Suc @ SY1411 ) )
| ( SV48 = SY1411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1530,plain,
! [SV49: $i] :
( ( ! [SY1412: $i] :
( ( ( c_Suc @ SV49 )
!= ( c_Suc @ SY1412 ) )
| ( SV49 = SY1412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1531,plain,
! [SV50: $i] :
( ( ! [SY1413: $i,SY1414: $i,SY1415: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SY1413 ) @ SY1414 ) @ SY1415 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY1414 ) @ SY1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1532,plain,
! [SV51: $i] :
( ( ! [SY1416: $i,SY1417: $i] :
( ! [SY1418: $i] :
( ( c_List_Ofilter @ SV51 @ ( c_List_Oreplicate @ SY1416 @ SY1417 @ SY1418 ) @ SY1418 )
= ( c_List_Oreplicate @ SY1416 @ SY1417 @ SY1418 ) )
| ~ ( hBOOL @ ( hAPP @ SV51 @ SY1417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1533,plain,
! [SV52: $i] :
( ( ! [SY1419: $i,SY1420: $i,SY1421: $i,SY1422: $i] :
( ( ( c_List_Omap @ SV52 @ SY1419 @ SY1420 @ SY1421 )
!= ( c_List_Omap @ SV52 @ SY1422 @ SY1420 @ SY1421 ) )
| ( ( c_Nat_Osize__class_Osize @ SY1419 @ ( tc_List_Olist @ SY1420 ) )
= ( c_Nat_Osize__class_Osize @ SY1422 @ ( tc_List_Olist @ SY1420 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1534,plain,
! [SV53: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV53 ) @ ( tc_List_Olist @ SV53 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1535,plain,
! [SV54: $i] :
( ( ! [SY1423: $i] :
( ( SV54 = SY1423 )
| ( c_HOL_Oord__class_Oless @ SV54 @ SY1423 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SY1423 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1536,plain,
! [SV55: $i] :
( ( ! [SY1424: $i] :
( ( SV55 = SY1424 )
| ~ ( c_HOL_Oord__class_Oless @ SY1424 @ ( c_Suc @ SV55 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1424 @ SV55 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1537,plain,
! [SV56: $i] :
( ( ! [SY1425: $i] :
( ( SV56 = SY1425 )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ ( c_Suc @ SY1425 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV56 @ SY1425 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1538,plain,
! [SV57: $i] :
( ( ! [SY1426: $i,SY1427: $i,SY1428: $i] :
( ! [SY1429: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV57 @ SY1426 @ SY1427 ) @ SY1428 @ SY1429 @ SY1427 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV57 @ SY1428 @ SY1429 @ SY1427 ) @ SY1426 @ SY1427 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1428 @ ( c_Nat_Osize__class_Osize @ SV57 @ ( tc_List_Olist @ SY1427 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1539,plain,
! [SV58: $i] :
( ( ! [SY1430: $i,SY1431: $i,SY1432: $i] :
( ! [SY1433: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV58 @ SY1430 @ SY1431 ) @ SY1432 @ SY1433 @ SY1431 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV58 @ SY1432 @ SY1433 @ SY1431 ) @ SY1430 @ SY1431 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1432 @ ( c_Nat_Osize__class_Osize @ SV58 @ ( tc_List_Olist @ SY1431 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1540,plain,
! [SV59: $i] :
( ( ! [SY1434: $i,SY1435: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ SV59 @ SY1434 @ SY1435 ) @ ( tc_List_Olist @ SY1435 ) )
= ( c_Nat_Osize__class_Osize @ SY1434 @ ( tc_List_Olist @ SY1435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1541,plain,
! [SV60: $i] :
( ( ! [SY1436: $i] :
( ( c_List_Olist_ONil @ SV60 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1436 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1542,plain,
! [SV61: $i] :
( ( ! [SY1437: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ SV61 @ SY1437 ) @ ( tc_List_Olist @ SY1437 ) )
= ( c_Nat_Osize__class_Osize @ SV61 @ ( tc_List_Olist @ SY1437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1543,plain,
! [SV62: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV62 @ SV62 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1544,plain,
! [SV63: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV63 @ SV63 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1545,plain,
! [SV64: $i] :
( ( ~ ( class_Orderings_Oorder @ SV64 )
| ! [SY1438: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1438 @ SY1438 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1546,plain,
! [SV65: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV65 )
| ! [SY1439: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1439 @ SY1439 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1547,plain,
! [SV66: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV66 )
| ! [SY1440: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1440 @ SY1440 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1548,plain,
! [SV67: $i] :
( ( ! [SY1441: $i,SY1442: $i,SY1443: $i] :
( ( c_ListOrder_Ostep1 @ SV67 @ SY1441 @ SY1442 @ SY1443 )
| ( SY1442 = SY1441 )
| ! [SY1444: $i,SY1445: $i] :
~ ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SY1444 @ SY1441 @ SY1443 ) @ ( c_List_Olist_OCons @ SY1445 @ SY1442 @ SY1443 ) @ SY1443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1549,plain,
! [SV68: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV68 )
| ! [SY1446: $i,SY1447: $i] :
( ( c_HOL_Oord__class_Oless @ SY1446 @ SY1447 @ SV68 )
| ( SY1447 = SY1446 )
| ( c_HOL_Oord__class_Oless @ SY1447 @ SY1446 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1550,plain,
! [SV69: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV69 )
| ! [SY1448: $i,SY1449: $i] :
( ( SY1448 = SY1449 )
| ( c_HOL_Oord__class_Oless @ SY1449 @ SY1448 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SY1448 @ SY1449 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1551,plain,
! [SV70: $i] :
( ( ! [SY1450: $i] :
( ( c_HOL_Oord__class_Oless @ SV70 @ SY1450 @ tc_nat )
| ( SY1450 = SV70 )
| ( c_HOL_Oord__class_Oless @ SY1450 @ SV70 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1552,plain,
! [SV71: $i] :
( ( ! [SY1451: $i,SY1452: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SY1451 ) @ SY1452 ) )
| ( c_HOL_Oord__class_Oless @ SY1451 @ SY1452 @ tc_nat )
| ( SY1452 = SY1451 )
| ( c_HOL_Oord__class_Oless @ SY1452 @ SY1451 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1553,plain,
! [SV72: $i] :
( ( ! [SY1453: $i] :
( ( c_HOL_Oord__class_Oless @ SV72 @ SY1453 @ tc_nat )
| ( SY1453 = SV72 )
| ( c_HOL_Oord__class_Oless @ SY1453 @ SV72 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1554,plain,
! [SV73: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV73 )
| ! [SY1454: $i,SY1455: $i] :
( ( c_HOL_Oord__class_Oless @ SY1454 @ SY1455 @ SV73 )
| ( SY1455 = SY1454 )
| ( c_HOL_Oord__class_Oless @ SY1455 @ SY1454 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1555,plain,
! [SV74: $i] :
( ( ! [SY1456: $i,SY1457: $i,SY1458: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SY1456 @ SY1457 ) @ ( c_List_Oreplicate @ SY1458 @ SY1456 @ SY1457 ) @ SY1457 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY1458 @ SY1456 @ SY1457 ) @ ( c_List_Oreplicate @ SV74 @ SY1456 @ SY1457 ) @ SY1457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1556,plain,
! [SV75: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV75 )
| ! [SY1459: $i,SY1460: $i] :
( ( c_HOL_Oord__class_Oless @ SY1459 @ SY1460 @ SV75 )
| ( SY1460 = SY1459 )
| ( c_HOL_Oord__class_Oless @ SY1460 @ SY1459 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1557,plain,
! [SV76: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV76 )
| ! [SY1461: $i,SY1462: $i] :
( ( SY1461 = SY1462 )
| ( c_HOL_Oord__class_Oless @ SY1461 @ SY1462 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SY1462 @ SY1461 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1558,plain,
! [SV77: $i] :
( ( ! [SY1463: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV77 )
| ! [SY1464: $i,SY1465: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1463 @ SY1464 @ SV77 ) @ SY1465 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SY1464 @ SY1465 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1559,plain,
! [SV78: $i] :
( ( ! [SY1466: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV78 )
| ! [SY1467: $i,SY1468: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1466 @ SY1467 @ SV78 ) @ SY1468 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SY1466 @ SY1468 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1560,plain,
! [SV79: $i] :
( ( ( c_Suc @ SV79 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1561,plain,
! [SV80: $i] :
( ( ( c_Suc @ SV80 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1562,plain,
! [SV81: $i] :
( ( c_HOL_Oord__class_Oless @ SV81 @ ( c_Suc @ SV81 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1563,plain,
! [SV82: $i] :
( ( c_HOL_Oord__class_Oless @ SV82 @ ( c_Suc @ SV82 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1564,plain,
! [SV83: $i] :
( ( ! [SY1469: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV83 ) @ SY1469 @ tc_nat )
| ! [SY1470: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1470 @ SY1469 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV83 @ SY1470 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1565,plain,
! [SV84: $i] :
( ( ! [SY1471: $i,SY1472: $i] :
( ( c_List_Oreplicate @ SV84 @ SY1471 @ SY1472 )
!= ( c_List_Olist_ONil @ SY1472 ) )
| ( SV84
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1566,plain,
! [SV85: $i] :
( ( ( SV85
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV85 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1567,plain,
! [SV86: $i] :
( ( ! [SY1473: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV86 @ SY1473 )
= SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1568,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1569,plain,
! [SV87: $i] :
( ( ! [SY1474: $i,SY1475: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV87 @ SY1474 @ SY1475 ) @ ( tc_List_Olist @ SY1475 ) )
= SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1570,plain,
! [SV88: $i] :
( ( ! [SY1476: $i] :
( ! [SY1477: $i] :
( ( c_List_Olist_ONil @ SV88 )
!= ( c_List_Oreplicate @ SY1476 @ SY1477 @ SV88 ) )
| ( SY1476
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1571,plain,
! [SV89: $i] :
( ( ! [SY1478: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV89 @ ( tc_List_Olist @ SY1478 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV89
= ( c_List_Olist_ONil @ SY1478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1572,plain,
! [SV90: $i] :
( ( ( c_Suc @ SV90 )
!= SV90 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1573,plain,
! [SV91: $i] :
( ( SV91
!= ( c_Suc @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1574,plain,
! [SV92: $i] :
( ( ! [SY1479: $i,SY1480: $i,SY1481: $i] :
( ( c_ListOrder_Ostep1 @ SV92 @ SY1479 @ SY1480 @ SY1481 )
| ! [SY1482: $i,SY1483: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY1482 ) @ SY1483 ) )
| ~ ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SY1482 @ SY1479 @ SY1481 ) @ ( c_List_Olist_OCons @ SY1483 @ SY1480 @ SY1481 ) @ SY1481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1575,plain,
! [SV93: $i] :
( ( ! [SY1484: $i,SY1485: $i,SY1486: $i,SY1487: $i] :
( ( c_ListOrder_Ostep1 @ SV93 @ ( c_List_Olist_OCons @ SY1484 @ SY1485 @ SY1486 ) @ ( c_List_Olist_OCons @ SY1484 @ SY1487 @ SY1486 ) @ SY1486 )
| ~ ( c_ListOrder_Ostep1 @ SV93 @ SY1485 @ SY1487 @ SY1486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1576,plain,
! [SV94: $i] :
( ( ! [SY1488: $i] :
( ( c_HOL_Oord__class_Oless @ SV94 @ SY1488 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SY1488 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1577,plain,
! [SV95: $i] :
( ( ! [SY1489: $i] :
( ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Suc @ SY1489 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV95 @ SY1489 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1578,plain,
! [SV96: $i] :
( ( ! [SY1490: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV96 @ SY1490 ) @ ( tc_List_Olist @ SY1490 ) )
= ( c_Nat_Osize__class_Osize @ SV96 @ ( tc_List_Olist @ SY1490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1579,plain,
! [SV97: $i] :
( ( ! [SY1491: $i,SY1492: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ SV97 @ SY1491 @ SY1492 ) @ SY1492 )
= ( c_List_Orotate @ SV97 @ ( c_List_Orotate1 @ SY1491 @ SY1492 ) @ SY1492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1580,plain,
! [SV98: $i] :
( ( ~ ( class_Orderings_Oorder @ SV98 )
| ! [SY1493: $i,SY1494: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1493 @ SY1494 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY1494 @ SY1493 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1581,plain,
! [SV99: $i] :
( ( ! [SY1495: $i,SY1496: $i,SY1497: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SY1495 ) @ SY1496 ) @ SY1497 ) )
| ! [SY1498: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SY1495 ) @ SY1498 ) @ SY1497 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SY1496 ) @ SY1498 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1582,plain,
! [SV100: $i] :
( ( ! [SY1499: $i,SY1500: $i,SY1501: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SY1499 ) @ SY1500 ) @ SY1501 ) )
| ! [SY1502: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SY1502 ) @ SY1501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SY1499 ) @ SY1500 ) @ SY1502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1583,plain,
! [SV101: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV101 )
| ! [SY1503: $i,SY1504: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1503 @ SY1504 @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SY1504 @ SY1503 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1584,plain,
! [SV102: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV102 )
| ! [SY1505: $i,SY1506: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1505 @ SY1506 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SY1506 @ SY1505 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1585,plain,
! [SV103: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV103 )
| ! [SY1507: $i,SY1508: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1507 @ SY1508 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SY1508 @ SY1507 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1586,plain,
! [SV104: $i] :
( ( ! [SY1509: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV104 @ SY1509 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV104 @ SY1509 ) @ ( c_List_Olist_ONil @ SY1509 ) @ SY1509 ) @ SY1509 )
= SV104 )
| ( SV104
= ( c_List_Olist_ONil @ SY1509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1587,plain,
! [SV105: $i] :
( ( ! [SY1510: $i,SY1511: $i] :
( ( SV105
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SY1510 ) @ SY1511 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SY1510 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SY1510 ) @ ( c_List_Oappend @ SY1511 @ ( c_List_Olist_OCons @ SY1510 @ ( 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)],[1161]) ).
thf(1588,plain,
! [SV106: $i] :
( ( ! [SY1512: $i,SY1513: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV106 @ SY1512 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1513 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV106 @ ( c_List_Oappend @ SY1512 @ ( c_List_Olist_OCons @ SY1513 @ ( 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)],[1162]) ).
thf(1589,plain,
! [SV107: $i] :
( ( ! [SY1514: $i] :
( ( ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SY1514 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ! [SY1515: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1515 @ SV107 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1514 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1515 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SY1514 @ ( 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)],[1163]) ).
thf(1590,plain,
! [SV108: $i] :
( ( ! [SY1516: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV108 ) @ SY1516 @ SV108 )
= ( c_Lambda_Oliftn @ SV108 @ SY1516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ SV108 @ SV108 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1591,plain,
! [SV109: $i] :
( ( ! [SY1517: $i,SY1518: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV109 @ SY1517 @ SY1518 ) @ SY1518 )
= ( c_List_Olast @ SY1517 @ SY1518 ) )
| ( SY1517
= ( c_List_Olist_ONil @ SY1518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1592,plain,
! [SV110: $i] :
( ( ! [SY1519: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV110 @ ( c_List_Olist_ONil @ SY1519 ) @ SY1519 ) @ SY1519 )
= ( c_List_Olist_ONil @ SY1519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1593,plain,
! [SV111: $i] :
( ( ! [SY1520: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ SV111 @ ( c_List_Olist_ONil @ SY1520 ) @ SY1520 ) @ SY1520 )
= SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1594,plain,
! [SV112: $i] :
( ( ! [SY1521: $i,SY1522: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV112 @ SY1521 @ SY1522 ) @ SY1522 )
= ( c_List_Olist_OCons @ SV112 @ ( c_List_Obutlast @ SY1521 @ SY1522 ) @ SY1522 ) )
| ( SY1521
= ( c_List_Olist_ONil @ SY1522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1595,plain,
! [SV113: $i] :
( ( ! [SY1523: $i,SY1524: $i,SY1525: $i,SY1526: $i] :
( ( ( c_List_Oappend @ SV113 @ SY1523 @ SY1524 )
!= ( c_List_Olist_OCons @ SY1525 @ SY1526 @ SY1524 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1525 @ SY1526 @ SV113 @ SY1523 @ SY1524 ) @ SY1523 @ SY1524 )
= SY1526 )
| ( SY1523
= ( c_List_Olist_OCons @ SY1525 @ SY1526 @ SY1524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1596,plain,
! [SV114: $i] :
( ( ! [SY1527: $i,SY1528: $i,SY1529: $i,SY1530: $i] :
( ( ( c_List_Olist_OCons @ SV114 @ SY1527 @ SY1528 )
!= ( c_List_Oappend @ SY1529 @ SY1530 @ SY1528 ) )
| ( ( c_List_Olist_OCons @ SV114 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV114 @ SY1527 @ SY1529 @ SY1530 @ SY1528 ) @ SY1528 )
= SY1529 )
| ( ( c_List_Olist_OCons @ SV114 @ SY1527 @ SY1528 )
= SY1530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1597,plain,
! [SV115: $i] :
( ( ! [SY1531: $i,SY1532: $i,SY1533: $i,SY1534: $i] :
( ( ( c_List_Oappend @ SV115 @ SY1531 @ SY1532 )
!= ( c_List_Olist_OCons @ SY1533 @ SY1534 @ SY1532 ) )
| ( SV115
= ( c_List_Olist_OCons @ SY1533 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1533 @ SY1534 @ SV115 @ SY1531 @ SY1532 ) @ SY1532 ) )
| ( SY1531
= ( c_List_Olist_OCons @ SY1533 @ SY1534 @ SY1532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1598,plain,
! [SV116: $i] :
( ( ! [SY1535: $i,SY1536: $i,SY1537: $i,SY1538: $i] :
( ( ( c_List_Olist_OCons @ SV116 @ SY1535 @ SY1536 )
!= ( c_List_Oappend @ SY1537 @ SY1538 @ SY1536 ) )
| ( SY1535
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV116 @ SY1535 @ SY1537 @ SY1538 @ SY1536 ) @ SY1538 @ SY1536 ) )
| ( ( c_List_Olist_OCons @ SV116 @ SY1535 @ SY1536 )
= SY1538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1599,plain,
! [SV117: $i] :
( ( ! [SY1539: $i,SY1540: $i,SY1541: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV117 @ SY1539 @ SY1540 ) @ ( c_List_Olist_OCons @ SY1539 @ SY1541 @ SY1540 ) @ SY1540 )
= ( c_List_Olist_OCons @ SY1539 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV117 @ SY1539 @ SY1540 ) @ SY1541 @ SY1540 ) @ SY1540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1600,plain,
! [SV118: $i] :
( ( ! [SY1542: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV118 @ ( c_List_Olist_ONil @ SY1542 ) @ SY1542 ) @ SY1542 )
= ( c_List_Obutlast @ SV118 @ SY1542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1601,plain,
! [SV119: $i] :
( ( ! [SY1543: $i,SY1544: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV119 @ SY1543 @ SY1544 ) @ SY1544 )
= ( c_List_Olast @ SY1543 @ SY1544 ) )
| ( SY1543
= ( c_List_Olist_ONil @ SY1544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1602,plain,
! [SV120: $i] :
( ( ! [SY1545: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV120 @ ( c_List_Olist_ONil @ SY1545 ) @ SY1545 ) @ SY1545 )
= ( c_List_Olast @ SV120 @ SY1545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1603,plain,
! [SV121: $i] :
( ( ! [SY1546: $i,SY1547: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV121 @ SY1546 @ SY1547 ) @ SY1547 )
= ( c_List_Oappend @ SV121 @ ( c_List_Obutlast @ SY1546 @ SY1547 ) @ SY1547 ) )
| ( SY1546
= ( c_List_Olist_ONil @ SY1547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1604,plain,
! [SV122: $i] :
( ( ! [SY1548: $i,SY1549: $i,SY1550: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SY1548 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1549 ) @ SY1550 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1548 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SY1549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1605,plain,
! [SV123: $i] :
( ( ! [SY1551: $i,SY1552: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SY1551 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1552 ) @ SY1551 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SY1552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1606,plain,
! [SV124: $i] :
( ( ! [SY1553: $i,SY1554: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SY1553 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SY1554 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1553 ) @ SY1554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1607,plain,
! [SV125: $i] :
( ( ! [SY1555: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV125 ) ) @ ( c_Lambda_OdB_OAbs @ SY1555 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV125 ) @ SY1555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1608,plain,
! [SV126: $i] :
( ( ! [SY1556: $i,SY1557: $i] :
( ! [SY1558: $i] :
( ( c_List_Ofilter @ SV126 @ ( c_List_Oreplicate @ SY1556 @ SY1557 @ SY1558 ) @ SY1558 )
= ( c_List_Olist_ONil @ SY1558 ) )
| ( hBOOL @ ( hAPP @ SV126 @ SY1557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1609,plain,
! [SV127: $i] :
( ( ! [SY1559: $i,SY1560: $i,SY1561: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV127 @ SY1559 @ SY1560 ) ) @ ( c_Lambda_Osubst @ SV127 @ SY1561 @ SY1560 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1559 ) @ SY1561 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1610,plain,
! [SV128: $i] :
( ( ! [SY1562: $i,SY1563: $i,SY1564: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV128 @ SY1562 @ SY1563 ) ) @ ( c_Lambda_Osubst @ SY1564 @ SY1562 @ SY1563 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SY1564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1611,plain,
! [SV129: $i] :
( ( ! [SY1565: $i,SY1566: $i,SY1567: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SY1565 @ SY1566 ) ) @ ( c_Lambda_Osubst @ SV129 @ SY1567 @ SY1566 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1565 ) @ SY1567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1612,plain,
! [SV130: $i] :
( ( ! [SY1568: $i,SY1569: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV130 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1568 @ SV130 @ SY1569 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1568 ) @ SV130 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1613,plain,
! [SV131: $i] :
( ( ! [SY1570: $i,SY1571: $i,SY1572: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV131 @ SY1570 @ SY1571 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1572 @ SY1571 )
= ( c_List_Olist_OCons @ SY1572 @ SY1570 @ SY1571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1614,plain,
! [SV132: $i] :
( ( ! [SY1573: $i,SY1574: $i,SY1575: $i,SY1576: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV132 @ SY1573 @ SY1574 ) @ ( c_Suc @ SY1575 ) @ SY1576 @ SY1574 )
= ( c_List_Olist_OCons @ SV132 @ ( c_List_Olist__update @ SY1573 @ SY1575 @ SY1576 @ SY1574 ) @ SY1574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1615,plain,
! [SV133: $i] :
( ( ! [SY1577: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV133 ) @ SY1577 @ SV133 )
= SY1577 )
| ( c_HOL_Oord__class_Oless @ SV133 @ SV133 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1616,plain,
! [SV134: $i] :
( ( ! [SY1578: $i,SY1579: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV134 ) @ SY1578 @ SY1579 )
= ( c_Lambda_OdB_OVar @ SV134 ) )
| ( SV134 = SY1579 )
| ( c_HOL_Oord__class_Oless @ SY1579 @ SV134 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1617,plain,
! [SV135: $i] :
( ( ! [SY1580: $i,SY1581: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV135 ) @ SY1580 @ SY1581 )
= ( c_Lambda_OdB_OVar @ SV135 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV135 @ SY1581 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1618,plain,
! [SV136: $i] :
( ( ! [SY1582: $i,SY1583: $i] :
( ( c_Type_Otyping @ SV136 @ SY1582 @ SY1583 )
| ! [SY1584: $i] :
( ~ ( c_Type_Otyping @ SV136 @ SY1584 @ SY1583 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1584 ) @ SY1582 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1619,plain,
! [SV137: $i] :
( ( ! [SY1585: $i,SY1586: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV137 @ SY1585 ) ) @ ( c_Lambda_Olift @ SY1586 @ SY1585 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV137 ) @ SY1586 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1620,plain,
! [SV138: $i] :
( ( ! [SY1587: $i,SY1588: $i,SY1589: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV138 @ ( tc_List_Olist @ SY1587 ) )
!= ( c_Nat_Osize__class_Osize @ SY1588 @ ( tc_List_Olist @ SY1589 ) ) )
| ! [SY1590: $i,SY1591: $i] :
( ( c_Map_Omap__upds @ SY1590 @ ( c_List_Oappend @ SV138 @ SY1591 @ SY1587 ) @ SY1588 @ SY1587 @ SY1589 )
= ( c_Map_Omap__upds @ SY1590 @ SV138 @ SY1588 @ SY1587 @ SY1589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1621,plain,
! [SV139: $i] :
( ( ! [SY1592: $i,SY1593: $i,SY1594: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV139 @ ( tc_List_Olist @ SY1592 ) )
!= ( c_Nat_Osize__class_Osize @ SY1593 @ ( tc_List_Olist @ SY1594 ) ) )
| ! [SY1595: $i,SY1596: $i] :
( ( c_Map_Omap__upds @ SY1595 @ SV139 @ ( c_List_Oappend @ SY1593 @ SY1596 @ SY1594 ) @ SY1592 @ SY1594 )
= ( c_Map_Omap__upds @ SY1595 @ SV139 @ SY1593 @ SY1592 @ SY1594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1622,plain,
! [SV140: $i] :
( ( ! [SY1597: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV140 ) @ SY1597 )
= ( c_Lambda_OdB_OVar @ SV140 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV140 @ SY1597 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1623,plain,
! [SV141: $i] :
( ( ! [SY1598: $i,SY1599: $i] :
( ( ( c_Lambda_Oliftn @ SV141 @ ( c_Lambda_OdB_OVar @ SY1598 ) @ SY1599 )
= ( c_Lambda_OdB_OVar @ SY1598 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1598 @ SY1599 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1624,plain,
! [SV142: $i] :
( ( ! [SY1600: $i] :
( ( hBOOL @ ( hAPP @ SV142 @ SY1600 ) )
| ! [SY1601: $i,SY1602: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV142 @ SY1601 @ ( tc_fun @ SY1602 @ tc_bool ) ) @ SY1600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1625,plain,
! [SV143: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV143 )
| ! [SY1603: $i] : ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1603 @ ( c_List_Olist_ONil @ SV143 ) @ SV143 ) @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1626,plain,
! [SV144: $i] :
( ( ! [SY1604: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV144 ) ) @ ( c_Lambda_OdB_OAbs @ SY1604 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV144 ) @ SY1604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1627,plain,
! [SV145: $i] :
( ( ! [SY1605: $i,SY1606: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV145 @ SY1605 @ SY1606 ) @ SY1606 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1605 @ SY1606 ) @ ( c_List_Orev @ SV145 @ SY1606 ) @ SY1606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1628,plain,
! [SV146: $i] :
( ( ! [SY1607: $i,SY1608: $i,SY1609: $i,SY1610: $i,SY1611: $i] :
( ( c_List_Ofoldl @ SV146 @ SY1607 @ ( c_List_Oappend @ SY1608 @ SY1609 @ SY1610 ) @ SY1611 @ SY1610 )
= ( c_List_Ofoldl @ SV146 @ ( c_List_Ofoldl @ SV146 @ SY1607 @ SY1608 @ SY1611 @ SY1610 ) @ SY1609 @ SY1611 @ SY1610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1629,plain,
! [SV147: $i] :
( ( ! [SY1612: $i,SY1613: $i,SY1614: $i] :
( ( c_List_Ofilter @ SV147 @ ( c_List_Oappend @ SY1612 @ SY1613 @ SY1614 ) @ SY1614 )
= ( c_List_Oappend @ ( c_List_Ofilter @ SV147 @ SY1612 @ SY1614 ) @ ( c_List_Ofilter @ SV147 @ SY1613 @ SY1614 ) @ SY1614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1630,plain,
! [SV148: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV148 ) @ ( c_List_Olist_ONil @ SV148 ) @ SV148 )
= ( c_List_Olist_ONil @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1631,plain,
! [SV149: $i] :
( ( ! [SY1615: $i,SY1616: $i] :
( ! [SY1617: $i] :
( ( c_List_Omap @ SV149 @ SY1615 @ SY1616 @ SY1617 )
!= ( c_List_Olist_ONil @ SY1617 ) )
| ( SY1615
= ( c_List_Olist_ONil @ SY1616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1632,plain,
! [SV150: $i] :
( ( ! [SY1618: $i] :
( ( SV150
= ( c_List_Olist_ONil @ SY1618 ) )
| ~ ( c_List_Onull @ SV150 @ SY1618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1633,plain,
! [SV151: $i] :
( ( ( c_List_Olist_ONil @ SV151 )
= ( c_List_Orev @ ( c_List_Olist_ONil @ SV151 ) @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1634,plain,
! [SV152: $i] :
( ( ( c_List_Olist_ONil @ SV152 )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ SV152 ) @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1635,plain,
! [SV153: $i] :
( ( ! [SY1619: $i,SY1620: $i] :
( ( SV153
!= ( c_List_Oappend @ SY1619 @ SV153 @ SY1620 ) )
| ( SY1619
= ( c_List_Olist_ONil @ SY1620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1636,plain,
! [SV154: $i] :
( ( ! [SY1621: $i,SY1622: $i] :
( ( ( c_List_Oappend @ SV154 @ SY1621 @ SY1622 )
!= SY1621 )
| ( SV154
= ( c_List_Olist_ONil @ SY1622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1637,plain,
! [SV155: $i] :
( ( ! [SY1623: $i,SY1624: $i] :
( ( SV155
!= ( c_List_Oappend @ SV155 @ SY1623 @ SY1624 ) )
| ( SY1623
= ( c_List_Olist_ONil @ SY1624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1638,plain,
! [SV156: $i] :
( ( ! [SY1625: $i,SY1626: $i] :
( ( ( c_List_Oappend @ SV156 @ SY1625 @ SY1626 )
!= SV156 )
| ( SY1625
= ( c_List_Olist_ONil @ SY1626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1639,plain,
! [SV157: $i] :
( ( ! [SY1627: $i] :
( ( ( c_List_Oremdups @ SV157 @ SY1627 )
!= ( c_List_Olist_ONil @ SY1627 ) )
| ( SV157
= ( c_List_Olist_ONil @ SY1627 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1640,plain,
! [SV158: $i] :
( ( ! [SY1628: $i,SY1629: $i] :
( ( ( c_List_Orotate @ SV158 @ SY1628 @ SY1629 )
!= ( c_List_Olist_ONil @ SY1629 ) )
| ( SY1628
= ( c_List_Olist_ONil @ SY1629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1641,plain,
! [SV159: $i] :
( ( ! [SY1630: $i] :
( ( ( c_List_Olist_ONil @ SV159 )
!= ( c_List_Orev @ SY1630 @ SV159 ) )
| ( SY1630
= ( c_List_Olist_ONil @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1642,plain,
! [SV160: $i] :
( ( ! [SY1631: $i,SY1632: $i] :
( ( c_List_Olist_ONil @ SV160 )
!= ( c_List_Olist_OCons @ SY1631 @ SY1632 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1643,plain,
! [SV161: $i] :
( ( ! [SY1633: $i,SY1634: $i] :
( ( ( c_List_Oappend @ SV161 @ SY1633 @ SY1634 )
!= ( c_List_Olist_ONil @ SY1634 ) )
| ( SY1633
= ( c_List_Olist_ONil @ SY1634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1644,plain,
! [SV162: $i] :
( ( ! [SY1635: $i,SY1636: $i] :
( ( ( c_List_Oappend @ SV162 @ SY1635 @ SY1636 )
!= ( c_List_Olist_ONil @ SY1636 ) )
| ( SV162
= ( c_List_Olist_ONil @ SY1636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1645,plain,
! [SV163: $i] :
( ( ! [SY1637: $i,SY1638: $i] :
( ( ( c_List_Olist_ONil @ SV163 )
!= ( c_List_Oappend @ SY1637 @ SY1638 @ SV163 ) )
| ( SY1638
= ( c_List_Olist_ONil @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1646,plain,
! [SV164: $i] :
( ( ! [SY1639: $i] :
( ! [SY1640: $i] :
( ( c_List_Olist_ONil @ SV164 )
!= ( c_List_Oappend @ SY1639 @ SY1640 @ SV164 ) )
| ( SY1639
= ( c_List_Olist_ONil @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1647,plain,
! [SV165: $i] :
( ( ! [SY1641: $i,SY1642: $i,SY1643: $i] :
( ( c_List_Ofoldl @ SV165 @ SY1641 @ ( c_List_Olist_ONil @ SY1642 ) @ SY1643 @ SY1642 )
= SY1641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1648,plain,
! [SV166: $i] :
( ( ( c_List_Oremdups @ ( c_List_Olist_ONil @ SV166 ) @ SV166 )
= ( c_List_Olist_ONil @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1649,plain,
! [SV167: $i] :
( ( ! [SY1644: $i,SY1645: $i,SY1646: $i] :
( ( ( c_List_Olist_ONil @ SV167 )
!= ( c_List_Omap @ SY1644 @ SY1645 @ SY1646 @ SV167 ) )
| ( SY1645
= ( c_List_Olist_ONil @ SY1646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1650,plain,
! [SV168: $i] :
( ( ! [SY1647: $i] :
( SV168
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1647 ) @ SV168 @ SY1647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1651,plain,
! [SV169: $i] :
( ( ! [SY1648: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV169 ) @ SY1648 @ SV169 )
= SY1648 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1652,plain,
! [SV170: $i] :
( ( ! [SY1649: $i] :
( SV170
= ( c_List_Oappend @ SV170 @ ( c_List_Olist_ONil @ SY1649 ) @ SY1649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1653,plain,
! [SV171: $i] :
( ( ! [SY1650: $i] :
( SV171
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1650 ) @ SV171 @ SY1650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1654,plain,
! [SV172: $i] :
( ( ! [SY1651: $i] :
( ( c_List_Oappend @ SV172 @ ( c_List_Olist_ONil @ SY1651 ) @ SY1651 )
= SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1655,plain,
! [SV173: $i] :
( ( ! [SY1652: $i,SY1653: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV173 ) ) @ SY1652 ) @ SY1653 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY1652 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV173 @ SY1652 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1653 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1656,plain,
! [SV174: $i] :
( ( ! [SY1654: $i,SY1655: $i] :
( ( SV174
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1654 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY1654 @ SY1655 @ SV174 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1654 ) @ SY1655 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1657,plain,
! [SV175: $i] :
( ( ! [SY1656: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV175 ) ) @ SY1656 ) ) @ ( c_Lambda_Osubst @ SV175 @ SY1656 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1658,plain,
! [SV176: $i] :
( ( ! [SY1657: $i] : ( hBOOL @ ( hAPP @ SV176 @ SY1657 ) )
| ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV176 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV176 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1659,plain,
! [SV177: $i] :
( ( ! [SY1658: $i] : ( hBOOL @ ( hAPP @ SV177 @ SY1658 ) )
| ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV177 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV177 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1660,plain,
! [SV178: $i] :
( ( ! [SY1659: $i] : ( hBOOL @ ( hAPP @ SV178 @ SY1659 ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV178 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV178 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1661,plain,
! [SV179: $i] :
( ( ! [SY1660: $i] : ( hBOOL @ ( hAPP @ SV179 @ SY1660 ) )
| ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV179 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV179 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1662,plain,
! [SV180: $i] :
( ( ! [SY1661: $i] : ( hBOOL @ ( hAPP @ SV180 @ SY1661 ) )
| ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV180 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV180 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1663,plain,
! [SV181: $i] :
( ( ! [SY1662: $i] : ( hBOOL @ ( hAPP @ SV181 @ SY1662 ) )
| ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV181 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV181 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1664,plain,
! [SV182: $i] :
( ( ! [SY1663: $i] : ( hBOOL @ ( hAPP @ SV182 @ SY1663 ) )
| ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV182 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV182 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1665,plain,
! [SV183: $i] :
( ( ! [SY1664: $i] : ( hBOOL @ ( hAPP @ SV183 @ SY1664 ) )
| ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV183 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV183 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1666,plain,
! [SV184: $i] :
( ( ! [SY1665: $i] : ( hBOOL @ ( hAPP @ SV184 @ SY1665 ) )
| ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV184 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV184 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1667,plain,
! [SV185: $i] :
( ( ! [SY1666: $i,SY1667: $i] :
( ( c_Lambda_Osubstn @ SV185 @ SY1666 @ SY1667 )
= ( c_Lambda_Osubst @ SV185 @ ( c_Lambda_Oliftn @ SY1667 @ SY1666 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1668,plain,
! [SV186: $i] :
( ( ! [SY1668: $i,SY1669: $i,SY1670: $i,SY1671: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SY1668 @ SY1669 @ SY1670 ) @ SY1670 ) @ ( c_Nat_Osize__class_Osize @ SV186 @ ( tc_List_Olist @ SY1670 ) ) @ SY1671 @ SY1670 )
= ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SY1671 @ SY1669 @ SY1670 ) @ SY1670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1669,plain,
! [SV187: $i] :
( ( ! [SY1672: $i,SY1673: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV187 @ SY1672 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1673 @ SY1672 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV187 ) @ SY1673 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1670,plain,
! [SV188: $i] :
( ( ! [SY1674: $i,SY1675: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SY1674 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SY1675 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY1674 @ SY1675 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1671,plain,
! [SV189: $i] :
( ( ! [SY1676: $i,SY1677: $i] :
( ~ ( hBOOL @ ( hAPP @ SV189 @ SY1676 ) )
| ! [SY1678: $i] :
( ! [SY1679: $i] :
( ( c_List_Olist_OCons @ SY1676 @ ( c_List_Ofilter @ SV189 @ SY1679 @ SY1678 ) @ SY1678 )
= ( c_List_Ofilter @ SV189 @ ( c_List_Oappend @ SY1677 @ ( c_List_Olist_OCons @ SY1676 @ SY1679 @ SY1678 ) @ SY1678 ) @ SY1678 ) )
| ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ SV189 @ SY1677 @ SY1678 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1672,plain,
! [SV190: $i] :
( ( ! [SY1680: $i,SY1681: $i] :
( ~ ( hBOOL @ ( hAPP @ SV190 @ SY1680 ) )
| ! [SY1682: $i] :
( ! [SY1683: $i] :
( ( c_List_Ofilter @ SV190 @ ( c_List_Oappend @ SY1681 @ ( c_List_Olist_OCons @ SY1680 @ SY1683 @ SY1682 ) @ SY1682 ) @ SY1682 )
= ( c_List_Olist_OCons @ SY1680 @ ( c_List_Ofilter @ SV190 @ SY1683 @ SY1682 ) @ SY1682 ) )
| ( hBOOL @ ( hAPP @ SV190 @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ SV190 @ SY1681 @ SY1682 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1673,plain,
! [SV191: $i] :
( ( ! [SY1684: $i,SY1685: $i,SY1686: $i,SY1687: $i] :
( ( ( c_List_Olist_OCons @ SV191 @ SY1684 @ SY1685 )
!= ( c_List_Oappend @ SY1686 @ SY1687 @ SY1685 ) )
| ( SY1684
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV191 @ SY1684 @ SY1686 @ SY1687 @ SY1685 ) @ SY1687 @ SY1685 ) )
| ( SY1686
= ( c_List_Olist_ONil @ SY1685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1674,plain,
! [SV192: $i] :
( ( ! [SY1688: $i,SY1689: $i,SY1690: $i,SY1691: $i] :
( ( ( c_List_Oappend @ SV192 @ SY1688 @ SY1689 )
!= ( c_List_Olist_OCons @ SY1690 @ SY1691 @ SY1689 ) )
| ( SV192
= ( c_List_Olist_OCons @ SY1690 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1690 @ SY1691 @ SV192 @ SY1688 @ SY1689 ) @ SY1689 ) )
| ( SV192
= ( c_List_Olist_ONil @ SY1689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1675,plain,
! [SV193: $i] :
( ( ! [SY1692: $i,SY1693: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV193 @ ( c_List_Olist_OCons @ SY1692 @ ( c_List_Olist_ONil @ SY1693 ) @ SY1693 ) @ SY1693 ) @ SY1693 )
= SY1692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1676,plain,
! [SV194: $i] :
( ( ! [SY1694: $i,SY1695: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV194 @ ( c_List_Olist_OCons @ SY1694 @ ( c_List_Olist_ONil @ SY1695 ) @ SY1695 ) @ SY1695 ) @ SY1695 )
= SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1677,plain,
! [SV195: $i] :
( ( ! [SY1696: $i,SY1697: $i,SY1698: $i] :
( ( SV195 = SY1696 )
| ( SY1697 = SY1698 )
| ! [SY1699: $i,SY1700: $i] :
~ ( c_ListOrder_Ostep1 @ SY1699 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SY1697 @ ( c_List_Olist_ONil @ SY1700 ) @ SY1700 ) @ SY1700 ) @ ( c_List_Oappend @ SY1696 @ ( c_List_Olist_OCons @ SY1698 @ ( c_List_Olist_ONil @ SY1700 ) @ SY1700 ) @ SY1700 ) @ SY1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1678,plain,
! [SV196: $i] :
( ( ! [SY1701: $i,SY1702: $i,SY1703: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SY1701 ) @ SY1702 ) )
| ( SY1701 = SY1702 )
| ! [SY1704: $i,SY1705: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SY1703 @ ( c_List_Olist_OCons @ SY1701 @ ( c_List_Olist_ONil @ SY1704 ) @ SY1704 ) @ SY1704 ) @ ( c_List_Oappend @ SY1705 @ ( c_List_Olist_OCons @ SY1702 @ ( c_List_Olist_ONil @ SY1704 ) @ SY1704 ) @ SY1704 ) @ SY1704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1679,plain,
! [SV197: $i] :
( ( ! [SY1706: $i,SY1707: $i,SY1708: $i,SY1709: $i] :
( ( ( c_List_Oappend @ SV197 @ SY1706 @ SY1707 )
!= ( c_List_Olist_OCons @ SY1708 @ SY1709 @ SY1707 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY1708 @ SY1709 @ SV197 @ SY1706 @ SY1707 ) @ SY1706 @ SY1707 )
= SY1709 )
| ( SV197
= ( c_List_Olist_ONil @ SY1707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1680,plain,
! [SV198: $i] :
( ( ! [SY1710: $i,SY1711: $i,SY1712: $i,SY1713: $i] :
( ( ( c_List_Olist_OCons @ SV198 @ SY1710 @ SY1711 )
!= ( c_List_Oappend @ SY1712 @ SY1713 @ SY1711 ) )
| ( ( c_List_Olist_OCons @ SV198 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV198 @ SY1710 @ SY1712 @ SY1713 @ SY1711 ) @ SY1711 )
= SY1712 )
| ( SY1712
= ( c_List_Olist_ONil @ SY1711 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1681,plain,
! [SV199: $i] :
( ( ! [SY1714: $i,SY1715: $i,SY1716: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SY1714 ) @ SY1715 ) )
| ! [SY1717: $i,SY1718: $i] :
( ( c_ListOrder_Ostep1 @ SV199 @ SY1716 @ SY1717 @ SY1718 )
| ~ ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SY1716 @ ( c_List_Olist_OCons @ SY1714 @ ( c_List_Olist_ONil @ SY1718 ) @ SY1718 ) @ SY1718 ) @ ( c_List_Oappend @ SY1717 @ ( c_List_Olist_OCons @ SY1715 @ ( c_List_Olist_ONil @ SY1718 ) @ SY1718 ) @ SY1718 ) @ SY1718 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1682,plain,
! [SV200: $i] :
( ( ! [SY1719: $i,SY1720: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV200 @ SY1719 @ SY1720 ) @ SY1720 )
= ( c_List_Oappend @ SY1719 @ ( c_List_Olist_OCons @ SV200 @ ( c_List_Olist_ONil @ SY1720 ) @ SY1720 ) @ SY1720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1683,plain,
! [SV201: $i] :
( ( ! [SY1721: $i,SY1722: $i,SY1723: $i] :
( ( SV201 = SY1721 )
| ( c_ListOrder_Ostep1 @ SY1722 @ SV201 @ SY1721 @ SY1723 )
| ! [SY1724: $i,SY1725: $i] :
~ ( c_ListOrder_Ostep1 @ SY1722 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SY1724 @ ( c_List_Olist_ONil @ SY1723 ) @ SY1723 ) @ SY1723 ) @ ( c_List_Oappend @ SY1721 @ ( c_List_Olist_OCons @ SY1725 @ ( c_List_Olist_ONil @ SY1723 ) @ SY1723 ) @ SY1723 ) @ SY1723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1684,plain,
! [SV202: $i] :
( ( ! [SY1726: $i,SY1727: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV202 @ SY1726 @ SY1727 ) @ ( c_List_Olist_OCons @ SY1726 @ ( c_List_Olist_ONil @ SY1727 ) @ SY1727 ) @ SY1727 )
= ( c_List_Olist_OCons @ SY1726 @ ( c_List_Oreplicate @ SV202 @ SY1726 @ SY1727 ) @ SY1727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1685,plain,
! [SV203: $i] :
( ( ! [SY1728: $i,SY1729: $i,SY1730: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV203 ) @ SY1728 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1729 @ SY1730 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1730
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV203 @ SY1728 @ SY1729 @ SY1730 ) @ ( c_List_Olist_OCons @ SY1728 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY1730
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1686,plain,
! [SV204: $i] :
( ( ! [SY1731: $i,SY1732: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ SV204 ) @ SY1731 @ SY1732 )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV204 @ SY1731 @ SY1732 ) @ SY1732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1687,plain,
! [SV205: $i] :
( ( ! [SY1733: $i,SY1734: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV205 ) @ SY1733 @ SY1734 )
= ( c_Lambda_OdB_OVar @ SV205 ) )
| ( SV205 = SY1734 )
| ( c_HOL_Oord__class_Oless @ SY1734 @ SV205 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1688,plain,
! [SV206: $i] :
( ( ! [SY1735: $i] :
( ( c_Lambda_Osubstn @ SV206 @ SY1735 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ SV206 @ SY1735 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1689,plain,
! [SV207: $i] :
( ( ! [SY1736: $i] :
( ( hBOOL @ ( hAPP @ SV207 @ SY1736 ) )
| ! [SY1737: $i,SY1738: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1737 @ SV207 @ ( tc_fun @ SY1738 @ tc_bool ) ) @ SY1736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1690,plain,
! [SV208: $i] :
( ( ! [SY1739: $i,SY1740: $i,SY1741: $i,SY1742: $i] :
( ( c_List_Ofoldl @ SV208 @ SY1739 @ SY1740 @ SY1741 @ SY1742 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV208 @ SY1741 @ SY1742 @ SY1741 ) @ ( c_List_Orev @ SY1740 @ SY1742 ) @ SY1739 @ SY1742 @ SY1741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1691,plain,
! [SV209: $i] :
( ( ! [SY1743: $i] :
( ( c_List_Olist_OCons @ SV209 @ ( c_List_Olist_ONil @ SY1743 ) @ SY1743 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV209 @ ( c_List_Olist_ONil @ SY1743 ) @ SY1743 ) @ SY1743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1692,plain,
! [SV210: $i] :
( ( ! [SY1744: $i,SY1745: $i,SY1746: $i,SY1747: $i,SY1748: $i] :
( ( c_List_Omap @ SV210 @ ( c_List_Olist__update @ SY1744 @ SY1745 @ SY1746 @ SY1747 ) @ SY1747 @ SY1748 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV210 @ SY1744 @ SY1747 @ SY1748 ) @ SY1745 @ ( hAPP @ SV210 @ SY1746 ) @ SY1748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1693,plain,
! [SV211: $i] :
( ( ! [SY1749: $i,SY1750: $i] :
( ( c_List_Olist_OCons @ SV211 @ SY1749 @ SY1750 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1750 ) @ ( c_List_Olist_OCons @ SV211 @ SY1749 @ SY1750 ) @ SY1750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1694,plain,
! [SV212: $i] :
( ( ! [SY1751: $i,SY1752: $i] :
( SV212
!= ( c_List_Olist_OCons @ SY1751 @ SV212 @ SY1752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1695,plain,
! [SV213: $i] :
( ( ! [SY1753: $i,SY1754: $i] :
( ( c_List_Olist_OCons @ SV213 @ SY1753 @ SY1754 )
!= SY1753 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1696,plain,
! [SV214: $i] :
( ( ! [SY1755: $i,SY1756: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV214 @ SY1755 ) ) @ ( c_Lambda_Olift @ SY1756 @ SY1755 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV214 ) @ SY1756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1697,plain,
! [SV215: $i] :
( ( ! [SY1757: $i] :
( ( hBOOL @ ( hAPP @ SV215 @ SY1757 ) )
| ! [SY1758: $i] :
( ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY1758 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY1758 @ SV215 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1758 @ SY1757 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1698,plain,
! [SV216: $i] :
( ( ! [SY1759: $i,SY1760: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV216 @ SY1759 ) @ SY1760 @ SY1759 )
= SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1699,plain,
! [SV217: $i] :
( ( ! [SY1761: $i] :
( ( hBOOL @ ( hAPP @ SV217 @ SY1761 ) )
| ! [SY1762: $i] :
( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY1762 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY1762 @ SV217 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1762 @ SY1761 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1700,plain,
! [SV218: $i] :
( ( ! [SY1763: $i,SY1764: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV218 @ SY1763 ) @ ( c_List_Olist_OCons @ SY1764 @ ( c_List_Olist_ONil @ SY1763 ) @ SY1763 ) @ SY1763 ) @ SY1763 )
= ( c_List_Olist_OCons @ SY1764 @ SV218 @ SY1763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1701,plain,
! [SV219: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV219 )
| ! [SY1765: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1765 @ SV219 )
| ! [SY1766: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1766 @ SY1765 @ SV219 ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1702,plain,
! [SV220: $i] :
( ( ! [SY1767: $i,SY1768: $i,SY1769: $i] :
( ( c_List_Olist_OCons @ SV220 @ ( c_List_Oappend @ SY1767 @ SY1768 @ SY1769 ) @ SY1769 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV220 @ SY1767 @ SY1769 ) @ SY1768 @ SY1769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1703,plain,
! [SV221: $i] :
( ( ! [SY1770: $i,SY1771: $i,SY1772: $i] :
( ( c_List_Olist_OCons @ SV221 @ ( c_List_Oappend @ SY1770 @ SY1771 @ SY1772 ) @ SY1772 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV221 @ SY1770 @ SY1772 ) @ SY1771 @ SY1772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1704,plain,
! [SV222: $i] :
( ( ! [SY1773: $i,SY1774: $i] :
( ( c_List_Oremove1 @ SV222 @ ( c_List_Olist_OCons @ SV222 @ SY1773 @ SY1774 ) @ SY1774 )
= SY1773 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1705,plain,
! [SV223: $i] :
( ( ! [SY1775: $i,SY1776: $i,SY1777: $i,SY1778: $i,SY1779: $i] :
( ( c_List_Olist_Olist__case @ SV223 @ SY1775 @ ( c_List_Olist_OCons @ SY1776 @ SY1777 @ SY1778 ) @ SY1779 @ SY1778 )
= ( hAPP @ ( hAPP @ SY1775 @ SY1776 ) @ SY1777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1706,plain,
! [SV224: $i] :
( ( ! [SY1780: $i,SY1781: $i,SY1782: $i,SY1783: $i] :
( ( c_List_Omap @ SV224 @ ( c_List_Olist_OCons @ SY1780 @ SY1781 @ SY1782 ) @ SY1782 @ SY1783 )
= ( c_List_Olist_OCons @ ( hAPP @ SV224 @ SY1780 ) @ ( c_List_Omap @ SV224 @ SY1781 @ SY1782 @ SY1783 ) @ SY1783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1707,plain,
! [SV225: $i] :
( ( ! [SY1784: $i,SY1785: $i,SY1786: $i,SY1787: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV225 @ SY1784 ) @ ( c_List_Omap @ SV225 @ SY1785 @ SY1786 @ SY1787 ) @ SY1787 )
= ( c_List_Omap @ SV225 @ ( c_List_Olist_OCons @ SY1784 @ SY1785 @ SY1786 ) @ SY1786 @ SY1787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1708,plain,
! [SV226: $i] :
( ( ! [SY1788: $i,SY1789: $i,SY1790: $i,SY1791: $i] :
( ( c_List_Omap @ SV226 @ ( c_List_Olist_OCons @ SY1788 @ SY1789 @ SY1790 ) @ SY1790 @ SY1791 )
= ( c_List_Olist_OCons @ ( hAPP @ SV226 @ SY1788 ) @ ( c_List_Omap @ SV226 @ SY1789 @ SY1790 @ SY1791 ) @ SY1791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1709,plain,
! [SV227: $i] :
( ( ! [SY1792: $i,SY1793: $i,SY1794: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV227 @ SY1792 @ SY1793 ) @ SY1794 @ SY1793 )
= ( c_List_Olist_OCons @ SV227 @ ( c_List_Oappend @ SY1792 @ SY1794 @ SY1793 ) @ SY1793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1710,plain,
! [SV228: $i] :
( ( ! [SY1795: $i,SY1796: $i,SY1797: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV228 @ SY1795 @ SY1796 ) @ SY1797 @ SY1796 )
= ( c_List_Olist_OCons @ SV228 @ ( c_List_Oappend @ SY1795 @ SY1797 @ SY1796 ) @ SY1796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1711,plain,
! [SV229: $i] :
( ( ! [SY1798: $i] :
( ! [SY1799: $i] :
( ( c_Lambda_OdB_OAbs @ SV229 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1798 @ SY1799 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV229 )
= SY1798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1712,plain,
! [SV230: $i] :
( ( ! [SY1800: $i] :
( ~ ( class_Orderings_Olinorder @ SV230 )
| ! [SY1801: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1800 @ SY1801 @ SV230 ) @ SV230 )
| ! [SY1802: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1802 @ ( c_List_Olist_OCons @ SY1800 @ SY1801 @ SV230 ) @ SV230 ) @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1713,plain,
! [SV231: $i] :
( ( ~ ( class_Lattices_Olattice @ SV231 )
| ! [SY1803: $i,SY1804: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1803 @ SY1804 @ SV231 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1804 @ SY1803 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1714,plain,
! [SV232: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV232 )
| ! [SY1805: $i,SY1806: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1805 @ SY1806 @ SV232 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1806 @ SY1805 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1715,plain,
! [SV233: $i] :
( ( ! [SY1807: $i,SY1808: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV233 @ SY1807 @ ( tc_fun @ SY1808 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1807 @ SV233 @ ( tc_fun @ SY1808 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1716,plain,
! [SV234: $i] :
( ( ! [SY1809: $i,SY1810: $i,SY1811: $i] :
( ( ( c_List_Orev @ SV234 @ SY1809 )
!= ( c_List_Olist_OCons @ SY1810 @ SY1811 @ SY1809 ) )
| ( SV234
= ( c_List_Oappend @ ( c_List_Orev @ SY1811 @ SY1809 ) @ ( c_List_Olist_OCons @ SY1810 @ ( c_List_Olist_ONil @ SY1809 ) @ SY1809 ) @ SY1809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1717,plain,
! [SV235: $i] :
( ( ! [SY1812: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV235 @ ( c_List_Olist_ONil @ SY1812 ) @ SY1812 ) @ SY1812 )
= ( c_List_Olist_OCons @ SV235 @ ( c_List_Olist_ONil @ SY1812 ) @ SY1812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1718,plain,
! [SV236: $i] :
( ( ! [SY1813: $i,SY1814: $i,SY1815: $i,SY1816: $i,SY1817: $i] :
( ( c_List_Ofoldl @ SV236 @ SY1813 @ ( c_List_Olist_OCons @ SY1814 @ SY1815 @ SY1816 ) @ SY1817 @ SY1816 )
= ( c_List_Ofoldl @ SV236 @ ( hAPP @ ( hAPP @ SV236 @ SY1813 ) @ SY1814 ) @ SY1815 @ SY1817 @ SY1816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1719,plain,
! [SV237: $i] :
( ( ! [SY1818: $i,SY1819: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV237 @ SY1818 @ SY1819 ) @ SY1819 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1818 @ SY1819 ) @ ( c_List_Olist_OCons @ SV237 @ ( c_List_Olist_ONil @ SY1819 ) @ SY1819 ) @ SY1819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1720,plain,
! [SV238: $i] :
( ( ! [SY1820: $i,SY1821: $i,SY1822: $i] :
( ! [SY1823: $i] :
( ( c_List_Olist_OCons @ SV238 @ SY1820 @ SY1821 )
!= ( c_List_Ofilter @ SY1822 @ SY1823 @ SY1821 ) )
| ( hBOOL @ ( hAPP @ SY1822 @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1721,plain,
! [SV239: $i] :
( ( ! [SY1824: $i,SY1825: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ SV239 @ SY1824 @ SY1825 ) @ SY1825 )
= ( c_List_Ofilter @ SV239 @ ( c_List_Oremdups @ SY1824 @ SY1825 ) @ SY1825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1722,plain,
! [SV240: $i] :
( ( ! [SY1826: $i] :
( ! [SY1827: $i,SY1828: $i] :
( ( c_List_Ofilter @ SV240 @ ( c_List_Olist_OCons @ SY1826 @ SY1827 @ SY1828 ) @ SY1828 )
= ( c_List_Olist_OCons @ SY1826 @ ( c_List_Ofilter @ SV240 @ SY1827 @ SY1828 ) @ SY1828 ) )
| ~ ( hBOOL @ ( hAPP @ SV240 @ SY1826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1723,plain,
! [SV241: $i] :
( ( ! [SY1829: $i,SY1830: $i] :
( ( ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SY1829 ) @ SY1829 )
!= ( c_List_Orev @ SY1830 @ SY1829 ) )
| ( SY1830
= ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SY1829 ) @ SY1829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1724,plain,
! [SV242: $i] :
( ( ! [SY1831: $i,SY1832: $i,SY1833: $i,SY1834: $i] :
( ( c_Lambda_OdB_OdB__case @ SV242 @ SY1831 @ SY1832 @ ( c_Lambda_OdB_OAbs @ SY1833 ) @ SY1834 )
= ( hAPP @ SY1832 @ SY1833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1725,plain,
! [SV243: $i] :
( ( ! [SY1835: $i,SY1836: $i,SY1837: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV243 @ SY1835 @ SY1836 ) ) @ ( c_Lambda_Osubst @ SY1837 @ SY1835 @ SY1836 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV243 ) @ SY1837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1726,plain,
! [SV244: $i] :
( ( ! [SY1838: $i,SY1839: $i,SY1840: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV244 @ SY1838 @ SY1839 @ SY1840 ) @ SY1840 )
= ( c_List_Omap @ SV244 @ ( c_List_Orev @ SY1838 @ SY1839 ) @ SY1839 @ SY1840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1727,plain,
! [SV245: $i] :
( ( ! [SY1841: $i,SY1842: $i,SY1843: $i] :
( ( ( c_List_Oappend @ SV245 @ SY1841 @ SY1842 )
!= ( c_List_Oappend @ SY1843 @ SY1841 @ SY1842 ) )
| ( SV245 = SY1843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1728,plain,
! [SV246: $i] :
( ( ! [SY1844: $i,SY1845: $i,SY1846: $i] :
( ( ( c_List_Oappend @ SV246 @ SY1844 @ SY1845 )
!= ( c_List_Oappend @ SV246 @ SY1846 @ SY1845 ) )
| ( SY1844 = SY1846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1729,plain,
! [SV247: $i] :
( ( ! [SY1847: $i,SY1848: $i,SY1849: $i] :
( ! [SY1850: $i] :
( ( c_List_Ofilter @ SV247 @ SY1847 @ SY1848 )
!= ( c_List_Olist_OCons @ SY1849 @ SY1850 @ SY1848 ) )
| ( hBOOL @ ( hAPP @ SV247 @ SY1849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1730,plain,
! [SV248: $i] :
( ( ! [SY1851: $i,SY1852: $i,SY1853: $i,SY1854: $i] :
( ( c_List_Orotate @ SV248 @ ( c_List_Omap @ SY1851 @ SY1852 @ SY1853 @ SY1854 ) @ SY1854 )
= ( c_List_Omap @ SY1851 @ ( c_List_Orotate @ SV248 @ SY1852 @ SY1853 ) @ SY1853 @ SY1854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1731,plain,
! [SV249: $i] :
( ( ! [SY1855: $i] :
( SV249
= ( c_List_Orev @ ( c_List_Orev @ SV249 @ SY1855 ) @ SY1855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1732,plain,
! [SV250: $i] :
( ( ! [SY1856: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV250 @ SY1856 ) @ SY1856 )
= SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1733,plain,
! [SV251: $i] :
( ( ! [SY1857: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV251 @ SY1857 ) @ SY1857 )
= SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1734,plain,
! [SV252: $i] :
( ( ! [SY1858: $i,SY1859: $i,SY1860: $i,SY1861: $i,SY1862: $i] :
( ( c_List_Ofoldr @ SV252 @ ( c_List_Oappend @ SY1858 @ SY1859 @ SY1860 ) @ SY1861 @ SY1860 @ SY1862 )
= ( c_List_Ofoldr @ SV252 @ SY1858 @ ( c_List_Ofoldr @ SV252 @ SY1859 @ SY1861 @ SY1860 @ SY1862 ) @ SY1860 @ SY1862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1735,plain,
! [SV253: $i] :
( ( ! [SY1863: $i] :
( ! [SY1864: $i,SY1865: $i] : ( c_List_Olist__ex @ SV253 @ ( c_List_Olist_OCons @ SY1863 @ SY1864 @ SY1865 ) @ SY1865 )
| ~ ( hBOOL @ ( hAPP @ SV253 @ SY1863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1736,plain,
! [SV254: $i] :
( ( ! [SY1866: $i,SY1867: $i] :
( ( ( c_List_Orev @ SV254 @ SY1866 )
!= ( c_List_Olist_OCons @ SY1867 @ ( c_List_Olist_ONil @ SY1866 ) @ SY1866 ) )
| ( SV254
= ( c_List_Olist_OCons @ SY1867 @ ( c_List_Olist_ONil @ SY1866 ) @ SY1866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1737,plain,
! [SV255: $i] :
( ( ! [SY1868: $i,SY1869: $i,SY1870: $i] :
( ( c_List_Olist__ex @ SV255 @ ( c_List_Olist_OCons @ SY1868 @ SY1869 @ SY1870 ) @ SY1870 )
| ~ ( c_List_Olist__ex @ SV255 @ SY1869 @ SY1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1738,plain,
! [SV256: $i] :
( ( ! [SY1871: $i,SY1872: $i] :
( ( c_List_Olist__ex @ SV256 @ SY1871 @ SY1872 )
| ! [SY1873: $i] :
( ( hBOOL @ ( hAPP @ SV256 @ SY1873 ) )
| ~ ( c_List_Olist__ex @ SV256 @ ( c_List_Olist_OCons @ SY1873 @ SY1871 @ SY1872 ) @ SY1872 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1739,plain,
! [SV257: $i] :
( ( ! [SY1874: $i,SY1875: $i,SY1876: $i,SY1877: $i,SY1878: $i] :
( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SY1874 @ SY1875 @ SY1876 ) @ ( c_List_Olist_OCons @ SY1877 @ SY1878 @ SY1876 ) @ SY1876 )
| ~ ( c_List_Olistrelp @ SV257 @ SY1875 @ SY1878 @ SY1876 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SY1874 ) @ SY1877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1740,plain,
! [SV258: $i] :
( ( ! [SY1879: $i] :
( ~ ( class_Lattices_Olattice @ SV258 )
| ! [SY1880: $i,SY1881: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1879 @ SY1880 @ SV258 ) @ SY1881 @ SV258 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1879 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1880 @ SY1881 @ SV258 ) @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1741,plain,
! [SV259: $i] :
( ( ! [SY1882: $i] :
( ~ ( class_Lattices_Olattice @ SV259 )
| ! [SY1883: $i,SY1884: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1882 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1883 @ SY1884 @ SV259 ) @ SV259 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1883 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1882 @ SY1884 @ SV259 ) @ SV259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1742,plain,
! [SV260: $i] :
( ( ! [SY1885: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV260 )
| ! [SY1886: $i,SY1887: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1885 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1886 @ SY1887 @ SV260 ) @ SV260 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1886 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1885 @ SY1887 @ SV260 ) @ SV260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1743,plain,
! [SV261: $i] :
( ( ! [SY1888: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV261 )
| ! [SY1889: $i,SY1890: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1888 @ SY1889 @ SV261 ) @ SY1890 @ SV261 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1888 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1889 @ SY1890 @ SV261 ) @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1744,plain,
! [SV262: $i] :
( ( ! [SY1891: $i,SY1892: $i,SY1893: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 @ SY1891 @ ( tc_fun @ SY1892 @ tc_bool ) ) @ SY1893 @ ( tc_fun @ SY1892 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1891 @ SY1893 @ ( tc_fun @ SY1892 @ tc_bool ) ) @ ( tc_fun @ SY1892 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1745,plain,
! [SV263: $i] :
( ( ! [SY1894: $i,SY1895: $i,SY1896: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1894 @ SY1895 @ ( tc_fun @ SY1896 @ tc_bool ) ) @ ( tc_fun @ SY1896 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1894 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SY1895 @ ( tc_fun @ SY1896 @ tc_bool ) ) @ ( tc_fun @ SY1896 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1746,plain,
! [SV264: $i] :
( ( ! [SY1897: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV264 )
!= ( c_Lambda_OdB_OAbs @ SY1897 ) )
| ( SV264 = SY1897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1747,plain,
! [SV265: $i] :
( ( ! [SY1898: $i] :
( ! [SY1899: $i,SY1900: $i] :
( ( c_List_Oremove1 @ SV265 @ ( c_List_Olist_OCons @ SY1898 @ SY1899 @ SY1900 ) @ SY1900 )
= ( c_List_Olist_OCons @ SY1898 @ ( c_List_Oremove1 @ SV265 @ SY1899 @ SY1900 ) @ SY1900 ) )
| ( SV265 = SY1898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1748,plain,
! [SV266: $i] :
( ( ! [SY1901: $i,SY1902: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV266 @ SY1901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1902 @ SY1901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV266 ) @ SY1902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1749,plain,
! [SV267: $i] :
( ( ! [SY1903: $i,SY1904: $i,SY1905: $i,SY1906: $i] :
( ( c_List_Omap @ SV267 @ ( c_List_Oappend @ SY1903 @ SY1904 @ SY1905 ) @ SY1905 @ SY1906 )
= ( c_List_Oappend @ ( c_List_Omap @ SV267 @ SY1903 @ SY1905 @ SY1906 ) @ ( c_List_Omap @ SV267 @ SY1904 @ SY1905 @ SY1906 ) @ SY1906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1750,plain,
! [SV268: $i] :
( ( ! [SY1907: $i] :
( ( SV268
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SY1907 @ SV268 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SY1907 @ SV268 ) @ t_a ) )
| ( SV268
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SY1907 @ SV268 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1751,plain,
! [SV269: $i] :
( ( ! [SY1908: $i,SY1909: $i,SY1910: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV269 ) @ SY1908 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1909 ) @ SY1910 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1908 = SY1910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1752,plain,
! [SV270: $i] :
( ( ! [SY1911: $i,SY1912: $i] :
( ! [SY1913: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV270 ) @ SY1911 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1912 ) @ SY1913 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV270 = SY1912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1753,plain,
! [SV271: $i] :
( ( ! [SY1914: $i,SY1915: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV271 @ SY1914 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1915 ) )
| ( SV271
= ( c_Lambda_OdB_OAbs @ SY1915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1754,plain,
! [SV272: $i] :
( ( ! [SY1916: $i] :
( ! [SY1917: $i,SY1918: $i] :
( ( c_List_Oremove1 @ SV272 @ ( c_List_Ofilter @ SY1916 @ SY1917 @ SY1918 ) @ SY1918 )
= ( c_List_Ofilter @ SY1916 @ SY1917 @ SY1918 ) )
| ( hBOOL @ ( hAPP @ SY1916 @ SV272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1755,plain,
! [SV273: $i] :
( ( ! [SY1919: $i,SY1920: $i,SY1921: $i,SY1922: $i,SY1923: $i] :
( ( c_List_Olist_Olist__rec @ SV273 @ SY1919 @ ( c_List_Olist_OCons @ SY1920 @ SY1921 @ SY1922 ) @ SY1923 @ SY1922 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY1919 @ SY1920 ) @ SY1921 ) @ ( c_List_Olist_Olist__rec @ SV273 @ SY1919 @ SY1921 @ SY1923 @ SY1922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1756,plain,
! [SV274: $i] :
( ( ! [SY1924: $i,SY1925: $i] :
( ( ( c_List_Orev @ SV274 @ SY1924 )
!= ( c_List_Orev @ SY1925 @ SY1924 ) )
| ( SV274 = SY1925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1757,plain,
! [SV275: $i] :
( ( ! [SY1926: $i,SY1927: $i,SY1928: $i,SY1929: $i] :
( ( c_List_Ofoldr @ SV275 @ SY1926 @ SY1927 @ SY1928 @ SY1929 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV275 @ SY1928 @ SY1929 @ SY1929 ) @ SY1927 @ ( c_List_Orev @ SY1926 @ SY1928 ) @ SY1929 @ SY1928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1758,plain,
! [SV276: $i] :
( ( ! [SY1930: $i,SY1931: $i,SY1932: $i,SY1933: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV276 @ SY1930 @ SY1931 @ ( c_Lambda_OdB_OAbs @ SY1932 ) @ SY1933 )
= ( hAPP @ ( hAPP @ SY1931 @ SY1932 ) @ ( c_Lambda_OdB_OdB__rec @ SV276 @ SY1930 @ SY1931 @ SY1932 @ SY1933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1759,plain,
! [SV277: $i] :
( ( ! [SY1934: $i,SY1935: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ SV277 @ SY1934 @ SY1935 ) @ SY1935 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1760,plain,
! [SV278: $i] :
( ( ~ ( class_Lattices_Olattice @ SV278 )
| ! [SY1936: $i,SY1937: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ SY1937 @ SV278 ) @ SV278 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ SY1937 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1761,plain,
! [SV279: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV279 )
| ! [SY1938: $i,SY1939: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ SY1939 @ SV279 ) @ SV279 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ SY1939 @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1762,plain,
! [SV280: $i] :
( ( ! [SY1940: $i,SY1941: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SY1940 @ ( tc_fun @ SY1941 @ tc_bool ) ) @ ( tc_fun @ SY1941 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SY1940 @ ( tc_fun @ SY1941 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1763,plain,
! [SV281: $i] :
( ( ! [SY1942: $i,SY1943: $i,SY1944: $i,SY1945: $i,SY1946: $i] :
( ( c_List_Ofoldr @ SV281 @ ( c_List_Olist_OCons @ SY1942 @ SY1943 @ SY1944 ) @ SY1945 @ SY1944 @ SY1946 )
= ( hAPP @ ( hAPP @ SV281 @ SY1942 ) @ ( c_List_Ofoldr @ SV281 @ SY1943 @ SY1945 @ SY1944 @ SY1946 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1764,plain,
! [SV282: $i] :
( ( ! [SY1947: $i,SY1948: $i,SY1949: $i,SY1950: $i] :
( ~ ( hBOOL @ ( hAPP @ SV282 @ ( c_Lambda_OdB_OdB__case @ SY1947 @ SY1948 @ SY1949 @ ( c_Lambda_OdB_OAbs @ SY1950 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ SY1949 @ SY1950 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1765,plain,
! [SV283: $i] :
( ( ! [SY1951: $i,SY1952: $i,SY1953: $i,SY1954: $i] :
( ~ ( hBOOL @ ( hAPP @ SV283 @ ( c_Lambda_OdB_OdB__case @ SY1951 @ SY1952 @ SY1953 @ ( c_Lambda_OdB_OAbs @ SY1954 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ SY1953 @ SY1954 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1766,plain,
! [SV284: $i] :
( ( ! [SY1955: $i,SY1956: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV284 ) @ ( c_List_Olist_OCons @ SY1955 @ SY1956 @ SV284 ) @ SV284 )
= ( c_List_Olist_OCons @ SY1955 @ SY1956 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1767,plain,
! [SV285: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV285 )
| ! [SY1957: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1957 @ SY1957 @ SV285 )
= SY1957 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1768,plain,
! [SV286: $i] :
( ( ! [SY1958: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV286 @ SV286 @ ( tc_fun @ SY1958 @ tc_bool ) )
= SV286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1769,plain,
! [SV287: $i] :
( ( ! [SY1959: $i,SY1960: $i,SY1961: $i] :
( ! [SY1962: $i] :
( ( c_List_Olist_OCons @ SV287 @ SY1959 @ SY1960 )
!= ( c_List_Olist_OCons @ SY1961 @ SY1962 @ SY1960 ) )
| ( SV287 = SY1961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1770,plain,
! [SV288: $i] :
( ( ! [SY1963: $i,SY1964: $i,SY1965: $i,SY1966: $i] :
( ( ( c_List_Olist_OCons @ SV288 @ SY1963 @ SY1964 )
!= ( c_List_Olist_OCons @ SY1965 @ SY1966 @ SY1964 ) )
| ( SY1963 = SY1966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1771,plain,
! [SV289: $i] :
( ( ! [SY1967: $i,SY1968: $i] :
( ( c_Type_Otyping @ SV289 @ SY1967 @ SY1968 )
| ! [SY1969: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1969 ) @ SY1967 ) )
| ~ ( c_Type_Otyping @ SV289 @ SY1969 @ SY1968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1772,plain,
! [SV290: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV290 )
| ! [SY1970: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1970 @ SV290 )
| ! [SY1971: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY1970 @ SY1971 @ SV290 ) @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1773,plain,
! [SV291: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV291 )
| ! [SY1972: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1972 @ SV291 )
| ! [SY1973: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY1973 @ SY1972 @ SV291 ) @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1774,plain,
! [SV292: $i] :
( ( ! [SY1974: $i,SY1975: $i,SY1976: $i,SY1977: $i] :
( ! [SY1978: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SY1974 @ SY1975 @ SY1976 ) @ SY1977 @ SY1978 @ SY1976 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SY1977 @ SY1978 @ SY1976 ) @ SY1974 @ SY1975 @ SY1976 ) )
| ( SY1974 = SY1977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1775,plain,
! [SV293: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV293 )
| ! [SY1979: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SY1979 @ SV293 ) @ SV293 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1979 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1776,plain,
! [SV294: $i] :
( ( ! [SY1980: $i] :
( ! [SY1981: $i,SY1982: $i] :
( ( c_List_Ofilter @ SV294 @ ( c_List_Olist_OCons @ SY1980 @ SY1981 @ SY1982 ) @ SY1982 )
= ( c_List_Ofilter @ SV294 @ SY1981 @ SY1982 ) )
| ( hBOOL @ ( hAPP @ SV294 @ SY1980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1777,plain,
! [SV295: $i] :
( ( ! [SY1983: $i,SY1984: $i,SY1985: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV295 @ SY1983 @ ( tc_fun @ SY1984 @ tc_bool ) ) @ SY1985 ) )
| ~ ( hBOOL @ ( hAPP @ SY1983 @ SY1985 ) )
| ~ ( hBOOL @ ( hAPP @ SV295 @ SY1985 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1778,plain,
! [SV296: $i] :
( ( ! [SY1986: $i,SY1987: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ SV296 @ SY1986 @ SY1987 ) @ SY1987 )
= ( c_List_Ofilter @ SV296 @ ( c_List_Orev @ SY1986 @ SY1987 ) @ SY1987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1779,plain,
! [SV297: $i] :
( ( ! [SY1988: $i,SY1989: $i,SY1990: $i] :
( ! [SY1991: $i] :
( ( c_List_Oappend @ SV297 @ ( c_List_Olist_OCons @ SY1988 @ ( c_List_Olist_ONil @ SY1989 ) @ SY1989 ) @ SY1989 )
!= ( c_List_Oappend @ SY1990 @ ( c_List_Olist_OCons @ SY1991 @ ( c_List_Olist_ONil @ SY1989 ) @ SY1989 ) @ SY1989 ) )
| ( SV297 = SY1990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1780,plain,
! [SV298: $i] :
( ( ! [SY1992: $i,SY1993: $i,SY1994: $i,SY1995: $i] :
( ( ( c_List_Oappend @ SV298 @ ( c_List_Olist_OCons @ SY1992 @ ( c_List_Olist_ONil @ SY1993 ) @ SY1993 ) @ SY1993 )
!= ( c_List_Oappend @ SY1994 @ ( c_List_Olist_OCons @ SY1995 @ ( c_List_Olist_ONil @ SY1993 ) @ SY1993 ) @ SY1993 ) )
| ( SY1992 = SY1995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1781,plain,
! [SV299: $i] :
( ( ! [SY1996: $i,SY1997: $i,SY1998: $i,SY1999: $i] :
( ~ ( hBOOL @ ( hAPP @ SV299 @ ( c_List_Olist_Olist__case @ SY1996 @ SY1997 @ ( c_List_Olist_OCons @ SY1998 @ SY1999 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV299 @ ( hAPP @ ( hAPP @ SY1997 @ SY1998 ) @ SY1999 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1782,plain,
! [SV300: $i] :
( ( ! [SY2000: $i,SY2001: $i,SY2002: $i,SY2003: $i] :
( ~ ( hBOOL @ ( hAPP @ SV300 @ ( c_List_Olist_Olist__case @ SY2000 @ SY2001 @ ( c_List_Olist_OCons @ SY2002 @ SY2003 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV300 @ ( hAPP @ ( hAPP @ SY2001 @ SY2002 ) @ SY2003 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1783,plain,
! [SV301: $i] :
( ( ! [SY2004: $i,SY2005: $i,SY2006: $i,SY2007: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV301 @ SY2004 @ SY2005 @ SY2006 ) @ SY2004 @ SY2007 @ SY2006 )
= ( c_List_Olist__update @ SV301 @ SY2004 @ SY2007 @ SY2006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1784,plain,
! [SV302: $i] :
( ( ! [SY2008: $i,SY2009: $i,SY2010: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV302 @ SY2008 @ SY2009 ) @ SY2010 @ SY2009 )
= ( c_List_Oappend @ SV302 @ ( c_List_Oappend @ SY2008 @ SY2010 @ SY2009 ) @ SY2009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1785,plain,
! [SV303: $i] :
( ( ! [SY2011: $i,SY2012: $i,SY2013: $i] :
( ( c_List_Oappend @ SV303 @ ( c_List_Oappend @ SY2011 @ SY2012 @ SY2013 ) @ SY2013 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV303 @ SY2011 @ SY2013 ) @ SY2012 @ SY2013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1786,plain,
! [SV304: $i] :
( ( ! [SY2014: $i,SY2015: $i,SY2016: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV304 @ SY2014 @ SY2015 ) @ SY2016 @ SY2015 )
= ( c_List_Oappend @ SV304 @ ( c_List_Oappend @ SY2014 @ SY2016 @ SY2015 ) @ SY2015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1787,plain,
! [SV305: $i] :
( ( ! [SY2017: $i,SY2018: $i,SY2019: $i] :
( ( c_List_Oappend @ SV305 @ ( c_List_Oappend @ SY2017 @ SY2018 @ SY2019 ) @ SY2019 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV305 @ SY2017 @ SY2019 ) @ SY2018 @ SY2019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1788,plain,
! [SV306: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV306 )
| ! [SY2020: $i,SY2021: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SY2020 @ SY2021 @ SV306 ) @ SV306 )
| ~ ( c_List_Olinorder__class_Osorted @ SY2021 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1789,plain,
! [SV307: $i] :
( ( ! [SY2022: $i] :
~ ( c_List_Olist__ex @ SV307 @ ( c_List_Olist_ONil @ SY2022 ) @ SY2022 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1790,plain,
! [SV308: $i] :
( ( c_List_Onull @ ( c_List_Olist_ONil @ SV308 ) @ SV308 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1791,plain,
! [SV309: $i] :
( ( ! [SY2023: $i] :
( ! [SY2024: $i] :
~ ( hBOOL @ ( hAPP @ SV309 @ ( c_List_Olist_Olist__case @ SY2023 @ SY2024 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV309 @ SY2023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1792,plain,
! [SV310: $i] :
( ( ! [SY2025: $i,SY2026: $i,SY2027: $i] :
( ( c_List_Ofoldr @ SV310 @ ( c_List_Olist_ONil @ SY2025 ) @ SY2026 @ SY2025 @ SY2027 )
= SY2026 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1793,plain,
! [SV311: $i] :
( ( ! [SY2028: $i] : ( hBOOL @ ( hAPP @ SV311 @ SY2028 ) )
| ( hBOOL @ ( hAPP @ SV311 @ ( v_sko__List__Xzip__Xinduct__2 @ SV311 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1794,plain,
! [SV312: $i] :
( ( ! [SY2029: $i,SY2030: $i] :
( ( c_List_Omap @ SV312 @ ( c_List_Olist_ONil @ SY2029 ) @ SY2029 @ SY2030 )
= ( c_List_Olist_ONil @ SY2030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1795,plain,
! [SV313: $i] :
( ( ! [SY2031: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ SV313 ) @ SY2031 @ SV313 )
= ( c_List_Olist_ONil @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1796,plain,
! [SV314: $i] :
( ( ! [SY2032: $i] : ( hBOOL @ ( hAPP @ SV314 @ SY2032 ) )
| ( hBOOL @ ( hAPP @ SV314 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV314 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV314 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1797,plain,
! [SV315: $i] :
( ( ! [SY2033: $i,SY2034: $i,SY2035: $i] :
( ( c_List_Olist_Olist__rec @ SV315 @ SY2033 @ ( c_List_Olist_ONil @ SY2034 ) @ SY2035 @ SY2034 )
= SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1798,plain,
! [SV316: $i] :
( ( ! [SY2036: $i] : ( hBOOL @ ( hAPP @ SV316 @ SY2036 ) )
| ( hBOOL @ ( hAPP @ SV316 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV316 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV316 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1799,plain,
! [SV317: $i] :
( ( ! [SY2037: $i] : ( hBOOL @ ( hAPP @ SV317 @ SY2037 ) )
| ( hBOOL @ ( hAPP @ SV317 @ ( v_sko__List__Xtake__Xinduct__2 @ SV317 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV317 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1800,plain,
! [SV318: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV318 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV318 ) @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1801,plain,
! [SV319: $i] :
( ( ! [SY2038: $i,SY2039: $i] :
( ( c_List_Ofiltermap @ SV319 @ ( c_List_Olist_ONil @ SY2038 ) @ SY2038 @ SY2039 )
= ( c_List_Olist_ONil @ SY2039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1802,plain,
! [SV320: $i] :
( ( ! [SY2040: $i] :
( ( ( c_List_Olist_ONil @ SV320 )
!= ( c_List_Oremdups @ SY2040 @ SV320 ) )
| ( SY2040
= ( c_List_Olist_ONil @ SV320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1803,plain,
! [SV321: $i] :
( ( ! [SY2041: $i] :
( ( c_List_Ofilter @ SV321 @ ( c_List_Olist_ONil @ SY2041 ) @ SY2041 )
= ( c_List_Olist_ONil @ SY2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1804,plain,
! [SV322: $i] :
( ( ! [SY2042: $i,SY2043: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV322 ) @ SY2042 @ SY2043 @ SV322 )
= ( c_List_Olist_ONil @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1805,plain,
! [SV323: $i] :
( ( ! [SY2044: $i,SY2045: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV323 ) @ SY2044 @ SY2045 @ SV323 )
= ( c_List_Olist_ONil @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1806,plain,
! [SV324: $i] :
( ( ! [SY2046: $i,SY2047: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV324 ) @ SY2046 @ SY2047 @ SV324 )
= ( c_List_Olist_ONil @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1807,plain,
! [SV325: $i] :
( ( ! [SY2048: $i] : ( hBOOL @ ( hAPP @ SV325 @ SY2048 ) )
| ( hBOOL @ ( hAPP @ SV325 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV325 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV325 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1808,plain,
! [SV326: $i] :
( ( ! [SY2049: $i,SY2050: $i] :
( ( c_List_Olist_OCons @ SV326 @ SY2049 @ SY2050 )
!= ( c_List_Olist_ONil @ SY2050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1809,plain,
! [SV327: $i] :
( ( ! [SY2051: $i,SY2052: $i] :
( ( c_List_Olist_OCons @ SV327 @ SY2051 @ SY2052 )
!= ( c_List_Olist_ONil @ SY2052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1810,plain,
! [SV328: $i] :
( ( ! [SY2053: $i] :
( ( c_List_Oremove1 @ SV328 @ ( c_List_Olist_ONil @ SY2053 ) @ SY2053 )
= ( c_List_Olist_ONil @ SY2053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1811,plain,
! [SV329: $i] :
( ( ! [SY2054: $i] : ( hBOOL @ ( hAPP @ SV329 @ SY2054 ) )
| ( hBOOL @ ( hAPP @ SV329 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV329 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1812,plain,
! [SV330: $i] :
( ( ! [SY2055: $i,SY2056: $i,SY2057: $i] :
( ( c_Map_Omap__upds @ SV330 @ SY2055 @ ( c_List_Olist_ONil @ SY2056 ) @ SY2057 @ SY2056 )
= SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1813,plain,
! [SV331: $i] :
( ( ! [SY2058: $i,SY2059: $i,SY2060: $i] :
( ( c_Map_Omap__upds @ SV331 @ ( c_List_Olist_ONil @ SY2058 ) @ SY2059 @ SY2058 @ SY2060 )
= SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1814,plain,
! [SV332: $i] :
( ( ! [SY2061: $i] : ( hBOOL @ ( hAPP @ SV332 @ SY2061 ) )
| ( hBOOL @ ( hAPP @ SV332 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV332 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV332 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1815,plain,
! [SV333: $i] :
( ( ! [SY2062: $i,SY2063: $i,SY2064: $i] :
( ( c_List_Olist_Olist__case @ SV333 @ SY2062 @ ( c_List_Olist_ONil @ SY2063 ) @ SY2064 @ SY2063 )
= SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1816,plain,
! [SV334: $i] :
( ( ! [SY2065: $i] :
( ( ( c_List_Orev @ SV334 @ SY2065 )
!= ( c_List_Olist_ONil @ SY2065 ) )
| ( SV334
= ( c_List_Olist_ONil @ SY2065 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1817,plain,
! [SV335: $i] :
( ( ! [SY2066: $i] :
( ( c_List_Orotate @ SV335 @ ( c_List_Olist_ONil @ SY2066 ) @ SY2066 )
= ( c_List_Olist_ONil @ SY2066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1818,plain,
! [SV336: $i] :
( ( ! [SY2067: $i] : ( hBOOL @ ( hAPP @ SV336 @ SY2067 ) )
| ( hBOOL @ ( hAPP @ SV336 @ ( v_sko__List__Xlist__Xinduct__2 @ SV336 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV336 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1819,plain,
! [SV337: $i] :
( ( ! [SY2068: $i,SY2069: $i] :
( ( c_List_Olist_ONil @ SV337 )
= ( c_List_Omap @ SY2068 @ ( c_List_Olist_ONil @ SY2069 ) @ SY2069 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1820,plain,
! [SV338: $i] :
( ( ( c_List_Olist_ONil @ SV338 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV338 ) @ ( c_List_Olist_ONil @ SV338 ) @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1821,plain,
! [SV339: $i] :
( ( ! [SY2070: $i] : ( c_List_Olistrelp @ SV339 @ ( c_List_Olist_ONil @ SY2070 ) @ ( c_List_Olist_ONil @ SY2070 ) @ SY2070 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1822,plain,
! [SV340: $i] :
( ( ! [SY2071: $i] : ( hBOOL @ ( hAPP @ SV340 @ SY2071 ) )
| ( hBOOL @ ( hAPP @ SV340 @ ( v_sko__List__Xmap__Xinduct__2 @ SV340 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV340 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1823,plain,
! [SV341: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_ONil @ SV341 ) @ SV341 )
= ( c_List_Olist_ONil @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1824,plain,
! [SV342: $i] :
( ( ! [SY2072: $i,SY2073: $i,SY2074: $i] :
( ( ( c_List_Olist__update @ SV342 @ SY2072 @ SY2073 @ SY2074 )
!= ( c_List_Olist_ONil @ SY2074 ) )
| ( SV342
= ( c_List_Olist_ONil @ SY2074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1825,plain,
! [SV343: $i] :
( ( ! [SY2075: $i,SY2076: $i,SY2077: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV343 ) @ SY2075 ) @ SY2076 @ SY2077 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV343 @ SY2076 @ SY2077 ) ) @ ( c_Lambda_Osubst @ SY2075 @ SY2076 @ SY2077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1826,plain,
! [SV344: $i] :
( ( ! [SY2078: $i,SY2079: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV344 ) @ SY2078 )
!= ( c_Lambda_OdB_OAbs @ SY2079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1827,plain,
! [SV345: $i] :
( ( ! [SY2080: $i,SY2081: $i] :
( ( c_Lambda_OdB_OAbs @ SV345 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2080 ) @ SY2081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1828,plain,
! [SV346: $i] :
( ( ! [SY2082: $i,SY2083: $i,SY2084: $i,SY2085: $i,SY2086: $i] :
( ~ ( hBOOL @ ( hAPP @ SV346 @ ( c_Lambda_OdB_OdB__case @ SY2082 @ SY2083 @ SY2084 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2085 ) @ SY2086 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ SY2083 @ SY2085 ) @ SY2086 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1829,plain,
! [SV347: $i] :
( ( ! [SY2087: $i,SY2088: $i,SY2089: $i,SY2090: $i,SY2091: $i] :
( ~ ( hBOOL @ ( hAPP @ SV347 @ ( c_Lambda_OdB_OdB__case @ SY2087 @ SY2088 @ SY2089 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2090 ) @ SY2091 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV347 @ ( hAPP @ ( hAPP @ SY2088 @ SY2090 ) @ SY2091 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1830,plain,
! [SV348: $i] :
( ( ! [SY2092: $i,SY2093: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SY2092 ) @ SY2093 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV348 @ SY2093 ) ) @ ( c_Lambda_Olift @ SY2092 @ SY2093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1831,plain,
! [SV349: $i] :
( ( ! [SY2094: $i,SY2095: $i,SY2096: $i,SY2097: $i,SY2098: $i] :
( ( c_Lambda_OdB_OdB__case @ SV349 @ SY2094 @ SY2095 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2096 ) @ SY2097 ) @ SY2098 )
= ( hAPP @ ( hAPP @ SY2094 @ SY2096 ) @ SY2097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1832,plain,
! [SV350: $i] :
( ( ! [SY2099: $i,SY2100: $i,SY2101: $i,SY2102: $i,SY2103: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV350 @ SY2099 @ SY2100 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2101 ) @ SY2102 ) @ SY2103 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SY2099 @ SY2101 ) @ SY2102 ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SY2099 @ SY2100 @ SY2101 @ SY2103 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SY2099 @ SY2100 @ SY2102 @ SY2103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1833,plain,
! [SV351: $i] :
( ( ! [SY2104: $i,SY2105: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV351 @ SY2104 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2105 @ SY2104 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV351 = SY2105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1834,plain,
! [SV352: $i] :
( ( ! [SY2106: $i,SY2107: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SY2106 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SY2107 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2106 ) @ SY2107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1835,plain,
! [SV353: $i] :
( ( ! [SY2108: $i,SY2109: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SY2108 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2109 ) @ SY2108 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV353 ) @ SY2109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1836,plain,
! [SV354: $i] :
( ( ! [SY2110: $i,SY2111: $i,SY2112: $i] :
( ( c_Lambda_Oliftn @ SV354 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2110 ) @ SY2111 ) @ SY2112 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV354 @ SY2110 @ SY2112 ) ) @ ( c_Lambda_Oliftn @ SV354 @ SY2111 @ SY2112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1837,plain,
! [SV355: $i] :
( ( ! [SY2113: $i,SY2114: $i,SY2115: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV355 ) @ SY2113 ) @ SY2114 @ SY2115 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV355 @ SY2114 @ SY2115 ) ) @ ( c_Lambda_Osubstn @ SY2113 @ SY2114 @ SY2115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1838,plain,
! [SV356: $i] :
( ( ! [SY2116: $i,SY2117: $i] :
( ( SV356 = SY2116 )
| ! [SY2118: $i,SY2119: $i] :
( ~ ( c_Type_Otyping @ SY2117 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2118 ) @ SY2119 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2116 )
| ~ ( c_Type_Otyping @ SY2117 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2118 ) @ SY2119 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1839,plain,
! [SV357: $i] :
( ( ! [SY2120: $i,SY2121: $i,SY2122: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV357 ) @ SY2120 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2121 ) @ SY2122 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1840,plain,
! [SV358: $i] :
( ( ! [SY2123: $i,SY2124: $i,SY2125: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV358 ) ) @ SY2123 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2124 ) @ SY2125 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1841,plain,
! [SV359: $i] :
( ( ! [SY2126: $i] :
( ( c_Lambda_OdB_OAbs @ SV359 )
!= ( c_Lambda_OdB_OVar @ SY2126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1842,plain,
! [SV360: $i] :
( ( ! [SY2127: $i,SY2128: $i,SY2129: $i,SY2130: $i] :
( ~ ( hBOOL @ ( hAPP @ SV360 @ ( c_Lambda_OdB_OdB__case @ SY2127 @ SY2128 @ SY2129 @ ( c_Lambda_OdB_OVar @ SY2130 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV360 @ ( hAPP @ SY2127 @ SY2130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1843,plain,
! [SV361: $i] :
( ( ! [SY2131: $i,SY2132: $i,SY2133: $i,SY2134: $i] :
( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Lambda_OdB_OdB__case @ SY2131 @ SY2132 @ SY2133 @ ( c_Lambda_OdB_OVar @ SY2134 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( hAPP @ SY2131 @ SY2134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1844,plain,
! [SV362: $i] :
( ( ! [SY2135: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV362 ) @ SY2135 @ SV362 )
= SY2135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1845,plain,
! [SV363: $i] :
( ( ! [SY2136: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV363 ) ) @ SY2136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1846,plain,
! [SV364: $i] :
( ( ! [SY2137: $i,SY2138: $i,SY2139: $i,SY2140: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV364 @ SY2137 @ SY2138 @ ( c_Lambda_OdB_OVar @ SY2139 ) @ SY2140 )
= ( hAPP @ SV364 @ SY2139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1847,plain,
! [SV365: $i] :
( ( ! [SY2141: $i] :
( ( c_Lambda_OdB_OVar @ SV365 )
!= ( c_Lambda_OdB_OAbs @ SY2141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1848,plain,
! [SV366: $i] :
( ( ! [SY2142: $i,SY2143: $i] :
( ( ( hAPP @ SV366 @ SY2142 )
= SY2143 )
| ~ ( c_Type_Otyping @ SV366 @ ( c_Lambda_OdB_OVar @ SY2142 ) @ SY2143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1849,plain,
! [SV367: $i] :
( ( ! [SY2144: $i,SY2145: $i,SY2146: $i,SY2147: $i] :
( ( c_Lambda_OdB_OdB__case @ SV367 @ SY2144 @ SY2145 @ ( c_Lambda_OdB_OVar @ SY2146 ) @ SY2147 )
= ( hAPP @ SV367 @ SY2146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1850,plain,
! [SV368: $i] :
( ( ! [SY2148: $i] : ( c_Type_Otyping @ SV368 @ ( c_Lambda_OdB_OVar @ SY2148 ) @ ( hAPP @ SV368 @ SY2148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1851,plain,
! [SV369: $i] :
( ( ! [SY2149: $i,SY2150: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV369 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2149 @ SY2150 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2150
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1852,plain,
! [SV370: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV370 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV370 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1853,plain,
! [SV371: $i] :
( ( ! [SY2151: $i,SY2152: $i,SY2153: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV371 ) @ SY2151 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2152 @ SY2153 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV371
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2152 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV371 @ SY2151 @ SY2152 @ SY2153 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2153
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1854,plain,
! [SV372: $i] :
( ( ! [SY2154: $i] :
( ! [SY2155: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV372 @ SY2154 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2155 ) )
| ( SY2154
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1855,plain,
! [SV373: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV373 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1856,plain,
! [SV374: $i] :
( ( ! [SY2156: $i,SY2157: $i,SY2158: $i] :
( ( c_List_Olistsp @ SV374 @ ( c_List_Oappend @ SY2156 @ SY2157 @ SY2158 ) @ SY2158 )
| ~ ( c_List_Olistsp @ SV374 @ SY2157 @ SY2158 )
| ~ ( c_List_Olistsp @ SV374 @ SY2156 @ SY2158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1857,plain,
! [SV375: $i] :
( ( ! [SY2159: $i,SY2160: $i] :
( ( c_List_Olistsp @ SV375 @ SY2159 @ SY2160 )
| ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV375 @ SY2159 @ SY2160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1858,plain,
! [SV376: $i] :
( ( ! [SY2161: $i,SY2162: $i,SY2163: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SY2161 @ ( tc_fun @ SY2162 @ tc_bool ) ) @ SY2163 @ SY2162 )
| ~ ( c_List_Olistsp @ SY2161 @ SY2163 @ SY2162 )
| ~ ( c_List_Olistsp @ SV376 @ SY2163 @ SY2162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1859,plain,
! [SV377: $i] :
( ( ! [SY2164: $i,SY2165: $i] :
( ( c_List_Olistsp @ SV377 @ SY2164 @ SY2165 )
| ! [SY2166: $i] :
~ ( c_List_Olistsp @ SV377 @ ( c_List_Oappend @ SY2166 @ SY2164 @ SY2165 ) @ SY2165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1860,plain,
! [SV378: $i] :
( ( ! [SY2167: $i,SY2168: $i] :
( ( c_List_Olistsp @ SV378 @ SY2167 @ SY2168 )
| ! [SY2169: $i] :
~ ( c_List_Olistsp @ SV378 @ ( c_List_Oappend @ SY2167 @ SY2169 @ SY2168 ) @ SY2168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1861,plain,
! [SV379: $i] :
( ( ! [SY2170: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV379 @ SY2170 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1862,plain,
! [SV380: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV380 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1863,plain,
! [SV381: $i] :
( ( ! [SY2171: $i,SY2172: $i] :
( ! [SY2173: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV381 ) @ SY2171 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2172 ) @ SY2173 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV381 = SY2172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1864,plain,
! [SV382: $i] :
( ( ! [SY2174: $i,SY2175: $i,SY2176: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV382 ) @ SY2174 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2175 ) @ SY2176 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2174 = SY2176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1865,plain,
! [SV383: $i] :
( ( ! [SY2177: $i] :
( ! [SY2178: $i] :
( ( c_Lambda_OdB_OVar @ SV383 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2177 @ SY2178 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV383 )
= SY2177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1866,plain,
! [SV384: $i] :
( ( ! [SY2179: $i] :
( ( hBOOL @ ( hAPP @ SV384 @ SY2179 ) )
| ! [SY2180: $i] :
( ( hBOOL @ ( hAPP @ SY2180 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY2180 @ SV384 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2180 @ SY2179 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1867,plain,
! [SV385: $i] :
( ( ! [SY2181: $i] :
( ( hBOOL @ ( hAPP @ SV385 @ SY2181 ) )
| ! [SY2182: $i] :
( ( hBOOL @ ( hAPP @ SV385 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2182 @ SV385 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV385 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2182 @ SY2181 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1868,plain,
! [SV386: $i] :
( ( ! [SY2183: $i] :
( ( hBOOL @ ( hAPP @ SV386 @ SY2183 ) )
| ! [SY2184: $i] :
( ( hBOOL @ ( hAPP @ SY2184 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY2184 @ SV386 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2184 @ SY2183 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1869,plain,
! [SV387: $i] :
( ( ! [SY2185: $i] :
( ( hBOOL @ ( hAPP @ SV387 @ SY2185 ) )
| ! [SY2186: $i] :
( ( hBOOL @ ( hAPP @ SV387 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2186 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2186 @ SY2185 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1870,plain,
! [SV388: $i] :
( ( ! [SY2187: $i] :
( ( c_List_Olistsp @ SV388 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV388 @ SY2187 ) @ t_a )
| ( SY2187
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV388 @ SY2187 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1871,plain,
! [SV389: $i] :
( ( ! [SY2188: $i] :
( ( hBOOL @ ( hAPP @ SV389 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV389 @ SY2188 ) ) )
| ( SY2188
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV389 @ SY2188 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1872,plain,
! [SV390: $i] :
( ( ! [SY2189: $i] :
( ( hBOOL @ ( hAPP @ SV390 @ SY2189 ) )
| ! [SY2190: $i] :
( ( c_List_Olistsp @ SY2190 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2190 @ SV390 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV390 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2190 @ SY2189 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1873,plain,
! [SV391: $i] :
( ( ! [SY2191: $i] :
( ( hBOOL @ ( hAPP @ SV391 @ SY2191 ) )
| ! [SY2192: $i] :
( ( c_List_Olistsp @ SY2192 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2192 @ SV391 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2192 @ SY2191 @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1874,plain,
! [SV392: $i] :
( ( ! [SY2193: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV392 ) @ SY2193 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV392 ) @ SY2193 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1875,plain,
! [SV393: $i] :
( ( ! [SY2194: $i,SY2195: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SY2194 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2195 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SY2194 )
= SY2195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1876,plain,
! [SV394: $i] :
( ( ! [SY2196: $i,SY2197: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV394 @ ( c_Lambda_OdB_OVar @ SY2196 ) @ SY2197 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1877,plain,
! [SV395: $i] :
( ( ( c_Lambda_OdB_OVar @ SV395 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV395 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1878,plain,
! [SV396: $i] :
( ( ! [SY2198: $i,SY2199: $i] :
( ( ( c_Lambda_OdB_OVar @ SV396 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2198 @ SY2199 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2199
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1879,plain,
! [SV397: $i] :
( ( ! [SY2200: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV397 ) @ SY2200 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY2200 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1880,plain,
! [SV398: $i] :
( ( ! [SY2201: $i] :
( ( ( c_Lambda_OdB_OVar @ SV398 )
!= ( c_Lambda_OdB_OVar @ SY2201 ) )
| ( SV398 = SY2201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1881,plain,
! [SV399: $i] :
( ( ! [SY2202: $i,SY2203: $i] :
( ! [SY2204: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV399 ) @ SY2202 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2203 ) @ SY2204 ) )
| ( SV399 = SY2203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1882,plain,
! [SV400: $i] :
( ( ! [SY2205: $i,SY2206: $i,SY2207: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV400 ) @ SY2205 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2206 ) @ SY2207 ) )
| ( SY2205 = SY2207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1883,plain,
! [SV401: $i] :
( ( ! [SY2208: $i,SY2209: $i] :
( ( c_Lambda_OdB_OVar @ SV401 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2208 ) @ SY2209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1884,plain,
! [SV402: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1885,plain,
! [SV403: $i] :
( ( ! [SY2210: $i] : ( c_List_Olistsp @ SV403 @ ( c_List_Olist_ONil @ SY2210 ) @ SY2210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1886,plain,
! [SV404: $i] :
( ( ! [SY2211: $i,SY2212: $i,SY2213: $i,SY2214: $i,SY2215: $i] :
( ( hAPP @ ( c_COMBB @ SV404 @ SY2211 @ SY2212 @ SY2213 @ SY2214 ) @ SY2215 )
= ( hAPP @ SV404 @ ( hAPP @ SY2211 @ SY2215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1887,plain,
! [SV405: $i] :
( ( ! [SY2216: $i,SY2217: $i,SY2218: $i,SY2219: $i,SY2220: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV405 @ SY2216 @ SY2217 @ SY2218 ) @ SY2219 ) @ SY2220 )
= ( hAPP @ ( hAPP @ SV405 @ SY2220 ) @ SY2219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1888,plain,
! [SV406: $i] :
( ( ! [SY2221: $i,SY2222: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SY2221 )
!= ( c_Lambda_OdB_OVar @ SY2222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1889,plain,
! [SV407: $i] :
( ( ! [SY2223: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV407 @ SY2223 ) )
| ~ ( class_Lattices_Olattice @ SY2223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1890,plain,
! [SV408: $i] :
( ( ! [SY2224: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV408 @ SY2224 ) )
| ~ ( class_Orderings_Opreorder @ SY2224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1891,plain,
! [SV409: $i] :
( ( ! [SY2225: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV409 @ SY2225 ) )
| ~ ( class_Lattices_Olattice @ SY2225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1892,plain,
! [SV410: $i] :
( ( ! [SY2226: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV410 @ SY2226 ) )
| ~ ( class_Orderings_Oorder @ SY2226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1893,plain,
! [SV411: $i] :
( ( ! [SY2227: $i,SY2228: $i,SY2229: $i,SY2230: $i,SY2231: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV411 @ SY2227 @ SY2228 @ SY2229 ) @ SY2230 ) @ SY2231 )
= ( hAPP @ ( hAPP @ SV411 @ SY2231 ) @ SY2230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1894,plain,
! [SV412: $i] :
( ( ! [SY2232: $i,SY2233: $i,SY2234: $i,SY2235: $i,SY2236: $i] :
( ( hAPP @ ( c_COMBB @ SV412 @ SY2232 @ SY2233 @ SY2234 @ SY2235 ) @ SY2236 )
= ( hAPP @ SV412 @ ( hAPP @ SY2232 @ SY2236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1895,plain,
! [SV413: $i] :
( ( ! [SY2237: $i] : ( c_fequal @ SV413 @ SV413 @ SY2237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1896,plain,
! [SV414: $i] :
( ( ! [SY2238: $i] :
( ( SV414 = SY2238 )
| ! [SY2239: $i] :
~ ( c_fequal @ SV414 @ SY2238 @ SY2239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1897,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1898,plain,
! [SV415: $i,SV1: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ SV1 @ SV415 ) @ ( tc_List_Olist @ SV415 ) )
!= ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SV415 ) ) )
| ( ( c_List_Oremdups @ SV1 @ SV415 )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1899,plain,
! [SV2: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1900,plain,
! [SV3: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1901,plain,
! [SV416: $i,SV4: $i] :
( ( ! [SY2240: $i,SY2241: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SY2240 ) @ SY2241 ) )
| ! [SY2242: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SY2242 ) @ SY2241 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SY2240 ) @ SY2242 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1902,plain,
! [SV417: $i,SV5: $i] :
( ( ! [SY2243: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV5 @ SV417 ) @ SY2243 ) @ SY2243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1903,plain,
! [SV418: $i,SV6: $i] :
( ( ! [SY2244: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV6 @ SV418 ) @ SY2244 ) @ SY2244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1904,plain,
! [SV419: $i,SV7: $i] :
( ( ! [SY2245: $i,SY2246: $i] :
( ! [SY2247: $i] :
( ( c_List_Oreplicate @ SV7 @ SV419 @ SY2245 )
!= ( c_List_Oreplicate @ SY2246 @ SY2247 @ SY2245 ) )
| ( SV7 = SY2246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1905,plain,
! [SV420: $i,SV8: $i] :
( ( ! [SY2248: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV8 @ SV420 ) @ SY2248 ) )
| ! [SY2249: $i,SY2250: $i] : ( c_ListOrder_Ostep1 @ SV8 @ ( c_List_Olist_OCons @ SV420 @ SY2249 @ SY2250 ) @ ( c_List_Olist_OCons @ SY2248 @ SY2249 @ SY2250 ) @ SY2250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1906,plain,
! [SV421: $i,SV9: $i] :
( ( ! [SY2251: $i,SY2252: $i] :
( ( SV9 = SV421 )
| ( SY2251 = SY2252 )
| ! [SY2253: $i,SY2254: $i] :
~ ( c_ListOrder_Ostep1 @ SY2253 @ ( c_List_Olist_OCons @ SV421 @ SY2252 @ SY2254 ) @ ( c_List_Olist_OCons @ SV9 @ SY2251 @ SY2254 ) @ SY2254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1907,plain,
! [SV10: $i] :
( ( ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1908,plain,
! [SV422: $i,SV11: $i] :
( ( ! [SY2255: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SV422 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SY2255 @ SV11 @ SV422 ) @ ( tc_List_Olist @ SV422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1909,plain,
! [SV423: $i,SV12: $i] :
( ( ! [SY2256: $i,SY2257: $i,SY2258: $i] :
( ( c_ListOrder_Ostep1 @ SV12 @ ( c_List_Oappend @ SV423 @ SY2256 @ SY2257 ) @ ( c_List_Oappend @ SV423 @ SY2258 @ SY2257 ) @ SY2257 )
| ~ ( c_ListOrder_Ostep1 @ SV12 @ SY2256 @ SY2258 @ SY2257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1910,plain,
! [SV424: $i,SV13: $i] :
( ( ! [SY2259: $i,SY2260: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV13 @ SV424 @ SY2259 @ SY2260 )
| ! [SY2261: $i] : ( c_ListOrder_Ostep1 @ SV13 @ ( c_List_Oappend @ SV424 @ SY2261 @ SY2260 ) @ ( c_List_Oappend @ SY2259 @ SY2261 @ SY2260 ) @ SY2260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1911,plain,
! [SV425: $i,SV14: $i] :
( ( ! [SY2262: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV14 @ SV425 @ SY2262 ) @ ( tc_List_Olist @ SY2262 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV425 @ ( tc_List_Olist @ SY2262 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1912,plain,
! [SV426: $i,SV15: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV15 )
| ! [SY2263: $i] :
( ( c_HOL_Oord__class_Oless @ SV426 @ SY2263 @ SV15 )
| ! [SY2264: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2264 @ SY2263 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV426 @ SY2264 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1913,plain,
! [SV427: $i,SV16: $i] :
( ( ~ ( class_Orderings_Oorder @ SV16 )
| ! [SY2265: $i] :
( ( c_HOL_Oord__class_Oless @ SV427 @ SY2265 @ SV16 )
| ! [SY2266: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV427 @ SY2266 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SY2266 @ SY2265 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1914,plain,
! [SV17: $i] :
( ( c_HOL_Oord__class_Oless @ SV17 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1915,plain,
! [SV18: $i] :
( ( c_HOL_Oord__class_Oless @ SV18 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1916,plain,
! [SV428: $i,SV19: $i] :
( ( ! [SY2267: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV19 ) @ SV428 @ SY2267 )
= ( c_List_Olist_OCons @ SV428 @ ( c_List_Oreplicate @ SV19 @ SV428 @ SY2267 ) @ SY2267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1917,plain,
! [SV429: $i,SV22: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV22 ) @ SV429 @ tc_nat )
| ( ( c_Suc @ SV22 )
= SV429 )
| ~ ( c_HOL_Oord__class_Oless @ SV22 @ SV429 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1918,plain,
! [SV430: $i,SV23: $i] :
( ( ( SV23
= ( c_List_Olist_ONil @ SV430 ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV23 @ ( tc_List_Olist @ SV430 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1919,plain,
! [SV431: $i,SV24: $i] :
( ( ! [SY2268: $i,SY2269: $i] :
( ( SV24 = SV431 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2268 @ SV431 ) @ SV24 ) )
| ! [SY2270: $i,SY2271: $i] :
~ ( c_ListOrder_Ostep1 @ SY2268 @ ( c_List_Olist_OCons @ SV431 @ SY2269 @ SY2270 ) @ ( c_List_Olist_OCons @ SV24 @ SY2271 @ SY2270 ) @ SY2270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1920,plain,
! [SV432: $i,SV25: $i] :
( ( ! [SY2272: $i] :
( ( c_List_Orotate @ ( c_Suc @ SV25 ) @ SV432 @ SY2272 )
= ( c_List_Orotate1 @ ( c_List_Orotate @ SV25 @ SV432 @ SY2272 ) @ SY2272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1921,plain,
! [SV26: $i] :
( ( ( ! [SY1378: $i,SY1379: $i] :
( ( c_List_Olast @ ( c_List_Oreplicate @ SV26 @ SY1378 @ SY1379 ) @ SY1379 )
= SY1378 ) )
= $true )
| ( ( SV26
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1922,plain,
! [SV433: $i,SV27: $i] :
( ( ! [SY2273: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV27 @ SV433 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2273 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1923,plain,
! [SV434: $i,SV28: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV28 @ SV434 )
= ( c_List_Olist_ONil @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1924,plain,
! [SV435: $i,SV29: $i] :
( ( ! [SY2274: $i,SY2275: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV29 @ SV435 @ SY2274 @ SY2275 ) @ ( tc_List_Olist @ SY2275 ) )
= ( c_Nat_Osize__class_Osize @ SV29 @ ( tc_List_Olist @ SY2275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1925,plain,
! [SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV30 @ SV30 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV30 @ ( c_Suc @ SV30 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1926,plain,
! [SV436: $i,SV31: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV31 @ SV436 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV436 @ ( c_Suc @ SV31 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1927,plain,
! [SV437: $i,SV32: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV32 @ ( c_Suc @ SV437 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV437 @ SV32 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1928,plain,
! [SV438: $i,SV33: $i] :
( ( ! [SY2276: $i,SY2277: $i,SY2278: $i] :
( ( ( c_List_Oreplicate @ SV33 @ SV438 @ SY2276 )
!= ( c_List_Oreplicate @ SY2277 @ SY2278 @ SY2276 ) )
| ( SV438 = SY2278 )
| ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1929,plain,
! [SV439: $i,SV34: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV34 @ SV439 ) @ SV439 )
= ( c_Transitive__Closure_Ortranclp @ SV34 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1930,plain,
! [SV35: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV35 ) @ ( tc_List_Olist @ SV35 ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1931,plain,
! [SV440: $i,SV36: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV36 ) @ ( c_Suc @ SV440 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV36 @ SV440 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1932,plain,
! [SV441: $i,SV37: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV37 @ SV441 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV37 ) @ ( c_Suc @ SV441 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1933,plain,
! [SV442: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV38 ) @ ( c_Suc @ SV442 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV442 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1934,plain,
! [SV443: $i,SV40: $i] :
( ( ! [SY2279: $i] :
~ ( c_ListOrder_Ostep1 @ SV40 @ SV443 @ ( c_List_Olist_ONil @ SY2279 ) @ SY2279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1935,plain,
! [SV444: $i,SV41: $i] :
( ( ! [SY2280: $i] :
~ ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Olist_ONil @ SV444 ) @ SY2280 @ SV444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1936,plain,
! [SV445: $i,SV42: $i] :
( ( ( ( c_List_Orotate1 @ SV42 @ SV445 )
!= ( c_List_Olist_ONil @ SV445 ) )
| ( SV42
= ( c_List_Olist_ONil @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1937,plain,
! [SV446: $i,SV44: $i] :
( ( ( ( c_List_Oremdups @ SV44 @ SV446 )
!= SV44 )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ SV44 @ SV446 ) @ ( tc_List_Olist @ SV446 ) )
= ( c_Nat_Osize__class_Osize @ SV44 @ ( tc_List_Olist @ SV446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1938,plain,
! [SV447: $i,SV45: $i] :
( ( ! [SY2281: $i,SY2282: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV45 @ SV447 @ SY2281 @ SY2282 ) @ ( tc_List_Olist @ SY2282 ) )
= ( c_Nat_Osize__class_Osize @ SV447 @ ( tc_List_Olist @ SY2281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1939,plain,
! [SV448: $i,SV46: $i] :
( ( ! [SY2283: $i,SY2284: $i,SY2285: $i] :
( ( c_List_Omap @ SV46 @ ( c_List_Oreplicate @ SV448 @ SY2283 @ SY2284 ) @ SY2284 @ SY2285 )
= ( c_List_Oreplicate @ SV448 @ ( hAPP @ SV46 @ SY2283 ) @ SY2285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1940,plain,
! [SV449: $i,SV47: $i] :
( ( ! [SY2286: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV47 @ SV449 @ SY2286 ) @ SY2286 )
= ( c_List_Oreplicate @ SV47 @ SV449 @ SY2286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1941,plain,
! [SV450: $i,SV48: $i] :
( ( ( ( c_Suc @ SV48 )
!= ( c_Suc @ SV450 ) )
| ( SV48 = SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1942,plain,
! [SV451: $i,SV49: $i] :
( ( ( ( c_Suc @ SV49 )
!= ( c_Suc @ SV451 ) )
| ( SV49 = SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1943,plain,
! [SV452: $i,SV50: $i] :
( ( ! [SY2287: $i,SY2288: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV452 ) @ SY2287 ) @ SY2288 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY2287 ) @ SY2288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1944,plain,
! [SV453: $i,SV51: $i] :
( ( ! [SY2289: $i] :
( ! [SY2290: $i] :
( ( c_List_Ofilter @ SV51 @ ( c_List_Oreplicate @ SV453 @ SY2289 @ SY2290 ) @ SY2290 )
= ( c_List_Oreplicate @ SV453 @ SY2289 @ SY2290 ) )
| ~ ( hBOOL @ ( hAPP @ SV51 @ SY2289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1945,plain,
! [SV454: $i,SV52: $i] :
( ( ! [SY2291: $i,SY2292: $i,SY2293: $i] :
( ( ( c_List_Omap @ SV52 @ SV454 @ SY2291 @ SY2292 )
!= ( c_List_Omap @ SV52 @ SY2293 @ SY2291 @ SY2292 ) )
| ( ( c_Nat_Osize__class_Osize @ SV454 @ ( tc_List_Olist @ SY2291 ) )
= ( c_Nat_Osize__class_Osize @ SY2293 @ ( tc_List_Olist @ SY2291 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1946,plain,
! [SV455: $i,SV54: $i] :
( ( ( SV54 = SV455 )
| ( c_HOL_Oord__class_Oless @ SV54 @ SV455 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SV455 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1947,plain,
! [SV456: $i,SV55: $i] :
( ( ( SV55 = SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV456 @ ( c_Suc @ SV55 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV456 @ SV55 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1948,plain,
! [SV457: $i,SV56: $i] :
( ( ( SV56 = SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ ( c_Suc @ SV457 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV56 @ SV457 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1949,plain,
! [SV458: $i,SV57: $i] :
( ( ! [SY2294: $i,SY2295: $i] :
( ! [SY2296: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV57 @ SV458 @ SY2294 ) @ SY2295 @ SY2296 @ SY2294 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV57 @ SY2295 @ SY2296 @ SY2294 ) @ SV458 @ SY2294 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2295 @ ( c_Nat_Osize__class_Osize @ SV57 @ ( tc_List_Olist @ SY2294 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1950,plain,
! [SV459: $i,SV58: $i] :
( ( ! [SY2297: $i,SY2298: $i] :
( ! [SY2299: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV58 @ SV459 @ SY2297 ) @ SY2298 @ SY2299 @ SY2297 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV58 @ SY2298 @ SY2299 @ SY2297 ) @ SV459 @ SY2297 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2298 @ ( c_Nat_Osize__class_Osize @ SV58 @ ( tc_List_Olist @ SY2297 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1951,plain,
! [SV460: $i,SV59: $i] :
( ( ! [SY2300: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ SV59 @ SV460 @ SY2300 ) @ ( tc_List_Olist @ SY2300 ) )
= ( c_Nat_Osize__class_Osize @ SV460 @ ( tc_List_Olist @ SY2300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1952,plain,
! [SV461: $i,SV60: $i] :
( ( ( c_List_Olist_ONil @ SV60 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV461 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1953,plain,
! [SV462: $i,SV61: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ SV61 @ SV462 ) @ ( tc_List_Olist @ SV462 ) )
= ( c_Nat_Osize__class_Osize @ SV61 @ ( tc_List_Olist @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1954,plain,
! [SV62: $i] :
( ( c_HOL_Oord__class_Oless @ SV62 @ SV62 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1955,plain,
! [SV63: $i] :
( ( c_HOL_Oord__class_Oless @ SV63 @ SV63 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1956,plain,
! [SV64: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV64 ) )
= $true )
| ( ( ! [SY1438: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1438 @ SY1438 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1957,plain,
! [SV65: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV65 ) )
= $true )
| ( ( ! [SY1439: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1439 @ SY1439 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1958,plain,
! [SV66: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV66 ) )
= $true )
| ( ( ! [SY1440: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1440 @ SY1440 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1959,plain,
! [SV463: $i,SV67: $i] :
( ( ! [SY2301: $i,SY2302: $i] :
( ( c_ListOrder_Ostep1 @ SV67 @ SV463 @ SY2301 @ SY2302 )
| ( SY2301 = SV463 )
| ! [SY2303: $i,SY2304: $i] :
~ ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SY2303 @ SV463 @ SY2302 ) @ ( c_List_Olist_OCons @ SY2304 @ SY2301 @ SY2302 ) @ SY2302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1960,plain,
! [SV68: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV68 ) )
= $true )
| ( ( ! [SY1446: $i,SY1447: $i] :
( ( c_HOL_Oord__class_Oless @ SY1446 @ SY1447 @ SV68 )
| ( SY1447 = SY1446 )
| ( c_HOL_Oord__class_Oless @ SY1447 @ SY1446 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1961,plain,
! [SV69: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV69 ) )
= $true )
| ( ( ! [SY1448: $i,SY1449: $i] :
( ( SY1448 = SY1449 )
| ( c_HOL_Oord__class_Oless @ SY1449 @ SY1448 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SY1448 @ SY1449 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1962,plain,
! [SV464: $i,SV70: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV70 @ SV464 @ tc_nat )
| ( SV464 = SV70 )
| ( c_HOL_Oord__class_Oless @ SV464 @ SV70 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1963,plain,
! [SV465: $i,SV71: $i] :
( ( ! [SY2305: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV465 ) @ SY2305 ) )
| ( c_HOL_Oord__class_Oless @ SV465 @ SY2305 @ tc_nat )
| ( SY2305 = SV465 )
| ( c_HOL_Oord__class_Oless @ SY2305 @ SV465 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1964,plain,
! [SV466: $i,SV72: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV72 @ SV466 @ tc_nat )
| ( SV466 = SV72 )
| ( c_HOL_Oord__class_Oless @ SV466 @ SV72 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1965,plain,
! [SV73: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV73 ) )
= $true )
| ( ( ! [SY1454: $i,SY1455: $i] :
( ( c_HOL_Oord__class_Oless @ SY1454 @ SY1455 @ SV73 )
| ( SY1455 = SY1454 )
| ( c_HOL_Oord__class_Oless @ SY1455 @ SY1454 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1966,plain,
! [SV467: $i,SV74: $i] :
( ( ! [SY2306: $i,SY2307: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV467 @ SY2306 ) @ ( c_List_Oreplicate @ SY2307 @ SV467 @ SY2306 ) @ SY2306 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY2307 @ SV467 @ SY2306 ) @ ( c_List_Oreplicate @ SV74 @ SV467 @ SY2306 ) @ SY2306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1967,plain,
! [SV75: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV75 ) )
= $true )
| ( ( ! [SY1459: $i,SY1460: $i] :
( ( c_HOL_Oord__class_Oless @ SY1459 @ SY1460 @ SV75 )
| ( SY1460 = SY1459 )
| ( c_HOL_Oord__class_Oless @ SY1460 @ SY1459 @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1968,plain,
! [SV76: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV76 ) )
= $true )
| ( ( ! [SY1461: $i,SY1462: $i] :
( ( SY1461 = SY1462 )
| ( c_HOL_Oord__class_Oless @ SY1461 @ SY1462 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SY1462 @ SY1461 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1969,plain,
! [SV468: $i,SV77: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV77 )
| ! [SY2308: $i,SY2309: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV468 @ SY2308 @ SV77 ) @ SY2309 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SY2308 @ SY2309 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1970,plain,
! [SV469: $i,SV78: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV78 )
| ! [SY2310: $i,SY2311: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV469 @ SY2310 @ SV78 ) @ SY2311 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SY2311 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1971,plain,
! [SV79: $i] :
( ( ( c_Suc @ SV79 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1972,plain,
! [SV80: $i] :
( ( ( c_Suc @ SV80 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1973,plain,
! [SV470: $i,SV83: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV83 ) @ SV470 @ tc_nat )
| ! [SY2312: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2312 @ SV470 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV83 @ SY2312 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1974,plain,
! [SV84: $i] :
( ( ( ! [SY1471: $i,SY1472: $i] :
( ( c_List_Oreplicate @ SV84 @ SY1471 @ SY1472 )
!= ( c_List_Olist_ONil @ SY1472 ) ) )
= $true )
| ( ( SV84
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1975,plain,
! [SV85: $i] :
( ( ( SV85
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV85 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1976,plain,
! [SV471: $i,SV86: $i] :
( ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV86 @ SV471 )
= SV86 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1977,plain,
! [SV472: $i,SV87: $i] :
( ( ! [SY2313: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV87 @ SV472 @ SY2313 ) @ ( tc_List_Olist @ SY2313 ) )
= SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1978,plain,
! [SV473: $i,SV88: $i] :
( ( ! [SY2314: $i] :
( ( c_List_Olist_ONil @ SV88 )
!= ( c_List_Oreplicate @ SV473 @ SY2314 @ SV88 ) )
| ( SV473
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1979,plain,
! [SV474: $i,SV89: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV89 @ ( tc_List_Olist @ SV474 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV89
= ( c_List_Olist_ONil @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1980,plain,
! [SV90: $i] :
( ( ( c_Suc @ SV90 )
= SV90 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1981,plain,
! [SV91: $i] :
( ( SV91
= ( c_Suc @ SV91 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1982,plain,
! [SV475: $i,SV92: $i] :
( ( ! [SY2315: $i,SY2316: $i] :
( ( c_ListOrder_Ostep1 @ SV92 @ SV475 @ SY2315 @ SY2316 )
| ! [SY2317: $i,SY2318: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY2317 ) @ SY2318 ) )
| ~ ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SY2317 @ SV475 @ SY2316 ) @ ( c_List_Olist_OCons @ SY2318 @ SY2315 @ SY2316 ) @ SY2316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1983,plain,
! [SV476: $i,SV93: $i] :
( ( ! [SY2319: $i,SY2320: $i,SY2321: $i] :
( ( c_ListOrder_Ostep1 @ SV93 @ ( c_List_Olist_OCons @ SV476 @ SY2319 @ SY2320 ) @ ( c_List_Olist_OCons @ SV476 @ SY2321 @ SY2320 ) @ SY2320 )
| ~ ( c_ListOrder_Ostep1 @ SV93 @ SY2319 @ SY2321 @ SY2320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1984,plain,
! [SV477: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV94 @ SV477 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV477 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1985,plain,
! [SV478: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Suc @ SV478 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV95 @ SV478 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1986,plain,
! [SV479: $i,SV96: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV96 @ SV479 ) @ ( tc_List_Olist @ SV479 ) )
= ( c_Nat_Osize__class_Osize @ SV96 @ ( tc_List_Olist @ SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1987,plain,
! [SV480: $i,SV97: $i] :
( ( ! [SY2322: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ SV97 @ SV480 @ SY2322 ) @ SY2322 )
= ( c_List_Orotate @ SV97 @ ( c_List_Orotate1 @ SV480 @ SY2322 ) @ SY2322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1988,plain,
! [SV98: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV98 ) )
= $true )
| ( ( ! [SY1493: $i,SY1494: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1493 @ SY1494 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY1494 @ SY1493 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1580]) ).
thf(1989,plain,
! [SV481: $i,SV99: $i] :
( ( ! [SY2323: $i,SY2324: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SY2323 ) @ SY2324 ) )
| ! [SY2325: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SY2325 ) @ SY2324 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SY2323 ) @ SY2325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1990,plain,
! [SV482: $i,SV100: $i] :
( ( ! [SY2326: $i,SY2327: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SY2326 ) @ SY2327 ) )
| ! [SY2328: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SY2328 ) @ SY2327 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SY2326 ) @ SY2328 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1991,plain,
! [SV101: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV101 ) )
= $true )
| ( ( ! [SY1503: $i,SY1504: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1503 @ SY1504 @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SY1504 @ SY1503 @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1992,plain,
! [SV102: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV102 ) )
= $true )
| ( ( ! [SY1505: $i,SY1506: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1505 @ SY1506 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SY1506 @ SY1505 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1993,plain,
! [SV103: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV103 ) )
= $true )
| ( ( ! [SY1507: $i,SY1508: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1507 @ SY1508 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SY1508 @ SY1507 @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1994,plain,
! [SV483: $i,SV104: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV104 @ SV483 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV104 @ SV483 ) @ ( c_List_Olist_ONil @ SV483 ) @ SV483 ) @ SV483 )
= SV104 )
| ( SV104
= ( c_List_Olist_ONil @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1995,plain,
! [SV484: $i,SV105: $i] :
( ( ! [SY2329: $i] :
( ( SV105
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 ) @ SY2329 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 ) @ ( c_List_Oappend @ SY2329 @ ( c_List_Olist_OCons @ SV484 @ ( 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)],[1587]) ).
thf(1996,plain,
! [SV485: $i,SV106: $i] :
( ( ! [SY2330: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV106 @ SV485 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2330 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV106 @ ( c_List_Oappend @ SV485 @ ( c_List_Olist_OCons @ SY2330 @ ( 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)],[1588]) ).
thf(1997,plain,
! [SV486: $i,SV107: $i] :
( ( ( ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV486 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ! [SY2331: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2331 @ SV107 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV486 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2331 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV486 @ ( 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)],[1589]) ).
thf(1998,plain,
! [SV108: $i] :
( ( ( ! [SY1516: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV108 ) @ SY1516 @ SV108 )
= ( c_Lambda_Oliftn @ SV108 @ SY1516 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV108 @ SV108 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1999,plain,
! [SV487: $i,SV109: $i] :
( ( ! [SY2332: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV109 @ SV487 @ SY2332 ) @ SY2332 )
= ( c_List_Olast @ SV487 @ SY2332 ) )
| ( SV487
= ( c_List_Olist_ONil @ SY2332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2000,plain,
! [SV488: $i,SV110: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV110 @ ( c_List_Olist_ONil @ SV488 ) @ SV488 ) @ SV488 )
= ( c_List_Olist_ONil @ SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2001,plain,
! [SV489: $i,SV111: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV111 @ ( c_List_Olist_ONil @ SV489 ) @ SV489 ) @ SV489 )
= SV111 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2002,plain,
! [SV490: $i,SV112: $i] :
( ( ! [SY2333: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV112 @ SV490 @ SY2333 ) @ SY2333 )
= ( c_List_Olist_OCons @ SV112 @ ( c_List_Obutlast @ SV490 @ SY2333 ) @ SY2333 ) )
| ( SV490
= ( c_List_Olist_ONil @ SY2333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2003,plain,
! [SV491: $i,SV113: $i] :
( ( ! [SY2334: $i,SY2335: $i,SY2336: $i] :
( ( ( c_List_Oappend @ SV113 @ SV491 @ SY2334 )
!= ( c_List_Olist_OCons @ SY2335 @ SY2336 @ SY2334 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2335 @ SY2336 @ SV113 @ SV491 @ SY2334 ) @ SV491 @ SY2334 )
= SY2336 )
| ( SV491
= ( c_List_Olist_OCons @ SY2335 @ SY2336 @ SY2334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2004,plain,
! [SV492: $i,SV114: $i] :
( ( ! [SY2337: $i,SY2338: $i,SY2339: $i] :
( ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SY2337 )
!= ( c_List_Oappend @ SY2338 @ SY2339 @ SY2337 ) )
| ( ( c_List_Olist_OCons @ SV114 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV114 @ SV492 @ SY2338 @ SY2339 @ SY2337 ) @ SY2337 )
= SY2338 )
| ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SY2337 )
= SY2339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2005,plain,
! [SV493: $i,SV115: $i] :
( ( ! [SY2340: $i,SY2341: $i,SY2342: $i] :
( ( ( c_List_Oappend @ SV115 @ SV493 @ SY2340 )
!= ( c_List_Olist_OCons @ SY2341 @ SY2342 @ SY2340 ) )
| ( SV115
= ( c_List_Olist_OCons @ SY2341 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2341 @ SY2342 @ SV115 @ SV493 @ SY2340 ) @ SY2340 ) )
| ( SV493
= ( c_List_Olist_OCons @ SY2341 @ SY2342 @ SY2340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2006,plain,
! [SV494: $i,SV116: $i] :
( ( ! [SY2343: $i,SY2344: $i,SY2345: $i] :
( ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SY2343 )
!= ( c_List_Oappend @ SY2344 @ SY2345 @ SY2343 ) )
| ( SV494
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV116 @ SV494 @ SY2344 @ SY2345 @ SY2343 ) @ SY2345 @ SY2343 ) )
| ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SY2343 )
= SY2345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2007,plain,
! [SV495: $i,SV117: $i] :
( ( ! [SY2346: $i,SY2347: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV117 @ SV495 @ SY2346 ) @ ( c_List_Olist_OCons @ SV495 @ SY2347 @ SY2346 ) @ SY2346 )
= ( c_List_Olist_OCons @ SV495 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV117 @ SV495 @ SY2346 ) @ SY2347 @ SY2346 ) @ SY2346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2008,plain,
! [SV496: $i,SV118: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV118 @ ( c_List_Olist_ONil @ SV496 ) @ SV496 ) @ SV496 )
= ( c_List_Obutlast @ SV118 @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2009,plain,
! [SV497: $i,SV119: $i] :
( ( ! [SY2348: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV119 @ SV497 @ SY2348 ) @ SY2348 )
= ( c_List_Olast @ SV497 @ SY2348 ) )
| ( SV497
= ( c_List_Olist_ONil @ SY2348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2010,plain,
! [SV498: $i,SV120: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV120 @ ( c_List_Olist_ONil @ SV498 ) @ SV498 ) @ SV498 )
= ( c_List_Olast @ SV120 @ SV498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2011,plain,
! [SV499: $i,SV121: $i] :
( ( ! [SY2349: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV121 @ SV499 @ SY2349 ) @ SY2349 )
= ( c_List_Oappend @ SV121 @ ( c_List_Obutlast @ SV499 @ SY2349 ) @ SY2349 ) )
| ( SV499
= ( c_List_Olist_ONil @ SY2349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2012,plain,
! [SV500: $i,SV122: $i] :
( ( ! [SY2350: $i,SY2351: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV500 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2350 ) @ SY2351 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV500 ) @ SY2351 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SY2350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2013,plain,
! [SV501: $i,SV123: $i] :
( ( ! [SY2352: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV501 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2352 ) @ SV501 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SY2352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2014,plain,
! [SV502: $i,SV124: $i] :
( ( ! [SY2353: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV502 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SY2353 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV502 ) @ SY2353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2015,plain,
! [SV503: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV125 ) ) @ ( c_Lambda_OdB_OAbs @ SV503 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV125 ) @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2016,plain,
! [SV504: $i,SV126: $i] :
( ( ! [SY2354: $i] :
( ! [SY2355: $i] :
( ( c_List_Ofilter @ SV126 @ ( c_List_Oreplicate @ SV504 @ SY2354 @ SY2355 ) @ SY2355 )
= ( c_List_Olist_ONil @ SY2355 ) )
| ( hBOOL @ ( hAPP @ SV126 @ SY2354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2017,plain,
! [SV505: $i,SV127: $i] :
( ( ! [SY2356: $i,SY2357: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV127 @ SV505 @ SY2356 ) ) @ ( c_Lambda_Osubst @ SV127 @ SY2357 @ SY2356 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV505 ) @ SY2357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2018,plain,
! [SV506: $i,SV128: $i] :
( ( ! [SY2358: $i,SY2359: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV128 @ SV506 @ SY2358 ) ) @ ( c_Lambda_Osubst @ SY2359 @ SV506 @ SY2358 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SY2359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2019,plain,
! [SV507: $i,SV129: $i] :
( ( ! [SY2360: $i,SY2361: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV507 @ SY2360 ) ) @ ( c_Lambda_Osubst @ SV129 @ SY2361 @ SY2360 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV507 ) @ SY2361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2020,plain,
! [SV508: $i,SV130: $i] :
( ( ! [SY2362: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV130 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV508 @ SV130 @ SY2362 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV508 ) @ SV130 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2021,plain,
! [SV509: $i,SV131: $i] :
( ( ! [SY2363: $i,SY2364: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV131 @ SV509 @ SY2363 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2364 @ SY2363 )
= ( c_List_Olist_OCons @ SY2364 @ SV509 @ SY2363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2022,plain,
! [SV510: $i,SV132: $i] :
( ( ! [SY2365: $i,SY2366: $i,SY2367: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV132 @ SV510 @ SY2365 ) @ ( c_Suc @ SY2366 ) @ SY2367 @ SY2365 )
= ( c_List_Olist_OCons @ SV132 @ ( c_List_Olist__update @ SV510 @ SY2366 @ SY2367 @ SY2365 ) @ SY2365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2023,plain,
! [SV133: $i] :
( ( ( ! [SY1577: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV133 ) @ SY1577 @ SV133 )
= SY1577 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV133 @ SV133 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(2024,plain,
! [SV511: $i,SV134: $i] :
( ( ! [SY2368: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV134 ) @ SV511 @ SY2368 )
= ( c_Lambda_OdB_OVar @ SV134 ) )
| ( SV134 = SY2368 )
| ( c_HOL_Oord__class_Oless @ SY2368 @ SV134 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2025,plain,
! [SV512: $i,SV135: $i] :
( ( ! [SY2369: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV135 ) @ SV512 @ SY2369 )
= ( c_Lambda_OdB_OVar @ SV135 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV135 @ SY2369 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2026,plain,
! [SV513: $i,SV136: $i] :
( ( ! [SY2370: $i] :
( ( c_Type_Otyping @ SV136 @ SV513 @ SY2370 )
| ! [SY2371: $i] :
( ~ ( c_Type_Otyping @ SV136 @ SY2371 @ SY2370 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2371 ) @ SV513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2027,plain,
! [SV514: $i,SV137: $i] :
( ( ! [SY2372: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV137 @ SV514 ) ) @ ( c_Lambda_Olift @ SY2372 @ SV514 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV137 ) @ SY2372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2028,plain,
! [SV515: $i,SV138: $i] :
( ( ! [SY2373: $i,SY2374: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV138 @ ( tc_List_Olist @ SV515 ) )
!= ( c_Nat_Osize__class_Osize @ SY2373 @ ( tc_List_Olist @ SY2374 ) ) )
| ! [SY2375: $i,SY2376: $i] :
( ( c_Map_Omap__upds @ SY2375 @ ( c_List_Oappend @ SV138 @ SY2376 @ SV515 ) @ SY2373 @ SV515 @ SY2374 )
= ( c_Map_Omap__upds @ SY2375 @ SV138 @ SY2373 @ SV515 @ SY2374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2029,plain,
! [SV516: $i,SV139: $i] :
( ( ! [SY2377: $i,SY2378: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV139 @ ( tc_List_Olist @ SV516 ) )
!= ( c_Nat_Osize__class_Osize @ SY2377 @ ( tc_List_Olist @ SY2378 ) ) )
| ! [SY2379: $i,SY2380: $i] :
( ( c_Map_Omap__upds @ SY2379 @ SV139 @ ( c_List_Oappend @ SY2377 @ SY2380 @ SY2378 ) @ SV516 @ SY2378 )
= ( c_Map_Omap__upds @ SY2379 @ SV139 @ SY2377 @ SV516 @ SY2378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2030,plain,
! [SV517: $i,SV140: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV140 ) @ SV517 )
= ( c_Lambda_OdB_OVar @ SV140 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV140 @ SV517 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2031,plain,
! [SV518: $i,SV141: $i] :
( ( ! [SY2381: $i] :
( ( ( c_Lambda_Oliftn @ SV141 @ ( c_Lambda_OdB_OVar @ SV518 ) @ SY2381 )
= ( c_Lambda_OdB_OVar @ SV518 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV518 @ SY2381 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2032,plain,
! [SV519: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP @ SV142 @ SV519 ) )
| ! [SY2382: $i,SY2383: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV142 @ SY2382 @ ( tc_fun @ SY2383 @ tc_bool ) ) @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2033,plain,
! [SV143: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV143 ) )
= $true )
| ( ( ! [SY1603: $i] : ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1603 @ ( c_List_Olist_ONil @ SV143 ) @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(2034,plain,
! [SV520: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV144 ) ) @ ( c_Lambda_OdB_OAbs @ SV520 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV144 ) @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2035,plain,
! [SV521: $i,SV145: $i] :
( ( ! [SY2384: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV145 @ SV521 @ SY2384 ) @ SY2384 )
= ( c_List_Oappend @ ( c_List_Orev @ SV521 @ SY2384 ) @ ( c_List_Orev @ SV145 @ SY2384 ) @ SY2384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2036,plain,
! [SV522: $i,SV146: $i] :
( ( ! [SY2385: $i,SY2386: $i,SY2387: $i,SY2388: $i] :
( ( c_List_Ofoldl @ SV146 @ SV522 @ ( c_List_Oappend @ SY2385 @ SY2386 @ SY2387 ) @ SY2388 @ SY2387 )
= ( c_List_Ofoldl @ SV146 @ ( c_List_Ofoldl @ SV146 @ SV522 @ SY2385 @ SY2388 @ SY2387 ) @ SY2386 @ SY2388 @ SY2387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2037,plain,
! [SV523: $i,SV147: $i] :
( ( ! [SY2389: $i,SY2390: $i] :
( ( c_List_Ofilter @ SV147 @ ( c_List_Oappend @ SV523 @ SY2389 @ SY2390 ) @ SY2390 )
= ( c_List_Oappend @ ( c_List_Ofilter @ SV147 @ SV523 @ SY2390 ) @ ( c_List_Ofilter @ SV147 @ SY2389 @ SY2390 ) @ SY2390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2038,plain,
! [SV524: $i,SV149: $i] :
( ( ! [SY2391: $i] :
( ! [SY2392: $i] :
( ( c_List_Omap @ SV149 @ SV524 @ SY2391 @ SY2392 )
!= ( c_List_Olist_ONil @ SY2392 ) )
| ( SV524
= ( c_List_Olist_ONil @ SY2391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2039,plain,
! [SV525: $i,SV150: $i] :
( ( ( SV150
= ( c_List_Olist_ONil @ SV525 ) )
| ~ ( c_List_Onull @ SV150 @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2040,plain,
! [SV526: $i,SV153: $i] :
( ( ! [SY2393: $i] :
( ( SV153
!= ( c_List_Oappend @ SV526 @ SV153 @ SY2393 ) )
| ( SV526
= ( c_List_Olist_ONil @ SY2393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2041,plain,
! [SV527: $i,SV154: $i] :
( ( ! [SY2394: $i] :
( ( ( c_List_Oappend @ SV154 @ SV527 @ SY2394 )
!= SV527 )
| ( SV154
= ( c_List_Olist_ONil @ SY2394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2042,plain,
! [SV528: $i,SV155: $i] :
( ( ! [SY2395: $i] :
( ( SV155
!= ( c_List_Oappend @ SV155 @ SV528 @ SY2395 ) )
| ( SV528
= ( c_List_Olist_ONil @ SY2395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2043,plain,
! [SV529: $i,SV156: $i] :
( ( ! [SY2396: $i] :
( ( ( c_List_Oappend @ SV156 @ SV529 @ SY2396 )
!= SV156 )
| ( SV529
= ( c_List_Olist_ONil @ SY2396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2044,plain,
! [SV530: $i,SV157: $i] :
( ( ( ( c_List_Oremdups @ SV157 @ SV530 )
!= ( c_List_Olist_ONil @ SV530 ) )
| ( SV157
= ( c_List_Olist_ONil @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2045,plain,
! [SV531: $i,SV158: $i] :
( ( ! [SY2397: $i] :
( ( ( c_List_Orotate @ SV158 @ SV531 @ SY2397 )
!= ( c_List_Olist_ONil @ SY2397 ) )
| ( SV531
= ( c_List_Olist_ONil @ SY2397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2046,plain,
! [SV532: $i,SV159: $i] :
( ( ( ( c_List_Olist_ONil @ SV159 )
!= ( c_List_Orev @ SV532 @ SV159 ) )
| ( SV532
= ( c_List_Olist_ONil @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2047,plain,
! [SV533: $i,SV160: $i] :
( ( ! [SY2398: $i] :
( ( c_List_Olist_ONil @ SV160 )
!= ( c_List_Olist_OCons @ SV533 @ SY2398 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2048,plain,
! [SV534: $i,SV161: $i] :
( ( ! [SY2399: $i] :
( ( ( c_List_Oappend @ SV161 @ SV534 @ SY2399 )
!= ( c_List_Olist_ONil @ SY2399 ) )
| ( SV534
= ( c_List_Olist_ONil @ SY2399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2049,plain,
! [SV535: $i,SV162: $i] :
( ( ! [SY2400: $i] :
( ( ( c_List_Oappend @ SV162 @ SV535 @ SY2400 )
!= ( c_List_Olist_ONil @ SY2400 ) )
| ( SV162
= ( c_List_Olist_ONil @ SY2400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2050,plain,
! [SV536: $i,SV163: $i] :
( ( ! [SY2401: $i] :
( ( ( c_List_Olist_ONil @ SV163 )
!= ( c_List_Oappend @ SV536 @ SY2401 @ SV163 ) )
| ( SY2401
= ( c_List_Olist_ONil @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2051,plain,
! [SV537: $i,SV164: $i] :
( ( ! [SY2402: $i] :
( ( c_List_Olist_ONil @ SV164 )
!= ( c_List_Oappend @ SV537 @ SY2402 @ SV164 ) )
| ( SV537
= ( c_List_Olist_ONil @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2052,plain,
! [SV538: $i,SV165: $i] :
( ( ! [SY2403: $i,SY2404: $i] :
( ( c_List_Ofoldl @ SV165 @ SV538 @ ( c_List_Olist_ONil @ SY2403 ) @ SY2404 @ SY2403 )
= SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2053,plain,
! [SV539: $i,SV167: $i] :
( ( ! [SY2405: $i,SY2406: $i] :
( ( ( c_List_Olist_ONil @ SV167 )
!= ( c_List_Omap @ SV539 @ SY2405 @ SY2406 @ SV167 ) )
| ( SY2405
= ( c_List_Olist_ONil @ SY2406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2054,plain,
! [SV540: $i,SV168: $i] :
( ( SV168
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV540 ) @ SV168 @ SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2055,plain,
! [SV541: $i,SV169: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV169 ) @ SV541 @ SV169 )
= SV541 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2056,plain,
! [SV542: $i,SV170: $i] :
( ( SV170
= ( c_List_Oappend @ SV170 @ ( c_List_Olist_ONil @ SV542 ) @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2057,plain,
! [SV543: $i,SV171: $i] :
( ( SV171
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV543 ) @ SV171 @ SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2058,plain,
! [SV544: $i,SV172: $i] :
( ( ( c_List_Oappend @ SV172 @ ( c_List_Olist_ONil @ SV544 ) @ SV544 )
= SV172 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2059,plain,
! [SV545: $i,SV173: $i] :
( ( ! [SY2407: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV173 ) ) @ SV545 ) @ SY2407 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV545 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV173 @ SV545 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2407 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2060,plain,
! [SV546: $i,SV174: $i] :
( ( ! [SY2408: $i] :
( ( SV174
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV546 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV546 @ SY2408 @ SV174 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV546 ) @ SY2408 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2061,plain,
! [SV547: $i,SV175: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV175 ) ) @ SV547 ) ) @ ( c_Lambda_Osubst @ SV175 @ SV547 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2062,plain,
! [SV176: $i] :
( ( ( ! [SY1657: $i] : ( hBOOL @ ( hAPP @ SV176 @ SY1657 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV176 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV176 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(2063,plain,
! [SV177: $i] :
( ( ( ! [SY1658: $i] : ( hBOOL @ ( hAPP @ SV177 @ SY1658 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV177 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV177 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(2064,plain,
! [SV178: $i] :
( ( ( ! [SY1659: $i] : ( hBOOL @ ( hAPP @ SV178 @ SY1659 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV178 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV178 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(2065,plain,
! [SV179: $i] :
( ( ( ! [SY1660: $i] : ( hBOOL @ ( hAPP @ SV179 @ SY1660 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV179 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV179 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(2066,plain,
! [SV180: $i] :
( ( ( ! [SY1661: $i] : ( hBOOL @ ( hAPP @ SV180 @ SY1661 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV180 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV180 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(2067,plain,
! [SV181: $i] :
( ( ( ! [SY1662: $i] : ( hBOOL @ ( hAPP @ SV181 @ SY1662 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV181 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV181 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(2068,plain,
! [SV182: $i] :
( ( ( ! [SY1663: $i] : ( hBOOL @ ( hAPP @ SV182 @ SY1663 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV182 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV182 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(2069,plain,
! [SV183: $i] :
( ( ( ! [SY1664: $i] : ( hBOOL @ ( hAPP @ SV183 @ SY1664 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV183 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV183 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(2070,plain,
! [SV184: $i] :
( ( ( ! [SY1665: $i] : ( hBOOL @ ( hAPP @ SV184 @ SY1665 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV184 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV184 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(2071,plain,
! [SV548: $i,SV185: $i] :
( ( ! [SY2409: $i] :
( ( c_Lambda_Osubstn @ SV185 @ SV548 @ SY2409 )
= ( c_Lambda_Osubst @ SV185 @ ( c_Lambda_Oliftn @ SY2409 @ SV548 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2072,plain,
! [SV549: $i,SV186: $i] :
( ( ! [SY2410: $i,SY2411: $i,SY2412: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SV549 @ SY2410 @ SY2411 ) @ SY2411 ) @ ( c_Nat_Osize__class_Osize @ SV186 @ ( tc_List_Olist @ SY2411 ) ) @ SY2412 @ SY2411 )
= ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SY2412 @ SY2410 @ SY2411 ) @ SY2411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2073,plain,
! [SV550: $i,SV187: $i] :
( ( ! [SY2413: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV187 @ SV550 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2413 @ SV550 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV187 ) @ SY2413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2074,plain,
! [SV551: $i,SV188: $i] :
( ( ! [SY2414: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV551 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SY2414 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV551 @ SY2414 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2075,plain,
! [SV552: $i,SV189: $i] :
( ( ! [SY2415: $i] :
( ~ ( hBOOL @ ( hAPP @ SV189 @ SV552 ) )
| ! [SY2416: $i] :
( ! [SY2417: $i] :
( ( c_List_Olist_OCons @ SV552 @ ( c_List_Ofilter @ SV189 @ SY2417 @ SY2416 ) @ SY2416 )
= ( c_List_Ofilter @ SV189 @ ( c_List_Oappend @ SY2415 @ ( c_List_Olist_OCons @ SV552 @ SY2417 @ SY2416 ) @ SY2416 ) @ SY2416 ) )
| ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ SV189 @ SY2415 @ SY2416 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2076,plain,
! [SV553: $i,SV190: $i] :
( ( ! [SY2418: $i] :
( ~ ( hBOOL @ ( hAPP @ SV190 @ SV553 ) )
| ! [SY2419: $i] :
( ! [SY2420: $i] :
( ( c_List_Ofilter @ SV190 @ ( c_List_Oappend @ SY2418 @ ( c_List_Olist_OCons @ SV553 @ SY2420 @ SY2419 ) @ SY2419 ) @ SY2419 )
= ( c_List_Olist_OCons @ SV553 @ ( c_List_Ofilter @ SV190 @ SY2420 @ SY2419 ) @ SY2419 ) )
| ( hBOOL @ ( hAPP @ SV190 @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ SV190 @ SY2418 @ SY2419 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2077,plain,
! [SV554: $i,SV191: $i] :
( ( ! [SY2421: $i,SY2422: $i,SY2423: $i] :
( ( ( c_List_Olist_OCons @ SV191 @ SV554 @ SY2421 )
!= ( c_List_Oappend @ SY2422 @ SY2423 @ SY2421 ) )
| ( SV554
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV191 @ SV554 @ SY2422 @ SY2423 @ SY2421 ) @ SY2423 @ SY2421 ) )
| ( SY2422
= ( c_List_Olist_ONil @ SY2421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2078,plain,
! [SV555: $i,SV192: $i] :
( ( ! [SY2424: $i,SY2425: $i,SY2426: $i] :
( ( ( c_List_Oappend @ SV192 @ SV555 @ SY2424 )
!= ( c_List_Olist_OCons @ SY2425 @ SY2426 @ SY2424 ) )
| ( SV192
= ( c_List_Olist_OCons @ SY2425 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2425 @ SY2426 @ SV192 @ SV555 @ SY2424 ) @ SY2424 ) )
| ( SV192
= ( c_List_Olist_ONil @ SY2424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2079,plain,
! [SV556: $i,SV193: $i] :
( ( ! [SY2427: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV193 @ ( c_List_Olist_OCons @ SV556 @ ( c_List_Olist_ONil @ SY2427 ) @ SY2427 ) @ SY2427 ) @ SY2427 )
= SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2080,plain,
! [SV557: $i,SV194: $i] :
( ( ! [SY2428: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV194 @ ( c_List_Olist_OCons @ SV557 @ ( c_List_Olist_ONil @ SY2428 ) @ SY2428 ) @ SY2428 ) @ SY2428 )
= SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2081,plain,
! [SV558: $i,SV195: $i] :
( ( ! [SY2429: $i,SY2430: $i] :
( ( SV195 = SV558 )
| ( SY2429 = SY2430 )
| ! [SY2431: $i,SY2432: $i] :
~ ( c_ListOrder_Ostep1 @ SY2431 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SY2429 @ ( c_List_Olist_ONil @ SY2432 ) @ SY2432 ) @ SY2432 ) @ ( c_List_Oappend @ SV558 @ ( c_List_Olist_OCons @ SY2430 @ ( c_List_Olist_ONil @ SY2432 ) @ SY2432 ) @ SY2432 ) @ SY2432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2082,plain,
! [SV559: $i,SV196: $i] :
( ( ! [SY2433: $i,SY2434: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SV559 ) @ SY2433 ) )
| ( SV559 = SY2433 )
| ! [SY2435: $i,SY2436: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SY2434 @ ( c_List_Olist_OCons @ SV559 @ ( c_List_Olist_ONil @ SY2435 ) @ SY2435 ) @ SY2435 ) @ ( c_List_Oappend @ SY2436 @ ( c_List_Olist_OCons @ SY2433 @ ( c_List_Olist_ONil @ SY2435 ) @ SY2435 ) @ SY2435 ) @ SY2435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2083,plain,
! [SV560: $i,SV197: $i] :
( ( ! [SY2437: $i,SY2438: $i,SY2439: $i] :
( ( ( c_List_Oappend @ SV197 @ SV560 @ SY2437 )
!= ( c_List_Olist_OCons @ SY2438 @ SY2439 @ SY2437 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2438 @ SY2439 @ SV197 @ SV560 @ SY2437 ) @ SV560 @ SY2437 )
= SY2439 )
| ( SV197
= ( c_List_Olist_ONil @ SY2437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2084,plain,
! [SV561: $i,SV198: $i] :
( ( ! [SY2440: $i,SY2441: $i,SY2442: $i] :
( ( ( c_List_Olist_OCons @ SV198 @ SV561 @ SY2440 )
!= ( c_List_Oappend @ SY2441 @ SY2442 @ SY2440 ) )
| ( ( c_List_Olist_OCons @ SV198 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV198 @ SV561 @ SY2441 @ SY2442 @ SY2440 ) @ SY2440 )
= SY2441 )
| ( SY2441
= ( c_List_Olist_ONil @ SY2440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2085,plain,
! [SV562: $i,SV199: $i] :
( ( ! [SY2443: $i,SY2444: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SV562 ) @ SY2443 ) )
| ! [SY2445: $i,SY2446: $i] :
( ( c_ListOrder_Ostep1 @ SV199 @ SY2444 @ SY2445 @ SY2446 )
| ~ ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SY2444 @ ( c_List_Olist_OCons @ SV562 @ ( c_List_Olist_ONil @ SY2446 ) @ SY2446 ) @ SY2446 ) @ ( c_List_Oappend @ SY2445 @ ( c_List_Olist_OCons @ SY2443 @ ( c_List_Olist_ONil @ SY2446 ) @ SY2446 ) @ SY2446 ) @ SY2446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2086,plain,
! [SV563: $i,SV200: $i] :
( ( ! [SY2447: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV200 @ SV563 @ SY2447 ) @ SY2447 )
= ( c_List_Oappend @ SV563 @ ( c_List_Olist_OCons @ SV200 @ ( c_List_Olist_ONil @ SY2447 ) @ SY2447 ) @ SY2447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2087,plain,
! [SV564: $i,SV201: $i] :
( ( ! [SY2448: $i,SY2449: $i] :
( ( SV201 = SV564 )
| ( c_ListOrder_Ostep1 @ SY2448 @ SV201 @ SV564 @ SY2449 )
| ! [SY2450: $i,SY2451: $i] :
~ ( c_ListOrder_Ostep1 @ SY2448 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SY2450 @ ( c_List_Olist_ONil @ SY2449 ) @ SY2449 ) @ SY2449 ) @ ( c_List_Oappend @ SV564 @ ( c_List_Olist_OCons @ SY2451 @ ( c_List_Olist_ONil @ SY2449 ) @ SY2449 ) @ SY2449 ) @ SY2449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2088,plain,
! [SV565: $i,SV202: $i] :
( ( ! [SY2452: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV202 @ SV565 @ SY2452 ) @ ( c_List_Olist_OCons @ SV565 @ ( c_List_Olist_ONil @ SY2452 ) @ SY2452 ) @ SY2452 )
= ( c_List_Olist_OCons @ SV565 @ ( c_List_Oreplicate @ SV202 @ SV565 @ SY2452 ) @ SY2452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2089,plain,
! [SV566: $i,SV203: $i] :
( ( ! [SY2453: $i,SY2454: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV203 ) @ SV566 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2453 @ SY2454 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2454
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV203 @ SV566 @ SY2453 @ SY2454 ) @ ( c_List_Olist_OCons @ SV566 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY2454
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2090,plain,
! [SV567: $i,SV204: $i] :
( ( ! [SY2455: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ SV204 ) @ SV567 @ SY2455 )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV204 @ SV567 @ SY2455 ) @ SY2455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2091,plain,
! [SV568: $i,SV205: $i] :
( ( ! [SY2456: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV205 ) @ SV568 @ SY2456 )
= ( c_Lambda_OdB_OVar @ SV205 ) )
| ( SV205 = SY2456 )
| ( c_HOL_Oord__class_Oless @ SY2456 @ SV205 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2092,plain,
! [SV569: $i,SV206: $i] :
( ( ( c_Lambda_Osubstn @ SV206 @ SV569 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ SV206 @ SV569 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2093,plain,
! [SV570: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP @ SV207 @ SV570 ) )
| ! [SY2457: $i,SY2458: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2457 @ SV207 @ ( tc_fun @ SY2458 @ tc_bool ) ) @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2094,plain,
! [SV571: $i,SV208: $i] :
( ( ! [SY2459: $i,SY2460: $i,SY2461: $i] :
( ( c_List_Ofoldl @ SV208 @ SV571 @ SY2459 @ SY2460 @ SY2461 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV208 @ SY2460 @ SY2461 @ SY2460 ) @ ( c_List_Orev @ SY2459 @ SY2461 ) @ SV571 @ SY2461 @ SY2460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2095,plain,
! [SV572: $i,SV209: $i] :
( ( ( c_List_Olist_OCons @ SV209 @ ( c_List_Olist_ONil @ SV572 ) @ SV572 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV209 @ ( c_List_Olist_ONil @ SV572 ) @ SV572 ) @ SV572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2096,plain,
! [SV573: $i,SV210: $i] :
( ( ! [SY2462: $i,SY2463: $i,SY2464: $i,SY2465: $i] :
( ( c_List_Omap @ SV210 @ ( c_List_Olist__update @ SV573 @ SY2462 @ SY2463 @ SY2464 ) @ SY2464 @ SY2465 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV210 @ SV573 @ SY2464 @ SY2465 ) @ SY2462 @ ( hAPP @ SV210 @ SY2463 ) @ SY2465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2097,plain,
! [SV574: $i,SV211: $i] :
( ( ! [SY2466: $i] :
( ( c_List_Olist_OCons @ SV211 @ SV574 @ SY2466 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2466 ) @ ( c_List_Olist_OCons @ SV211 @ SV574 @ SY2466 ) @ SY2466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2098,plain,
! [SV575: $i,SV212: $i] :
( ( ! [SY2467: $i] :
( SV212
!= ( c_List_Olist_OCons @ SV575 @ SV212 @ SY2467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2099,plain,
! [SV576: $i,SV213: $i] :
( ( ! [SY2468: $i] :
( ( c_List_Olist_OCons @ SV213 @ SV576 @ SY2468 )
!= SV576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2100,plain,
! [SV577: $i,SV214: $i] :
( ( ! [SY2469: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV214 @ SV577 ) ) @ ( c_Lambda_Olift @ SY2469 @ SV577 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV214 ) @ SY2469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2101,plain,
! [SV578: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ SV215 @ SV578 ) )
| ! [SY2470: $i] :
( ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY2470 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2470 @ SV215 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2470 @ SV578 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2102,plain,
! [SV579: $i,SV216: $i] :
( ( ! [SY2471: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV216 @ SV579 ) @ SY2471 @ SV579 )
= SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2103,plain,
! [SV580: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ SV580 ) )
| ! [SY2472: $i] :
( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY2472 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2472 @ SV217 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2472 @ SV580 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2104,plain,
! [SV581: $i,SV218: $i] :
( ( ! [SY2473: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV218 @ SV581 ) @ ( c_List_Olist_OCons @ SY2473 @ ( c_List_Olist_ONil @ SV581 ) @ SV581 ) @ SV581 ) @ SV581 )
= ( c_List_Olist_OCons @ SY2473 @ SV218 @ SV581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2105,plain,
! [SV219: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV219 ) )
= $true )
| ( ( ! [SY1765: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1765 @ SV219 )
| ! [SY1766: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1766 @ SY1765 @ SV219 ) @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(2106,plain,
! [SV582: $i,SV220: $i] :
( ( ! [SY2474: $i,SY2475: $i] :
( ( c_List_Olist_OCons @ SV220 @ ( c_List_Oappend @ SV582 @ SY2474 @ SY2475 ) @ SY2475 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV220 @ SV582 @ SY2475 ) @ SY2474 @ SY2475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2107,plain,
! [SV583: $i,SV221: $i] :
( ( ! [SY2476: $i,SY2477: $i] :
( ( c_List_Olist_OCons @ SV221 @ ( c_List_Oappend @ SV583 @ SY2476 @ SY2477 ) @ SY2477 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV221 @ SV583 @ SY2477 ) @ SY2476 @ SY2477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2108,plain,
! [SV584: $i,SV222: $i] :
( ( ! [SY2478: $i] :
( ( c_List_Oremove1 @ SV222 @ ( c_List_Olist_OCons @ SV222 @ SV584 @ SY2478 ) @ SY2478 )
= SV584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2109,plain,
! [SV585: $i,SV223: $i] :
( ( ! [SY2479: $i,SY2480: $i,SY2481: $i,SY2482: $i] :
( ( c_List_Olist_Olist__case @ SV223 @ SV585 @ ( c_List_Olist_OCons @ SY2479 @ SY2480 @ SY2481 ) @ SY2482 @ SY2481 )
= ( hAPP @ ( hAPP @ SV585 @ SY2479 ) @ SY2480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2110,plain,
! [SV586: $i,SV224: $i] :
( ( ! [SY2483: $i,SY2484: $i,SY2485: $i] :
( ( c_List_Omap @ SV224 @ ( c_List_Olist_OCons @ SV586 @ SY2483 @ SY2484 ) @ SY2484 @ SY2485 )
= ( c_List_Olist_OCons @ ( hAPP @ SV224 @ SV586 ) @ ( c_List_Omap @ SV224 @ SY2483 @ SY2484 @ SY2485 ) @ SY2485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2111,plain,
! [SV587: $i,SV225: $i] :
( ( ! [SY2486: $i,SY2487: $i,SY2488: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV225 @ SV587 ) @ ( c_List_Omap @ SV225 @ SY2486 @ SY2487 @ SY2488 ) @ SY2488 )
= ( c_List_Omap @ SV225 @ ( c_List_Olist_OCons @ SV587 @ SY2486 @ SY2487 ) @ SY2487 @ SY2488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2112,plain,
! [SV588: $i,SV226: $i] :
( ( ! [SY2489: $i,SY2490: $i,SY2491: $i] :
( ( c_List_Omap @ SV226 @ ( c_List_Olist_OCons @ SV588 @ SY2489 @ SY2490 ) @ SY2490 @ SY2491 )
= ( c_List_Olist_OCons @ ( hAPP @ SV226 @ SV588 ) @ ( c_List_Omap @ SV226 @ SY2489 @ SY2490 @ SY2491 ) @ SY2491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2113,plain,
! [SV589: $i,SV227: $i] :
( ( ! [SY2492: $i,SY2493: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV227 @ SV589 @ SY2492 ) @ SY2493 @ SY2492 )
= ( c_List_Olist_OCons @ SV227 @ ( c_List_Oappend @ SV589 @ SY2493 @ SY2492 ) @ SY2492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2114,plain,
! [SV590: $i,SV228: $i] :
( ( ! [SY2494: $i,SY2495: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV228 @ SV590 @ SY2494 ) @ SY2495 @ SY2494 )
= ( c_List_Olist_OCons @ SV228 @ ( c_List_Oappend @ SV590 @ SY2495 @ SY2494 ) @ SY2494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2115,plain,
! [SV591: $i,SV229: $i] :
( ( ! [SY2496: $i] :
( ( c_Lambda_OdB_OAbs @ SV229 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV591 @ SY2496 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV229 )
= SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2116,plain,
! [SV592: $i,SV230: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV230 )
| ! [SY2497: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV592 @ SY2497 @ SV230 ) @ SV230 )
| ! [SY2498: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2498 @ ( c_List_Olist_OCons @ SV592 @ SY2497 @ SV230 ) @ SV230 ) @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2117,plain,
! [SV231: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV231 ) )
= $true )
| ( ( ! [SY1803: $i,SY1804: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1803 @ SY1804 @ SV231 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1804 @ SY1803 @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(2118,plain,
! [SV232: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV232 ) )
= $true )
| ( ( ! [SY1805: $i,SY1806: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1805 @ SY1806 @ SV232 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1806 @ SY1805 @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(2119,plain,
! [SV593: $i,SV233: $i] :
( ( ! [SY2499: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV233 @ SV593 @ ( tc_fun @ SY2499 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV593 @ SV233 @ ( tc_fun @ SY2499 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2120,plain,
! [SV594: $i,SV234: $i] :
( ( ! [SY2500: $i,SY2501: $i] :
( ( ( c_List_Orev @ SV234 @ SV594 )
!= ( c_List_Olist_OCons @ SY2500 @ SY2501 @ SV594 ) )
| ( SV234
= ( c_List_Oappend @ ( c_List_Orev @ SY2501 @ SV594 ) @ ( c_List_Olist_OCons @ SY2500 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2121,plain,
! [SV595: $i,SV235: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV235 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 ) @ SV595 )
= ( c_List_Olist_OCons @ SV235 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2122,plain,
! [SV596: $i,SV236: $i] :
( ( ! [SY2502: $i,SY2503: $i,SY2504: $i,SY2505: $i] :
( ( c_List_Ofoldl @ SV236 @ SV596 @ ( c_List_Olist_OCons @ SY2502 @ SY2503 @ SY2504 ) @ SY2505 @ SY2504 )
= ( c_List_Ofoldl @ SV236 @ ( hAPP @ ( hAPP @ SV236 @ SV596 ) @ SY2502 ) @ SY2503 @ SY2505 @ SY2504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2123,plain,
! [SV597: $i,SV237: $i] :
( ( ! [SY2506: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV237 @ SV597 @ SY2506 ) @ SY2506 )
= ( c_List_Oappend @ ( c_List_Orev @ SV597 @ SY2506 ) @ ( c_List_Olist_OCons @ SV237 @ ( c_List_Olist_ONil @ SY2506 ) @ SY2506 ) @ SY2506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2124,plain,
! [SV598: $i,SV238: $i] :
( ( ! [SY2507: $i,SY2508: $i] :
( ! [SY2509: $i] :
( ( c_List_Olist_OCons @ SV238 @ SV598 @ SY2507 )
!= ( c_List_Ofilter @ SY2508 @ SY2509 @ SY2507 ) )
| ( hBOOL @ ( hAPP @ SY2508 @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2125,plain,
! [SV599: $i,SV239: $i] :
( ( ! [SY2510: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ SV239 @ SV599 @ SY2510 ) @ SY2510 )
= ( c_List_Ofilter @ SV239 @ ( c_List_Oremdups @ SV599 @ SY2510 ) @ SY2510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2126,plain,
! [SV600: $i,SV240: $i] :
( ( ! [SY2511: $i,SY2512: $i] :
( ( c_List_Ofilter @ SV240 @ ( c_List_Olist_OCons @ SV600 @ SY2511 @ SY2512 ) @ SY2512 )
= ( c_List_Olist_OCons @ SV600 @ ( c_List_Ofilter @ SV240 @ SY2511 @ SY2512 ) @ SY2512 ) )
| ~ ( hBOOL @ ( hAPP @ SV240 @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2127,plain,
! [SV601: $i,SV241: $i] :
( ( ! [SY2513: $i] :
( ( ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SV601 ) @ SV601 )
!= ( c_List_Orev @ SY2513 @ SV601 ) )
| ( SY2513
= ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SV601 ) @ SV601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2128,plain,
! [SV602: $i,SV242: $i] :
( ( ! [SY2514: $i,SY2515: $i,SY2516: $i] :
( ( c_Lambda_OdB_OdB__case @ SV242 @ SV602 @ SY2514 @ ( c_Lambda_OdB_OAbs @ SY2515 ) @ SY2516 )
= ( hAPP @ SY2514 @ SY2515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2129,plain,
! [SV603: $i,SV243: $i] :
( ( ! [SY2517: $i,SY2518: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV243 @ SV603 @ SY2517 ) ) @ ( c_Lambda_Osubst @ SY2518 @ SV603 @ SY2517 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV243 ) @ SY2518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2130,plain,
! [SV604: $i,SV244: $i] :
( ( ! [SY2519: $i,SY2520: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV244 @ SV604 @ SY2519 @ SY2520 ) @ SY2520 )
= ( c_List_Omap @ SV244 @ ( c_List_Orev @ SV604 @ SY2519 ) @ SY2519 @ SY2520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2131,plain,
! [SV605: $i,SV245: $i] :
( ( ! [SY2521: $i,SY2522: $i] :
( ( ( c_List_Oappend @ SV245 @ SV605 @ SY2521 )
!= ( c_List_Oappend @ SY2522 @ SV605 @ SY2521 ) )
| ( SV245 = SY2522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2132,plain,
! [SV606: $i,SV246: $i] :
( ( ! [SY2523: $i,SY2524: $i] :
( ( ( c_List_Oappend @ SV246 @ SV606 @ SY2523 )
!= ( c_List_Oappend @ SV246 @ SY2524 @ SY2523 ) )
| ( SV606 = SY2524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2133,plain,
! [SV607: $i,SV247: $i] :
( ( ! [SY2525: $i,SY2526: $i] :
( ! [SY2527: $i] :
( ( c_List_Ofilter @ SV247 @ SV607 @ SY2525 )
!= ( c_List_Olist_OCons @ SY2526 @ SY2527 @ SY2525 ) )
| ( hBOOL @ ( hAPP @ SV247 @ SY2526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2134,plain,
! [SV608: $i,SV248: $i] :
( ( ! [SY2528: $i,SY2529: $i,SY2530: $i] :
( ( c_List_Orotate @ SV248 @ ( c_List_Omap @ SV608 @ SY2528 @ SY2529 @ SY2530 ) @ SY2530 )
= ( c_List_Omap @ SV608 @ ( c_List_Orotate @ SV248 @ SY2528 @ SY2529 ) @ SY2529 @ SY2530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2135,plain,
! [SV609: $i,SV249: $i] :
( ( SV249
= ( c_List_Orev @ ( c_List_Orev @ SV249 @ SV609 ) @ SV609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2136,plain,
! [SV610: $i,SV250: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV250 @ SV610 ) @ SV610 )
= SV250 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2137,plain,
! [SV611: $i,SV251: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV251 @ SV611 ) @ SV611 )
= SV251 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2138,plain,
! [SV612: $i,SV252: $i] :
( ( ! [SY2531: $i,SY2532: $i,SY2533: $i,SY2534: $i] :
( ( c_List_Ofoldr @ SV252 @ ( c_List_Oappend @ SV612 @ SY2531 @ SY2532 ) @ SY2533 @ SY2532 @ SY2534 )
= ( c_List_Ofoldr @ SV252 @ SV612 @ ( c_List_Ofoldr @ SV252 @ SY2531 @ SY2533 @ SY2532 @ SY2534 ) @ SY2532 @ SY2534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2139,plain,
! [SV613: $i,SV253: $i] :
( ( ! [SY2535: $i,SY2536: $i] : ( c_List_Olist__ex @ SV253 @ ( c_List_Olist_OCons @ SV613 @ SY2535 @ SY2536 ) @ SY2536 )
| ~ ( hBOOL @ ( hAPP @ SV253 @ SV613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2140,plain,
! [SV614: $i,SV254: $i] :
( ( ! [SY2537: $i] :
( ( ( c_List_Orev @ SV254 @ SV614 )
!= ( c_List_Olist_OCons @ SY2537 @ ( c_List_Olist_ONil @ SV614 ) @ SV614 ) )
| ( SV254
= ( c_List_Olist_OCons @ SY2537 @ ( c_List_Olist_ONil @ SV614 ) @ SV614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2141,plain,
! [SV615: $i,SV255: $i] :
( ( ! [SY2538: $i,SY2539: $i] :
( ( c_List_Olist__ex @ SV255 @ ( c_List_Olist_OCons @ SV615 @ SY2538 @ SY2539 ) @ SY2539 )
| ~ ( c_List_Olist__ex @ SV255 @ SY2538 @ SY2539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2142,plain,
! [SV616: $i,SV256: $i] :
( ( ! [SY2540: $i] :
( ( c_List_Olist__ex @ SV256 @ SV616 @ SY2540 )
| ! [SY2541: $i] :
( ( hBOOL @ ( hAPP @ SV256 @ SY2541 ) )
| ~ ( c_List_Olist__ex @ SV256 @ ( c_List_Olist_OCons @ SY2541 @ SV616 @ SY2540 ) @ SY2540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2143,plain,
! [SV617: $i,SV257: $i] :
( ( ! [SY2542: $i,SY2543: $i,SY2544: $i,SY2545: $i] :
( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SY2542 @ SY2543 ) @ ( c_List_Olist_OCons @ SY2544 @ SY2545 @ SY2543 ) @ SY2543 )
| ~ ( c_List_Olistrelp @ SV257 @ SY2542 @ SY2545 @ SY2543 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SY2544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2144,plain,
! [SV618: $i,SV258: $i] :
( ( ~ ( class_Lattices_Olattice @ SV258 )
| ! [SY2546: $i,SY2547: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ SY2546 @ SV258 ) @ SY2547 @ SV258 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2546 @ SY2547 @ SV258 ) @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2145,plain,
! [SV619: $i,SV259: $i] :
( ( ~ ( class_Lattices_Olattice @ SV259 )
| ! [SY2548: $i,SY2549: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2548 @ SY2549 @ SV259 ) @ SV259 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2548 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ SY2549 @ SV259 ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2146,plain,
! [SV620: $i,SV260: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV260 )
| ! [SY2550: $i,SY2551: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2550 @ SY2551 @ SV260 ) @ SV260 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2550 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ SY2551 @ SV260 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2147,plain,
! [SV621: $i,SV261: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV261 )
| ! [SY2552: $i,SY2553: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ SY2552 @ SV261 ) @ SY2553 @ SV261 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2552 @ SY2553 @ SV261 ) @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2148,plain,
! [SV622: $i,SV262: $i] :
( ( ! [SY2554: $i,SY2555: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 @ SV622 @ ( tc_fun @ SY2554 @ tc_bool ) ) @ SY2555 @ ( tc_fun @ SY2554 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV622 @ SY2555 @ ( tc_fun @ SY2554 @ tc_bool ) ) @ ( tc_fun @ SY2554 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2149,plain,
! [SV623: $i,SV263: $i] :
( ( ! [SY2556: $i,SY2557: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV623 @ SY2556 @ ( tc_fun @ SY2557 @ tc_bool ) ) @ ( tc_fun @ SY2557 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV623 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SY2556 @ ( tc_fun @ SY2557 @ tc_bool ) ) @ ( tc_fun @ SY2557 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2150,plain,
! [SV624: $i,SV264: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV264 )
!= ( c_Lambda_OdB_OAbs @ SV624 ) )
| ( SV264 = SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2151,plain,
! [SV625: $i,SV265: $i] :
( ( ! [SY2558: $i,SY2559: $i] :
( ( c_List_Oremove1 @ SV265 @ ( c_List_Olist_OCons @ SV625 @ SY2558 @ SY2559 ) @ SY2559 )
= ( c_List_Olist_OCons @ SV625 @ ( c_List_Oremove1 @ SV265 @ SY2558 @ SY2559 ) @ SY2559 ) )
| ( SV265 = SV625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2152,plain,
! [SV626: $i,SV266: $i] :
( ( ! [SY2560: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV266 @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2560 @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV266 ) @ SY2560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2153,plain,
! [SV627: $i,SV267: $i] :
( ( ! [SY2561: $i,SY2562: $i,SY2563: $i] :
( ( c_List_Omap @ SV267 @ ( c_List_Oappend @ SV627 @ SY2561 @ SY2562 ) @ SY2562 @ SY2563 )
= ( c_List_Oappend @ ( c_List_Omap @ SV267 @ SV627 @ SY2562 @ SY2563 ) @ ( c_List_Omap @ SV267 @ SY2561 @ SY2562 @ SY2563 ) @ SY2563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2154,plain,
! [SV628: $i,SV268: $i] :
( ( ( SV268
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SV628 @ SV268 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SV628 @ SV268 ) @ t_a ) )
| ( SV268
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV628 @ SV268 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2155,plain,
! [SV629: $i,SV269: $i] :
( ( ! [SY2564: $i,SY2565: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV269 ) @ SV629 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2564 ) @ SY2565 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV629 = SY2565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2156,plain,
! [SV630: $i,SV270: $i] :
( ( ! [SY2566: $i] :
( ! [SY2567: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV270 ) @ SV630 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2566 ) @ SY2567 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV270 = SY2566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2157,plain,
! [SV631: $i,SV271: $i] :
( ( ! [SY2568: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV271 @ SV631 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2568 ) )
| ( SV271
= ( c_Lambda_OdB_OAbs @ SY2568 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2158,plain,
! [SV632: $i,SV272: $i] :
( ( ! [SY2569: $i,SY2570: $i] :
( ( c_List_Oremove1 @ SV272 @ ( c_List_Ofilter @ SV632 @ SY2569 @ SY2570 ) @ SY2570 )
= ( c_List_Ofilter @ SV632 @ SY2569 @ SY2570 ) )
| ( hBOOL @ ( hAPP @ SV632 @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2159,plain,
! [SV633: $i,SV273: $i] :
( ( ! [SY2571: $i,SY2572: $i,SY2573: $i,SY2574: $i] :
( ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ ( c_List_Olist_OCons @ SY2571 @ SY2572 @ SY2573 ) @ SY2574 @ SY2573 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV633 @ SY2571 ) @ SY2572 ) @ ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ SY2572 @ SY2574 @ SY2573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2160,plain,
! [SV634: $i,SV274: $i] :
( ( ! [SY2575: $i] :
( ( ( c_List_Orev @ SV274 @ SV634 )
!= ( c_List_Orev @ SY2575 @ SV634 ) )
| ( SV274 = SY2575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2161,plain,
! [SV635: $i,SV275: $i] :
( ( ! [SY2576: $i,SY2577: $i,SY2578: $i] :
( ( c_List_Ofoldr @ SV275 @ SV635 @ SY2576 @ SY2577 @ SY2578 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV275 @ SY2577 @ SY2578 @ SY2578 ) @ SY2576 @ ( c_List_Orev @ SV635 @ SY2577 ) @ SY2578 @ SY2577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2162,plain,
! [SV636: $i,SV276: $i] :
( ( ! [SY2579: $i,SY2580: $i,SY2581: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV276 @ SV636 @ SY2579 @ ( c_Lambda_OdB_OAbs @ SY2580 ) @ SY2581 )
= ( hAPP @ ( hAPP @ SY2579 @ SY2580 ) @ ( c_Lambda_OdB_OdB__rec @ SV276 @ SV636 @ SY2579 @ SY2580 @ SY2581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2163,plain,
! [SV637: $i,SV277: $i] :
( ( ! [SY2582: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ SV277 @ SV637 @ SY2582 ) @ SY2582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2164,plain,
! [SV278: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV278 ) )
= $true )
| ( ( ! [SY1936: $i,SY1937: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ SY1937 @ SV278 ) @ SV278 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ SY1937 @ SV278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(2165,plain,
! [SV279: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV279 ) )
= $true )
| ( ( ! [SY1938: $i,SY1939: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ SY1939 @ SV279 ) @ SV279 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ SY1939 @ SV279 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(2166,plain,
! [SV638: $i,SV280: $i] :
( ( ! [SY2583: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SV638 @ ( tc_fun @ SY2583 @ tc_bool ) ) @ ( tc_fun @ SY2583 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SV638 @ ( tc_fun @ SY2583 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2167,plain,
! [SV639: $i,SV281: $i] :
( ( ! [SY2584: $i,SY2585: $i,SY2586: $i,SY2587: $i] :
( ( c_List_Ofoldr @ SV281 @ ( c_List_Olist_OCons @ SV639 @ SY2584 @ SY2585 ) @ SY2586 @ SY2585 @ SY2587 )
= ( hAPP @ ( hAPP @ SV281 @ SV639 ) @ ( c_List_Ofoldr @ SV281 @ SY2584 @ SY2586 @ SY2585 @ SY2587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2168,plain,
! [SV640: $i,SV282: $i] :
( ( ! [SY2588: $i,SY2589: $i,SY2590: $i] :
( ~ ( hBOOL @ ( hAPP @ SV282 @ ( c_Lambda_OdB_OdB__case @ SV640 @ SY2588 @ SY2589 @ ( c_Lambda_OdB_OAbs @ SY2590 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ SY2589 @ SY2590 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2169,plain,
! [SV641: $i,SV283: $i] :
( ( ! [SY2591: $i,SY2592: $i,SY2593: $i] :
( ~ ( hBOOL @ ( hAPP @ SV283 @ ( c_Lambda_OdB_OdB__case @ SV641 @ SY2591 @ SY2592 @ ( c_Lambda_OdB_OAbs @ SY2593 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ SY2592 @ SY2593 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2170,plain,
! [SV642: $i,SV284: $i] :
( ( ! [SY2594: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV284 ) @ ( c_List_Olist_OCons @ SV642 @ SY2594 @ SV284 ) @ SV284 )
= ( c_List_Olist_OCons @ SV642 @ SY2594 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2171,plain,
! [SV285: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV285 ) )
= $true )
| ( ( ! [SY1957: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1957 @ SY1957 @ SV285 )
= SY1957 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(2172,plain,
! [SV643: $i,SV286: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV286 @ SV286 @ ( tc_fun @ SV643 @ tc_bool ) )
= SV286 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2173,plain,
! [SV644: $i,SV287: $i] :
( ( ! [SY2595: $i,SY2596: $i] :
( ! [SY2597: $i] :
( ( c_List_Olist_OCons @ SV287 @ SV644 @ SY2595 )
!= ( c_List_Olist_OCons @ SY2596 @ SY2597 @ SY2595 ) )
| ( SV287 = SY2596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2174,plain,
! [SV645: $i,SV288: $i] :
( ( ! [SY2598: $i,SY2599: $i,SY2600: $i] :
( ( ( c_List_Olist_OCons @ SV288 @ SV645 @ SY2598 )
!= ( c_List_Olist_OCons @ SY2599 @ SY2600 @ SY2598 ) )
| ( SV645 = SY2600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2175,plain,
! [SV646: $i,SV289: $i] :
( ( ! [SY2601: $i] :
( ( c_Type_Otyping @ SV289 @ SV646 @ SY2601 )
| ! [SY2602: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2602 ) @ SV646 ) )
| ~ ( c_Type_Otyping @ SV289 @ SY2602 @ SY2601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2176,plain,
! [SV290: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV290 ) )
= $true )
| ( ( ! [SY1970: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1970 @ SV290 )
| ! [SY1971: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY1970 @ SY1971 @ SV290 ) @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(2177,plain,
! [SV291: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV291 ) )
= $true )
| ( ( ! [SY1972: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1972 @ SV291 )
| ! [SY1973: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY1973 @ SY1972 @ SV291 ) @ SV291 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(2178,plain,
! [SV647: $i,SV292: $i] :
( ( ! [SY2603: $i,SY2604: $i,SY2605: $i] :
( ! [SY2606: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV647 @ SY2603 @ SY2604 ) @ SY2605 @ SY2606 @ SY2604 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SY2605 @ SY2606 @ SY2604 ) @ SV647 @ SY2603 @ SY2604 ) )
| ( SV647 = SY2605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2179,plain,
! [SV293: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV293 ) )
= $true )
| ( ( ! [SY1979: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SY1979 @ SV293 ) @ SV293 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1979 @ SV293 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(2180,plain,
! [SV648: $i,SV294: $i] :
( ( ! [SY2607: $i,SY2608: $i] :
( ( c_List_Ofilter @ SV294 @ ( c_List_Olist_OCons @ SV648 @ SY2607 @ SY2608 ) @ SY2608 )
= ( c_List_Ofilter @ SV294 @ SY2607 @ SY2608 ) )
| ( hBOOL @ ( hAPP @ SV294 @ SV648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2181,plain,
! [SV649: $i,SV295: $i] :
( ( ! [SY2609: $i,SY2610: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV295 @ SV649 @ ( tc_fun @ SY2609 @ tc_bool ) ) @ SY2610 ) )
| ~ ( hBOOL @ ( hAPP @ SV649 @ SY2610 ) )
| ~ ( hBOOL @ ( hAPP @ SV295 @ SY2610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2182,plain,
! [SV650: $i,SV296: $i] :
( ( ! [SY2611: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ SV296 @ SV650 @ SY2611 ) @ SY2611 )
= ( c_List_Ofilter @ SV296 @ ( c_List_Orev @ SV650 @ SY2611 ) @ SY2611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2183,plain,
! [SV651: $i,SV297: $i] :
( ( ! [SY2612: $i,SY2613: $i] :
( ! [SY2614: $i] :
( ( c_List_Oappend @ SV297 @ ( c_List_Olist_OCons @ SV651 @ ( c_List_Olist_ONil @ SY2612 ) @ SY2612 ) @ SY2612 )
!= ( c_List_Oappend @ SY2613 @ ( c_List_Olist_OCons @ SY2614 @ ( c_List_Olist_ONil @ SY2612 ) @ SY2612 ) @ SY2612 ) )
| ( SV297 = SY2613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2184,plain,
! [SV652: $i,SV298: $i] :
( ( ! [SY2615: $i,SY2616: $i,SY2617: $i] :
( ( ( c_List_Oappend @ SV298 @ ( c_List_Olist_OCons @ SV652 @ ( c_List_Olist_ONil @ SY2615 ) @ SY2615 ) @ SY2615 )
!= ( c_List_Oappend @ SY2616 @ ( c_List_Olist_OCons @ SY2617 @ ( c_List_Olist_ONil @ SY2615 ) @ SY2615 ) @ SY2615 ) )
| ( SV652 = SY2617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2185,plain,
! [SV653: $i,SV299: $i] :
( ( ! [SY2618: $i,SY2619: $i,SY2620: $i] :
( ~ ( hBOOL @ ( hAPP @ SV299 @ ( c_List_Olist_Olist__case @ SV653 @ SY2618 @ ( c_List_Olist_OCons @ SY2619 @ SY2620 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV299 @ ( hAPP @ ( hAPP @ SY2618 @ SY2619 ) @ SY2620 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2186,plain,
! [SV654: $i,SV300: $i] :
( ( ! [SY2621: $i,SY2622: $i,SY2623: $i] :
( ~ ( hBOOL @ ( hAPP @ SV300 @ ( c_List_Olist_Olist__case @ SV654 @ SY2621 @ ( c_List_Olist_OCons @ SY2622 @ SY2623 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV300 @ ( hAPP @ ( hAPP @ SY2621 @ SY2622 ) @ SY2623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2187,plain,
! [SV655: $i,SV301: $i] :
( ( ! [SY2624: $i,SY2625: $i,SY2626: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV301 @ SV655 @ SY2624 @ SY2625 ) @ SV655 @ SY2626 @ SY2625 )
= ( c_List_Olist__update @ SV301 @ SV655 @ SY2626 @ SY2625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2188,plain,
! [SV656: $i,SV302: $i] :
( ( ! [SY2627: $i,SY2628: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV302 @ SV656 @ SY2627 ) @ SY2628 @ SY2627 )
= ( c_List_Oappend @ SV302 @ ( c_List_Oappend @ SV656 @ SY2628 @ SY2627 ) @ SY2627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2189,plain,
! [SV657: $i,SV303: $i] :
( ( ! [SY2629: $i,SY2630: $i] :
( ( c_List_Oappend @ SV303 @ ( c_List_Oappend @ SV657 @ SY2629 @ SY2630 ) @ SY2630 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV303 @ SV657 @ SY2630 ) @ SY2629 @ SY2630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2190,plain,
! [SV658: $i,SV304: $i] :
( ( ! [SY2631: $i,SY2632: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV304 @ SV658 @ SY2631 ) @ SY2632 @ SY2631 )
= ( c_List_Oappend @ SV304 @ ( c_List_Oappend @ SV658 @ SY2632 @ SY2631 ) @ SY2631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2191,plain,
! [SV659: $i,SV305: $i] :
( ( ! [SY2633: $i,SY2634: $i] :
( ( c_List_Oappend @ SV305 @ ( c_List_Oappend @ SV659 @ SY2633 @ SY2634 ) @ SY2634 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV305 @ SV659 @ SY2634 ) @ SY2633 @ SY2634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2192,plain,
! [SV306: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV306 ) )
= $true )
| ( ( ! [SY2020: $i,SY2021: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SY2020 @ SY2021 @ SV306 ) @ SV306 )
| ~ ( c_List_Olinorder__class_Osorted @ SY2021 @ SV306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(2193,plain,
! [SV660: $i,SV307: $i] :
( ( ~ ( c_List_Olist__ex @ SV307 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2194,plain,
! [SV661: $i,SV309: $i] :
( ( ! [SY2635: $i] :
~ ( hBOOL @ ( hAPP @ SV309 @ ( c_List_Olist_Olist__case @ SV661 @ SY2635 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV309 @ SV661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2195,plain,
! [SV662: $i,SV310: $i] :
( ( ! [SY2636: $i,SY2637: $i] :
( ( c_List_Ofoldr @ SV310 @ ( c_List_Olist_ONil @ SV662 ) @ SY2636 @ SV662 @ SY2637 )
= SY2636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2196,plain,
! [SV311: $i] :
( ( ( ! [SY2028: $i] : ( hBOOL @ ( hAPP @ SV311 @ SY2028 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV311 @ ( v_sko__List__Xzip__Xinduct__2 @ SV311 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(2197,plain,
! [SV663: $i,SV312: $i] :
( ( ! [SY2638: $i] :
( ( c_List_Omap @ SV312 @ ( c_List_Olist_ONil @ SV663 ) @ SV663 @ SY2638 )
= ( c_List_Olist_ONil @ SY2638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2198,plain,
! [SV664: $i,SV313: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_ONil @ SV313 ) @ SV664 @ SV313 )
= ( c_List_Olist_ONil @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2199,plain,
! [SV314: $i] :
( ( ( ! [SY2032: $i] : ( hBOOL @ ( hAPP @ SV314 @ SY2032 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV314 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV314 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV314 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(2200,plain,
! [SV665: $i,SV315: $i] :
( ( ! [SY2639: $i,SY2640: $i] :
( ( c_List_Olist_Olist__rec @ SV315 @ SV665 @ ( c_List_Olist_ONil @ SY2639 ) @ SY2640 @ SY2639 )
= SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2201,plain,
! [SV316: $i] :
( ( ( ! [SY2036: $i] : ( hBOOL @ ( hAPP @ SV316 @ SY2036 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV316 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV316 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV316 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(2202,plain,
! [SV317: $i] :
( ( ( ! [SY2037: $i] : ( hBOOL @ ( hAPP @ SV317 @ SY2037 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV317 @ ( v_sko__List__Xtake__Xinduct__2 @ SV317 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV317 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(2203,plain,
! [SV318: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV318 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV318 ) @ SV318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(2204,plain,
! [SV666: $i,SV319: $i] :
( ( ! [SY2641: $i] :
( ( c_List_Ofiltermap @ SV319 @ ( c_List_Olist_ONil @ SV666 ) @ SV666 @ SY2641 )
= ( c_List_Olist_ONil @ SY2641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2205,plain,
! [SV667: $i,SV320: $i] :
( ( ( ( c_List_Olist_ONil @ SV320 )
!= ( c_List_Oremdups @ SV667 @ SV320 ) )
| ( SV667
= ( c_List_Olist_ONil @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2206,plain,
! [SV668: $i,SV321: $i] :
( ( ( c_List_Ofilter @ SV321 @ ( c_List_Olist_ONil @ SV668 ) @ SV668 )
= ( c_List_Olist_ONil @ SV668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2207,plain,
! [SV669: $i,SV322: $i] :
( ( ! [SY2642: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV322 ) @ SV669 @ SY2642 @ SV322 )
= ( c_List_Olist_ONil @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2208,plain,
! [SV670: $i,SV323: $i] :
( ( ! [SY2643: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV323 ) @ SV670 @ SY2643 @ SV323 )
= ( c_List_Olist_ONil @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2209,plain,
! [SV671: $i,SV324: $i] :
( ( ! [SY2644: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV324 ) @ SV671 @ SY2644 @ SV324 )
= ( c_List_Olist_ONil @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2210,plain,
! [SV325: $i] :
( ( ( ! [SY2048: $i] : ( hBOOL @ ( hAPP @ SV325 @ SY2048 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV325 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV325 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV325 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(2211,plain,
! [SV672: $i,SV326: $i] :
( ( ! [SY2645: $i] :
( ( c_List_Olist_OCons @ SV326 @ SV672 @ SY2645 )
!= ( c_List_Olist_ONil @ SY2645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2212,plain,
! [SV673: $i,SV327: $i] :
( ( ! [SY2646: $i] :
( ( c_List_Olist_OCons @ SV327 @ SV673 @ SY2646 )
!= ( c_List_Olist_ONil @ SY2646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2213,plain,
! [SV674: $i,SV328: $i] :
( ( ( c_List_Oremove1 @ SV328 @ ( c_List_Olist_ONil @ SV674 ) @ SV674 )
= ( c_List_Olist_ONil @ SV674 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2214,plain,
! [SV329: $i] :
( ( ( ! [SY2054: $i] : ( hBOOL @ ( hAPP @ SV329 @ SY2054 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV329 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV329 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(2215,plain,
! [SV675: $i,SV330: $i] :
( ( ! [SY2647: $i,SY2648: $i] :
( ( c_Map_Omap__upds @ SV330 @ SV675 @ ( c_List_Olist_ONil @ SY2647 ) @ SY2648 @ SY2647 )
= SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2216,plain,
! [SV676: $i,SV331: $i] :
( ( ! [SY2649: $i,SY2650: $i] :
( ( c_Map_Omap__upds @ SV331 @ ( c_List_Olist_ONil @ SV676 ) @ SY2649 @ SV676 @ SY2650 )
= SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2217,plain,
! [SV332: $i] :
( ( ( ! [SY2061: $i] : ( hBOOL @ ( hAPP @ SV332 @ SY2061 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV332 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV332 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV332 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(2218,plain,
! [SV677: $i,SV333: $i] :
( ( ! [SY2651: $i,SY2652: $i] :
( ( c_List_Olist_Olist__case @ SV333 @ SV677 @ ( c_List_Olist_ONil @ SY2651 ) @ SY2652 @ SY2651 )
= SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2219,plain,
! [SV678: $i,SV334: $i] :
( ( ( ( c_List_Orev @ SV334 @ SV678 )
!= ( c_List_Olist_ONil @ SV678 ) )
| ( SV334
= ( c_List_Olist_ONil @ SV678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2220,plain,
! [SV679: $i,SV335: $i] :
( ( ( c_List_Orotate @ SV335 @ ( c_List_Olist_ONil @ SV679 ) @ SV679 )
= ( c_List_Olist_ONil @ SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2221,plain,
! [SV336: $i] :
( ( ( ! [SY2067: $i] : ( hBOOL @ ( hAPP @ SV336 @ SY2067 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV336 @ ( v_sko__List__Xlist__Xinduct__2 @ SV336 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV336 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(2222,plain,
! [SV680: $i,SV337: $i] :
( ( ! [SY2653: $i] :
( ( c_List_Olist_ONil @ SV337 )
= ( c_List_Omap @ SV680 @ ( c_List_Olist_ONil @ SY2653 ) @ SY2653 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2223,plain,
! [SV681: $i,SV339: $i] :
( ( c_List_Olistrelp @ SV339 @ ( c_List_Olist_ONil @ SV681 ) @ ( c_List_Olist_ONil @ SV681 ) @ SV681 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2224,plain,
! [SV340: $i] :
( ( ( ! [SY2071: $i] : ( hBOOL @ ( hAPP @ SV340 @ SY2071 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV340 @ ( v_sko__List__Xmap__Xinduct__2 @ SV340 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV340 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(2225,plain,
! [SV682: $i,SV342: $i] :
( ( ! [SY2654: $i,SY2655: $i] :
( ( ( c_List_Olist__update @ SV342 @ SV682 @ SY2654 @ SY2655 )
!= ( c_List_Olist_ONil @ SY2655 ) )
| ( SV342
= ( c_List_Olist_ONil @ SY2655 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2226,plain,
! [SV683: $i,SV343: $i] :
( ( ! [SY2656: $i,SY2657: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV343 ) @ SV683 ) @ SY2656 @ SY2657 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV343 @ SY2656 @ SY2657 ) ) @ ( c_Lambda_Osubst @ SV683 @ SY2656 @ SY2657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2227,plain,
! [SV684: $i,SV344: $i] :
( ( ! [SY2658: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV344 ) @ SV684 )
!= ( c_Lambda_OdB_OAbs @ SY2658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2228,plain,
! [SV685: $i,SV345: $i] :
( ( ! [SY2659: $i] :
( ( c_Lambda_OdB_OAbs @ SV345 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV685 ) @ SY2659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2229,plain,
! [SV686: $i,SV346: $i] :
( ( ! [SY2660: $i,SY2661: $i,SY2662: $i,SY2663: $i] :
( ~ ( hBOOL @ ( hAPP @ SV346 @ ( c_Lambda_OdB_OdB__case @ SV686 @ SY2660 @ SY2661 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2662 ) @ SY2663 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ SY2660 @ SY2662 ) @ SY2663 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2230,plain,
! [SV687: $i,SV347: $i] :
( ( ! [SY2664: $i,SY2665: $i,SY2666: $i,SY2667: $i] :
( ~ ( hBOOL @ ( hAPP @ SV347 @ ( c_Lambda_OdB_OdB__case @ SV687 @ SY2664 @ SY2665 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2666 ) @ SY2667 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV347 @ ( hAPP @ ( hAPP @ SY2664 @ SY2666 ) @ SY2667 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2231,plain,
! [SV688: $i,SV348: $i] :
( ( ! [SY2668: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SV688 ) @ SY2668 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV348 @ SY2668 ) ) @ ( c_Lambda_Olift @ SV688 @ SY2668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2232,plain,
! [SV689: $i,SV349: $i] :
( ( ! [SY2669: $i,SY2670: $i,SY2671: $i,SY2672: $i] :
( ( c_Lambda_OdB_OdB__case @ SV349 @ SV689 @ SY2669 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2670 ) @ SY2671 ) @ SY2672 )
= ( hAPP @ ( hAPP @ SV689 @ SY2670 ) @ SY2671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2233,plain,
! [SV690: $i,SV350: $i] :
( ( ! [SY2673: $i,SY2674: $i,SY2675: $i,SY2676: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SY2673 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2674 ) @ SY2675 ) @ SY2676 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV690 @ SY2674 ) @ SY2675 ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SY2673 @ SY2674 @ SY2676 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SY2673 @ SY2675 @ SY2676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2234,plain,
! [SV691: $i,SV351: $i] :
( ( ! [SY2677: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV351 @ SV691 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2677 @ SV691 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV351 = SY2677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2235,plain,
! [SV692: $i,SV352: $i] :
( ( ! [SY2678: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV692 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SY2678 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV692 ) @ SY2678 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2236,plain,
! [SV693: $i,SV353: $i] :
( ( ! [SY2679: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV693 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2679 ) @ SV693 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV353 ) @ SY2679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2237,plain,
! [SV694: $i,SV354: $i] :
( ( ! [SY2680: $i,SY2681: $i] :
( ( c_Lambda_Oliftn @ SV354 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV694 ) @ SY2680 ) @ SY2681 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV354 @ SV694 @ SY2681 ) ) @ ( c_Lambda_Oliftn @ SV354 @ SY2680 @ SY2681 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2238,plain,
! [SV695: $i,SV355: $i] :
( ( ! [SY2682: $i,SY2683: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV355 ) @ SV695 ) @ SY2682 @ SY2683 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV355 @ SY2682 @ SY2683 ) ) @ ( c_Lambda_Osubstn @ SV695 @ SY2682 @ SY2683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2239,plain,
! [SV696: $i,SV356: $i] :
( ( ! [SY2684: $i] :
( ( SV356 = SV696 )
| ! [SY2685: $i,SY2686: $i] :
( ~ ( c_Type_Otyping @ SY2684 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2685 ) @ SY2686 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV696 )
| ~ ( c_Type_Otyping @ SY2684 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2685 ) @ SY2686 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2240,plain,
! [SV697: $i,SV357: $i] :
( ( ! [SY2687: $i,SY2688: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV357 ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY2687 ) @ SY2688 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2241,plain,
! [SV698: $i,SV358: $i] :
( ( ! [SY2689: $i,SY2690: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV358 ) ) @ SV698 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2689 ) @ SY2690 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2242,plain,
! [SV699: $i,SV359: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV359 )
!= ( c_Lambda_OdB_OVar @ SV699 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2243,plain,
! [SV700: $i,SV360: $i] :
( ( ! [SY2691: $i,SY2692: $i,SY2693: $i] :
( ~ ( hBOOL @ ( hAPP @ SV360 @ ( c_Lambda_OdB_OdB__case @ SV700 @ SY2691 @ SY2692 @ ( c_Lambda_OdB_OVar @ SY2693 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV360 @ ( hAPP @ SV700 @ SY2693 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2244,plain,
! [SV701: $i,SV361: $i] :
( ( ! [SY2694: $i,SY2695: $i,SY2696: $i] :
( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Lambda_OdB_OdB__case @ SV701 @ SY2694 @ SY2695 @ ( c_Lambda_OdB_OVar @ SY2696 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( hAPP @ SV701 @ SY2696 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2245,plain,
! [SV702: $i,SV362: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV362 ) @ SV702 @ SV362 )
= SV702 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2246,plain,
! [SV703: $i,SV363: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV363 ) ) @ SV703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2247,plain,
! [SV704: $i,SV364: $i] :
( ( ! [SY2697: $i,SY2698: $i,SY2699: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV364 @ SV704 @ SY2697 @ ( c_Lambda_OdB_OVar @ SY2698 ) @ SY2699 )
= ( hAPP @ SV364 @ SY2698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2248,plain,
! [SV705: $i,SV365: $i] :
( ( ( c_Lambda_OdB_OVar @ SV365 )
!= ( c_Lambda_OdB_OAbs @ SV705 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2249,plain,
! [SV706: $i,SV366: $i] :
( ( ! [SY2700: $i] :
( ( ( hAPP @ SV366 @ SV706 )
= SY2700 )
| ~ ( c_Type_Otyping @ SV366 @ ( c_Lambda_OdB_OVar @ SV706 ) @ SY2700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2250,plain,
! [SV707: $i,SV367: $i] :
( ( ! [SY2701: $i,SY2702: $i,SY2703: $i] :
( ( c_Lambda_OdB_OdB__case @ SV367 @ SV707 @ SY2701 @ ( c_Lambda_OdB_OVar @ SY2702 ) @ SY2703 )
= ( hAPP @ SV367 @ SY2702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2251,plain,
! [SV708: $i,SV368: $i] :
( ( c_Type_Otyping @ SV368 @ ( c_Lambda_OdB_OVar @ SV708 ) @ ( hAPP @ SV368 @ SV708 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2252,plain,
! [SV709: $i,SV369: $i] :
( ( ! [SY2704: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV369 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV709 @ SY2704 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2704
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2253,plain,
! [SV710: $i,SV371: $i] :
( ( ! [SY2705: $i,SY2706: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV371 ) @ SV710 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2705 @ SY2706 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV371
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2705 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV371 @ SV710 @ SY2705 @ SY2706 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2706
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2254,plain,
! [SV711: $i,SV372: $i] :
( ( ! [SY2707: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV372 @ SV711 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2707 ) )
| ( SV711
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2255,plain,
! [SV712: $i,SV374: $i] :
( ( ! [SY2708: $i,SY2709: $i] :
( ( c_List_Olistsp @ SV374 @ ( c_List_Oappend @ SV712 @ SY2708 @ SY2709 ) @ SY2709 )
| ~ ( c_List_Olistsp @ SV374 @ SY2708 @ SY2709 )
| ~ ( c_List_Olistsp @ SV374 @ SV712 @ SY2709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2256,plain,
! [SV713: $i,SV375: $i] :
( ( ! [SY2710: $i] :
( ( c_List_Olistsp @ SV375 @ SV713 @ SY2710 )
| ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV375 @ SV713 @ SY2710 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2257,plain,
! [SV714: $i,SV376: $i] :
( ( ! [SY2711: $i,SY2712: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV714 @ ( tc_fun @ SY2711 @ tc_bool ) ) @ SY2712 @ SY2711 )
| ~ ( c_List_Olistsp @ SV714 @ SY2712 @ SY2711 )
| ~ ( c_List_Olistsp @ SV376 @ SY2712 @ SY2711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2258,plain,
! [SV715: $i,SV377: $i] :
( ( ! [SY2713: $i] :
( ( c_List_Olistsp @ SV377 @ SV715 @ SY2713 )
| ! [SY2714: $i] :
~ ( c_List_Olistsp @ SV377 @ ( c_List_Oappend @ SY2714 @ SV715 @ SY2713 ) @ SY2713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2259,plain,
! [SV716: $i,SV378: $i] :
( ( ! [SY2715: $i] :
( ( c_List_Olistsp @ SV378 @ SV716 @ SY2715 )
| ! [SY2716: $i] :
~ ( c_List_Olistsp @ SV378 @ ( c_List_Oappend @ SV716 @ SY2716 @ SY2715 ) @ SY2715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2260,plain,
! [SV379: $i] :
( ( ( ! [SY2170: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV379 @ SY2170 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV379 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2261,plain,
! [SV380: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV380 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV380 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2262,plain,
! [SV717: $i,SV381: $i] :
( ( ! [SY2717: $i] :
( ! [SY2718: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV381 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2717 ) @ SY2718 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV381 = SY2717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2263,plain,
! [SV718: $i,SV382: $i] :
( ( ! [SY2719: $i,SY2720: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV382 ) @ SV718 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2719 ) @ SY2720 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV718 = SY2720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2264,plain,
! [SV719: $i,SV383: $i] :
( ( ! [SY2721: $i] :
( ( c_Lambda_OdB_OVar @ SV383 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV719 @ SY2721 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV383 )
= SV719 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2265,plain,
! [SV720: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP @ SV384 @ SV720 ) )
| ! [SY2722: $i] :
( ( hBOOL @ ( hAPP @ SY2722 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY2722 @ SV384 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2722 @ SV720 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2266,plain,
! [SV721: $i,SV385: $i] :
( ( ( hBOOL @ ( hAPP @ SV385 @ SV721 ) )
| ! [SY2723: $i] :
( ( hBOOL @ ( hAPP @ SV385 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2723 @ SV385 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV385 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2723 @ SV721 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2267,plain,
! [SV722: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP @ SV386 @ SV722 ) )
| ! [SY2724: $i] :
( ( hBOOL @ ( hAPP @ SY2724 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY2724 @ SV386 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2724 @ SV722 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2268,plain,
! [SV723: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ SV387 @ SV723 ) )
| ! [SY2725: $i] :
( ( hBOOL @ ( hAPP @ SV387 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2725 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2725 @ SV723 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2269,plain,
! [SV724: $i,SV388: $i] :
( ( ( c_List_Olistsp @ SV388 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV388 @ SV724 ) @ t_a )
| ( SV724
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV388 @ SV724 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2270,plain,
! [SV725: $i,SV389: $i] :
( ( ( hBOOL @ ( hAPP @ SV389 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV389 @ SV725 ) ) )
| ( SV725
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV389 @ SV725 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2271,plain,
! [SV726: $i,SV390: $i] :
( ( ( hBOOL @ ( hAPP @ SV390 @ SV726 ) )
| ! [SY2726: $i] :
( ( c_List_Olistsp @ SY2726 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2726 @ SV390 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV390 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2726 @ SV726 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2272,plain,
! [SV727: $i,SV391: $i] :
( ( ( hBOOL @ ( hAPP @ SV391 @ SV727 ) )
| ! [SY2727: $i] :
( ( c_List_Olistsp @ SY2727 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2727 @ SV391 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2727 @ SV727 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2273,plain,
! [SV728: $i,SV392: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV392 ) @ SV728 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV392 ) @ SV728 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2274,plain,
! [SV729: $i,SV393: $i] :
( ( ! [SY2728: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV729 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2728 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV729 )
= SY2728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2275,plain,
! [SV394: $i] :
( ( ( ! [SY2196: $i,SY2197: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV394 @ ( c_Lambda_OdB_OVar @ SY2196 ) @ SY2197 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV394 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2276,plain,
! [SV730: $i,SV396: $i] :
( ( ! [SY2729: $i] :
( ( ( c_Lambda_OdB_OVar @ SV396 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV730 @ SY2729 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2729
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2277,plain,
! [SV731: $i,SV397: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV397 ) @ SV731 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV731 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2278,plain,
! [SV732: $i,SV398: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV398 )
!= ( c_Lambda_OdB_OVar @ SV732 ) )
| ( SV398 = SV732 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2279,plain,
! [SV733: $i,SV399: $i] :
( ( ! [SY2730: $i] :
( ! [SY2731: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV399 ) @ SV733 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2730 ) @ SY2731 ) )
| ( SV399 = SY2730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2280,plain,
! [SV734: $i,SV400: $i] :
( ( ! [SY2732: $i,SY2733: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV400 ) @ SV734 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2732 ) @ SY2733 ) )
| ( SV734 = SY2733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2281,plain,
! [SV735: $i,SV401: $i] :
( ( ! [SY2734: $i] :
( ( c_Lambda_OdB_OVar @ SV401 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV735 ) @ SY2734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2282,plain,
! [SV736: $i,SV403: $i] :
( ( c_List_Olistsp @ SV403 @ ( c_List_Olist_ONil @ SV736 ) @ SV736 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2283,plain,
! [SV737: $i,SV404: $i] :
( ( ! [SY2735: $i,SY2736: $i,SY2737: $i,SY2738: $i] :
( ( hAPP @ ( c_COMBB @ SV404 @ SV737 @ SY2735 @ SY2736 @ SY2737 ) @ SY2738 )
= ( hAPP @ SV404 @ ( hAPP @ SV737 @ SY2738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2284,plain,
! [SV738: $i,SV405: $i] :
( ( ! [SY2739: $i,SY2740: $i,SY2741: $i,SY2742: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV405 @ SV738 @ SY2739 @ SY2740 ) @ SY2741 ) @ SY2742 )
= ( hAPP @ ( hAPP @ SV405 @ SY2742 ) @ SY2741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2285,plain,
! [SV739: $i,SV406: $i] :
( ( ! [SY2743: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV739 )
!= ( c_Lambda_OdB_OVar @ SY2743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2286,plain,
! [SV740: $i,SV407: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV407 @ SV740 ) )
| ~ ( class_Lattices_Olattice @ SV740 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2287,plain,
! [SV741: $i,SV408: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV408 @ SV741 ) )
| ~ ( class_Orderings_Opreorder @ SV741 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2288,plain,
! [SV742: $i,SV409: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV409 @ SV742 ) )
| ~ ( class_Lattices_Olattice @ SV742 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2289,plain,
! [SV743: $i,SV410: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV410 @ SV743 ) )
| ~ ( class_Orderings_Oorder @ SV743 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2290,plain,
! [SV744: $i,SV411: $i] :
( ( ! [SY2744: $i,SY2745: $i,SY2746: $i,SY2747: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV411 @ SV744 @ SY2744 @ SY2745 ) @ SY2746 ) @ SY2747 )
= ( hAPP @ ( hAPP @ SV411 @ SY2747 ) @ SY2746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2291,plain,
! [SV745: $i,SV412: $i] :
( ( ! [SY2748: $i,SY2749: $i,SY2750: $i,SY2751: $i] :
( ( hAPP @ ( c_COMBB @ SV412 @ SV745 @ SY2748 @ SY2749 @ SY2750 ) @ SY2751 )
= ( hAPP @ SV412 @ ( hAPP @ SV745 @ SY2751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2292,plain,
! [SV746: $i,SV413: $i] :
( ( c_fequal @ SV413 @ SV413 @ SV746 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2293,plain,
! [SV747: $i,SV414: $i] :
( ( ( SV414 = SV747 )
| ! [SY2752: $i] :
~ ( c_fequal @ SV414 @ SV747 @ SY2752 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2294,plain,
! [SV415: $i,SV1: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ SV1 @ SV415 ) @ ( tc_List_Olist @ SV415 ) )
!= ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SV415 ) ) )
= $true )
| ( ( ( c_List_Oremdups @ SV1 @ SV415 )
= SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2295,plain,
! [SV748: $i,SV416: $i,SV4: $i] :
( ( ! [SY2753: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SY2753 ) )
| ! [SY2754: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SY2754 ) @ SY2753 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SY2754 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2296,plain,
! [SV749: $i,SV417: $i,SV5: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV5 @ SV417 ) @ SV749 ) @ SV749 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2297,plain,
! [SV750: $i,SV418: $i,SV6: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV6 @ SV418 ) @ SV750 ) @ SV750 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2298,plain,
! [SV751: $i,SV419: $i,SV7: $i] :
( ( ! [SY2755: $i] :
( ! [SY2756: $i] :
( ( c_List_Oreplicate @ SV7 @ SV419 @ SV751 )
!= ( c_List_Oreplicate @ SY2755 @ SY2756 @ SV751 ) )
| ( SV7 = SY2755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2299,plain,
! [SV752: $i,SV420: $i,SV8: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV8 @ SV420 ) @ SV752 ) )
| ! [SY2757: $i,SY2758: $i] : ( c_ListOrder_Ostep1 @ SV8 @ ( c_List_Olist_OCons @ SV420 @ SY2757 @ SY2758 ) @ ( c_List_Olist_OCons @ SV752 @ SY2757 @ SY2758 ) @ SY2758 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2300,plain,
! [SV753: $i,SV421: $i,SV9: $i] :
( ( ! [SY2759: $i] :
( ( SV9 = SV421 )
| ( SV753 = SY2759 )
| ! [SY2760: $i,SY2761: $i] :
~ ( c_ListOrder_Ostep1 @ SY2760 @ ( c_List_Olist_OCons @ SV421 @ SY2759 @ SY2761 ) @ ( c_List_Olist_OCons @ SV9 @ SV753 @ SY2761 ) @ SY2761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2301,plain,
! [SV10: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV10 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(2302,plain,
! [SV754: $i,SV422: $i,SV11: $i] :
( ( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV11 @ ( tc_List_Olist @ SV422 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV754 @ SV11 @ SV422 ) @ ( tc_List_Olist @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2303,plain,
! [SV755: $i,SV423: $i,SV12: $i] :
( ( ! [SY2762: $i,SY2763: $i] :
( ( c_ListOrder_Ostep1 @ SV12 @ ( c_List_Oappend @ SV423 @ SV755 @ SY2762 ) @ ( c_List_Oappend @ SV423 @ SY2763 @ SY2762 ) @ SY2762 )
| ~ ( c_ListOrder_Ostep1 @ SV12 @ SV755 @ SY2763 @ SY2762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2304,plain,
! [SV756: $i,SV424: $i,SV13: $i] :
( ( ! [SY2764: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV13 @ SV424 @ SV756 @ SY2764 )
| ! [SY2765: $i] : ( c_ListOrder_Ostep1 @ SV13 @ ( c_List_Oappend @ SV424 @ SY2765 @ SY2764 ) @ ( c_List_Oappend @ SV756 @ SY2765 @ SY2764 ) @ SY2764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2305,plain,
! [SV757: $i,SV425: $i,SV14: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV14 @ SV425 @ SV757 ) @ ( tc_List_Olist @ SV757 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV425 @ ( tc_List_Olist @ SV757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2306,plain,
! [SV426: $i,SV15: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV15 ) )
= $true )
| ( ( ! [SY2263: $i] :
( ( c_HOL_Oord__class_Oless @ SV426 @ SY2263 @ SV15 )
| ! [SY2264: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2264 @ SY2263 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV426 @ SY2264 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(2307,plain,
! [SV427: $i,SV16: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV16 ) )
= $true )
| ( ( ! [SY2265: $i] :
( ( c_HOL_Oord__class_Oless @ SV427 @ SY2265 @ SV16 )
| ! [SY2266: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV427 @ SY2266 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SY2266 @ SY2265 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(2308,plain,
! [SV758: $i,SV428: $i,SV19: $i] :
( ( ( c_List_Oreplicate @ ( c_Suc @ SV19 ) @ SV428 @ SV758 )
= ( c_List_Olist_OCons @ SV428 @ ( c_List_Oreplicate @ SV19 @ SV428 @ SV758 ) @ SV758 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2309,plain,
! [SV429: $i,SV22: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV22 ) @ SV429 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV22 )
= SV429 )
| ~ ( c_HOL_Oord__class_Oless @ SV22 @ SV429 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2310,plain,
! [SV430: $i,SV23: $i] :
( ( ( SV23
= ( c_List_Olist_ONil @ SV430 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV23 @ ( tc_List_Olist @ SV430 ) ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2311,plain,
! [SV759: $i,SV431: $i,SV24: $i] :
( ( ! [SY2766: $i] :
( ( SV24 = SV431 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ SV431 ) @ SV24 ) )
| ! [SY2767: $i,SY2768: $i] :
~ ( c_ListOrder_Ostep1 @ SV759 @ ( c_List_Olist_OCons @ SV431 @ SY2766 @ SY2767 ) @ ( c_List_Olist_OCons @ SV24 @ SY2768 @ SY2767 ) @ SY2767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2312,plain,
! [SV760: $i,SV432: $i,SV25: $i] :
( ( ( c_List_Orotate @ ( c_Suc @ SV25 ) @ SV432 @ SV760 )
= ( c_List_Orotate1 @ ( c_List_Orotate @ SV25 @ SV432 @ SV760 ) @ SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2313,plain,
! [SV761: $i,SV26: $i] :
( ( ( ! [SY2769: $i] :
( ( c_List_Olast @ ( c_List_Oreplicate @ SV26 @ SV761 @ SY2769 ) @ SY2769 )
= SV761 ) )
= $true )
| ( ( SV26
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2314,plain,
! [SV762: $i,SV433: $i,SV27: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV27 @ SV433 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV762 @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2315,plain,
! [SV763: $i,SV435: $i,SV29: $i] :
( ( ! [SY2770: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV29 @ SV435 @ SV763 @ SY2770 ) @ ( tc_List_Olist @ SY2770 ) )
= ( c_Nat_Osize__class_Osize @ SV29 @ ( tc_List_Olist @ SY2770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2316,plain,
! [SV436: $i,SV31: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV31 @ SV436 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV436 @ ( c_Suc @ SV31 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2317,plain,
! [SV437: $i,SV32: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV32 @ ( c_Suc @ SV437 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV437 @ SV32 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2318,plain,
! [SV764: $i,SV438: $i,SV33: $i] :
( ( ! [SY2771: $i,SY2772: $i] :
( ( ( c_List_Oreplicate @ SV33 @ SV438 @ SV764 )
!= ( c_List_Oreplicate @ SY2771 @ SY2772 @ SV764 ) )
| ( SV438 = SY2772 )
| ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2319,plain,
! [SV440: $i,SV36: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV36 ) @ ( c_Suc @ SV440 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV36 @ SV440 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2320,plain,
! [SV441: $i,SV37: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV37 @ SV441 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV37 ) @ ( c_Suc @ SV441 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2321,plain,
! [SV442: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV38 ) @ ( c_Suc @ SV442 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV442 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2322,plain,
! [SV765: $i,SV443: $i,SV40: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV40 @ SV443 @ ( c_List_Olist_ONil @ SV765 ) @ SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2323,plain,
! [SV766: $i,SV444: $i,SV41: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Olist_ONil @ SV444 ) @ SV766 @ SV444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2324,plain,
! [SV445: $i,SV42: $i] :
( ( ( ( c_List_Orotate1 @ SV42 @ SV445 )
!= ( c_List_Olist_ONil @ SV445 ) )
= $true )
| ( ( SV42
= ( c_List_Olist_ONil @ SV445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2325,plain,
! [SV446: $i,SV44: $i] :
( ( ( ( c_List_Oremdups @ SV44 @ SV446 )
!= SV44 )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ SV44 @ SV446 ) @ ( tc_List_Olist @ SV446 ) )
= ( c_Nat_Osize__class_Osize @ SV44 @ ( tc_List_Olist @ SV446 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2326,plain,
! [SV767: $i,SV447: $i,SV45: $i] :
( ( ! [SY2773: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV45 @ SV447 @ SV767 @ SY2773 ) @ ( tc_List_Olist @ SY2773 ) )
= ( c_Nat_Osize__class_Osize @ SV447 @ ( tc_List_Olist @ SV767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2327,plain,
! [SV768: $i,SV448: $i,SV46: $i] :
( ( ! [SY2774: $i,SY2775: $i] :
( ( c_List_Omap @ SV46 @ ( c_List_Oreplicate @ SV448 @ SV768 @ SY2774 ) @ SY2774 @ SY2775 )
= ( c_List_Oreplicate @ SV448 @ ( hAPP @ SV46 @ SV768 ) @ SY2775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2328,plain,
! [SV769: $i,SV449: $i,SV47: $i] :
( ( ( c_List_Orev @ ( c_List_Oreplicate @ SV47 @ SV449 @ SV769 ) @ SV769 )
= ( c_List_Oreplicate @ SV47 @ SV449 @ SV769 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2329,plain,
! [SV450: $i,SV48: $i] :
( ( ( ( c_Suc @ SV48 )
!= ( c_Suc @ SV450 ) )
= $true )
| ( ( SV48 = SV450 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2330,plain,
! [SV451: $i,SV49: $i] :
( ( ( ( c_Suc @ SV49 )
!= ( c_Suc @ SV451 ) )
= $true )
| ( ( SV49 = SV451 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(2331,plain,
! [SV770: $i,SV452: $i,SV50: $i] :
( ( ! [SY2776: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV452 ) @ SV770 ) @ SY2776 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV770 ) @ SY2776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2332,plain,
! [SV771: $i,SV453: $i,SV51: $i] :
( ( ! [SY2777: $i] :
( ( c_List_Ofilter @ SV51 @ ( c_List_Oreplicate @ SV453 @ SV771 @ SY2777 ) @ SY2777 )
= ( c_List_Oreplicate @ SV453 @ SV771 @ SY2777 ) )
| ~ ( hBOOL @ ( hAPP @ SV51 @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2333,plain,
! [SV772: $i,SV454: $i,SV52: $i] :
( ( ! [SY2778: $i,SY2779: $i] :
( ( ( c_List_Omap @ SV52 @ SV454 @ SV772 @ SY2778 )
!= ( c_List_Omap @ SV52 @ SY2779 @ SV772 @ SY2778 ) )
| ( ( c_Nat_Osize__class_Osize @ SV454 @ ( tc_List_Olist @ SV772 ) )
= ( c_Nat_Osize__class_Osize @ SY2779 @ ( tc_List_Olist @ SV772 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2334,plain,
! [SV455: $i,SV54: $i] :
( ( ( SV54 = SV455 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV455 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SV455 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2335,plain,
! [SV456: $i,SV55: $i] :
( ( ( SV55 = SV456 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV456 @ ( c_Suc @ SV55 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV456 @ SV55 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2336,plain,
! [SV457: $i,SV56: $i] :
( ( ( SV56 = SV457 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV56 @ ( c_Suc @ SV457 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV56 @ SV457 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2337,plain,
! [SV773: $i,SV458: $i,SV57: $i] :
( ( ! [SY2780: $i] :
( ! [SY2781: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV57 @ SV458 @ SV773 ) @ SY2780 @ SY2781 @ SV773 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV57 @ SY2780 @ SY2781 @ SV773 ) @ SV458 @ SV773 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2780 @ ( c_Nat_Osize__class_Osize @ SV57 @ ( tc_List_Olist @ SV773 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2338,plain,
! [SV774: $i,SV459: $i,SV58: $i] :
( ( ! [SY2782: $i] :
( ! [SY2783: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV58 @ SV459 @ SV774 ) @ SY2782 @ SY2783 @ SV774 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV58 @ SY2782 @ SY2783 @ SV774 ) @ SV459 @ SV774 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2782 @ ( c_Nat_Osize__class_Osize @ SV58 @ ( tc_List_Olist @ SV774 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2339,plain,
! [SV775: $i,SV460: $i,SV59: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ SV59 @ SV460 @ SV775 ) @ ( tc_List_Olist @ SV775 ) )
= ( c_Nat_Osize__class_Osize @ SV460 @ ( tc_List_Olist @ SV775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2340,plain,
! [SV64: $i] :
( ( ( class_Orderings_Oorder @ SV64 )
= $false )
| ( ( ! [SY1438: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1438 @ SY1438 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2341,plain,
! [SV65: $i] :
( ( ( class_Orderings_Olinorder @ SV65 )
= $false )
| ( ( ! [SY1439: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1439 @ SY1439 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2342,plain,
! [SV66: $i] :
( ( ( class_Orderings_Opreorder @ SV66 )
= $false )
| ( ( ! [SY1440: $i] :
~ ( c_HOL_Oord__class_Oless @ SY1440 @ SY1440 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2343,plain,
! [SV776: $i,SV463: $i,SV67: $i] :
( ( ! [SY2784: $i] :
( ( c_ListOrder_Ostep1 @ SV67 @ SV463 @ SV776 @ SY2784 )
| ( SV776 = SV463 )
| ! [SY2785: $i,SY2786: $i] :
~ ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SY2785 @ SV463 @ SY2784 ) @ ( c_List_Olist_OCons @ SY2786 @ SV776 @ SY2784 ) @ SY2784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2344,plain,
! [SV68: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV68 )
= $false )
| ( ( ! [SY1446: $i,SY1447: $i] :
( ( c_HOL_Oord__class_Oless @ SY1446 @ SY1447 @ SV68 )
| ( SY1447 = SY1446 )
| ( c_HOL_Oord__class_Oless @ SY1447 @ SY1446 @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2345,plain,
! [SV69: $i] :
( ( ( class_Orderings_Olinorder @ SV69 )
= $false )
| ( ( ! [SY1448: $i,SY1449: $i] :
( ( SY1448 = SY1449 )
| ( c_HOL_Oord__class_Oless @ SY1449 @ SY1448 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SY1448 @ SY1449 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2346,plain,
! [SV464: $i,SV70: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV70 @ SV464 @ tc_nat )
= $true )
| ( ( ( SV464 = SV70 )
| ( c_HOL_Oord__class_Oless @ SV464 @ SV70 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2347,plain,
! [SV777: $i,SV465: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV465 ) @ SV777 ) )
| ( c_HOL_Oord__class_Oless @ SV465 @ SV777 @ tc_nat )
| ( SV777 = SV465 )
| ( c_HOL_Oord__class_Oless @ SV777 @ SV465 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2348,plain,
! [SV466: $i,SV72: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV72 @ SV466 @ tc_nat )
= $true )
| ( ( ( SV466 = SV72 )
| ( c_HOL_Oord__class_Oless @ SV466 @ SV72 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2349,plain,
! [SV73: $i] :
( ( ( class_Orderings_Olinorder @ SV73 )
= $false )
| ( ( ! [SY1454: $i,SY1455: $i] :
( ( c_HOL_Oord__class_Oless @ SY1454 @ SY1455 @ SV73 )
| ( SY1455 = SY1454 )
| ( c_HOL_Oord__class_Oless @ SY1455 @ SY1454 @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2350,plain,
! [SV778: $i,SV467: $i,SV74: $i] :
( ( ! [SY2787: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV467 @ SV778 ) @ ( c_List_Oreplicate @ SY2787 @ SV467 @ SV778 ) @ SV778 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY2787 @ SV467 @ SV778 ) @ ( c_List_Oreplicate @ SV74 @ SV467 @ SV778 ) @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2351,plain,
! [SV75: $i] :
( ( ( class_Orderings_Olinorder @ SV75 )
= $false )
| ( ( ! [SY1459: $i,SY1460: $i] :
( ( c_HOL_Oord__class_Oless @ SY1459 @ SY1460 @ SV75 )
| ( SY1460 = SY1459 )
| ( c_HOL_Oord__class_Oless @ SY1460 @ SY1459 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2352,plain,
! [SV76: $i] :
( ( ( class_Orderings_Olinorder @ SV76 )
= $false )
| ( ( ! [SY1461: $i,SY1462: $i] :
( ( SY1461 = SY1462 )
| ( c_HOL_Oord__class_Oless @ SY1461 @ SY1462 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SY1462 @ SY1461 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2353,plain,
! [SV468: $i,SV77: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV77 ) )
= $true )
| ( ( ! [SY2308: $i,SY2309: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV468 @ SY2308 @ SV77 ) @ SY2309 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SY2308 @ SY2309 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2354,plain,
! [SV469: $i,SV78: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV78 ) )
= $true )
| ( ( ! [SY2310: $i,SY2311: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV469 @ SY2310 @ SV78 ) @ SY2311 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SY2311 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(2355,plain,
! [SV470: $i,SV83: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV83 ) @ SV470 @ tc_nat )
= $true )
| ( ( ! [SY2312: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2312 @ SV470 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV83 @ SY2312 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2356,plain,
! [SV779: $i,SV84: $i] :
( ( ( ! [SY2788: $i] :
( ( c_List_Oreplicate @ SV84 @ SV779 @ SY2788 )
!= ( c_List_Olist_ONil @ SY2788 ) ) )
= $true )
| ( ( SV84
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2357,plain,
! [SV780: $i,SV472: $i,SV87: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV87 @ SV472 @ SV780 ) @ ( tc_List_Olist @ SV780 ) )
= SV87 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2358,plain,
! [SV473: $i,SV88: $i] :
( ( ( ! [SY2314: $i] :
( ( c_List_Olist_ONil @ SV88 )
!= ( c_List_Oreplicate @ SV473 @ SY2314 @ SV88 ) ) )
= $true )
| ( ( SV473
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2359,plain,
! [SV474: $i,SV89: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV89 @ ( tc_List_Olist @ SV474 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV89
= ( c_List_Olist_ONil @ SV474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2360,plain,
! [SV781: $i,SV475: $i,SV92: $i] :
( ( ! [SY2789: $i] :
( ( c_ListOrder_Ostep1 @ SV92 @ SV475 @ SV781 @ SY2789 )
| ! [SY2790: $i,SY2791: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY2790 ) @ SY2791 ) )
| ~ ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SY2790 @ SV475 @ SY2789 ) @ ( c_List_Olist_OCons @ SY2791 @ SV781 @ SY2789 ) @ SY2789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2361,plain,
! [SV782: $i,SV476: $i,SV93: $i] :
( ( ! [SY2792: $i,SY2793: $i] :
( ( c_ListOrder_Ostep1 @ SV93 @ ( c_List_Olist_OCons @ SV476 @ SV782 @ SY2792 ) @ ( c_List_Olist_OCons @ SV476 @ SY2793 @ SY2792 ) @ SY2792 )
| ~ ( c_ListOrder_Ostep1 @ SV93 @ SV782 @ SY2793 @ SY2792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2362,plain,
! [SV477: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV94 @ SV477 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV477 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2363,plain,
! [SV478: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Suc @ SV478 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV95 @ SV478 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2364,plain,
! [SV783: $i,SV480: $i,SV97: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Orotate @ SV97 @ SV480 @ SV783 ) @ SV783 )
= ( c_List_Orotate @ SV97 @ ( c_List_Orotate1 @ SV480 @ SV783 ) @ SV783 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2365,plain,
! [SV98: $i] :
( ( ( class_Orderings_Oorder @ SV98 )
= $false )
| ( ( ! [SY1493: $i,SY1494: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1493 @ SY1494 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY1494 @ SY1493 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2366,plain,
! [SV784: $i,SV481: $i,SV99: $i] :
( ( ! [SY2794: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV784 ) @ SY2794 ) )
| ! [SY2795: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SY2795 ) @ SY2794 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SV784 ) @ SY2795 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2367,plain,
! [SV785: $i,SV482: $i,SV100: $i] :
( ( ! [SY2796: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SY2796 ) )
| ! [SY2797: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SY2797 ) @ SY2796 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SY2797 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2368,plain,
! [SV101: $i] :
( ( ( class_Orderings_Olinorder @ SV101 )
= $false )
| ( ( ! [SY1503: $i,SY1504: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1503 @ SY1504 @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SY1504 @ SY1503 @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2369,plain,
! [SV102: $i] :
( ( ( class_Orderings_Opreorder @ SV102 )
= $false )
| ( ( ! [SY1505: $i,SY1506: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1505 @ SY1506 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SY1506 @ SY1505 @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2370,plain,
! [SV103: $i] :
( ( ( class_Orderings_Opreorder @ SV103 )
= $false )
| ( ( ! [SY1507: $i,SY1508: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY1507 @ SY1508 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SY1508 @ SY1507 @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2371,plain,
! [SV483: $i,SV104: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV104 @ SV483 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV104 @ SV483 ) @ ( c_List_Olist_ONil @ SV483 ) @ SV483 ) @ SV483 )
= SV104 )
= $true )
| ( ( SV104
= ( c_List_Olist_ONil @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2372,plain,
! [SV786: $i,SV484: $i,SV105: $i] :
( ( ( SV105
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 ) @ SV786 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 ) @ ( c_List_Oappend @ SV786 @ ( c_List_Olist_OCons @ SV484 @ ( 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)],[1995]) ).
thf(2373,plain,
! [SV787: $i,SV485: $i,SV106: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV106 @ SV485 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV787 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV106 @ ( c_List_Oappend @ SV485 @ ( c_List_Olist_OCons @ SV787 @ ( 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)],[1996]) ).
thf(2374,plain,
! [SV486: $i,SV107: $i] :
( ( ( ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV486 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ! [SY2331: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2331 @ SV107 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV486 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2331 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV486 @ ( 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)],[1997]) ).
thf(2375,plain,
! [SV788: $i,SV108: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV108 ) @ SV788 @ SV108 )
= ( c_Lambda_Oliftn @ SV108 @ SV788 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV108 @ SV108 @ tc_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2376,plain,
! [SV789: $i,SV487: $i,SV109: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV109 @ SV487 @ SV789 ) @ SV789 )
= ( c_List_Olast @ SV487 @ SV789 ) )
| ( SV487
= ( c_List_Olist_ONil @ SV789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2377,plain,
! [SV790: $i,SV490: $i,SV112: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV112 @ SV490 @ SV790 ) @ SV790 )
= ( c_List_Olist_OCons @ SV112 @ ( c_List_Obutlast @ SV490 @ SV790 ) @ SV790 ) )
| ( SV490
= ( c_List_Olist_ONil @ SV790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2378,plain,
! [SV791: $i,SV491: $i,SV113: $i] :
( ( ! [SY2798: $i,SY2799: $i] :
( ( ( c_List_Oappend @ SV113 @ SV491 @ SV791 )
!= ( c_List_Olist_OCons @ SY2798 @ SY2799 @ SV791 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2798 @ SY2799 @ SV113 @ SV491 @ SV791 ) @ SV491 @ SV791 )
= SY2799 )
| ( SV491
= ( c_List_Olist_OCons @ SY2798 @ SY2799 @ SV791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2379,plain,
! [SV792: $i,SV492: $i,SV114: $i] :
( ( ! [SY2800: $i,SY2801: $i] :
( ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
!= ( c_List_Oappend @ SY2800 @ SY2801 @ SV792 ) )
| ( ( c_List_Olist_OCons @ SV114 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV114 @ SV492 @ SY2800 @ SY2801 @ SV792 ) @ SV792 )
= SY2800 )
| ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
= SY2801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2380,plain,
! [SV793: $i,SV493: $i,SV115: $i] :
( ( ! [SY2802: $i,SY2803: $i] :
( ( ( c_List_Oappend @ SV115 @ SV493 @ SV793 )
!= ( c_List_Olist_OCons @ SY2802 @ SY2803 @ SV793 ) )
| ( SV115
= ( c_List_Olist_OCons @ SY2802 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2802 @ SY2803 @ SV115 @ SV493 @ SV793 ) @ SV793 ) )
| ( SV493
= ( c_List_Olist_OCons @ SY2802 @ SY2803 @ SV793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2381,plain,
! [SV794: $i,SV494: $i,SV116: $i] :
( ( ! [SY2804: $i,SY2805: $i] :
( ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
!= ( c_List_Oappend @ SY2804 @ SY2805 @ SV794 ) )
| ( SV494
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV116 @ SV494 @ SY2804 @ SY2805 @ SV794 ) @ SY2805 @ SV794 ) )
| ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
= SY2805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2382,plain,
! [SV795: $i,SV495: $i,SV117: $i] :
( ( ! [SY2806: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV117 @ SV495 @ SV795 ) @ ( c_List_Olist_OCons @ SV495 @ SY2806 @ SV795 ) @ SV795 )
= ( c_List_Olist_OCons @ SV495 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV117 @ SV495 @ SV795 ) @ SY2806 @ SV795 ) @ SV795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2383,plain,
! [SV796: $i,SV497: $i,SV119: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV119 @ SV497 @ SV796 ) @ SV796 )
= ( c_List_Olast @ SV497 @ SV796 ) )
| ( SV497
= ( c_List_Olist_ONil @ SV796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2384,plain,
! [SV797: $i,SV499: $i,SV121: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV121 @ SV499 @ SV797 ) @ SV797 )
= ( c_List_Oappend @ SV121 @ ( c_List_Obutlast @ SV499 @ SV797 ) @ SV797 ) )
| ( SV499
= ( c_List_Olist_ONil @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2385,plain,
! [SV798: $i,SV500: $i,SV122: $i] :
( ( ! [SY2807: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV500 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV798 ) @ SY2807 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV500 ) @ SY2807 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2386,plain,
! [SV799: $i,SV501: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV501 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV799 ) @ SV501 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SV799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2387,plain,
! [SV800: $i,SV502: $i,SV124: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV502 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV800 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV502 ) @ SV800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2388,plain,
! [SV503: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV125 ) ) @ ( c_Lambda_OdB_OAbs @ SV503 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV125 ) @ SV503 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2389,plain,
! [SV801: $i,SV504: $i,SV126: $i] :
( ( ! [SY2808: $i] :
( ( c_List_Ofilter @ SV126 @ ( c_List_Oreplicate @ SV504 @ SV801 @ SY2808 ) @ SY2808 )
= ( c_List_Olist_ONil @ SY2808 ) )
| ( hBOOL @ ( hAPP @ SV126 @ SV801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2390,plain,
! [SV802: $i,SV505: $i,SV127: $i] :
( ( ! [SY2809: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV127 @ SV505 @ SV802 ) ) @ ( c_Lambda_Osubst @ SV127 @ SY2809 @ SV802 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV505 ) @ SY2809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2391,plain,
! [SV803: $i,SV506: $i,SV128: $i] :
( ( ! [SY2810: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV128 @ SV506 @ SV803 ) ) @ ( c_Lambda_Osubst @ SY2810 @ SV506 @ SV803 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SY2810 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2392,plain,
! [SV804: $i,SV507: $i,SV129: $i] :
( ( ! [SY2811: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV507 @ SV804 ) ) @ ( c_Lambda_Osubst @ SV129 @ SY2811 @ SV804 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV507 ) @ SY2811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2393,plain,
! [SV805: $i,SV508: $i,SV130: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV130 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV508 @ SV130 @ SV805 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV508 ) @ SV130 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2394,plain,
! [SV806: $i,SV509: $i,SV131: $i] :
( ( ! [SY2812: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV131 @ SV509 @ SV806 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2812 @ SV806 )
= ( c_List_Olist_OCons @ SY2812 @ SV509 @ SV806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2395,plain,
! [SV807: $i,SV510: $i,SV132: $i] :
( ( ! [SY2813: $i,SY2814: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV132 @ SV510 @ SV807 ) @ ( c_Suc @ SY2813 ) @ SY2814 @ SV807 )
= ( c_List_Olist_OCons @ SV132 @ ( c_List_Olist__update @ SV510 @ SY2813 @ SY2814 @ SV807 ) @ SV807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2396,plain,
! [SV808: $i,SV133: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV133 ) @ SV808 @ SV133 )
= SV808 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV133 @ SV133 @ tc_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2397,plain,
! [SV809: $i,SV511: $i,SV134: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV134 ) @ SV511 @ SV809 )
= ( c_Lambda_OdB_OVar @ SV134 ) )
| ( SV134 = SV809 )
| ( c_HOL_Oord__class_Oless @ SV809 @ SV134 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2398,plain,
! [SV810: $i,SV512: $i,SV135: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV135 ) @ SV512 @ SV810 )
= ( c_Lambda_OdB_OVar @ SV135 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV135 @ SV810 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2399,plain,
! [SV811: $i,SV513: $i,SV136: $i] :
( ( ( c_Type_Otyping @ SV136 @ SV513 @ SV811 )
| ! [SY2815: $i] :
( ~ ( c_Type_Otyping @ SV136 @ SY2815 @ SV811 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2815 ) @ SV513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2400,plain,
! [SV812: $i,SV514: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV137 @ SV514 ) ) @ ( c_Lambda_Olift @ SV812 @ SV514 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV137 ) @ SV812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2401,plain,
! [SV813: $i,SV515: $i,SV138: $i] :
( ( ! [SY2816: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV138 @ ( tc_List_Olist @ SV515 ) )
!= ( c_Nat_Osize__class_Osize @ SV813 @ ( tc_List_Olist @ SY2816 ) ) )
| ! [SY2817: $i,SY2818: $i] :
( ( c_Map_Omap__upds @ SY2817 @ ( c_List_Oappend @ SV138 @ SY2818 @ SV515 ) @ SV813 @ SV515 @ SY2816 )
= ( c_Map_Omap__upds @ SY2817 @ SV138 @ SV813 @ SV515 @ SY2816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2402,plain,
! [SV814: $i,SV516: $i,SV139: $i] :
( ( ! [SY2819: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV139 @ ( tc_List_Olist @ SV516 ) )
!= ( c_Nat_Osize__class_Osize @ SV814 @ ( tc_List_Olist @ SY2819 ) ) )
| ! [SY2820: $i,SY2821: $i] :
( ( c_Map_Omap__upds @ SY2820 @ SV139 @ ( c_List_Oappend @ SV814 @ SY2821 @ SY2819 ) @ SV516 @ SY2819 )
= ( c_Map_Omap__upds @ SY2820 @ SV139 @ SV814 @ SV516 @ SY2819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2403,plain,
! [SV517: $i,SV140: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV140 ) @ SV517 )
= ( c_Lambda_OdB_OVar @ SV140 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV140 @ SV517 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2404,plain,
! [SV815: $i,SV518: $i,SV141: $i] :
( ( ( ( c_Lambda_Oliftn @ SV141 @ ( c_Lambda_OdB_OVar @ SV518 ) @ SV815 )
= ( c_Lambda_OdB_OVar @ SV518 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV518 @ SV815 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2405,plain,
! [SV519: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP @ SV142 @ SV519 ) )
= $true )
| ( ( ! [SY2382: $i,SY2383: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV142 @ SY2382 @ ( tc_fun @ SY2383 @ tc_bool ) ) @ SV519 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2406,plain,
! [SV143: $i] :
( ( ( class_Orderings_Olinorder @ SV143 )
= $false )
| ( ( ! [SY1603: $i] : ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1603 @ ( c_List_Olist_ONil @ SV143 ) @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2407,plain,
! [SV520: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV144 ) ) @ ( c_Lambda_OdB_OAbs @ SV520 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV144 ) @ SV520 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2408,plain,
! [SV816: $i,SV521: $i,SV145: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ SV145 @ SV521 @ SV816 ) @ SV816 )
= ( c_List_Oappend @ ( c_List_Orev @ SV521 @ SV816 ) @ ( c_List_Orev @ SV145 @ SV816 ) @ SV816 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2409,plain,
! [SV817: $i,SV522: $i,SV146: $i] :
( ( ! [SY2822: $i,SY2823: $i,SY2824: $i] :
( ( c_List_Ofoldl @ SV146 @ SV522 @ ( c_List_Oappend @ SV817 @ SY2822 @ SY2823 ) @ SY2824 @ SY2823 )
= ( c_List_Ofoldl @ SV146 @ ( c_List_Ofoldl @ SV146 @ SV522 @ SV817 @ SY2824 @ SY2823 ) @ SY2822 @ SY2824 @ SY2823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2410,plain,
! [SV818: $i,SV523: $i,SV147: $i] :
( ( ! [SY2825: $i] :
( ( c_List_Ofilter @ SV147 @ ( c_List_Oappend @ SV523 @ SV818 @ SY2825 ) @ SY2825 )
= ( c_List_Oappend @ ( c_List_Ofilter @ SV147 @ SV523 @ SY2825 ) @ ( c_List_Ofilter @ SV147 @ SV818 @ SY2825 ) @ SY2825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2411,plain,
! [SV819: $i,SV524: $i,SV149: $i] :
( ( ! [SY2826: $i] :
( ( c_List_Omap @ SV149 @ SV524 @ SV819 @ SY2826 )
!= ( c_List_Olist_ONil @ SY2826 ) )
| ( SV524
= ( c_List_Olist_ONil @ SV819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2412,plain,
! [SV525: $i,SV150: $i] :
( ( ( SV150
= ( c_List_Olist_ONil @ SV525 ) )
= $true )
| ( ( ~ ( c_List_Onull @ SV150 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2039]) ).
thf(2413,plain,
! [SV820: $i,SV526: $i,SV153: $i] :
( ( ( SV153
!= ( c_List_Oappend @ SV526 @ SV153 @ SV820 ) )
| ( SV526
= ( c_List_Olist_ONil @ SV820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2414,plain,
! [SV821: $i,SV527: $i,SV154: $i] :
( ( ( ( c_List_Oappend @ SV154 @ SV527 @ SV821 )
!= SV527 )
| ( SV154
= ( c_List_Olist_ONil @ SV821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2415,plain,
! [SV822: $i,SV528: $i,SV155: $i] :
( ( ( SV155
!= ( c_List_Oappend @ SV155 @ SV528 @ SV822 ) )
| ( SV528
= ( c_List_Olist_ONil @ SV822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2416,plain,
! [SV823: $i,SV529: $i,SV156: $i] :
( ( ( ( c_List_Oappend @ SV156 @ SV529 @ SV823 )
!= SV156 )
| ( SV529
= ( c_List_Olist_ONil @ SV823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2417,plain,
! [SV530: $i,SV157: $i] :
( ( ( ( c_List_Oremdups @ SV157 @ SV530 )
!= ( c_List_Olist_ONil @ SV530 ) )
= $true )
| ( ( SV157
= ( c_List_Olist_ONil @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2418,plain,
! [SV824: $i,SV531: $i,SV158: $i] :
( ( ( ( c_List_Orotate @ SV158 @ SV531 @ SV824 )
!= ( c_List_Olist_ONil @ SV824 ) )
| ( SV531
= ( c_List_Olist_ONil @ SV824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2419,plain,
! [SV532: $i,SV159: $i] :
( ( ( ( c_List_Olist_ONil @ SV159 )
!= ( c_List_Orev @ SV532 @ SV159 ) )
= $true )
| ( ( SV532
= ( c_List_Olist_ONil @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2420,plain,
! [SV825: $i,SV533: $i,SV160: $i] :
( ( ( c_List_Olist_ONil @ SV160 )
!= ( c_List_Olist_OCons @ SV533 @ SV825 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2421,plain,
! [SV826: $i,SV534: $i,SV161: $i] :
( ( ( ( c_List_Oappend @ SV161 @ SV534 @ SV826 )
!= ( c_List_Olist_ONil @ SV826 ) )
| ( SV534
= ( c_List_Olist_ONil @ SV826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2422,plain,
! [SV827: $i,SV535: $i,SV162: $i] :
( ( ( ( c_List_Oappend @ SV162 @ SV535 @ SV827 )
!= ( c_List_Olist_ONil @ SV827 ) )
| ( SV162
= ( c_List_Olist_ONil @ SV827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2423,plain,
! [SV828: $i,SV536: $i,SV163: $i] :
( ( ( ( c_List_Olist_ONil @ SV163 )
!= ( c_List_Oappend @ SV536 @ SV828 @ SV163 ) )
| ( SV828
= ( c_List_Olist_ONil @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2424,plain,
! [SV537: $i,SV164: $i] :
( ( ( ! [SY2402: $i] :
( ( c_List_Olist_ONil @ SV164 )
!= ( c_List_Oappend @ SV537 @ SY2402 @ SV164 ) ) )
= $true )
| ( ( SV537
= ( c_List_Olist_ONil @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2425,plain,
! [SV829: $i,SV538: $i,SV165: $i] :
( ( ! [SY2827: $i] :
( ( c_List_Ofoldl @ SV165 @ SV538 @ ( c_List_Olist_ONil @ SV829 ) @ SY2827 @ SV829 )
= SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2426,plain,
! [SV830: $i,SV539: $i,SV167: $i] :
( ( ! [SY2828: $i] :
( ( ( c_List_Olist_ONil @ SV167 )
!= ( c_List_Omap @ SV539 @ SV830 @ SY2828 @ SV167 ) )
| ( SV830
= ( c_List_Olist_ONil @ SY2828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2427,plain,
! [SV831: $i,SV545: $i,SV173: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV173 ) ) @ SV545 ) @ SV831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV545 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV173 @ SV545 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2428,plain,
! [SV832: $i,SV546: $i,SV174: $i] :
( ( ( SV174
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV546 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV546 @ SV832 @ SV174 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV546 ) @ SV832 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2429,plain,
! [SV833: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ SV176 @ SV833 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV176 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV176 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2430,plain,
! [SV834: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ SV177 @ SV834 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV177 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV177 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2431,plain,
! [SV835: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ SV178 @ SV835 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV178 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV178 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2432,plain,
! [SV836: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ SV179 @ SV836 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV179 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV179 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2433,plain,
! [SV837: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ SV180 @ SV837 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV180 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV180 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2434,plain,
! [SV838: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ SV181 @ SV838 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV181 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV181 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2435,plain,
! [SV839: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ SV182 @ SV839 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV182 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV182 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2436,plain,
! [SV840: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ SV183 @ SV840 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV183 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV183 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2437,plain,
! [SV841: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ SV184 @ SV841 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV184 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV184 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2438,plain,
! [SV842: $i,SV548: $i,SV185: $i] :
( ( ( c_Lambda_Osubstn @ SV185 @ SV548 @ SV842 )
= ( c_Lambda_Osubst @ SV185 @ ( c_Lambda_Oliftn @ SV842 @ SV548 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV842 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2439,plain,
! [SV843: $i,SV549: $i,SV186: $i] :
( ( ! [SY2829: $i,SY2830: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SV549 @ SV843 @ SY2829 ) @ SY2829 ) @ ( c_Nat_Osize__class_Osize @ SV186 @ ( tc_List_Olist @ SY2829 ) ) @ SY2830 @ SY2829 )
= ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SY2830 @ SV843 @ SY2829 ) @ SY2829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2440,plain,
! [SV844: $i,SV550: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV187 @ SV550 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV844 @ SV550 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV187 ) @ SV844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2441,plain,
! [SV845: $i,SV551: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV551 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV845 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV551 @ SV845 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2442,plain,
! [SV846: $i,SV552: $i,SV189: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV189 @ SV552 ) )
| ! [SY2831: $i] :
( ! [SY2832: $i] :
( ( c_List_Olist_OCons @ SV552 @ ( c_List_Ofilter @ SV189 @ SY2832 @ SY2831 ) @ SY2831 )
= ( c_List_Ofilter @ SV189 @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV552 @ SY2832 @ SY2831 ) @ SY2831 ) @ SY2831 ) )
| ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ SV189 @ SV846 @ SY2831 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2443,plain,
! [SV847: $i,SV553: $i,SV190: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV190 @ SV553 ) )
| ! [SY2833: $i] :
( ! [SY2834: $i] :
( ( c_List_Ofilter @ SV190 @ ( c_List_Oappend @ SV847 @ ( c_List_Olist_OCons @ SV553 @ SY2834 @ SY2833 ) @ SY2833 ) @ SY2833 )
= ( c_List_Olist_OCons @ SV553 @ ( c_List_Ofilter @ SV190 @ SY2834 @ SY2833 ) @ SY2833 ) )
| ( hBOOL @ ( hAPP @ SV190 @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ SV190 @ SV847 @ SY2833 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2444,plain,
! [SV848: $i,SV554: $i,SV191: $i] :
( ( ! [SY2835: $i,SY2836: $i] :
( ( ( c_List_Olist_OCons @ SV191 @ SV554 @ SV848 )
!= ( c_List_Oappend @ SY2835 @ SY2836 @ SV848 ) )
| ( SV554
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV191 @ SV554 @ SY2835 @ SY2836 @ SV848 ) @ SY2836 @ SV848 ) )
| ( SY2835
= ( c_List_Olist_ONil @ SV848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2445,plain,
! [SV849: $i,SV555: $i,SV192: $i] :
( ( ! [SY2837: $i,SY2838: $i] :
( ( ( c_List_Oappend @ SV192 @ SV555 @ SV849 )
!= ( c_List_Olist_OCons @ SY2837 @ SY2838 @ SV849 ) )
| ( SV192
= ( c_List_Olist_OCons @ SY2837 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2837 @ SY2838 @ SV192 @ SV555 @ SV849 ) @ SV849 ) )
| ( SV192
= ( c_List_Olist_ONil @ SV849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2446,plain,
! [SV850: $i,SV556: $i,SV193: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV193 @ ( c_List_Olist_OCons @ SV556 @ ( c_List_Olist_ONil @ SV850 ) @ SV850 ) @ SV850 ) @ SV850 )
= SV556 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2447,plain,
! [SV851: $i,SV557: $i,SV194: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV194 @ ( c_List_Olist_OCons @ SV557 @ ( c_List_Olist_ONil @ SV851 ) @ SV851 ) @ SV851 ) @ SV851 )
= SV194 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2448,plain,
! [SV852: $i,SV558: $i,SV195: $i] :
( ( ! [SY2839: $i] :
( ( SV195 = SV558 )
| ( SV852 = SY2839 )
| ! [SY2840: $i,SY2841: $i] :
~ ( c_ListOrder_Ostep1 @ SY2840 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SV852 @ ( c_List_Olist_ONil @ SY2841 ) @ SY2841 ) @ SY2841 ) @ ( c_List_Oappend @ SV558 @ ( c_List_Olist_OCons @ SY2839 @ ( c_List_Olist_ONil @ SY2841 ) @ SY2841 ) @ SY2841 ) @ SY2841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2449,plain,
! [SV853: $i,SV559: $i,SV196: $i] :
( ( ! [SY2842: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SV559 ) @ SV853 ) )
| ( SV559 = SV853 )
| ! [SY2843: $i,SY2844: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SY2842 @ ( c_List_Olist_OCons @ SV559 @ ( c_List_Olist_ONil @ SY2843 ) @ SY2843 ) @ SY2843 ) @ ( c_List_Oappend @ SY2844 @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_ONil @ SY2843 ) @ SY2843 ) @ SY2843 ) @ SY2843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2450,plain,
! [SV854: $i,SV560: $i,SV197: $i] :
( ( ! [SY2845: $i,SY2846: $i] :
( ( ( c_List_Oappend @ SV197 @ SV560 @ SV854 )
!= ( c_List_Olist_OCons @ SY2845 @ SY2846 @ SV854 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SY2845 @ SY2846 @ SV197 @ SV560 @ SV854 ) @ SV560 @ SV854 )
= SY2846 )
| ( SV197
= ( c_List_Olist_ONil @ SV854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2451,plain,
! [SV855: $i,SV561: $i,SV198: $i] :
( ( ! [SY2847: $i,SY2848: $i] :
( ( ( c_List_Olist_OCons @ SV198 @ SV561 @ SV855 )
!= ( c_List_Oappend @ SY2847 @ SY2848 @ SV855 ) )
| ( ( c_List_Olist_OCons @ SV198 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV198 @ SV561 @ SY2847 @ SY2848 @ SV855 ) @ SV855 )
= SY2847 )
| ( SY2847
= ( c_List_Olist_ONil @ SV855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2452,plain,
! [SV856: $i,SV562: $i,SV199: $i] :
( ( ! [SY2849: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SV562 ) @ SV856 ) )
| ! [SY2850: $i,SY2851: $i] :
( ( c_ListOrder_Ostep1 @ SV199 @ SY2849 @ SY2850 @ SY2851 )
| ~ ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SY2849 @ ( c_List_Olist_OCons @ SV562 @ ( c_List_Olist_ONil @ SY2851 ) @ SY2851 ) @ SY2851 ) @ ( c_List_Oappend @ SY2850 @ ( c_List_Olist_OCons @ SV856 @ ( c_List_Olist_ONil @ SY2851 ) @ SY2851 ) @ SY2851 ) @ SY2851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2453,plain,
! [SV857: $i,SV563: $i,SV200: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV200 @ SV563 @ SV857 ) @ SV857 )
= ( c_List_Oappend @ SV563 @ ( c_List_Olist_OCons @ SV200 @ ( c_List_Olist_ONil @ SV857 ) @ SV857 ) @ SV857 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2454,plain,
! [SV858: $i,SV564: $i,SV201: $i] :
( ( ! [SY2852: $i] :
( ( SV201 = SV564 )
| ( c_ListOrder_Ostep1 @ SV858 @ SV201 @ SV564 @ SY2852 )
| ! [SY2853: $i,SY2854: $i] :
~ ( c_ListOrder_Ostep1 @ SV858 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SY2853 @ ( c_List_Olist_ONil @ SY2852 ) @ SY2852 ) @ SY2852 ) @ ( c_List_Oappend @ SV564 @ ( c_List_Olist_OCons @ SY2854 @ ( c_List_Olist_ONil @ SY2852 ) @ SY2852 ) @ SY2852 ) @ SY2852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2455,plain,
! [SV859: $i,SV565: $i,SV202: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV202 @ SV565 @ SV859 ) @ ( c_List_Olist_OCons @ SV565 @ ( c_List_Olist_ONil @ SV859 ) @ SV859 ) @ SV859 )
= ( c_List_Olist_OCons @ SV565 @ ( c_List_Oreplicate @ SV202 @ SV565 @ SV859 ) @ SV859 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2456,plain,
! [SV860: $i,SV566: $i,SV203: $i] :
( ( ! [SY2855: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV203 ) @ SV566 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV860 @ SY2855 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2855
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV203 @ SV566 @ SV860 @ SY2855 ) @ ( c_List_Olist_OCons @ SV566 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY2855
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2457,plain,
! [SV861: $i,SV567: $i,SV204: $i] :
( ( ( c_Lambda_Oliftn @ ( c_Suc @ SV204 ) @ SV567 @ SV861 )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV204 @ SV567 @ SV861 ) @ SV861 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2458,plain,
! [SV862: $i,SV568: $i,SV205: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV205 ) @ SV568 @ SV862 )
= ( c_Lambda_OdB_OVar @ SV205 ) )
| ( SV205 = SV862 )
| ( c_HOL_Oord__class_Oless @ SV862 @ SV205 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2459,plain,
! [SV570: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP @ SV207 @ SV570 ) )
= $true )
| ( ( ! [SY2457: $i,SY2458: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2457 @ SV207 @ ( tc_fun @ SY2458 @ tc_bool ) ) @ SV570 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2460,plain,
! [SV863: $i,SV571: $i,SV208: $i] :
( ( ! [SY2856: $i,SY2857: $i] :
( ( c_List_Ofoldl @ SV208 @ SV571 @ SV863 @ SY2856 @ SY2857 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV208 @ SY2856 @ SY2857 @ SY2856 ) @ ( c_List_Orev @ SV863 @ SY2857 ) @ SV571 @ SY2857 @ SY2856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2461,plain,
! [SV864: $i,SV573: $i,SV210: $i] :
( ( ! [SY2858: $i,SY2859: $i,SY2860: $i] :
( ( c_List_Omap @ SV210 @ ( c_List_Olist__update @ SV573 @ SV864 @ SY2858 @ SY2859 ) @ SY2859 @ SY2860 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV210 @ SV573 @ SY2859 @ SY2860 ) @ SV864 @ ( hAPP @ SV210 @ SY2858 ) @ SY2860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2462,plain,
! [SV865: $i,SV574: $i,SV211: $i] :
( ( ( c_List_Olist_OCons @ SV211 @ SV574 @ SV865 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV865 ) @ ( c_List_Olist_OCons @ SV211 @ SV574 @ SV865 ) @ SV865 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2463,plain,
! [SV866: $i,SV575: $i,SV212: $i] :
( ( SV212
!= ( c_List_Olist_OCons @ SV575 @ SV212 @ SV866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2464,plain,
! [SV867: $i,SV576: $i,SV213: $i] :
( ( ( c_List_Olist_OCons @ SV213 @ SV576 @ SV867 )
!= SV576 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2465,plain,
! [SV868: $i,SV577: $i,SV214: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV214 @ SV577 ) ) @ ( c_Lambda_Olift @ SV868 @ SV577 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV214 ) @ SV868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2466,plain,
! [SV578: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ SV215 @ SV578 ) )
= $true )
| ( ( ! [SY2470: $i] :
( ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY2470 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2470 @ SV215 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2470 @ SV578 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2467,plain,
! [SV869: $i,SV579: $i,SV216: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV216 @ SV579 ) @ SV869 @ SV579 )
= SV216 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2468,plain,
! [SV580: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ SV580 ) )
= $true )
| ( ( ! [SY2472: $i] :
( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY2472 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2472 @ SV217 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2472 @ SV580 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2469,plain,
! [SV870: $i,SV581: $i,SV218: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV218 @ SV581 ) @ ( c_List_Olist_OCons @ SV870 @ ( c_List_Olist_ONil @ SV581 ) @ SV581 ) @ SV581 ) @ SV581 )
= ( c_List_Olist_OCons @ SV870 @ SV218 @ SV581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2470,plain,
! [SV219: $i] :
( ( ( class_Orderings_Olinorder @ SV219 )
= $false )
| ( ( ! [SY1765: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1765 @ SV219 )
| ! [SY1766: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1766 @ SY1765 @ SV219 ) @ SV219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2471,plain,
! [SV871: $i,SV582: $i,SV220: $i] :
( ( ! [SY2861: $i] :
( ( c_List_Olist_OCons @ SV220 @ ( c_List_Oappend @ SV582 @ SV871 @ SY2861 ) @ SY2861 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV220 @ SV582 @ SY2861 ) @ SV871 @ SY2861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2472,plain,
! [SV872: $i,SV583: $i,SV221: $i] :
( ( ! [SY2862: $i] :
( ( c_List_Olist_OCons @ SV221 @ ( c_List_Oappend @ SV583 @ SV872 @ SY2862 ) @ SY2862 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV221 @ SV583 @ SY2862 ) @ SV872 @ SY2862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2473,plain,
! [SV873: $i,SV584: $i,SV222: $i] :
( ( ( c_List_Oremove1 @ SV222 @ ( c_List_Olist_OCons @ SV222 @ SV584 @ SV873 ) @ SV873 )
= SV584 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2474,plain,
! [SV874: $i,SV585: $i,SV223: $i] :
( ( ! [SY2863: $i,SY2864: $i,SY2865: $i] :
( ( c_List_Olist_Olist__case @ SV223 @ SV585 @ ( c_List_Olist_OCons @ SV874 @ SY2863 @ SY2864 ) @ SY2865 @ SY2864 )
= ( hAPP @ ( hAPP @ SV585 @ SV874 ) @ SY2863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2475,plain,
! [SV875: $i,SV586: $i,SV224: $i] :
( ( ! [SY2866: $i,SY2867: $i] :
( ( c_List_Omap @ SV224 @ ( c_List_Olist_OCons @ SV586 @ SV875 @ SY2866 ) @ SY2866 @ SY2867 )
= ( c_List_Olist_OCons @ ( hAPP @ SV224 @ SV586 ) @ ( c_List_Omap @ SV224 @ SV875 @ SY2866 @ SY2867 ) @ SY2867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2476,plain,
! [SV876: $i,SV587: $i,SV225: $i] :
( ( ! [SY2868: $i,SY2869: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV225 @ SV587 ) @ ( c_List_Omap @ SV225 @ SV876 @ SY2868 @ SY2869 ) @ SY2869 )
= ( c_List_Omap @ SV225 @ ( c_List_Olist_OCons @ SV587 @ SV876 @ SY2868 ) @ SY2868 @ SY2869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2477,plain,
! [SV877: $i,SV588: $i,SV226: $i] :
( ( ! [SY2870: $i,SY2871: $i] :
( ( c_List_Omap @ SV226 @ ( c_List_Olist_OCons @ SV588 @ SV877 @ SY2870 ) @ SY2870 @ SY2871 )
= ( c_List_Olist_OCons @ ( hAPP @ SV226 @ SV588 ) @ ( c_List_Omap @ SV226 @ SV877 @ SY2870 @ SY2871 ) @ SY2871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2478,plain,
! [SV878: $i,SV589: $i,SV227: $i] :
( ( ! [SY2872: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV227 @ SV589 @ SV878 ) @ SY2872 @ SV878 )
= ( c_List_Olist_OCons @ SV227 @ ( c_List_Oappend @ SV589 @ SY2872 @ SV878 ) @ SV878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2479,plain,
! [SV879: $i,SV590: $i,SV228: $i] :
( ( ! [SY2873: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV228 @ SV590 @ SV879 ) @ SY2873 @ SV879 )
= ( c_List_Olist_OCons @ SV228 @ ( c_List_Oappend @ SV590 @ SY2873 @ SV879 ) @ SV879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2480,plain,
! [SV591: $i,SV229: $i] :
( ( ( ! [SY2496: $i] :
( ( c_Lambda_OdB_OAbs @ SV229 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV591 @ SY2496 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV229 )
= SV591 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2481,plain,
! [SV592: $i,SV230: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV230 ) )
= $true )
| ( ( ! [SY2497: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV592 @ SY2497 @ SV230 ) @ SV230 )
| ! [SY2498: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2498 @ ( c_List_Olist_OCons @ SV592 @ SY2497 @ SV230 ) @ SV230 ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2482,plain,
! [SV231: $i] :
( ( ( class_Lattices_Olattice @ SV231 )
= $false )
| ( ( ! [SY1803: $i,SY1804: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1803 @ SY1804 @ SV231 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1804 @ SY1803 @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2483,plain,
! [SV232: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV232 )
= $false )
| ( ( ! [SY1805: $i,SY1806: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1805 @ SY1806 @ SV232 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1806 @ SY1805 @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2484,plain,
! [SV880: $i,SV593: $i,SV233: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV233 @ SV593 @ ( tc_fun @ SV880 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV593 @ SV233 @ ( tc_fun @ SV880 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2485,plain,
! [SV881: $i,SV594: $i,SV234: $i] :
( ( ! [SY2874: $i] :
( ( ( c_List_Orev @ SV234 @ SV594 )
!= ( c_List_Olist_OCons @ SV881 @ SY2874 @ SV594 ) )
| ( SV234
= ( c_List_Oappend @ ( c_List_Orev @ SY2874 @ SV594 ) @ ( c_List_Olist_OCons @ SV881 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2486,plain,
! [SV882: $i,SV596: $i,SV236: $i] :
( ( ! [SY2875: $i,SY2876: $i,SY2877: $i] :
( ( c_List_Ofoldl @ SV236 @ SV596 @ ( c_List_Olist_OCons @ SV882 @ SY2875 @ SY2876 ) @ SY2877 @ SY2876 )
= ( c_List_Ofoldl @ SV236 @ ( hAPP @ ( hAPP @ SV236 @ SV596 ) @ SV882 ) @ SY2875 @ SY2877 @ SY2876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2487,plain,
! [SV883: $i,SV597: $i,SV237: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV237 @ SV597 @ SV883 ) @ SV883 )
= ( c_List_Oappend @ ( c_List_Orev @ SV597 @ SV883 ) @ ( c_List_Olist_OCons @ SV237 @ ( c_List_Olist_ONil @ SV883 ) @ SV883 ) @ SV883 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2488,plain,
! [SV884: $i,SV598: $i,SV238: $i] :
( ( ! [SY2878: $i] :
( ! [SY2879: $i] :
( ( c_List_Olist_OCons @ SV238 @ SV598 @ SV884 )
!= ( c_List_Ofilter @ SY2878 @ SY2879 @ SV884 ) )
| ( hBOOL @ ( hAPP @ SY2878 @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2489,plain,
! [SV885: $i,SV599: $i,SV239: $i] :
( ( ( c_List_Oremdups @ ( c_List_Ofilter @ SV239 @ SV599 @ SV885 ) @ SV885 )
= ( c_List_Ofilter @ SV239 @ ( c_List_Oremdups @ SV599 @ SV885 ) @ SV885 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2490,plain,
! [SV600: $i,SV240: $i] :
( ( ( ! [SY2511: $i,SY2512: $i] :
( ( c_List_Ofilter @ SV240 @ ( c_List_Olist_OCons @ SV600 @ SY2511 @ SY2512 ) @ SY2512 )
= ( c_List_Olist_OCons @ SV600 @ ( c_List_Ofilter @ SV240 @ SY2511 @ SY2512 ) @ SY2512 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV240 @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2491,plain,
! [SV886: $i,SV601: $i,SV241: $i] :
( ( ( ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SV601 ) @ SV601 )
!= ( c_List_Orev @ SV886 @ SV601 ) )
| ( SV886
= ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SV601 ) @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2492,plain,
! [SV887: $i,SV602: $i,SV242: $i] :
( ( ! [SY2880: $i,SY2881: $i] :
( ( c_Lambda_OdB_OdB__case @ SV242 @ SV602 @ SV887 @ ( c_Lambda_OdB_OAbs @ SY2880 ) @ SY2881 )
= ( hAPP @ SV887 @ SY2880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2493,plain,
! [SV888: $i,SV603: $i,SV243: $i] :
( ( ! [SY2882: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV243 @ SV603 @ SV888 ) ) @ ( c_Lambda_Osubst @ SY2882 @ SV603 @ SV888 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV243 ) @ SY2882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2494,plain,
! [SV889: $i,SV604: $i,SV244: $i] :
( ( ! [SY2883: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV244 @ SV604 @ SV889 @ SY2883 ) @ SY2883 )
= ( c_List_Omap @ SV244 @ ( c_List_Orev @ SV604 @ SV889 ) @ SV889 @ SY2883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2495,plain,
! [SV890: $i,SV605: $i,SV245: $i] :
( ( ! [SY2884: $i] :
( ( ( c_List_Oappend @ SV245 @ SV605 @ SV890 )
!= ( c_List_Oappend @ SY2884 @ SV605 @ SV890 ) )
| ( SV245 = SY2884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2496,plain,
! [SV891: $i,SV606: $i,SV246: $i] :
( ( ! [SY2885: $i] :
( ( ( c_List_Oappend @ SV246 @ SV606 @ SV891 )
!= ( c_List_Oappend @ SV246 @ SY2885 @ SV891 ) )
| ( SV606 = SY2885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2497,plain,
! [SV892: $i,SV607: $i,SV247: $i] :
( ( ! [SY2886: $i] :
( ! [SY2887: $i] :
( ( c_List_Ofilter @ SV247 @ SV607 @ SV892 )
!= ( c_List_Olist_OCons @ SY2886 @ SY2887 @ SV892 ) )
| ( hBOOL @ ( hAPP @ SV247 @ SY2886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2498,plain,
! [SV893: $i,SV608: $i,SV248: $i] :
( ( ! [SY2888: $i,SY2889: $i] :
( ( c_List_Orotate @ SV248 @ ( c_List_Omap @ SV608 @ SV893 @ SY2888 @ SY2889 ) @ SY2889 )
= ( c_List_Omap @ SV608 @ ( c_List_Orotate @ SV248 @ SV893 @ SY2888 ) @ SY2888 @ SY2889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2499,plain,
! [SV894: $i,SV612: $i,SV252: $i] :
( ( ! [SY2890: $i,SY2891: $i,SY2892: $i] :
( ( c_List_Ofoldr @ SV252 @ ( c_List_Oappend @ SV612 @ SV894 @ SY2890 ) @ SY2891 @ SY2890 @ SY2892 )
= ( c_List_Ofoldr @ SV252 @ SV612 @ ( c_List_Ofoldr @ SV252 @ SV894 @ SY2891 @ SY2890 @ SY2892 ) @ SY2890 @ SY2892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2500,plain,
! [SV613: $i,SV253: $i] :
( ( ( ! [SY2535: $i,SY2536: $i] : ( c_List_Olist__ex @ SV253 @ ( c_List_Olist_OCons @ SV613 @ SY2535 @ SY2536 ) @ SY2536 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV253 @ SV613 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2501,plain,
! [SV895: $i,SV614: $i,SV254: $i] :
( ( ( ( c_List_Orev @ SV254 @ SV614 )
!= ( c_List_Olist_OCons @ SV895 @ ( c_List_Olist_ONil @ SV614 ) @ SV614 ) )
| ( SV254
= ( c_List_Olist_OCons @ SV895 @ ( c_List_Olist_ONil @ SV614 ) @ SV614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2502,plain,
! [SV896: $i,SV615: $i,SV255: $i] :
( ( ! [SY2893: $i] :
( ( c_List_Olist__ex @ SV255 @ ( c_List_Olist_OCons @ SV615 @ SV896 @ SY2893 ) @ SY2893 )
| ~ ( c_List_Olist__ex @ SV255 @ SV896 @ SY2893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2503,plain,
! [SV897: $i,SV616: $i,SV256: $i] :
( ( ( c_List_Olist__ex @ SV256 @ SV616 @ SV897 )
| ! [SY2894: $i] :
( ( hBOOL @ ( hAPP @ SV256 @ SY2894 ) )
| ~ ( c_List_Olist__ex @ SV256 @ ( c_List_Olist_OCons @ SY2894 @ SV616 @ SV897 ) @ SV897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2504,plain,
! [SV898: $i,SV617: $i,SV257: $i] :
( ( ! [SY2895: $i,SY2896: $i,SY2897: $i] :
( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SV898 @ SY2895 ) @ ( c_List_Olist_OCons @ SY2896 @ SY2897 @ SY2895 ) @ SY2895 )
| ~ ( c_List_Olistrelp @ SV257 @ SV898 @ SY2897 @ SY2895 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SY2896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2505,plain,
! [SV618: $i,SV258: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV258 ) )
= $true )
| ( ( ! [SY2546: $i,SY2547: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ SY2546 @ SV258 ) @ SY2547 @ SV258 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2546 @ SY2547 @ SV258 ) @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2506,plain,
! [SV619: $i,SV259: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV259 ) )
= $true )
| ( ( ! [SY2548: $i,SY2549: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2548 @ SY2549 @ SV259 ) @ SV259 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2548 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ SY2549 @ SV259 ) @ SV259 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2507,plain,
! [SV620: $i,SV260: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV260 ) )
= $true )
| ( ( ! [SY2550: $i,SY2551: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2550 @ SY2551 @ SV260 ) @ SV260 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2550 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ SY2551 @ SV260 ) @ SV260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2508,plain,
! [SV621: $i,SV261: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV261 ) )
= $true )
| ( ( ! [SY2552: $i,SY2553: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ SY2552 @ SV261 ) @ SY2553 @ SV261 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2552 @ SY2553 @ SV261 ) @ SV261 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2509,plain,
! [SV899: $i,SV622: $i,SV262: $i] :
( ( ! [SY2898: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 @ SV622 @ ( tc_fun @ SV899 @ tc_bool ) ) @ SY2898 @ ( tc_fun @ SV899 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV622 @ SY2898 @ ( tc_fun @ SV899 @ tc_bool ) ) @ ( tc_fun @ SV899 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2510,plain,
! [SV900: $i,SV623: $i,SV263: $i] :
( ( ! [SY2899: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV623 @ SV900 @ ( tc_fun @ SY2899 @ tc_bool ) ) @ ( tc_fun @ SY2899 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV623 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV900 @ ( tc_fun @ SY2899 @ tc_bool ) ) @ ( tc_fun @ SY2899 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2511,plain,
! [SV624: $i,SV264: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV264 )
!= ( c_Lambda_OdB_OAbs @ SV624 ) )
= $true )
| ( ( SV264 = SV624 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2512,plain,
! [SV625: $i,SV265: $i] :
( ( ( ! [SY2558: $i,SY2559: $i] :
( ( c_List_Oremove1 @ SV265 @ ( c_List_Olist_OCons @ SV625 @ SY2558 @ SY2559 ) @ SY2559 )
= ( c_List_Olist_OCons @ SV625 @ ( c_List_Oremove1 @ SV265 @ SY2558 @ SY2559 ) @ SY2559 ) ) )
= $true )
| ( ( SV265 = SV625 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2513,plain,
! [SV901: $i,SV626: $i,SV266: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV266 @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV901 @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV266 ) @ SV901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2514,plain,
! [SV902: $i,SV627: $i,SV267: $i] :
( ( ! [SY2900: $i,SY2901: $i] :
( ( c_List_Omap @ SV267 @ ( c_List_Oappend @ SV627 @ SV902 @ SY2900 ) @ SY2900 @ SY2901 )
= ( c_List_Oappend @ ( c_List_Omap @ SV267 @ SV627 @ SY2900 @ SY2901 ) @ ( c_List_Omap @ SV267 @ SV902 @ SY2900 @ SY2901 ) @ SY2901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2515,plain,
! [SV628: $i,SV268: $i] :
( ( ( SV268
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SV628 @ SV268 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SV628 @ SV268 ) @ t_a ) )
= $true )
| ( ( ( SV268
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV628 @ SV268 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2516,plain,
! [SV903: $i,SV629: $i,SV269: $i] :
( ( ! [SY2902: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV269 ) @ SV629 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV903 ) @ SY2902 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV629 = SY2902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2517,plain,
! [SV904: $i,SV630: $i,SV270: $i] :
( ( ! [SY2903: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV270 ) @ SV630 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV904 ) @ SY2903 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV270 = SV904 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2518,plain,
! [SV905: $i,SV631: $i,SV271: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV271 @ SV631 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV905 ) )
| ( SV271
= ( c_Lambda_OdB_OAbs @ SV905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2519,plain,
! [SV632: $i,SV272: $i] :
( ( ( ! [SY2569: $i,SY2570: $i] :
( ( c_List_Oremove1 @ SV272 @ ( c_List_Ofilter @ SV632 @ SY2569 @ SY2570 ) @ SY2570 )
= ( c_List_Ofilter @ SV632 @ SY2569 @ SY2570 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV632 @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2520,plain,
! [SV906: $i,SV633: $i,SV273: $i] :
( ( ! [SY2904: $i,SY2905: $i,SY2906: $i] :
( ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ ( c_List_Olist_OCons @ SV906 @ SY2904 @ SY2905 ) @ SY2906 @ SY2905 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV633 @ SV906 ) @ SY2904 ) @ ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ SY2904 @ SY2906 @ SY2905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2521,plain,
! [SV907: $i,SV634: $i,SV274: $i] :
( ( ( ( c_List_Orev @ SV274 @ SV634 )
!= ( c_List_Orev @ SV907 @ SV634 ) )
| ( SV274 = SV907 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2522,plain,
! [SV908: $i,SV635: $i,SV275: $i] :
( ( ! [SY2907: $i,SY2908: $i] :
( ( c_List_Ofoldr @ SV275 @ SV635 @ SV908 @ SY2907 @ SY2908 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV275 @ SY2907 @ SY2908 @ SY2908 ) @ SV908 @ ( c_List_Orev @ SV635 @ SY2907 ) @ SY2908 @ SY2907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2523,plain,
! [SV909: $i,SV636: $i,SV276: $i] :
( ( ! [SY2909: $i,SY2910: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV276 @ SV636 @ SV909 @ ( c_Lambda_OdB_OAbs @ SY2909 ) @ SY2910 )
= ( hAPP @ ( hAPP @ SV909 @ SY2909 ) @ ( c_Lambda_OdB_OdB__rec @ SV276 @ SV636 @ SV909 @ SY2909 @ SY2910 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2524,plain,
! [SV910: $i,SV637: $i,SV277: $i] :
( ( ~ ( c_List_Onull @ ( c_List_Olist_OCons @ SV277 @ SV637 @ SV910 ) @ SV910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2525,plain,
! [SV278: $i] :
( ( ( class_Lattices_Olattice @ SV278 )
= $false )
| ( ( ! [SY1936: $i,SY1937: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ SY1937 @ SV278 ) @ SV278 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1936 @ SY1937 @ SV278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2526,plain,
! [SV279: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV279 )
= $false )
| ( ( ! [SY1938: $i,SY1939: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ SY1939 @ SV279 ) @ SV279 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1938 @ SY1939 @ SV279 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2527,plain,
! [SV911: $i,SV638: $i,SV280: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SV638 @ ( tc_fun @ SV911 @ tc_bool ) ) @ ( tc_fun @ SV911 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SV638 @ ( tc_fun @ SV911 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2528,plain,
! [SV912: $i,SV639: $i,SV281: $i] :
( ( ! [SY2911: $i,SY2912: $i,SY2913: $i] :
( ( c_List_Ofoldr @ SV281 @ ( c_List_Olist_OCons @ SV639 @ SV912 @ SY2911 ) @ SY2912 @ SY2911 @ SY2913 )
= ( hAPP @ ( hAPP @ SV281 @ SV639 ) @ ( c_List_Ofoldr @ SV281 @ SV912 @ SY2912 @ SY2911 @ SY2913 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2529,plain,
! [SV913: $i,SV640: $i,SV282: $i] :
( ( ! [SY2914: $i,SY2915: $i] :
( ~ ( hBOOL @ ( hAPP @ SV282 @ ( c_Lambda_OdB_OdB__case @ SV640 @ SV913 @ SY2914 @ ( c_Lambda_OdB_OAbs @ SY2915 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ SY2914 @ SY2915 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2530,plain,
! [SV914: $i,SV641: $i,SV283: $i] :
( ( ! [SY2916: $i,SY2917: $i] :
( ~ ( hBOOL @ ( hAPP @ SV283 @ ( c_Lambda_OdB_OdB__case @ SV641 @ SV914 @ SY2916 @ ( c_Lambda_OdB_OAbs @ SY2917 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ SY2916 @ SY2917 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2531,plain,
! [SV915: $i,SV642: $i,SV284: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV284 ) @ ( c_List_Olist_OCons @ SV642 @ SV915 @ SV284 ) @ SV284 )
= ( c_List_Olist_OCons @ SV642 @ SV915 @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2532,plain,
! [SV285: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV285 )
= $false )
| ( ( ! [SY1957: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1957 @ SY1957 @ SV285 )
= SY1957 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2533,plain,
! [SV916: $i,SV644: $i,SV287: $i] :
( ( ! [SY2918: $i] :
( ! [SY2919: $i] :
( ( c_List_Olist_OCons @ SV287 @ SV644 @ SV916 )
!= ( c_List_Olist_OCons @ SY2918 @ SY2919 @ SV916 ) )
| ( SV287 = SY2918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2534,plain,
! [SV917: $i,SV645: $i,SV288: $i] :
( ( ! [SY2920: $i,SY2921: $i] :
( ( ( c_List_Olist_OCons @ SV288 @ SV645 @ SV917 )
!= ( c_List_Olist_OCons @ SY2920 @ SY2921 @ SV917 ) )
| ( SV645 = SY2921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2535,plain,
! [SV918: $i,SV646: $i,SV289: $i] :
( ( ( c_Type_Otyping @ SV289 @ SV646 @ SV918 )
| ! [SY2922: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2922 ) @ SV646 ) )
| ~ ( c_Type_Otyping @ SV289 @ SY2922 @ SV918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2536,plain,
! [SV290: $i] :
( ( ( class_Orderings_Olinorder @ SV290 )
= $false )
| ( ( ! [SY1970: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1970 @ SV290 )
| ! [SY1971: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY1970 @ SY1971 @ SV290 ) @ SV290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2537,plain,
! [SV291: $i] :
( ( ( class_Orderings_Olinorder @ SV291 )
= $false )
| ( ( ! [SY1972: $i] :
( ( c_List_Olinorder__class_Osorted @ SY1972 @ SV291 )
| ! [SY1973: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY1973 @ SY1972 @ SV291 ) @ SV291 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2538,plain,
! [SV919: $i,SV647: $i,SV292: $i] :
( ( ! [SY2923: $i,SY2924: $i] :
( ! [SY2925: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV647 @ SV919 @ SY2923 ) @ SY2924 @ SY2925 @ SY2923 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SY2924 @ SY2925 @ SY2923 ) @ SV647 @ SV919 @ SY2923 ) )
| ( SV647 = SY2924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2539,plain,
! [SV293: $i] :
( ( ( class_Orderings_Olinorder @ SV293 )
= $false )
| ( ( ! [SY1979: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SY1979 @ SV293 ) @ SV293 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1979 @ SV293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2540,plain,
! [SV648: $i,SV294: $i] :
( ( ( ! [SY2607: $i,SY2608: $i] :
( ( c_List_Ofilter @ SV294 @ ( c_List_Olist_OCons @ SV648 @ SY2607 @ SY2608 ) @ SY2608 )
= ( c_List_Ofilter @ SV294 @ SY2607 @ SY2608 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV294 @ SV648 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2541,plain,
! [SV920: $i,SV649: $i,SV295: $i] :
( ( ! [SY2926: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV295 @ SV649 @ ( tc_fun @ SV920 @ tc_bool ) ) @ SY2926 ) )
| ~ ( hBOOL @ ( hAPP @ SV649 @ SY2926 ) )
| ~ ( hBOOL @ ( hAPP @ SV295 @ SY2926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2542,plain,
! [SV921: $i,SV650: $i,SV296: $i] :
( ( ( c_List_Orev @ ( c_List_Ofilter @ SV296 @ SV650 @ SV921 ) @ SV921 )
= ( c_List_Ofilter @ SV296 @ ( c_List_Orev @ SV650 @ SV921 ) @ SV921 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2543,plain,
! [SV922: $i,SV651: $i,SV297: $i] :
( ( ! [SY2927: $i] :
( ! [SY2928: $i] :
( ( c_List_Oappend @ SV297 @ ( c_List_Olist_OCons @ SV651 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 )
!= ( c_List_Oappend @ SY2927 @ ( c_List_Olist_OCons @ SY2928 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 ) )
| ( SV297 = SY2927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2544,plain,
! [SV923: $i,SV652: $i,SV298: $i] :
( ( ! [SY2929: $i,SY2930: $i] :
( ( ( c_List_Oappend @ SV298 @ ( c_List_Olist_OCons @ SV652 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 )
!= ( c_List_Oappend @ SY2929 @ ( c_List_Olist_OCons @ SY2930 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 ) )
| ( SV652 = SY2930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2545,plain,
! [SV924: $i,SV653: $i,SV299: $i] :
( ( ! [SY2931: $i,SY2932: $i] :
( ~ ( hBOOL @ ( hAPP @ SV299 @ ( c_List_Olist_Olist__case @ SV653 @ SV924 @ ( c_List_Olist_OCons @ SY2931 @ SY2932 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV299 @ ( hAPP @ ( hAPP @ SV924 @ SY2931 ) @ SY2932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2546,plain,
! [SV925: $i,SV654: $i,SV300: $i] :
( ( ! [SY2933: $i,SY2934: $i] :
( ~ ( hBOOL @ ( hAPP @ SV300 @ ( c_List_Olist_Olist__case @ SV654 @ SV925 @ ( c_List_Olist_OCons @ SY2933 @ SY2934 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV300 @ ( hAPP @ ( hAPP @ SV925 @ SY2933 ) @ SY2934 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2547,plain,
! [SV926: $i,SV655: $i,SV301: $i] :
( ( ! [SY2935: $i,SY2936: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV301 @ SV655 @ SV926 @ SY2935 ) @ SV655 @ SY2936 @ SY2935 )
= ( c_List_Olist__update @ SV301 @ SV655 @ SY2936 @ SY2935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2548,plain,
! [SV927: $i,SV656: $i,SV302: $i] :
( ( ! [SY2937: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV302 @ SV656 @ SV927 ) @ SY2937 @ SV927 )
= ( c_List_Oappend @ SV302 @ ( c_List_Oappend @ SV656 @ SY2937 @ SV927 ) @ SV927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2549,plain,
! [SV928: $i,SV657: $i,SV303: $i] :
( ( ! [SY2938: $i] :
( ( c_List_Oappend @ SV303 @ ( c_List_Oappend @ SV657 @ SV928 @ SY2938 ) @ SY2938 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV303 @ SV657 @ SY2938 ) @ SV928 @ SY2938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2550,plain,
! [SV929: $i,SV658: $i,SV304: $i] :
( ( ! [SY2939: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV304 @ SV658 @ SV929 ) @ SY2939 @ SV929 )
= ( c_List_Oappend @ SV304 @ ( c_List_Oappend @ SV658 @ SY2939 @ SV929 ) @ SV929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2551,plain,
! [SV930: $i,SV659: $i,SV305: $i] :
( ( ! [SY2940: $i] :
( ( c_List_Oappend @ SV305 @ ( c_List_Oappend @ SV659 @ SV930 @ SY2940 ) @ SY2940 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV305 @ SV659 @ SY2940 ) @ SV930 @ SY2940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2552,plain,
! [SV306: $i] :
( ( ( class_Orderings_Olinorder @ SV306 )
= $false )
| ( ( ! [SY2020: $i,SY2021: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SY2020 @ SY2021 @ SV306 ) @ SV306 )
| ~ ( c_List_Olinorder__class_Osorted @ SY2021 @ SV306 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2553,plain,
! [SV660: $i,SV307: $i] :
( ( c_List_Olist__ex @ SV307 @ ( c_List_Olist_ONil @ SV660 ) @ SV660 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2554,plain,
! [SV661: $i,SV309: $i] :
( ( ( ! [SY2635: $i] :
~ ( hBOOL @ ( hAPP @ SV309 @ ( c_List_Olist_Olist__case @ SV661 @ SY2635 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV661 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2555,plain,
! [SV931: $i,SV662: $i,SV310: $i] :
( ( ! [SY2941: $i] :
( ( c_List_Ofoldr @ SV310 @ ( c_List_Olist_ONil @ SV662 ) @ SV931 @ SV662 @ SY2941 )
= SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2556,plain,
! [SV932: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ SV932 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV311 @ ( v_sko__List__Xzip__Xinduct__2 @ SV311 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2557,plain,
! [SV933: $i,SV663: $i,SV312: $i] :
( ( ( c_List_Omap @ SV312 @ ( c_List_Olist_ONil @ SV663 ) @ SV663 @ SV933 )
= ( c_List_Olist_ONil @ SV933 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2558,plain,
! [SV934: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ SV934 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV314 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV314 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV314 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2559,plain,
! [SV935: $i,SV665: $i,SV315: $i] :
( ( ! [SY2942: $i] :
( ( c_List_Olist_Olist__rec @ SV315 @ SV665 @ ( c_List_Olist_ONil @ SV935 ) @ SY2942 @ SV935 )
= SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2560,plain,
! [SV936: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ SV316 @ SV936 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV316 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV316 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV316 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2561,plain,
! [SV937: $i,SV317: $i] :
( ( ( hBOOL @ ( hAPP @ SV317 @ SV937 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV317 @ ( v_sko__List__Xtake__Xinduct__2 @ SV317 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV317 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2562,plain,
! [SV318: $i] :
( ( ( class_Orderings_Olinorder @ SV318 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV318 ) @ SV318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2563,plain,
! [SV938: $i,SV666: $i,SV319: $i] :
( ( ( c_List_Ofiltermap @ SV319 @ ( c_List_Olist_ONil @ SV666 ) @ SV666 @ SV938 )
= ( c_List_Olist_ONil @ SV938 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2564,plain,
! [SV667: $i,SV320: $i] :
( ( ( ( c_List_Olist_ONil @ SV320 )
!= ( c_List_Oremdups @ SV667 @ SV320 ) )
= $true )
| ( ( SV667
= ( c_List_Olist_ONil @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2565,plain,
! [SV939: $i,SV669: $i,SV322: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV322 ) @ SV669 @ SV939 @ SV322 )
= ( c_List_Olist_ONil @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2566,plain,
! [SV940: $i,SV670: $i,SV323: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV323 ) @ SV670 @ SV940 @ SV323 )
= ( c_List_Olist_ONil @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2567,plain,
! [SV941: $i,SV671: $i,SV324: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV324 ) @ SV671 @ SV941 @ SV324 )
= ( c_List_Olist_ONil @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2568,plain,
! [SV942: $i,SV325: $i] :
( ( ( hBOOL @ ( hAPP @ SV325 @ SV942 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV325 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV325 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV325 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2569,plain,
! [SV943: $i,SV672: $i,SV326: $i] :
( ( ( c_List_Olist_OCons @ SV326 @ SV672 @ SV943 )
!= ( c_List_Olist_ONil @ SV943 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2570,plain,
! [SV944: $i,SV673: $i,SV327: $i] :
( ( ( c_List_Olist_OCons @ SV327 @ SV673 @ SV944 )
!= ( c_List_Olist_ONil @ SV944 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2571,plain,
! [SV945: $i,SV329: $i] :
( ( ( hBOOL @ ( hAPP @ SV329 @ SV945 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV329 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV329 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2572,plain,
! [SV946: $i,SV675: $i,SV330: $i] :
( ( ! [SY2943: $i] :
( ( c_Map_Omap__upds @ SV330 @ SV675 @ ( c_List_Olist_ONil @ SV946 ) @ SY2943 @ SV946 )
= SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2573,plain,
! [SV947: $i,SV676: $i,SV331: $i] :
( ( ! [SY2944: $i] :
( ( c_Map_Omap__upds @ SV331 @ ( c_List_Olist_ONil @ SV676 ) @ SV947 @ SV676 @ SY2944 )
= SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2574,plain,
! [SV948: $i,SV332: $i] :
( ( ( hBOOL @ ( hAPP @ SV332 @ SV948 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV332 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV332 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV332 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2575,plain,
! [SV949: $i,SV677: $i,SV333: $i] :
( ( ! [SY2945: $i] :
( ( c_List_Olist_Olist__case @ SV333 @ SV677 @ ( c_List_Olist_ONil @ SV949 ) @ SY2945 @ SV949 )
= SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2576,plain,
! [SV678: $i,SV334: $i] :
( ( ( ( c_List_Orev @ SV334 @ SV678 )
!= ( c_List_Olist_ONil @ SV678 ) )
= $true )
| ( ( SV334
= ( c_List_Olist_ONil @ SV678 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2577,plain,
! [SV950: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ SV336 @ SV950 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV336 @ ( v_sko__List__Xlist__Xinduct__2 @ SV336 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV336 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2578,plain,
! [SV951: $i,SV680: $i,SV337: $i] :
( ( ( c_List_Olist_ONil @ SV337 )
= ( c_List_Omap @ SV680 @ ( c_List_Olist_ONil @ SV951 ) @ SV951 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2579,plain,
! [SV952: $i,SV340: $i] :
( ( ( hBOOL @ ( hAPP @ SV340 @ SV952 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV340 @ ( v_sko__List__Xmap__Xinduct__2 @ SV340 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV340 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2580,plain,
! [SV953: $i,SV682: $i,SV342: $i] :
( ( ! [SY2946: $i] :
( ( ( c_List_Olist__update @ SV342 @ SV682 @ SV953 @ SY2946 )
!= ( c_List_Olist_ONil @ SY2946 ) )
| ( SV342
= ( c_List_Olist_ONil @ SY2946 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2581,plain,
! [SV954: $i,SV683: $i,SV343: $i] :
( ( ! [SY2947: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV343 ) @ SV683 ) @ SV954 @ SY2947 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV343 @ SV954 @ SY2947 ) ) @ ( c_Lambda_Osubst @ SV683 @ SV954 @ SY2947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2582,plain,
! [SV955: $i,SV684: $i,SV344: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV344 ) @ SV684 )
!= ( c_Lambda_OdB_OAbs @ SV955 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2583,plain,
! [SV956: $i,SV685: $i,SV345: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV345 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV685 ) @ SV956 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2584,plain,
! [SV957: $i,SV686: $i,SV346: $i] :
( ( ! [SY2948: $i,SY2949: $i,SY2950: $i] :
( ~ ( hBOOL @ ( hAPP @ SV346 @ ( c_Lambda_OdB_OdB__case @ SV686 @ SV957 @ SY2948 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2949 ) @ SY2950 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ SV957 @ SY2949 ) @ SY2950 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2585,plain,
! [SV958: $i,SV687: $i,SV347: $i] :
( ( ! [SY2951: $i,SY2952: $i,SY2953: $i] :
( ~ ( hBOOL @ ( hAPP @ SV347 @ ( c_Lambda_OdB_OdB__case @ SV687 @ SV958 @ SY2951 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2952 ) @ SY2953 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV347 @ ( hAPP @ ( hAPP @ SV958 @ SY2952 ) @ SY2953 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2586,plain,
! [SV959: $i,SV688: $i,SV348: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV348 ) @ SV688 ) @ SV959 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV348 @ SV959 ) ) @ ( c_Lambda_Olift @ SV688 @ SV959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2587,plain,
! [SV960: $i,SV689: $i,SV349: $i] :
( ( ! [SY2954: $i,SY2955: $i,SY2956: $i] :
( ( c_Lambda_OdB_OdB__case @ SV349 @ SV689 @ SV960 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2954 ) @ SY2955 ) @ SY2956 )
= ( hAPP @ ( hAPP @ SV689 @ SY2954 ) @ SY2955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2588,plain,
! [SV961: $i,SV690: $i,SV350: $i] :
( ( ! [SY2957: $i,SY2958: $i,SY2959: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2957 ) @ SY2958 ) @ SY2959 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV690 @ SY2957 ) @ SY2958 ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ SY2957 @ SY2959 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ SY2958 @ SY2959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2589,plain,
! [SV962: $i,SV691: $i,SV351: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV351 @ SV691 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV962 @ SV691 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV351 = SV962 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2590,plain,
! [SV963: $i,SV692: $i,SV352: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV692 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV963 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV692 ) @ SV963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2591,plain,
! [SV964: $i,SV693: $i,SV353: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV693 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV964 ) @ SV693 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV353 ) @ SV964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2592,plain,
! [SV965: $i,SV694: $i,SV354: $i] :
( ( ! [SY2960: $i] :
( ( c_Lambda_Oliftn @ SV354 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV694 ) @ SV965 ) @ SY2960 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV354 @ SV694 @ SY2960 ) ) @ ( c_Lambda_Oliftn @ SV354 @ SV965 @ SY2960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2593,plain,
! [SV966: $i,SV695: $i,SV355: $i] :
( ( ! [SY2961: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV355 ) @ SV695 ) @ SV966 @ SY2961 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV355 @ SV966 @ SY2961 ) ) @ ( c_Lambda_Osubstn @ SV695 @ SV966 @ SY2961 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2594,plain,
! [SV967: $i,SV696: $i,SV356: $i] :
( ( ( SV356 = SV696 )
| ! [SY2962: $i,SY2963: $i] :
( ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2962 ) @ SY2963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV696 )
| ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2962 ) @ SY2963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2595,plain,
! [SV968: $i,SV697: $i,SV357: $i] :
( ( ! [SY2964: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV357 ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV968 ) @ SY2964 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2596,plain,
! [SV969: $i,SV698: $i,SV358: $i] :
( ( ! [SY2965: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV358 ) ) @ SV698 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV969 ) @ SY2965 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2597,plain,
! [SV699: $i,SV359: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV359 )
= ( c_Lambda_OdB_OVar @ SV699 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2598,plain,
! [SV970: $i,SV700: $i,SV360: $i] :
( ( ! [SY2966: $i,SY2967: $i] :
( ~ ( hBOOL @ ( hAPP @ SV360 @ ( c_Lambda_OdB_OdB__case @ SV700 @ SV970 @ SY2966 @ ( c_Lambda_OdB_OVar @ SY2967 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV360 @ ( hAPP @ SV700 @ SY2967 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2599,plain,
! [SV971: $i,SV701: $i,SV361: $i] :
( ( ! [SY2968: $i,SY2969: $i] :
( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Lambda_OdB_OdB__case @ SV701 @ SV971 @ SY2968 @ ( c_Lambda_OdB_OVar @ SY2969 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( hAPP @ SV701 @ SY2969 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2600,plain,
! [SV703: $i,SV363: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV363 ) ) @ SV703 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2601,plain,
! [SV972: $i,SV704: $i,SV364: $i] :
( ( ! [SY2970: $i,SY2971: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV364 @ SV704 @ SV972 @ ( c_Lambda_OdB_OVar @ SY2970 ) @ SY2971 )
= ( hAPP @ SV364 @ SY2970 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2602,plain,
! [SV705: $i,SV365: $i] :
( ( ( c_Lambda_OdB_OVar @ SV365 )
= ( c_Lambda_OdB_OAbs @ SV705 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2603,plain,
! [SV973: $i,SV706: $i,SV366: $i] :
( ( ( ( hAPP @ SV366 @ SV706 )
= SV973 )
| ~ ( c_Type_Otyping @ SV366 @ ( c_Lambda_OdB_OVar @ SV706 ) @ SV973 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2604,plain,
! [SV974: $i,SV707: $i,SV367: $i] :
( ( ! [SY2972: $i,SY2973: $i] :
( ( c_Lambda_OdB_OdB__case @ SV367 @ SV707 @ SV974 @ ( c_Lambda_OdB_OVar @ SY2972 ) @ SY2973 )
= ( hAPP @ SV367 @ SY2972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2605,plain,
! [SV975: $i,SV709: $i,SV369: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV369 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV709 @ SV975 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV975
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2606,plain,
! [SV976: $i,SV710: $i,SV371: $i] :
( ( ! [SY2974: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV371 ) @ SV710 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ SY2974 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV371
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV371 @ SV710 @ SV976 @ SY2974 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY2974
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2607,plain,
! [SV711: $i,SV372: $i] :
( ( ( ! [SY2707: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV372 @ SV711 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY2707 ) ) )
= $true )
| ( ( SV711
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2608,plain,
! [SV977: $i,SV712: $i,SV374: $i] :
( ( ! [SY2975: $i] :
( ( c_List_Olistsp @ SV374 @ ( c_List_Oappend @ SV712 @ SV977 @ SY2975 ) @ SY2975 )
| ~ ( c_List_Olistsp @ SV374 @ SV977 @ SY2975 )
| ~ ( c_List_Olistsp @ SV374 @ SV712 @ SY2975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2609,plain,
! [SV978: $i,SV713: $i,SV375: $i] :
( ( ( c_List_Olistsp @ SV375 @ SV713 @ SV978 )
| ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV375 @ SV713 @ SV978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2610,plain,
! [SV979: $i,SV714: $i,SV376: $i] :
( ( ! [SY2976: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV714 @ ( tc_fun @ SV979 @ tc_bool ) ) @ SY2976 @ SV979 )
| ~ ( c_List_Olistsp @ SV714 @ SY2976 @ SV979 )
| ~ ( c_List_Olistsp @ SV376 @ SY2976 @ SV979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2611,plain,
! [SV980: $i,SV715: $i,SV377: $i] :
( ( ( c_List_Olistsp @ SV377 @ SV715 @ SV980 )
| ! [SY2977: $i] :
~ ( c_List_Olistsp @ SV377 @ ( c_List_Oappend @ SY2977 @ SV715 @ SV980 ) @ SV980 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2612,plain,
! [SV981: $i,SV716: $i,SV378: $i] :
( ( ( c_List_Olistsp @ SV378 @ SV716 @ SV981 )
| ! [SY2978: $i] :
~ ( c_List_Olistsp @ SV378 @ ( c_List_Oappend @ SV716 @ SY2978 @ SV981 ) @ SV981 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2613,plain,
! [SV982: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV379 @ SV982 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV379 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2614,plain,
! [SV380: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV380 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV380 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2615,plain,
! [SV983: $i,SV717: $i,SV381: $i] :
( ( ! [SY2979: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV381 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV983 ) @ SY2979 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV381 = SV983 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2616,plain,
! [SV984: $i,SV718: $i,SV382: $i] :
( ( ! [SY2980: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV382 ) @ SV718 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV984 ) @ SY2980 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV718 = SY2980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2617,plain,
! [SV719: $i,SV383: $i] :
( ( ( ! [SY2721: $i] :
( ( c_Lambda_OdB_OVar @ SV383 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV719 @ SY2721 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV383 )
= SV719 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2618,plain,
! [SV720: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP @ SV384 @ SV720 ) )
= $true )
| ( ( ! [SY2722: $i] :
( ( hBOOL @ ( hAPP @ SY2722 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY2722 @ SV384 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2722 @ SV720 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2619,plain,
! [SV721: $i,SV385: $i] :
( ( ( hBOOL @ ( hAPP @ SV385 @ SV721 ) )
= $true )
| ( ( ! [SY2723: $i] :
( ( hBOOL @ ( hAPP @ SV385 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2723 @ SV385 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV385 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2723 @ SV721 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2620,plain,
! [SV722: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP @ SV386 @ SV722 ) )
= $true )
| ( ( ! [SY2724: $i] :
( ( hBOOL @ ( hAPP @ SY2724 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY2724 @ SV386 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2724 @ SV722 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2621,plain,
! [SV723: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ SV387 @ SV723 ) )
= $true )
| ( ( ! [SY2725: $i] :
( ( hBOOL @ ( hAPP @ SV387 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2725 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2725 @ SV723 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2622,plain,
! [SV724: $i,SV388: $i] :
( ( ( c_List_Olistsp @ SV388 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV388 @ SV724 ) @ t_a )
= $true )
| ( ( ( SV724
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV388 @ SV724 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2623,plain,
! [SV725: $i,SV389: $i] :
( ( ( hBOOL @ ( hAPP @ SV389 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV389 @ SV725 ) ) )
= $true )
| ( ( ( SV725
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV389 @ SV725 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2624,plain,
! [SV726: $i,SV390: $i] :
( ( ( hBOOL @ ( hAPP @ SV390 @ SV726 ) )
= $true )
| ( ( ! [SY2726: $i] :
( ( c_List_Olistsp @ SY2726 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2726 @ SV390 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV390 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2726 @ SV726 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2625,plain,
! [SV727: $i,SV391: $i] :
( ( ( hBOOL @ ( hAPP @ SV391 @ SV727 ) )
= $true )
| ( ( ! [SY2727: $i] :
( ( c_List_Olistsp @ SY2727 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2727 @ SV391 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2727 @ SV727 @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2626,plain,
! [SV985: $i,SV729: $i,SV393: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV729 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV985 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV729 )
= SV985 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2627,plain,
! [SV986: $i,SV394: $i] :
( ( ( ! [SY2981: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV394 @ ( c_Lambda_OdB_OVar @ SV986 ) @ SY2981 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV394 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2628,plain,
! [SV987: $i,SV730: $i,SV396: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV396 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV730 @ SV987 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV987
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2629,plain,
! [SV731: $i,SV397: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV397 ) @ SV731 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV731 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2630,plain,
! [SV732: $i,SV398: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV398 )
!= ( c_Lambda_OdB_OVar @ SV732 ) )
= $true )
| ( ( SV398 = SV732 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2631,plain,
! [SV988: $i,SV733: $i,SV399: $i] :
( ( ! [SY2982: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV399 ) @ SV733 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV988 ) @ SY2982 ) )
| ( SV399 = SV988 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2632,plain,
! [SV989: $i,SV734: $i,SV400: $i] :
( ( ! [SY2983: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV400 ) @ SV734 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV989 ) @ SY2983 ) )
| ( SV734 = SY2983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2633,plain,
! [SV990: $i,SV735: $i,SV401: $i] :
( ( ( c_Lambda_OdB_OVar @ SV401 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV735 ) @ SV990 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2634,plain,
! [SV991: $i,SV737: $i,SV404: $i] :
( ( ! [SY2984: $i,SY2985: $i,SY2986: $i] :
( ( hAPP @ ( c_COMBB @ SV404 @ SV737 @ SV991 @ SY2984 @ SY2985 ) @ SY2986 )
= ( hAPP @ SV404 @ ( hAPP @ SV737 @ SY2986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2635,plain,
! [SV992: $i,SV738: $i,SV405: $i] :
( ( ! [SY2987: $i,SY2988: $i,SY2989: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV405 @ SV738 @ SV992 @ SY2987 ) @ SY2988 ) @ SY2989 )
= ( hAPP @ ( hAPP @ SV405 @ SY2989 ) @ SY2988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2636,plain,
! [SV993: $i,SV739: $i,SV406: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV739 )
!= ( c_Lambda_OdB_OVar @ SV993 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2637,plain,
! [SV740: $i,SV407: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV407 @ SV740 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV740 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2638,plain,
! [SV741: $i,SV408: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV408 @ SV741 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV741 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2639,plain,
! [SV742: $i,SV409: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV409 @ SV742 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV742 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2640,plain,
! [SV743: $i,SV410: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV410 @ SV743 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV743 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2641,plain,
! [SV994: $i,SV744: $i,SV411: $i] :
( ( ! [SY2990: $i,SY2991: $i,SY2992: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV411 @ SV744 @ SV994 @ SY2990 ) @ SY2991 ) @ SY2992 )
= ( hAPP @ ( hAPP @ SV411 @ SY2992 ) @ SY2991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2642,plain,
! [SV995: $i,SV745: $i,SV412: $i] :
( ( ! [SY2993: $i,SY2994: $i,SY2995: $i] :
( ( hAPP @ ( c_COMBB @ SV412 @ SV745 @ SV995 @ SY2993 @ SY2994 ) @ SY2995 )
= ( hAPP @ SV412 @ ( hAPP @ SV745 @ SY2995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2643,plain,
! [SV747: $i,SV414: $i] :
( ( ( SV414 = SV747 )
= $true )
| ( ( ! [SY2752: $i] :
~ ( c_fequal @ SV414 @ SV747 @ SY2752 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2644,plain,
! [SV415: $i,SV1: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ SV1 @ SV415 ) @ ( tc_List_Olist @ SV415 ) )
= ( c_Nat_Osize__class_Osize @ SV1 @ ( tc_List_Olist @ SV415 ) ) )
= $false )
| ( ( ( c_List_Oremdups @ SV1 @ SV415 )
= SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2645,plain,
! [SV996: $i,SV748: $i,SV416: $i,SV4: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV996 ) )
| ! [SY2996: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SY2996 ) @ SV996 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SY2996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2646,plain,
! [SV997: $i,SV751: $i,SV419: $i,SV7: $i] :
( ( ! [SY2997: $i] :
( ( c_List_Oreplicate @ SV7 @ SV419 @ SV751 )
!= ( c_List_Oreplicate @ SV997 @ SY2997 @ SV751 ) )
| ( SV7 = SV997 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2647,plain,
! [SV752: $i,SV420: $i,SV8: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV8 @ SV420 ) @ SV752 ) ) )
= $true )
| ( ( ! [SY2757: $i,SY2758: $i] : ( c_ListOrder_Ostep1 @ SV8 @ ( c_List_Olist_OCons @ SV420 @ SY2757 @ SY2758 ) @ ( c_List_Olist_OCons @ SV752 @ SY2757 @ SY2758 ) @ SY2758 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2648,plain,
! [SV998: $i,SV753: $i,SV421: $i,SV9: $i] :
( ( ( SV9 = SV421 )
| ( SV753 = SV998 )
| ! [SY2998: $i,SY2999: $i] :
~ ( c_ListOrder_Ostep1 @ SY2998 @ ( c_List_Olist_OCons @ SV421 @ SV998 @ SY2999 ) @ ( c_List_Olist_OCons @ SV9 @ SV753 @ SY2999 ) @ SY2999 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2649,plain,
! [SV999: $i,SV755: $i,SV423: $i,SV12: $i] :
( ( ! [SY3000: $i] :
( ( c_ListOrder_Ostep1 @ SV12 @ ( c_List_Oappend @ SV423 @ SV755 @ SV999 ) @ ( c_List_Oappend @ SV423 @ SY3000 @ SV999 ) @ SV999 )
| ~ ( c_ListOrder_Ostep1 @ SV12 @ SV755 @ SY3000 @ SV999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2650,plain,
! [SV1000: $i,SV756: $i,SV424: $i,SV13: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV13 @ SV424 @ SV756 @ SV1000 )
| ! [SY3001: $i] : ( c_ListOrder_Ostep1 @ SV13 @ ( c_List_Oappend @ SV424 @ SY3001 @ SV1000 ) @ ( c_List_Oappend @ SV756 @ SY3001 @ SV1000 ) @ SV1000 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2651,plain,
! [SV426: $i,SV15: $i] :
( ( ( class_Orderings_Opreorder @ SV15 )
= $false )
| ( ( ! [SY2263: $i] :
( ( c_HOL_Oord__class_Oless @ SV426 @ SY2263 @ SV15 )
| ! [SY2264: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2264 @ SY2263 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV426 @ SY2264 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2652,plain,
! [SV427: $i,SV16: $i] :
( ( ( class_Orderings_Oorder @ SV16 )
= $false )
| ( ( ! [SY2265: $i] :
( ( c_HOL_Oord__class_Oless @ SV427 @ SY2265 @ SV16 )
| ! [SY2266: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV427 @ SY2266 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SY2266 @ SY2265 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2653,plain,
! [SV429: $i,SV22: $i] :
( ( ( ( c_Suc @ SV22 )
= SV429 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV22 @ SV429 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV22 ) @ SV429 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2654,plain,
! [SV1001: $i,SV759: $i,SV431: $i,SV24: $i] :
( ( ( SV24 = SV431 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ SV431 ) @ SV24 ) )
| ! [SY3002: $i,SY3003: $i] :
~ ( c_ListOrder_Ostep1 @ SV759 @ ( c_List_Olist_OCons @ SV431 @ SV1001 @ SY3002 ) @ ( c_List_Olist_OCons @ SV24 @ SY3003 @ SY3002 ) @ SY3002 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2655,plain,
! [SV1002: $i,SV761: $i,SV26: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV26 @ SV761 @ SV1002 ) @ SV1002 )
= SV761 )
= $true )
| ( ( SV26
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2656,plain,
! [SV1003: $i,SV763: $i,SV435: $i,SV29: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV29 @ SV435 @ SV763 @ SV1003 ) @ ( tc_List_Olist @ SV1003 ) )
= ( c_Nat_Osize__class_Osize @ SV29 @ ( tc_List_Olist @ SV1003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2657,plain,
! [SV436: $i,SV31: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV31 @ SV436 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV436 @ ( c_Suc @ SV31 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2658,plain,
! [SV1004: $i,SV764: $i,SV438: $i,SV33: $i] :
( ( ! [SY3004: $i] :
( ( ( c_List_Oreplicate @ SV33 @ SV438 @ SV764 )
!= ( c_List_Oreplicate @ SV1004 @ SY3004 @ SV764 ) )
| ( SV438 = SY3004 )
| ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2659,plain,
! [SV440: $i,SV36: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV36 @ SV440 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV36 ) @ ( c_Suc @ SV440 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2660,plain,
! [SV441: $i,SV37: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV37 ) @ ( c_Suc @ SV441 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV37 @ SV441 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2661,plain,
! [SV442: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV38 @ SV442 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV38 ) @ ( c_Suc @ SV442 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2662,plain,
! [SV765: $i,SV443: $i,SV40: $i] :
( ( c_ListOrder_Ostep1 @ SV40 @ SV443 @ ( c_List_Olist_ONil @ SV765 ) @ SV765 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2663,plain,
! [SV766: $i,SV444: $i,SV41: $i] :
( ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Olist_ONil @ SV444 ) @ SV766 @ SV444 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2664,plain,
! [SV445: $i,SV42: $i] :
( ( ( ( c_List_Orotate1 @ SV42 @ SV445 )
= ( c_List_Olist_ONil @ SV445 ) )
= $false )
| ( ( SV42
= ( c_List_Olist_ONil @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2665,plain,
! [SV446: $i,SV44: $i] :
( ( ( ( c_List_Oremdups @ SV44 @ SV446 )
= SV44 )
= $false )
| ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ SV44 @ SV446 ) @ ( tc_List_Olist @ SV446 ) )
= ( c_Nat_Osize__class_Osize @ SV44 @ ( tc_List_Olist @ SV446 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2666,plain,
! [SV1005: $i,SV767: $i,SV447: $i,SV45: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV45 @ SV447 @ SV767 @ SV1005 ) @ ( tc_List_Olist @ SV1005 ) )
= ( c_Nat_Osize__class_Osize @ SV447 @ ( tc_List_Olist @ SV767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2667,plain,
! [SV1006: $i,SV768: $i,SV448: $i,SV46: $i] :
( ( ! [SY3005: $i] :
( ( c_List_Omap @ SV46 @ ( c_List_Oreplicate @ SV448 @ SV768 @ SV1006 ) @ SV1006 @ SY3005 )
= ( c_List_Oreplicate @ SV448 @ ( hAPP @ SV46 @ SV768 ) @ SY3005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2668,plain,
! [SV450: $i,SV48: $i] :
( ( ( ( c_Suc @ SV48 )
= ( c_Suc @ SV450 ) )
= $false )
| ( ( SV48 = SV450 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2669,plain,
! [SV451: $i,SV49: $i] :
( ( ( ( c_Suc @ SV49 )
= ( c_Suc @ SV451 ) )
= $false )
| ( ( SV49 = SV451 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2670,plain,
! [SV1007: $i,SV770: $i,SV452: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV452 ) @ SV770 ) @ SV1007 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV770 ) @ SV1007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2671,plain,
! [SV771: $i,SV453: $i,SV51: $i] :
( ( ( ! [SY2777: $i] :
( ( c_List_Ofilter @ SV51 @ ( c_List_Oreplicate @ SV453 @ SV771 @ SY2777 ) @ SY2777 )
= ( c_List_Oreplicate @ SV453 @ SV771 @ SY2777 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV51 @ SV771 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2672,plain,
! [SV1008: $i,SV772: $i,SV454: $i,SV52: $i] :
( ( ! [SY3006: $i] :
( ( ( c_List_Omap @ SV52 @ SV454 @ SV772 @ SV1008 )
!= ( c_List_Omap @ SV52 @ SY3006 @ SV772 @ SV1008 ) )
| ( ( c_Nat_Osize__class_Osize @ SV454 @ ( tc_List_Olist @ SV772 ) )
= ( c_Nat_Osize__class_Osize @ SY3006 @ ( tc_List_Olist @ SV772 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2673,plain,
! [SV455: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV455 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SV455 ) @ tc_nat ) )
= $true )
| ( ( SV54 = SV455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2674,plain,
! [SV55: $i,SV456: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV456 @ ( c_Suc @ SV55 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV456 @ SV55 @ tc_nat )
= $true )
| ( ( SV55 = SV456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2675,plain,
! [SV457: $i,SV56: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV56 @ ( c_Suc @ SV457 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV56 @ SV457 @ tc_nat )
= $true )
| ( ( SV56 = SV457 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2676,plain,
! [SV1009: $i,SV773: $i,SV458: $i,SV57: $i] :
( ( ! [SY3007: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV57 @ SV458 @ SV773 ) @ SV1009 @ SY3007 @ SV773 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV57 @ SV1009 @ SY3007 @ SV773 ) @ SV458 @ SV773 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_Nat_Osize__class_Osize @ SV57 @ ( tc_List_Olist @ SV773 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2677,plain,
! [SV1010: $i,SV774: $i,SV459: $i,SV58: $i] :
( ( ! [SY3008: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV58 @ SV459 @ SV774 ) @ SV1010 @ SY3008 @ SV774 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV58 @ SV1010 @ SY3008 @ SV774 ) @ SV459 @ SV774 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1010 @ ( c_Nat_Osize__class_Osize @ SV58 @ ( tc_List_Olist @ SV774 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2678,plain,
! [SV64: $i,SV1011: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SV1011 @ SV64 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2679,plain,
! [SV65: $i,SV1012: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1012 @ SV1012 @ SV65 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2680,plain,
! [SV66: $i,SV1013: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1013 @ SV1013 @ SV66 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2681,plain,
! [SV1014: $i,SV776: $i,SV463: $i,SV67: $i] :
( ( ( c_ListOrder_Ostep1 @ SV67 @ SV463 @ SV776 @ SV1014 )
| ( SV776 = SV463 )
| ! [SY3009: $i,SY3010: $i] :
~ ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SY3009 @ SV463 @ SV1014 ) @ ( c_List_Olist_OCons @ SY3010 @ SV776 @ SV1014 ) @ SV1014 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2682,plain,
! [SV68: $i,SV1015: $i] :
( ( ( ! [SY3011: $i] :
( ( c_HOL_Oord__class_Oless @ SV1015 @ SY3011 @ SV68 )
| ( SY3011 = SV1015 )
| ( c_HOL_Oord__class_Oless @ SY3011 @ SV1015 @ SV68 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2683,plain,
! [SV69: $i,SV1016: $i] :
( ( ( ! [SY3012: $i] :
( ( SV1016 = SY3012 )
| ( c_HOL_Oord__class_Oless @ SY3012 @ SV1016 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV1016 @ SY3012 @ SV69 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2684,plain,
! [SV70: $i,SV464: $i] :
( ( ( SV464 = SV70 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV70 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV70 @ SV464 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2685,plain,
! [SV777: $i,SV465: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV465 ) @ SV777 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV465 @ SV777 @ tc_nat )
| ( SV777 = SV465 )
| ( c_HOL_Oord__class_Oless @ SV777 @ SV465 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2686,plain,
! [SV72: $i,SV466: $i] :
( ( ( SV466 = SV72 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV466 @ SV72 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV72 @ SV466 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2687,plain,
! [SV73: $i,SV1017: $i] :
( ( ( ! [SY3013: $i] :
( ( c_HOL_Oord__class_Oless @ SV1017 @ SY3013 @ SV73 )
| ( SY3013 = SV1017 )
| ( c_HOL_Oord__class_Oless @ SY3013 @ SV1017 @ SV73 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2688,plain,
! [SV1018: $i,SV778: $i,SV467: $i,SV74: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV74 @ SV467 @ SV778 ) @ ( c_List_Oreplicate @ SV1018 @ SV467 @ SV778 ) @ SV778 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV1018 @ SV467 @ SV778 ) @ ( c_List_Oreplicate @ SV74 @ SV467 @ SV778 ) @ SV778 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2689,plain,
! [SV75: $i,SV1019: $i] :
( ( ( ! [SY3014: $i] :
( ( c_HOL_Oord__class_Oless @ SV1019 @ SY3014 @ SV75 )
| ( SY3014 = SV1019 )
| ( c_HOL_Oord__class_Oless @ SY3014 @ SV1019 @ SV75 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2690,plain,
! [SV76: $i,SV1020: $i] :
( ( ( ! [SY3015: $i] :
( ( SV1020 = SY3015 )
| ( c_HOL_Oord__class_Oless @ SV1020 @ SY3015 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SY3015 @ SV1020 @ SV76 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2691,plain,
! [SV468: $i,SV77: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV77 )
= $false )
| ( ( ! [SY2308: $i,SY2309: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV468 @ SY2308 @ SV77 ) @ SY2309 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SY2308 @ SY2309 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2692,plain,
! [SV469: $i,SV78: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV78 )
= $false )
| ( ( ! [SY2310: $i,SY2311: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV469 @ SY2310 @ SV78 ) @ SY2311 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SY2311 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2693,plain,
! [SV83: $i,SV470: $i,SV1021: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1021 @ SV470 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV83 @ SV1021 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV83 ) @ SV470 @ tc_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2694,plain,
! [SV1022: $i,SV779: $i,SV84: $i] :
( ( ( ( c_List_Oreplicate @ SV84 @ SV779 @ SV1022 )
!= ( c_List_Olist_ONil @ SV1022 ) )
= $true )
| ( ( SV84
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2695,plain,
! [SV1023: $i,SV473: $i,SV88: $i] :
( ( ( ( c_List_Olist_ONil @ SV88 )
!= ( c_List_Oreplicate @ SV473 @ SV1023 @ SV88 ) )
= $true )
| ( ( SV473
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2696,plain,
! [SV474: $i,SV89: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV89 @ ( tc_List_Olist @ SV474 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV89
= ( c_List_Olist_ONil @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2697,plain,
! [SV1024: $i,SV781: $i,SV475: $i,SV92: $i] :
( ( ( c_ListOrder_Ostep1 @ SV92 @ SV475 @ SV781 @ SV1024 )
| ! [SY3016: $i,SY3017: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY3016 ) @ SY3017 ) )
| ~ ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SY3016 @ SV475 @ SV1024 ) @ ( c_List_Olist_OCons @ SY3017 @ SV781 @ SV1024 ) @ SV1024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2698,plain,
! [SV1025: $i,SV782: $i,SV476: $i,SV93: $i] :
( ( ! [SY3018: $i] :
( ( c_ListOrder_Ostep1 @ SV93 @ ( c_List_Olist_OCons @ SV476 @ SV782 @ SV1025 ) @ ( c_List_Olist_OCons @ SV476 @ SY3018 @ SV1025 ) @ SV1025 )
| ~ ( c_ListOrder_Ostep1 @ SV93 @ SV782 @ SY3018 @ SV1025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2699,plain,
! [SV477: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV94 ) @ SV477 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV94 @ SV477 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2700,plain,
! [SV478: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ SV478 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Suc @ SV478 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2701,plain,
! [SV98: $i,SV1026: $i] :
( ( ( ! [SY3019: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV1026 @ SY3019 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY3019 @ SV1026 @ SV98 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2702,plain,
! [SV1027: $i,SV784: $i,SV481: $i,SV99: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV784 ) @ SV1027 ) )
| ! [SY3020: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SY3020 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SV784 ) @ SY3020 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2703,plain,
! [SV1028: $i,SV785: $i,SV482: $i,SV100: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1028 ) )
| ! [SY3021: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SY3021 ) @ SV1028 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SY3021 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2704,plain,
! [SV101: $i,SV1029: $i] :
( ( ( ! [SY3022: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SY3022 @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SY3022 @ SV1029 @ SV101 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2705,plain,
! [SV102: $i,SV1030: $i] :
( ( ( ! [SY3023: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV1030 @ SY3023 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SY3023 @ SV1030 @ SV102 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2706,plain,
! [SV103: $i,SV1031: $i] :
( ( ( ! [SY3024: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV1031 @ SY3024 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SY3024 @ SV1031 @ SV103 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2707,plain,
! [SV786: $i,SV484: $i,SV105: $i] :
( ( ( SV105
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 ) @ SV786 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 ) @ ( c_List_Oappend @ SV786 @ ( c_List_Olist_OCons @ SV484 @ ( 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)],[2372]) ).
thf(2708,plain,
! [SV486: $i,SV107: $i,SV1032: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1032 @ SV107 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV486 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1032 @ ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV486 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_List_Oappend @ SV107 @ ( c_List_Olist_OCons @ SV486 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2709,plain,
! [SV789: $i,SV487: $i,SV109: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV109 @ SV487 @ SV789 ) @ SV789 )
= ( c_List_Olast @ SV487 @ SV789 ) )
= $true )
| ( ( SV487
= ( c_List_Olist_ONil @ SV789 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2710,plain,
! [SV790: $i,SV490: $i,SV112: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV112 @ SV490 @ SV790 ) @ SV790 )
= ( c_List_Olist_OCons @ SV112 @ ( c_List_Obutlast @ SV490 @ SV790 ) @ SV790 ) )
= $true )
| ( ( SV490
= ( c_List_Olist_ONil @ SV790 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2711,plain,
! [SV1033: $i,SV791: $i,SV491: $i,SV113: $i] :
( ( ! [SY3025: $i] :
( ( ( c_List_Oappend @ SV113 @ SV491 @ SV791 )
!= ( c_List_Olist_OCons @ SV1033 @ SY3025 @ SV791 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1033 @ SY3025 @ SV113 @ SV491 @ SV791 ) @ SV491 @ SV791 )
= SY3025 )
| ( SV491
= ( c_List_Olist_OCons @ SV1033 @ SY3025 @ SV791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2712,plain,
! [SV1034: $i,SV792: $i,SV492: $i,SV114: $i] :
( ( ! [SY3026: $i] :
( ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
!= ( c_List_Oappend @ SV1034 @ SY3026 @ SV792 ) )
| ( ( c_List_Olist_OCons @ SV114 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV114 @ SV492 @ SV1034 @ SY3026 @ SV792 ) @ SV792 )
= SV1034 )
| ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
= SY3026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(2713,plain,
! [SV1035: $i,SV793: $i,SV493: $i,SV115: $i] :
( ( ! [SY3027: $i] :
( ( ( c_List_Oappend @ SV115 @ SV493 @ SV793 )
!= ( c_List_Olist_OCons @ SV1035 @ SY3027 @ SV793 ) )
| ( SV115
= ( c_List_Olist_OCons @ SV1035 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1035 @ SY3027 @ SV115 @ SV493 @ SV793 ) @ SV793 ) )
| ( SV493
= ( c_List_Olist_OCons @ SV1035 @ SY3027 @ SV793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(2714,plain,
! [SV1036: $i,SV794: $i,SV494: $i,SV116: $i] :
( ( ! [SY3028: $i] :
( ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
!= ( c_List_Oappend @ SV1036 @ SY3028 @ SV794 ) )
| ( SV494
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV116 @ SV494 @ SV1036 @ SY3028 @ SV794 ) @ SY3028 @ SV794 ) )
| ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
= SY3028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2715,plain,
! [SV1037: $i,SV795: $i,SV495: $i,SV117: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV117 @ SV495 @ SV795 ) @ ( c_List_Olist_OCons @ SV495 @ SV1037 @ SV795 ) @ SV795 )
= ( c_List_Olist_OCons @ SV495 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV117 @ SV495 @ SV795 ) @ SV1037 @ SV795 ) @ SV795 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2716,plain,
! [SV796: $i,SV497: $i,SV119: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV119 @ SV497 @ SV796 ) @ SV796 )
= ( c_List_Olast @ SV497 @ SV796 ) )
= $true )
| ( ( SV497
= ( c_List_Olist_ONil @ SV796 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2717,plain,
! [SV797: $i,SV499: $i,SV121: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV121 @ SV499 @ SV797 ) @ SV797 )
= ( c_List_Oappend @ SV121 @ ( c_List_Obutlast @ SV499 @ SV797 ) @ SV797 ) )
= $true )
| ( ( SV499
= ( c_List_Olist_ONil @ SV797 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2718,plain,
! [SV1038: $i,SV798: $i,SV500: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV500 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV798 ) @ SV1038 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV500 ) @ SV1038 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2719,plain,
! [SV799: $i,SV501: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV501 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV799 ) @ SV501 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SV799 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2720,plain,
! [SV800: $i,SV502: $i,SV124: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV502 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV800 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV502 ) @ SV800 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2721,plain,
! [SV503: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV125 ) @ SV503 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV125 ) ) @ ( c_Lambda_OdB_OAbs @ SV503 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2722,plain,
! [SV801: $i,SV504: $i,SV126: $i] :
( ( ( ! [SY2808: $i] :
( ( c_List_Ofilter @ SV126 @ ( c_List_Oreplicate @ SV504 @ SV801 @ SY2808 ) @ SY2808 )
= ( c_List_Olist_ONil @ SY2808 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV126 @ SV801 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2723,plain,
! [SV1039: $i,SV802: $i,SV505: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV127 @ SV505 @ SV802 ) ) @ ( c_Lambda_Osubst @ SV127 @ SV1039 @ SV802 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV505 ) @ SV1039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2724,plain,
! [SV1040: $i,SV803: $i,SV506: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV128 @ SV506 @ SV803 ) ) @ ( c_Lambda_Osubst @ SV1040 @ SV506 @ SV803 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SV1040 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2725,plain,
! [SV1041: $i,SV804: $i,SV507: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV507 @ SV804 ) ) @ ( c_Lambda_Osubst @ SV129 @ SV1041 @ SV804 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV507 ) @ SV1041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2726,plain,
! [SV805: $i,SV508: $i,SV130: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV130 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV508 @ SV130 @ SV805 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV508 ) @ SV130 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV805 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2727,plain,
! [SV1042: $i,SV806: $i,SV509: $i,SV131: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV131 @ SV509 @ SV806 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1042 @ SV806 )
= ( c_List_Olist_OCons @ SV1042 @ SV509 @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2728,plain,
! [SV1043: $i,SV807: $i,SV510: $i,SV132: $i] :
( ( ! [SY3029: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV132 @ SV510 @ SV807 ) @ ( c_Suc @ SV1043 ) @ SY3029 @ SV807 )
= ( c_List_Olist_OCons @ SV132 @ ( c_List_Olist__update @ SV510 @ SV1043 @ SY3029 @ SV807 ) @ SV807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2729,plain,
! [SV809: $i,SV511: $i,SV134: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV134 ) @ SV511 @ SV809 )
= ( c_Lambda_OdB_OVar @ SV134 ) )
= $true )
| ( ( ( SV134 = SV809 )
| ( c_HOL_Oord__class_Oless @ SV809 @ SV134 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(2730,plain,
! [SV810: $i,SV512: $i,SV135: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV135 ) @ SV512 @ SV810 )
= ( c_Lambda_OdB_OVar @ SV135 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV135 @ SV810 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2731,plain,
! [SV811: $i,SV513: $i,SV136: $i] :
( ( ( c_Type_Otyping @ SV136 @ SV513 @ SV811 )
= $true )
| ( ( ! [SY2815: $i] :
( ~ ( c_Type_Otyping @ SV136 @ SY2815 @ SV811 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2815 ) @ SV513 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2732,plain,
! [SV812: $i,SV514: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV137 @ SV514 ) ) @ ( c_Lambda_Olift @ SV812 @ SV514 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV137 ) @ SV812 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2733,plain,
! [SV1044: $i,SV813: $i,SV515: $i,SV138: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV138 @ ( tc_List_Olist @ SV515 ) )
!= ( c_Nat_Osize__class_Osize @ SV813 @ ( tc_List_Olist @ SV1044 ) ) )
| ! [SY3030: $i,SY3031: $i] :
( ( c_Map_Omap__upds @ SY3030 @ ( c_List_Oappend @ SV138 @ SY3031 @ SV515 ) @ SV813 @ SV515 @ SV1044 )
= ( c_Map_Omap__upds @ SY3030 @ SV138 @ SV813 @ SV515 @ SV1044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2734,plain,
! [SV1045: $i,SV814: $i,SV516: $i,SV139: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV139 @ ( tc_List_Olist @ SV516 ) )
!= ( c_Nat_Osize__class_Osize @ SV814 @ ( tc_List_Olist @ SV1045 ) ) )
| ! [SY3032: $i,SY3033: $i] :
( ( c_Map_Omap__upds @ SY3032 @ SV139 @ ( c_List_Oappend @ SV814 @ SY3033 @ SV1045 ) @ SV516 @ SV1045 )
= ( c_Map_Omap__upds @ SY3032 @ SV139 @ SV814 @ SV516 @ SV1045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2735,plain,
! [SV517: $i,SV140: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV140 @ SV517 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV140 ) @ SV517 )
= ( c_Lambda_OdB_OVar @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2736,plain,
! [SV815: $i,SV518: $i,SV141: $i] :
( ( ( ( c_Lambda_Oliftn @ SV141 @ ( c_Lambda_OdB_OVar @ SV518 ) @ SV815 )
= ( c_Lambda_OdB_OVar @ SV518 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV518 @ SV815 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2737,plain,
! [SV519: $i,SV1046: $i,SV142: $i] :
( ( ( ! [SY3034: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV142 @ SV1046 @ ( tc_fun @ SY3034 @ tc_bool ) ) @ SV519 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV142 @ SV519 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2738,plain,
! [SV143: $i,SV1047: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1047 @ ( c_List_Olist_ONil @ SV143 ) @ SV143 ) @ SV143 )
= $true )
| ( ( class_Orderings_Olinorder @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2739,plain,
! [SV520: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV144 ) @ SV520 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV144 ) ) @ ( c_Lambda_OdB_OAbs @ SV520 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2740,plain,
! [SV1048: $i,SV817: $i,SV522: $i,SV146: $i] :
( ( ! [SY3035: $i,SY3036: $i] :
( ( c_List_Ofoldl @ SV146 @ SV522 @ ( c_List_Oappend @ SV817 @ SV1048 @ SY3035 ) @ SY3036 @ SY3035 )
= ( c_List_Ofoldl @ SV146 @ ( c_List_Ofoldl @ SV146 @ SV522 @ SV817 @ SY3036 @ SY3035 ) @ SV1048 @ SY3036 @ SY3035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2741,plain,
! [SV1049: $i,SV818: $i,SV523: $i,SV147: $i] :
( ( ( c_List_Ofilter @ SV147 @ ( c_List_Oappend @ SV523 @ SV818 @ SV1049 ) @ SV1049 )
= ( c_List_Oappend @ ( c_List_Ofilter @ SV147 @ SV523 @ SV1049 ) @ ( c_List_Ofilter @ SV147 @ SV818 @ SV1049 ) @ SV1049 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2742,plain,
! [SV819: $i,SV524: $i,SV149: $i] :
( ( ( ! [SY2826: $i] :
( ( c_List_Omap @ SV149 @ SV524 @ SV819 @ SY2826 )
!= ( c_List_Olist_ONil @ SY2826 ) ) )
= $true )
| ( ( SV524
= ( c_List_Olist_ONil @ SV819 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2743,plain,
! [SV525: $i,SV150: $i] :
( ( ( c_List_Onull @ SV150 @ SV525 )
= $false )
| ( ( SV150
= ( c_List_Olist_ONil @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2744,plain,
! [SV820: $i,SV526: $i,SV153: $i] :
( ( ( SV153
!= ( c_List_Oappend @ SV526 @ SV153 @ SV820 ) )
= $true )
| ( ( SV526
= ( c_List_Olist_ONil @ SV820 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(2745,plain,
! [SV821: $i,SV527: $i,SV154: $i] :
( ( ( ( c_List_Oappend @ SV154 @ SV527 @ SV821 )
!= SV527 )
= $true )
| ( ( SV154
= ( c_List_Olist_ONil @ SV821 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2746,plain,
! [SV822: $i,SV528: $i,SV155: $i] :
( ( ( SV155
!= ( c_List_Oappend @ SV155 @ SV528 @ SV822 ) )
= $true )
| ( ( SV528
= ( c_List_Olist_ONil @ SV822 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2747,plain,
! [SV823: $i,SV529: $i,SV156: $i] :
( ( ( ( c_List_Oappend @ SV156 @ SV529 @ SV823 )
!= SV156 )
= $true )
| ( ( SV529
= ( c_List_Olist_ONil @ SV823 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2748,plain,
! [SV530: $i,SV157: $i] :
( ( ( ( c_List_Oremdups @ SV157 @ SV530 )
= ( c_List_Olist_ONil @ SV530 ) )
= $false )
| ( ( SV157
= ( c_List_Olist_ONil @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2749,plain,
! [SV824: $i,SV531: $i,SV158: $i] :
( ( ( ( c_List_Orotate @ SV158 @ SV531 @ SV824 )
!= ( c_List_Olist_ONil @ SV824 ) )
= $true )
| ( ( SV531
= ( c_List_Olist_ONil @ SV824 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2750,plain,
! [SV532: $i,SV159: $i] :
( ( ( ( c_List_Olist_ONil @ SV159 )
= ( c_List_Orev @ SV532 @ SV159 ) )
= $false )
| ( ( SV532
= ( c_List_Olist_ONil @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2751,plain,
! [SV825: $i,SV533: $i,SV160: $i] :
( ( ( c_List_Olist_ONil @ SV160 )
= ( c_List_Olist_OCons @ SV533 @ SV825 @ SV160 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2752,plain,
! [SV826: $i,SV534: $i,SV161: $i] :
( ( ( ( c_List_Oappend @ SV161 @ SV534 @ SV826 )
!= ( c_List_Olist_ONil @ SV826 ) )
= $true )
| ( ( SV534
= ( c_List_Olist_ONil @ SV826 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2753,plain,
! [SV827: $i,SV535: $i,SV162: $i] :
( ( ( ( c_List_Oappend @ SV162 @ SV535 @ SV827 )
!= ( c_List_Olist_ONil @ SV827 ) )
= $true )
| ( ( SV162
= ( c_List_Olist_ONil @ SV827 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2754,plain,
! [SV828: $i,SV536: $i,SV163: $i] :
( ( ( ( c_List_Olist_ONil @ SV163 )
!= ( c_List_Oappend @ SV536 @ SV828 @ SV163 ) )
= $true )
| ( ( SV828
= ( c_List_Olist_ONil @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2755,plain,
! [SV1050: $i,SV537: $i,SV164: $i] :
( ( ( ( c_List_Olist_ONil @ SV164 )
!= ( c_List_Oappend @ SV537 @ SV1050 @ SV164 ) )
= $true )
| ( ( SV537
= ( c_List_Olist_ONil @ SV164 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2756,plain,
! [SV1051: $i,SV829: $i,SV538: $i,SV165: $i] :
( ( ( c_List_Ofoldl @ SV165 @ SV538 @ ( c_List_Olist_ONil @ SV829 ) @ SV1051 @ SV829 )
= SV538 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(2757,plain,
! [SV1052: $i,SV830: $i,SV539: $i,SV167: $i] :
( ( ( ( c_List_Olist_ONil @ SV167 )
!= ( c_List_Omap @ SV539 @ SV830 @ SV1052 @ SV167 ) )
| ( SV830
= ( c_List_Olist_ONil @ SV1052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2758,plain,
! [SV831: $i,SV545: $i,SV173: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV173 ) ) @ SV545 ) @ SV831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV545 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV173 @ SV545 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2759,plain,
! [SV832: $i,SV546: $i,SV174: $i] :
( ( ( SV174
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV546 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV546 @ SV832 @ SV174 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV546 ) @ SV832 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2760,plain,
! [SV833: $i,SV176: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV176 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV176 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV176 @ SV833 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2761,plain,
! [SV834: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV177 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV177 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV177 @ SV834 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2762,plain,
! [SV835: $i,SV178: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV178 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV178 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV178 @ SV835 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2763,plain,
! [SV836: $i,SV179: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV179 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV179 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV179 @ SV836 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2764,plain,
! [SV837: $i,SV180: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV180 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV180 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV180 @ SV837 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2433]) ).
thf(2765,plain,
! [SV838: $i,SV181: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV181 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV181 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV181 @ SV838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2766,plain,
! [SV839: $i,SV182: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV182 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV182 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV182 @ SV839 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2767,plain,
! [SV840: $i,SV183: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV183 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV183 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV183 @ SV840 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2768,plain,
! [SV841: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV184 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV184 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV184 @ SV841 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2437]) ).
thf(2769,plain,
! [SV1053: $i,SV843: $i,SV549: $i,SV186: $i] :
( ( ! [SY3037: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SV549 @ SV843 @ SV1053 ) @ SV1053 ) @ ( c_Nat_Osize__class_Osize @ SV186 @ ( tc_List_Olist @ SV1053 ) ) @ SY3037 @ SV1053 )
= ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SY3037 @ SV843 @ SV1053 ) @ SV1053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(2770,plain,
! [SV844: $i,SV550: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV187 @ SV550 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV844 @ SV550 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV187 ) @ SV844 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2771,plain,
! [SV845: $i,SV551: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV551 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV845 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV551 @ SV845 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2772,plain,
! [SV846: $i,SV552: $i,SV189: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV189 @ SV552 ) ) )
= $true )
| ( ( ! [SY2831: $i] :
( ! [SY2832: $i] :
( ( c_List_Olist_OCons @ SV552 @ ( c_List_Ofilter @ SV189 @ SY2832 @ SY2831 ) @ SY2831 )
= ( c_List_Ofilter @ SV189 @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV552 @ SY2832 @ SY2831 ) @ SY2831 ) @ SY2831 ) )
| ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ SV189 @ SV846 @ SY2831 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2773,plain,
! [SV847: $i,SV553: $i,SV190: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV190 @ SV553 ) ) )
= $true )
| ( ( ! [SY2833: $i] :
( ! [SY2834: $i] :
( ( c_List_Ofilter @ SV190 @ ( c_List_Oappend @ SV847 @ ( c_List_Olist_OCons @ SV553 @ SY2834 @ SY2833 ) @ SY2833 ) @ SY2833 )
= ( c_List_Olist_OCons @ SV553 @ ( c_List_Ofilter @ SV190 @ SY2834 @ SY2833 ) @ SY2833 ) )
| ( hBOOL @ ( hAPP @ SV190 @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ SV190 @ SV847 @ SY2833 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2774,plain,
! [SV1054: $i,SV848: $i,SV554: $i,SV191: $i] :
( ( ! [SY3038: $i] :
( ( ( c_List_Olist_OCons @ SV191 @ SV554 @ SV848 )
!= ( c_List_Oappend @ SV1054 @ SY3038 @ SV848 ) )
| ( SV554
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV191 @ SV554 @ SV1054 @ SY3038 @ SV848 ) @ SY3038 @ SV848 ) )
| ( SV1054
= ( c_List_Olist_ONil @ SV848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(2775,plain,
! [SV1055: $i,SV849: $i,SV555: $i,SV192: $i] :
( ( ! [SY3039: $i] :
( ( ( c_List_Oappend @ SV192 @ SV555 @ SV849 )
!= ( c_List_Olist_OCons @ SV1055 @ SY3039 @ SV849 ) )
| ( SV192
= ( c_List_Olist_OCons @ SV1055 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1055 @ SY3039 @ SV192 @ SV555 @ SV849 ) @ SV849 ) )
| ( SV192
= ( c_List_Olist_ONil @ SV849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(2776,plain,
! [SV1056: $i,SV852: $i,SV558: $i,SV195: $i] :
( ( ( SV195 = SV558 )
| ( SV852 = SV1056 )
| ! [SY3040: $i,SY3041: $i] :
~ ( c_ListOrder_Ostep1 @ SY3040 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SV852 @ ( c_List_Olist_ONil @ SY3041 ) @ SY3041 ) @ SY3041 ) @ ( c_List_Oappend @ SV558 @ ( c_List_Olist_OCons @ SV1056 @ ( c_List_Olist_ONil @ SY3041 ) @ SY3041 ) @ SY3041 ) @ SY3041 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2777,plain,
! [SV1057: $i,SV853: $i,SV559: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SV559 ) @ SV853 ) )
| ( SV559 = SV853 )
| ! [SY3042: $i,SY3043: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SV1057 @ ( c_List_Olist_OCons @ SV559 @ ( c_List_Olist_ONil @ SY3042 ) @ SY3042 ) @ SY3042 ) @ ( c_List_Oappend @ SY3043 @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_ONil @ SY3042 ) @ SY3042 ) @ SY3042 ) @ SY3042 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2778,plain,
! [SV1058: $i,SV854: $i,SV560: $i,SV197: $i] :
( ( ! [SY3044: $i] :
( ( ( c_List_Oappend @ SV197 @ SV560 @ SV854 )
!= ( c_List_Olist_OCons @ SV1058 @ SY3044 @ SV854 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1058 @ SY3044 @ SV197 @ SV560 @ SV854 ) @ SV560 @ SV854 )
= SY3044 )
| ( SV197
= ( c_List_Olist_ONil @ SV854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2779,plain,
! [SV1059: $i,SV855: $i,SV561: $i,SV198: $i] :
( ( ! [SY3045: $i] :
( ( ( c_List_Olist_OCons @ SV198 @ SV561 @ SV855 )
!= ( c_List_Oappend @ SV1059 @ SY3045 @ SV855 ) )
| ( ( c_List_Olist_OCons @ SV198 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV198 @ SV561 @ SV1059 @ SY3045 @ SV855 ) @ SV855 )
= SV1059 )
| ( SV1059
= ( c_List_Olist_ONil @ SV855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2780,plain,
! [SV1060: $i,SV856: $i,SV562: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SV562 ) @ SV856 ) )
| ! [SY3046: $i,SY3047: $i] :
( ( c_ListOrder_Ostep1 @ SV199 @ SV1060 @ SY3046 @ SY3047 )
| ~ ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SV1060 @ ( c_List_Olist_OCons @ SV562 @ ( c_List_Olist_ONil @ SY3047 ) @ SY3047 ) @ SY3047 ) @ ( c_List_Oappend @ SY3046 @ ( c_List_Olist_OCons @ SV856 @ ( c_List_Olist_ONil @ SY3047 ) @ SY3047 ) @ SY3047 ) @ SY3047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2781,plain,
! [SV1061: $i,SV858: $i,SV564: $i,SV201: $i] :
( ( ( SV201 = SV564 )
| ( c_ListOrder_Ostep1 @ SV858 @ SV201 @ SV564 @ SV1061 )
| ! [SY3048: $i,SY3049: $i] :
~ ( c_ListOrder_Ostep1 @ SV858 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SY3048 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ ( c_List_Oappend @ SV564 @ ( c_List_Olist_OCons @ SY3049 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ SV1061 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2782,plain,
! [SV1062: $i,SV860: $i,SV566: $i,SV203: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV203 ) @ SV566 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV860 @ SV1062 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1062
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV203 @ SV566 @ SV860 @ SV1062 ) @ ( c_List_Olist_OCons @ SV566 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1062
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2783,plain,
! [SV862: $i,SV568: $i,SV205: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV205 ) @ SV568 @ SV862 )
= ( c_Lambda_OdB_OVar @ SV205 ) )
= $true )
| ( ( ( SV205 = SV862 )
| ( c_HOL_Oord__class_Oless @ SV862 @ SV205 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2784,plain,
! [SV570: $i,SV207: $i,SV1063: $i] :
( ( ( ! [SY3050: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1063 @ SV207 @ ( tc_fun @ SY3050 @ tc_bool ) ) @ SV570 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV207 @ SV570 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2785,plain,
! [SV1064: $i,SV863: $i,SV571: $i,SV208: $i] :
( ( ! [SY3051: $i] :
( ( c_List_Ofoldl @ SV208 @ SV571 @ SV863 @ SV1064 @ SY3051 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV208 @ SV1064 @ SY3051 @ SV1064 ) @ ( c_List_Orev @ SV863 @ SY3051 ) @ SV571 @ SY3051 @ SV1064 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(2786,plain,
! [SV1065: $i,SV864: $i,SV573: $i,SV210: $i] :
( ( ! [SY3052: $i,SY3053: $i] :
( ( c_List_Omap @ SV210 @ ( c_List_Olist__update @ SV573 @ SV864 @ SV1065 @ SY3052 ) @ SY3052 @ SY3053 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV210 @ SV573 @ SY3052 @ SY3053 ) @ SV864 @ ( hAPP @ SV210 @ SV1065 ) @ SY3053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2787,plain,
! [SV866: $i,SV575: $i,SV212: $i] :
( ( SV212
= ( c_List_Olist_OCons @ SV575 @ SV212 @ SV866 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2788,plain,
! [SV867: $i,SV576: $i,SV213: $i] :
( ( ( c_List_Olist_OCons @ SV213 @ SV576 @ SV867 )
= SV576 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2789,plain,
! [SV868: $i,SV577: $i,SV214: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV214 @ SV577 ) ) @ ( c_Lambda_Olift @ SV868 @ SV577 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV214 ) @ SV868 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2465]) ).
thf(2790,plain,
! [SV578: $i,SV1066: $i,SV215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1066 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1066 @ SV215 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1066 @ SV578 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV215 @ SV578 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2791,plain,
! [SV580: $i,SV1067: $i,SV217: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1067 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1067 @ SV217 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1067 @ SV580 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV217 @ SV580 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2792,plain,
! [SV219: $i,SV1068: $i] :
( ( ( ( c_List_Olinorder__class_Osorted @ SV1068 @ SV219 )
| ! [SY3054: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY3054 @ SV1068 @ SV219 ) @ SV219 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV219 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2793,plain,
! [SV1069: $i,SV871: $i,SV582: $i,SV220: $i] :
( ( ( c_List_Olist_OCons @ SV220 @ ( c_List_Oappend @ SV582 @ SV871 @ SV1069 ) @ SV1069 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV220 @ SV582 @ SV1069 ) @ SV871 @ SV1069 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2794,plain,
! [SV1070: $i,SV872: $i,SV583: $i,SV221: $i] :
( ( ( c_List_Olist_OCons @ SV221 @ ( c_List_Oappend @ SV583 @ SV872 @ SV1070 ) @ SV1070 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV221 @ SV583 @ SV1070 ) @ SV872 @ SV1070 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2795,plain,
! [SV1071: $i,SV874: $i,SV585: $i,SV223: $i] :
( ( ! [SY3055: $i,SY3056: $i] :
( ( c_List_Olist_Olist__case @ SV223 @ SV585 @ ( c_List_Olist_OCons @ SV874 @ SV1071 @ SY3055 ) @ SY3056 @ SY3055 )
= ( hAPP @ ( hAPP @ SV585 @ SV874 ) @ SV1071 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2796,plain,
! [SV1072: $i,SV875: $i,SV586: $i,SV224: $i] :
( ( ! [SY3057: $i] :
( ( c_List_Omap @ SV224 @ ( c_List_Olist_OCons @ SV586 @ SV875 @ SV1072 ) @ SV1072 @ SY3057 )
= ( c_List_Olist_OCons @ ( hAPP @ SV224 @ SV586 ) @ ( c_List_Omap @ SV224 @ SV875 @ SV1072 @ SY3057 ) @ SY3057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2797,plain,
! [SV1073: $i,SV876: $i,SV587: $i,SV225: $i] :
( ( ! [SY3058: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV225 @ SV587 ) @ ( c_List_Omap @ SV225 @ SV876 @ SV1073 @ SY3058 ) @ SY3058 )
= ( c_List_Omap @ SV225 @ ( c_List_Olist_OCons @ SV587 @ SV876 @ SV1073 ) @ SV1073 @ SY3058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2798,plain,
! [SV1074: $i,SV877: $i,SV588: $i,SV226: $i] :
( ( ! [SY3059: $i] :
( ( c_List_Omap @ SV226 @ ( c_List_Olist_OCons @ SV588 @ SV877 @ SV1074 ) @ SV1074 @ SY3059 )
= ( c_List_Olist_OCons @ ( hAPP @ SV226 @ SV588 ) @ ( c_List_Omap @ SV226 @ SV877 @ SV1074 @ SY3059 ) @ SY3059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2799,plain,
! [SV1075: $i,SV878: $i,SV589: $i,SV227: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV227 @ SV589 @ SV878 ) @ SV1075 @ SV878 )
= ( c_List_Olist_OCons @ SV227 @ ( c_List_Oappend @ SV589 @ SV1075 @ SV878 ) @ SV878 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2800,plain,
! [SV1076: $i,SV879: $i,SV590: $i,SV228: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV228 @ SV590 @ SV879 ) @ SV1076 @ SV879 )
= ( c_List_Olist_OCons @ SV228 @ ( c_List_Oappend @ SV590 @ SV1076 @ SV879 ) @ SV879 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2801,plain,
! [SV1077: $i,SV591: $i,SV229: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV229 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV591 @ SV1077 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV229 )
= SV591 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2802,plain,
! [SV592: $i,SV230: $i] :
( ( ( class_Orderings_Olinorder @ SV230 )
= $false )
| ( ( ! [SY2497: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV592 @ SY2497 @ SV230 ) @ SV230 )
| ! [SY2498: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2498 @ ( c_List_Olist_OCons @ SV592 @ SY2497 @ SV230 ) @ SV230 ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2803,plain,
! [SV231: $i,SV1078: $i] :
( ( ( ! [SY3060: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1078 @ SY3060 @ SV231 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3060 @ SV1078 @ SV231 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(2804,plain,
! [SV232: $i,SV1079: $i] :
( ( ( ! [SY3061: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1079 @ SY3061 @ SV232 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3061 @ SV1079 @ SV232 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(2805,plain,
! [SV1080: $i,SV881: $i,SV594: $i,SV234: $i] :
( ( ( ( c_List_Orev @ SV234 @ SV594 )
!= ( c_List_Olist_OCons @ SV881 @ SV1080 @ SV594 ) )
| ( SV234
= ( c_List_Oappend @ ( c_List_Orev @ SV1080 @ SV594 ) @ ( c_List_Olist_OCons @ SV881 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2806,plain,
! [SV1081: $i,SV882: $i,SV596: $i,SV236: $i] :
( ( ! [SY3062: $i,SY3063: $i] :
( ( c_List_Ofoldl @ SV236 @ SV596 @ ( c_List_Olist_OCons @ SV882 @ SV1081 @ SY3062 ) @ SY3063 @ SY3062 )
= ( c_List_Ofoldl @ SV236 @ ( hAPP @ ( hAPP @ SV236 @ SV596 ) @ SV882 ) @ SV1081 @ SY3063 @ SY3062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2807,plain,
! [SV1082: $i,SV884: $i,SV598: $i,SV238: $i] :
( ( ! [SY3064: $i] :
( ( c_List_Olist_OCons @ SV238 @ SV598 @ SV884 )
!= ( c_List_Ofilter @ SV1082 @ SY3064 @ SV884 ) )
| ( hBOOL @ ( hAPP @ SV1082 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(2808,plain,
! [SV1083: $i,SV600: $i,SV240: $i] :
( ( ( ! [SY3065: $i] :
( ( c_List_Ofilter @ SV240 @ ( c_List_Olist_OCons @ SV600 @ SV1083 @ SY3065 ) @ SY3065 )
= ( c_List_Olist_OCons @ SV600 @ ( c_List_Ofilter @ SV240 @ SV1083 @ SY3065 ) @ SY3065 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV240 @ SV600 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2809,plain,
! [SV886: $i,SV601: $i,SV241: $i] :
( ( ( ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SV601 ) @ SV601 )
!= ( c_List_Orev @ SV886 @ SV601 ) )
= $true )
| ( ( SV886
= ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SV601 ) @ SV601 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2810,plain,
! [SV1084: $i,SV887: $i,SV602: $i,SV242: $i] :
( ( ! [SY3066: $i] :
( ( c_Lambda_OdB_OdB__case @ SV242 @ SV602 @ SV887 @ ( c_Lambda_OdB_OAbs @ SV1084 ) @ SY3066 )
= ( hAPP @ SV887 @ SV1084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(2811,plain,
! [SV1085: $i,SV888: $i,SV603: $i,SV243: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV243 @ SV603 @ SV888 ) ) @ ( c_Lambda_Osubst @ SV1085 @ SV603 @ SV888 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV243 ) @ SV1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(2812,plain,
! [SV1086: $i,SV889: $i,SV604: $i,SV244: $i] :
( ( ( c_List_Orev @ ( c_List_Omap @ SV244 @ SV604 @ SV889 @ SV1086 ) @ SV1086 )
= ( c_List_Omap @ SV244 @ ( c_List_Orev @ SV604 @ SV889 ) @ SV889 @ SV1086 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2813,plain,
! [SV1087: $i,SV890: $i,SV605: $i,SV245: $i] :
( ( ( ( c_List_Oappend @ SV245 @ SV605 @ SV890 )
!= ( c_List_Oappend @ SV1087 @ SV605 @ SV890 ) )
| ( SV245 = SV1087 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(2814,plain,
! [SV1088: $i,SV891: $i,SV606: $i,SV246: $i] :
( ( ( ( c_List_Oappend @ SV246 @ SV606 @ SV891 )
!= ( c_List_Oappend @ SV246 @ SV1088 @ SV891 ) )
| ( SV606 = SV1088 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2815,plain,
! [SV1089: $i,SV892: $i,SV607: $i,SV247: $i] :
( ( ! [SY3067: $i] :
( ( c_List_Ofilter @ SV247 @ SV607 @ SV892 )
!= ( c_List_Olist_OCons @ SV1089 @ SY3067 @ SV892 ) )
| ( hBOOL @ ( hAPP @ SV247 @ SV1089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2816,plain,
! [SV1090: $i,SV893: $i,SV608: $i,SV248: $i] :
( ( ! [SY3068: $i] :
( ( c_List_Orotate @ SV248 @ ( c_List_Omap @ SV608 @ SV893 @ SV1090 @ SY3068 ) @ SY3068 )
= ( c_List_Omap @ SV608 @ ( c_List_Orotate @ SV248 @ SV893 @ SV1090 ) @ SV1090 @ SY3068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(2817,plain,
! [SV1091: $i,SV894: $i,SV612: $i,SV252: $i] :
( ( ! [SY3069: $i,SY3070: $i] :
( ( c_List_Ofoldr @ SV252 @ ( c_List_Oappend @ SV612 @ SV894 @ SV1091 ) @ SY3069 @ SV1091 @ SY3070 )
= ( c_List_Ofoldr @ SV252 @ SV612 @ ( c_List_Ofoldr @ SV252 @ SV894 @ SY3069 @ SV1091 @ SY3070 ) @ SV1091 @ SY3070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(2818,plain,
! [SV1092: $i,SV613: $i,SV253: $i] :
( ( ( ! [SY3071: $i] : ( c_List_Olist__ex @ SV253 @ ( c_List_Olist_OCons @ SV613 @ SV1092 @ SY3071 ) @ SY3071 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV253 @ SV613 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2819,plain,
! [SV895: $i,SV614: $i,SV254: $i] :
( ( ( ( c_List_Orev @ SV254 @ SV614 )
!= ( c_List_Olist_OCons @ SV895 @ ( c_List_Olist_ONil @ SV614 ) @ SV614 ) )
= $true )
| ( ( SV254
= ( c_List_Olist_OCons @ SV895 @ ( c_List_Olist_ONil @ SV614 ) @ SV614 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2820,plain,
! [SV1093: $i,SV896: $i,SV615: $i,SV255: $i] :
( ( ( c_List_Olist__ex @ SV255 @ ( c_List_Olist_OCons @ SV615 @ SV896 @ SV1093 ) @ SV1093 )
| ~ ( c_List_Olist__ex @ SV255 @ SV896 @ SV1093 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2821,plain,
! [SV897: $i,SV616: $i,SV256: $i] :
( ( ( c_List_Olist__ex @ SV256 @ SV616 @ SV897 )
= $true )
| ( ( ! [SY2894: $i] :
( ( hBOOL @ ( hAPP @ SV256 @ SY2894 ) )
| ~ ( c_List_Olist__ex @ SV256 @ ( c_List_Olist_OCons @ SY2894 @ SV616 @ SV897 ) @ SV897 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2822,plain,
! [SV1094: $i,SV898: $i,SV617: $i,SV257: $i] :
( ( ! [SY3072: $i,SY3073: $i] :
( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SV898 @ SV1094 ) @ ( c_List_Olist_OCons @ SY3072 @ SY3073 @ SV1094 ) @ SV1094 )
| ~ ( c_List_Olistrelp @ SV257 @ SV898 @ SY3073 @ SV1094 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SY3072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2823,plain,
! [SV618: $i,SV258: $i] :
( ( ( class_Lattices_Olattice @ SV258 )
= $false )
| ( ( ! [SY2546: $i,SY2547: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ SY2546 @ SV258 ) @ SY2547 @ SV258 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2546 @ SY2547 @ SV258 ) @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2824,plain,
! [SV619: $i,SV259: $i] :
( ( ( class_Lattices_Olattice @ SV259 )
= $false )
| ( ( ! [SY2548: $i,SY2549: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2548 @ SY2549 @ SV259 ) @ SV259 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2548 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ SY2549 @ SV259 ) @ SV259 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2825,plain,
! [SV620: $i,SV260: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV260 )
= $false )
| ( ( ! [SY2550: $i,SY2551: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2550 @ SY2551 @ SV260 ) @ SV260 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2550 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ SY2551 @ SV260 ) @ SV260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2826,plain,
! [SV621: $i,SV261: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV261 )
= $false )
| ( ( ! [SY2552: $i,SY2553: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ SY2552 @ SV261 ) @ SY2553 @ SV261 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2552 @ SY2553 @ SV261 ) @ SV261 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2827,plain,
! [SV1095: $i,SV899: $i,SV622: $i,SV262: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 @ SV622 @ ( tc_fun @ SV899 @ tc_bool ) ) @ SV1095 @ ( tc_fun @ SV899 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV622 @ SV1095 @ ( tc_fun @ SV899 @ tc_bool ) ) @ ( tc_fun @ SV899 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2828,plain,
! [SV1096: $i,SV900: $i,SV623: $i,SV263: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV623 @ SV900 @ ( tc_fun @ SV1096 @ tc_bool ) ) @ ( tc_fun @ SV1096 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV623 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 @ SV900 @ ( tc_fun @ SV1096 @ tc_bool ) ) @ ( tc_fun @ SV1096 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2829,plain,
! [SV624: $i,SV264: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV264 )
= ( c_Lambda_OdB_OAbs @ SV624 ) )
= $false )
| ( ( SV264 = SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2830,plain,
! [SV1097: $i,SV625: $i,SV265: $i] :
( ( ( ! [SY3074: $i] :
( ( c_List_Oremove1 @ SV265 @ ( c_List_Olist_OCons @ SV625 @ SV1097 @ SY3074 ) @ SY3074 )
= ( c_List_Olist_OCons @ SV625 @ ( c_List_Oremove1 @ SV265 @ SV1097 @ SY3074 ) @ SY3074 ) ) )
= $true )
| ( ( SV265 = SV625 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2831,plain,
! [SV901: $i,SV626: $i,SV266: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV266 @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV901 @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV266 ) @ SV901 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2832,plain,
! [SV1098: $i,SV902: $i,SV627: $i,SV267: $i] :
( ( ! [SY3075: $i] :
( ( c_List_Omap @ SV267 @ ( c_List_Oappend @ SV627 @ SV902 @ SV1098 ) @ SV1098 @ SY3075 )
= ( c_List_Oappend @ ( c_List_Omap @ SV267 @ SV627 @ SV1098 @ SY3075 ) @ ( c_List_Omap @ SV267 @ SV902 @ SV1098 @ SY3075 ) @ SY3075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(2833,plain,
! [SV628: $i,SV268: $i] :
( ( ( SV268
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV628 @ SV268 @ t_a ) )
= $true )
| ( ( SV268
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SV628 @ SV268 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SV628 @ SV268 ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2834,plain,
! [SV1099: $i,SV903: $i,SV629: $i,SV269: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV269 ) @ SV629 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV903 ) @ SV1099 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV629 = SV1099 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(2835,plain,
! [SV904: $i,SV630: $i,SV270: $i] :
( ( ( ! [SY2903: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV270 ) @ SV630 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV904 ) @ SY2903 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( SV270 = SV904 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2836,plain,
! [SV905: $i,SV631: $i,SV271: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV271 @ SV631 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV905 ) )
= $true )
| ( ( SV271
= ( c_Lambda_OdB_OAbs @ SV905 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2837,plain,
! [SV1100: $i,SV632: $i,SV272: $i] :
( ( ( ! [SY3076: $i] :
( ( c_List_Oremove1 @ SV272 @ ( c_List_Ofilter @ SV632 @ SV1100 @ SY3076 ) @ SY3076 )
= ( c_List_Ofilter @ SV632 @ SV1100 @ SY3076 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV632 @ SV272 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(2838,plain,
! [SV1101: $i,SV906: $i,SV633: $i,SV273: $i] :
( ( ! [SY3077: $i,SY3078: $i] :
( ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ ( c_List_Olist_OCons @ SV906 @ SV1101 @ SY3077 ) @ SY3078 @ SY3077 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV633 @ SV906 ) @ SV1101 ) @ ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ SV1101 @ SY3078 @ SY3077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(2839,plain,
! [SV907: $i,SV634: $i,SV274: $i] :
( ( ( ( c_List_Orev @ SV274 @ SV634 )
!= ( c_List_Orev @ SV907 @ SV634 ) )
= $true )
| ( ( SV274 = SV907 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(2840,plain,
! [SV1102: $i,SV908: $i,SV635: $i,SV275: $i] :
( ( ! [SY3079: $i] :
( ( c_List_Ofoldr @ SV275 @ SV635 @ SV908 @ SV1102 @ SY3079 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV275 @ SV1102 @ SY3079 @ SY3079 ) @ SV908 @ ( c_List_Orev @ SV635 @ SV1102 ) @ SY3079 @ SV1102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2841,plain,
! [SV1103: $i,SV909: $i,SV636: $i,SV276: $i] :
( ( ! [SY3080: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV276 @ SV636 @ SV909 @ ( c_Lambda_OdB_OAbs @ SV1103 ) @ SY3080 )
= ( hAPP @ ( hAPP @ SV909 @ SV1103 ) @ ( c_Lambda_OdB_OdB__rec @ SV276 @ SV636 @ SV909 @ SV1103 @ SY3080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(2842,plain,
! [SV910: $i,SV637: $i,SV277: $i] :
( ( c_List_Onull @ ( c_List_Olist_OCons @ SV277 @ SV637 @ SV910 ) @ SV910 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2843,plain,
! [SV278: $i,SV1104: $i] :
( ( ( ! [SY3081: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1104 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1104 @ SY3081 @ SV278 ) @ SV278 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1104 @ SY3081 @ SV278 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2844,plain,
! [SV279: $i,SV1105: $i] :
( ( ( ! [SY3082: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1105 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1105 @ SY3082 @ SV279 ) @ SV279 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1105 @ SY3082 @ SV279 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(2845,plain,
! [SV1106: $i,SV912: $i,SV639: $i,SV281: $i] :
( ( ! [SY3083: $i,SY3084: $i] :
( ( c_List_Ofoldr @ SV281 @ ( c_List_Olist_OCons @ SV639 @ SV912 @ SV1106 ) @ SY3083 @ SV1106 @ SY3084 )
= ( hAPP @ ( hAPP @ SV281 @ SV639 ) @ ( c_List_Ofoldr @ SV281 @ SV912 @ SY3083 @ SV1106 @ SY3084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(2846,plain,
! [SV1107: $i,SV913: $i,SV640: $i,SV282: $i] :
( ( ! [SY3085: $i] :
( ~ ( hBOOL @ ( hAPP @ SV282 @ ( c_Lambda_OdB_OdB__case @ SV640 @ SV913 @ SV1107 @ ( c_Lambda_OdB_OAbs @ SY3085 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ SV1107 @ SY3085 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2847,plain,
! [SV1108: $i,SV914: $i,SV641: $i,SV283: $i] :
( ( ! [SY3086: $i] :
( ~ ( hBOOL @ ( hAPP @ SV283 @ ( c_Lambda_OdB_OdB__case @ SV641 @ SV914 @ SV1108 @ ( c_Lambda_OdB_OAbs @ SY3086 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ SV1108 @ SY3086 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(2848,plain,
! [SV285: $i,SV1109: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1109 @ SV1109 @ SV285 )
= SV1109 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(2849,plain,
! [SV1110: $i,SV916: $i,SV644: $i,SV287: $i] :
( ( ! [SY3087: $i] :
( ( c_List_Olist_OCons @ SV287 @ SV644 @ SV916 )
!= ( c_List_Olist_OCons @ SV1110 @ SY3087 @ SV916 ) )
| ( SV287 = SV1110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(2850,plain,
! [SV1111: $i,SV917: $i,SV645: $i,SV288: $i] :
( ( ! [SY3088: $i] :
( ( ( c_List_Olist_OCons @ SV288 @ SV645 @ SV917 )
!= ( c_List_Olist_OCons @ SV1111 @ SY3088 @ SV917 ) )
| ( SV645 = SY3088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(2851,plain,
! [SV918: $i,SV646: $i,SV289: $i] :
( ( ( c_Type_Otyping @ SV289 @ SV646 @ SV918 )
= $true )
| ( ( ! [SY2922: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2922 ) @ SV646 ) )
| ~ ( c_Type_Otyping @ SV289 @ SY2922 @ SV918 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2852,plain,
! [SV290: $i,SV1112: $i] :
( ( ( ( c_List_Olinorder__class_Osorted @ SV1112 @ SV290 )
| ! [SY3089: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1112 @ SY3089 @ SV290 ) @ SV290 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(2853,plain,
! [SV291: $i,SV1113: $i] :
( ( ( ( c_List_Olinorder__class_Osorted @ SV1113 @ SV291 )
| ! [SY3090: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY3090 @ SV1113 @ SV291 ) @ SV291 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(2854,plain,
! [SV1114: $i,SV919: $i,SV647: $i,SV292: $i] :
( ( ! [SY3091: $i] :
( ! [SY3092: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV647 @ SV919 @ SV1114 ) @ SY3091 @ SY3092 @ SV1114 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SY3091 @ SY3092 @ SV1114 ) @ SV647 @ SV919 @ SV1114 ) )
| ( SV647 = SY3091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(2855,plain,
! [SV293: $i,SV1115: $i] :
( ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SV1115 @ SV293 ) @ SV293 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1115 @ SV293 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2856,plain,
! [SV1116: $i,SV648: $i,SV294: $i] :
( ( ( ! [SY3093: $i] :
( ( c_List_Ofilter @ SV294 @ ( c_List_Olist_OCons @ SV648 @ SV1116 @ SY3093 ) @ SY3093 )
= ( c_List_Ofilter @ SV294 @ SV1116 @ SY3093 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV294 @ SV648 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(2857,plain,
! [SV1117: $i,SV920: $i,SV649: $i,SV295: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV295 @ SV649 @ ( tc_fun @ SV920 @ tc_bool ) ) @ SV1117 ) )
| ~ ( hBOOL @ ( hAPP @ SV649 @ SV1117 ) )
| ~ ( hBOOL @ ( hAPP @ SV295 @ SV1117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(2858,plain,
! [SV1118: $i,SV922: $i,SV651: $i,SV297: $i] :
( ( ! [SY3094: $i] :
( ( c_List_Oappend @ SV297 @ ( c_List_Olist_OCons @ SV651 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 )
!= ( c_List_Oappend @ SV1118 @ ( c_List_Olist_OCons @ SY3094 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 ) )
| ( SV297 = SV1118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2859,plain,
! [SV1119: $i,SV923: $i,SV652: $i,SV298: $i] :
( ( ! [SY3095: $i] :
( ( ( c_List_Oappend @ SV298 @ ( c_List_Olist_OCons @ SV652 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 )
!= ( c_List_Oappend @ SV1119 @ ( c_List_Olist_OCons @ SY3095 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 ) )
| ( SV652 = SY3095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2860,plain,
! [SV1120: $i,SV924: $i,SV653: $i,SV299: $i] :
( ( ! [SY3096: $i] :
( ~ ( hBOOL @ ( hAPP @ SV299 @ ( c_List_Olist_Olist__case @ SV653 @ SV924 @ ( c_List_Olist_OCons @ SV1120 @ SY3096 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV299 @ ( hAPP @ ( hAPP @ SV924 @ SV1120 ) @ SY3096 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(2861,plain,
! [SV1121: $i,SV925: $i,SV654: $i,SV300: $i] :
( ( ! [SY3097: $i] :
( ~ ( hBOOL @ ( hAPP @ SV300 @ ( c_List_Olist_Olist__case @ SV654 @ SV925 @ ( c_List_Olist_OCons @ SV1121 @ SY3097 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV300 @ ( hAPP @ ( hAPP @ SV925 @ SV1121 ) @ SY3097 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(2862,plain,
! [SV1122: $i,SV926: $i,SV655: $i,SV301: $i] :
( ( ! [SY3098: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV301 @ SV655 @ SV926 @ SV1122 ) @ SV655 @ SY3098 @ SV1122 )
= ( c_List_Olist__update @ SV301 @ SV655 @ SY3098 @ SV1122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(2863,plain,
! [SV1123: $i,SV927: $i,SV656: $i,SV302: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV302 @ SV656 @ SV927 ) @ SV1123 @ SV927 )
= ( c_List_Oappend @ SV302 @ ( c_List_Oappend @ SV656 @ SV1123 @ SV927 ) @ SV927 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2864,plain,
! [SV1124: $i,SV928: $i,SV657: $i,SV303: $i] :
( ( ( c_List_Oappend @ SV303 @ ( c_List_Oappend @ SV657 @ SV928 @ SV1124 ) @ SV1124 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV303 @ SV657 @ SV1124 ) @ SV928 @ SV1124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2865,plain,
! [SV1125: $i,SV929: $i,SV658: $i,SV304: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV304 @ SV658 @ SV929 ) @ SV1125 @ SV929 )
= ( c_List_Oappend @ SV304 @ ( c_List_Oappend @ SV658 @ SV1125 @ SV929 ) @ SV929 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(2866,plain,
! [SV1126: $i,SV930: $i,SV659: $i,SV305: $i] :
( ( ( c_List_Oappend @ SV305 @ ( c_List_Oappend @ SV659 @ SV930 @ SV1126 ) @ SV1126 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV305 @ SV659 @ SV1126 ) @ SV930 @ SV1126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2867,plain,
! [SV306: $i,SV1127: $i] :
( ( ( ! [SY3099: $i] :
( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV1127 @ SY3099 @ SV306 ) @ SV306 )
| ~ ( c_List_Olinorder__class_Osorted @ SY3099 @ SV306 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV306 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(2868,plain,
! [SV1128: $i,SV661: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV309 @ ( c_List_Olist_Olist__case @ SV661 @ SV1128 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV661 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(2869,plain,
! [SV1129: $i,SV931: $i,SV662: $i,SV310: $i] :
( ( ( c_List_Ofoldr @ SV310 @ ( c_List_Olist_ONil @ SV662 ) @ SV931 @ SV662 @ SV1129 )
= SV931 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(2870,plain,
! [SV932: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ ( v_sko__List__Xzip__Xinduct__2 @ SV311 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV311 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV932 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2871,plain,
! [SV934: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV314 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV314 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV934 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2872,plain,
! [SV1130: $i,SV935: $i,SV665: $i,SV315: $i] :
( ( ( c_List_Olist_Olist__rec @ SV315 @ SV665 @ ( c_List_Olist_ONil @ SV935 ) @ SV1130 @ SV935 )
= SV315 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(2873,plain,
! [SV936: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ SV316 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV316 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV316 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV936 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2874,plain,
! [SV937: $i,SV317: $i] :
( ( ( hBOOL @ ( hAPP @ SV317 @ ( v_sko__List__Xtake__Xinduct__2 @ SV317 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV317 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV317 @ SV937 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2875,plain,
! [SV667: $i,SV320: $i] :
( ( ( ( c_List_Olist_ONil @ SV320 )
= ( c_List_Oremdups @ SV667 @ SV320 ) )
= $false )
| ( ( SV667
= ( c_List_Olist_ONil @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2876,plain,
! [SV942: $i,SV325: $i] :
( ( ( hBOOL @ ( hAPP @ SV325 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV325 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV325 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV325 @ SV942 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2877,plain,
! [SV943: $i,SV672: $i,SV326: $i] :
( ( ( c_List_Olist_OCons @ SV326 @ SV672 @ SV943 )
= ( c_List_Olist_ONil @ SV943 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2878,plain,
! [SV944: $i,SV673: $i,SV327: $i] :
( ( ( c_List_Olist_OCons @ SV327 @ SV673 @ SV944 )
= ( c_List_Olist_ONil @ SV944 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2879,plain,
! [SV945: $i,SV329: $i] :
( ( ( hBOOL @ ( hAPP @ SV329 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV329 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV329 @ SV945 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2571]) ).
thf(2880,plain,
! [SV1131: $i,SV946: $i,SV675: $i,SV330: $i] :
( ( ( c_Map_Omap__upds @ SV330 @ SV675 @ ( c_List_Olist_ONil @ SV946 ) @ SV1131 @ SV946 )
= SV330 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(2881,plain,
! [SV1132: $i,SV947: $i,SV676: $i,SV331: $i] :
( ( ( c_Map_Omap__upds @ SV331 @ ( c_List_Olist_ONil @ SV676 ) @ SV947 @ SV676 @ SV1132 )
= SV331 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2882,plain,
! [SV948: $i,SV332: $i] :
( ( ( hBOOL @ ( hAPP @ SV332 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV332 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV332 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV332 @ SV948 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2883,plain,
! [SV1133: $i,SV949: $i,SV677: $i,SV333: $i] :
( ( ( c_List_Olist_Olist__case @ SV333 @ SV677 @ ( c_List_Olist_ONil @ SV949 ) @ SV1133 @ SV949 )
= SV333 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(2884,plain,
! [SV678: $i,SV334: $i] :
( ( ( ( c_List_Orev @ SV334 @ SV678 )
= ( c_List_Olist_ONil @ SV678 ) )
= $false )
| ( ( SV334
= ( c_List_Olist_ONil @ SV678 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2885,plain,
! [SV950: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ SV336 @ ( v_sko__List__Xlist__Xinduct__2 @ SV336 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV336 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV336 @ SV950 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2886,plain,
! [SV952: $i,SV340: $i] :
( ( ( hBOOL @ ( hAPP @ SV340 @ ( v_sko__List__Xmap__Xinduct__2 @ SV340 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV340 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV340 @ SV952 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2579]) ).
thf(2887,plain,
! [SV1134: $i,SV953: $i,SV682: $i,SV342: $i] :
( ( ( ( c_List_Olist__update @ SV342 @ SV682 @ SV953 @ SV1134 )
!= ( c_List_Olist_ONil @ SV1134 ) )
| ( SV342
= ( c_List_Olist_ONil @ SV1134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(2888,plain,
! [SV1135: $i,SV954: $i,SV683: $i,SV343: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV343 ) @ SV683 ) @ SV954 @ SV1135 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV343 @ SV954 @ SV1135 ) ) @ ( c_Lambda_Osubst @ SV683 @ SV954 @ SV1135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(2889,plain,
! [SV955: $i,SV684: $i,SV344: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV344 ) @ SV684 )
= ( c_Lambda_OdB_OAbs @ SV955 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2890,plain,
! [SV956: $i,SV685: $i,SV345: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV345 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV685 ) @ SV956 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2891,plain,
! [SV1136: $i,SV957: $i,SV686: $i,SV346: $i] :
( ( ! [SY3100: $i,SY3101: $i] :
( ~ ( hBOOL @ ( hAPP @ SV346 @ ( c_Lambda_OdB_OdB__case @ SV686 @ SV957 @ SV1136 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3100 ) @ SY3101 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ SV957 @ SY3100 ) @ SY3101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(2892,plain,
! [SV1137: $i,SV958: $i,SV687: $i,SV347: $i] :
( ( ! [SY3102: $i,SY3103: $i] :
( ~ ( hBOOL @ ( hAPP @ SV347 @ ( c_Lambda_OdB_OdB__case @ SV687 @ SV958 @ SV1137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3102 ) @ SY3103 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV347 @ ( hAPP @ ( hAPP @ SV958 @ SY3102 ) @ SY3103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(2893,plain,
! [SV1138: $i,SV960: $i,SV689: $i,SV349: $i] :
( ( ! [SY3104: $i,SY3105: $i] :
( ( c_Lambda_OdB_OdB__case @ SV349 @ SV689 @ SV960 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1138 ) @ SY3104 ) @ SY3105 )
= ( hAPP @ ( hAPP @ SV689 @ SV1138 ) @ SY3104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(2894,plain,
! [SV1139: $i,SV961: $i,SV690: $i,SV350: $i] :
( ( ! [SY3106: $i,SY3107: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1139 ) @ SY3106 ) @ SY3107 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV690 @ SV1139 ) @ SY3106 ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ SV1139 @ SY3107 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ SY3106 @ SY3107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2895,plain,
! [SV962: $i,SV691: $i,SV351: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV351 @ SV691 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV962 @ SV691 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV351 = SV962 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2896,plain,
! [SV963: $i,SV692: $i,SV352: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV692 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV963 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV692 ) @ SV963 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2590]) ).
thf(2897,plain,
! [SV964: $i,SV693: $i,SV353: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV693 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV964 ) @ SV693 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV353 ) @ SV964 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2591]) ).
thf(2898,plain,
! [SV1140: $i,SV965: $i,SV694: $i,SV354: $i] :
( ( ( c_Lambda_Oliftn @ SV354 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV694 ) @ SV965 ) @ SV1140 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV354 @ SV694 @ SV1140 ) ) @ ( c_Lambda_Oliftn @ SV354 @ SV965 @ SV1140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(2899,plain,
! [SV1141: $i,SV966: $i,SV695: $i,SV355: $i] :
( ( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV355 ) @ SV695 ) @ SV966 @ SV1141 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV355 @ SV966 @ SV1141 ) ) @ ( c_Lambda_Osubstn @ SV695 @ SV966 @ SV1141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(2900,plain,
! [SV967: $i,SV696: $i,SV356: $i] :
( ( ( SV356 = SV696 )
= $true )
| ( ( ! [SY2962: $i,SY2963: $i] :
( ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2962 ) @ SY2963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV696 )
| ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2962 ) @ SY2963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2901,plain,
! [SV1142: $i,SV968: $i,SV697: $i,SV357: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV357 ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV968 ) @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(2902,plain,
! [SV1143: $i,SV969: $i,SV698: $i,SV358: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV358 ) ) @ SV698 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV969 ) @ SV1143 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(2903,plain,
! [SV1144: $i,SV970: $i,SV700: $i,SV360: $i] :
( ( ! [SY3108: $i] :
( ~ ( hBOOL @ ( hAPP @ SV360 @ ( c_Lambda_OdB_OdB__case @ SV700 @ SV970 @ SV1144 @ ( c_Lambda_OdB_OVar @ SY3108 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV360 @ ( hAPP @ SV700 @ SY3108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(2904,plain,
! [SV1145: $i,SV971: $i,SV701: $i,SV361: $i] :
( ( ! [SY3109: $i] :
( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Lambda_OdB_OdB__case @ SV701 @ SV971 @ SV1145 @ ( c_Lambda_OdB_OVar @ SY3109 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( hAPP @ SV701 @ SY3109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(2905,plain,
! [SV1146: $i,SV972: $i,SV704: $i,SV364: $i] :
( ( ! [SY3110: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV364 @ SV704 @ SV972 @ ( c_Lambda_OdB_OVar @ SV1146 ) @ SY3110 )
= ( hAPP @ SV364 @ SV1146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(2906,plain,
! [SV973: $i,SV706: $i,SV366: $i] :
( ( ( ( hAPP @ SV366 @ SV706 )
= SV973 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV366 @ ( c_Lambda_OdB_OVar @ SV706 ) @ SV973 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2603]) ).
thf(2907,plain,
! [SV1147: $i,SV974: $i,SV707: $i,SV367: $i] :
( ( ! [SY3111: $i] :
( ( c_Lambda_OdB_OdB__case @ SV367 @ SV707 @ SV974 @ ( c_Lambda_OdB_OVar @ SV1147 ) @ SY3111 )
= ( hAPP @ SV367 @ SV1147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(2908,plain,
! [SV975: $i,SV709: $i,SV369: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV369 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV709 @ SV975 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV975
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(2909,plain,
! [SV1148: $i,SV976: $i,SV710: $i,SV371: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV371 ) @ SV710 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ SV1148 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV371
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV371 @ SV710 @ SV976 @ SV1148 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1148
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(2910,plain,
! [SV1149: $i,SV711: $i,SV372: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV372 @ SV711 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1149 ) )
= $true )
| ( ( SV711
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(2911,plain,
! [SV1150: $i,SV977: $i,SV712: $i,SV374: $i] :
( ( ( c_List_Olistsp @ SV374 @ ( c_List_Oappend @ SV712 @ SV977 @ SV1150 ) @ SV1150 )
| ~ ( c_List_Olistsp @ SV374 @ SV977 @ SV1150 )
| ~ ( c_List_Olistsp @ SV374 @ SV712 @ SV1150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(2912,plain,
! [SV978: $i,SV713: $i,SV375: $i] :
( ( ( c_List_Olistsp @ SV375 @ SV713 @ SV978 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV375 @ SV713 @ SV978 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2913,plain,
! [SV1151: $i,SV979: $i,SV714: $i,SV376: $i] :
( ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV714 @ ( tc_fun @ SV979 @ tc_bool ) ) @ SV1151 @ SV979 )
| ~ ( c_List_Olistsp @ SV714 @ SV1151 @ SV979 )
| ~ ( c_List_Olistsp @ SV376 @ SV1151 @ SV979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(2914,plain,
! [SV980: $i,SV715: $i,SV377: $i] :
( ( ( c_List_Olistsp @ SV377 @ SV715 @ SV980 )
= $true )
| ( ( ! [SY2977: $i] :
~ ( c_List_Olistsp @ SV377 @ ( c_List_Oappend @ SY2977 @ SV715 @ SV980 ) @ SV980 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(2915,plain,
! [SV981: $i,SV716: $i,SV378: $i] :
( ( ( c_List_Olistsp @ SV378 @ SV716 @ SV981 )
= $true )
| ( ( ! [SY2978: $i] :
~ ( c_List_Olistsp @ SV378 @ ( c_List_Oappend @ SV716 @ SY2978 @ SV981 ) @ SV981 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2916,plain,
! [SV982: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV379 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV379 @ SV982 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2917,plain,
! [SV983: $i,SV717: $i,SV381: $i] :
( ( ( ! [SY2979: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV381 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV983 ) @ SY2979 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( SV381 = SV983 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2918,plain,
! [SV1152: $i,SV984: $i,SV718: $i,SV382: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV382 ) @ SV718 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV984 ) @ SV1152 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV718 = SV1152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(2919,plain,
! [SV1153: $i,SV719: $i,SV383: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV383 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV719 @ SV1153 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV383 )
= SV719 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(2920,plain,
! [SV720: $i,SV384: $i,SV1154: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV1154 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1154 @ SV384 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1154 @ SV720 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV384 @ SV720 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(2921,plain,
! [SV721: $i,SV1155: $i,SV385: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV385 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1155 @ SV385 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV385 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1155 @ SV721 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ SV721 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2922,plain,
! [SV722: $i,SV386: $i,SV1156: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV1156 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1156 @ SV386 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1156 @ SV722 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV386 @ SV722 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(2923,plain,
! [SV723: $i,SV1157: $i,SV387: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV387 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1157 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1157 @ SV723 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ SV723 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(2924,plain,
! [SV388: $i,SV724: $i] :
( ( ( SV724
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV388 @ SV724 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV388 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV388 @ SV724 ) @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(2925,plain,
! [SV389: $i,SV725: $i] :
( ( ( SV725
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV389 @ SV725 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV389 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV389 @ SV725 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2926,plain,
! [SV726: $i,SV390: $i,SV1158: $i] :
( ( ( ( c_List_Olistsp @ SV1158 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1158 @ SV390 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV390 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1158 @ SV726 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV390 @ SV726 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(2927,plain,
! [SV727: $i,SV391: $i,SV1159: $i] :
( ( ( ( c_List_Olistsp @ SV1159 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1159 @ SV391 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1159 @ SV727 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV391 @ SV727 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(2928,plain,
! [SV985: $i,SV729: $i,SV393: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV729 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV985 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV729 )
= SV985 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2929,plain,
! [SV1160: $i,SV986: $i,SV394: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV394 @ ( c_Lambda_OdB_OVar @ SV986 ) @ SV1160 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV394 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(2930,plain,
! [SV987: $i,SV730: $i,SV396: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV396 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV730 @ SV987 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV987
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2931,plain,
! [SV397: $i,SV731: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV731 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV397 ) @ SV731 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2932,plain,
! [SV732: $i,SV398: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV398 )
= ( c_Lambda_OdB_OVar @ SV732 ) )
= $false )
| ( ( SV398 = SV732 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2933,plain,
! [SV988: $i,SV733: $i,SV399: $i] :
( ( ( ! [SY2982: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV399 ) @ SV733 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV988 ) @ SY2982 ) ) )
= $true )
| ( ( SV399 = SV988 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2631]) ).
thf(2934,plain,
! [SV1161: $i,SV989: $i,SV734: $i,SV400: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV400 ) @ SV734 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV989 ) @ SV1161 ) )
| ( SV734 = SV1161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(2935,plain,
! [SV990: $i,SV735: $i,SV401: $i] :
( ( ( c_Lambda_OdB_OVar @ SV401 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV735 ) @ SV990 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2936,plain,
! [SV1162: $i,SV991: $i,SV737: $i,SV404: $i] :
( ( ! [SY3112: $i,SY3113: $i] :
( ( hAPP @ ( c_COMBB @ SV404 @ SV737 @ SV991 @ SV1162 @ SY3112 ) @ SY3113 )
= ( hAPP @ SV404 @ ( hAPP @ SV737 @ SY3113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(2937,plain,
! [SV1163: $i,SV992: $i,SV738: $i,SV405: $i] :
( ( ! [SY3114: $i,SY3115: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV405 @ SV738 @ SV992 @ SV1163 ) @ SY3114 ) @ SY3115 )
= ( hAPP @ ( hAPP @ SV405 @ SY3115 ) @ SY3114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(2938,plain,
! [SV993: $i,SV739: $i,SV406: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV406 ) @ SV739 )
= ( c_Lambda_OdB_OVar @ SV993 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2939,plain,
! [SV407: $i,SV740: $i] :
( ( ( class_Lattices_Olattice @ SV740 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV407 @ SV740 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2940,plain,
! [SV408: $i,SV741: $i] :
( ( ( class_Orderings_Opreorder @ SV741 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV408 @ SV741 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2941,plain,
! [SV409: $i,SV742: $i] :
( ( ( class_Lattices_Olattice @ SV742 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV409 @ SV742 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(2942,plain,
! [SV410: $i,SV743: $i] :
( ( ( class_Orderings_Oorder @ SV743 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV410 @ SV743 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2943,plain,
! [SV1164: $i,SV994: $i,SV744: $i,SV411: $i] :
( ( ! [SY3116: $i,SY3117: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV411 @ SV744 @ SV994 @ SV1164 ) @ SY3116 ) @ SY3117 )
= ( hAPP @ ( hAPP @ SV411 @ SY3117 ) @ SY3116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(2944,plain,
! [SV1165: $i,SV995: $i,SV745: $i,SV412: $i] :
( ( ! [SY3118: $i,SY3119: $i] :
( ( hAPP @ ( c_COMBB @ SV412 @ SV745 @ SV995 @ SV1165 @ SY3118 ) @ SY3119 )
= ( hAPP @ SV412 @ ( hAPP @ SV745 @ SY3119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(2945,plain,
! [SV1166: $i,SV747: $i,SV414: $i] :
( ( ( ~ ( c_fequal @ SV414 @ SV747 @ SV1166 ) )
= $true )
| ( ( SV414 = SV747 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(2946,plain,
! [SV996: $i,SV748: $i,SV416: $i,SV4: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV996 ) )
= $true )
| ( ( ! [SY2996: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SY2996 ) @ SV996 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SY2996 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2947,plain,
! [SV997: $i,SV751: $i,SV419: $i,SV7: $i] :
( ( ( ! [SY2997: $i] :
( ( c_List_Oreplicate @ SV7 @ SV419 @ SV751 )
!= ( c_List_Oreplicate @ SV997 @ SY2997 @ SV751 ) ) )
= $true )
| ( ( SV7 = SV997 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2948,plain,
! [SV752: $i,SV420: $i,SV8: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV8 @ SV420 ) @ SV752 ) )
= $false )
| ( ( ! [SY2757: $i,SY2758: $i] : ( c_ListOrder_Ostep1 @ SV8 @ ( c_List_Olist_OCons @ SV420 @ SY2757 @ SY2758 ) @ ( c_List_Olist_OCons @ SV752 @ SY2757 @ SY2758 ) @ SY2758 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2949,plain,
! [SV998: $i,SV753: $i,SV421: $i,SV9: $i] :
( ( ( SV9 = SV421 )
= $true )
| ( ( ( SV753 = SV998 )
| ! [SY2998: $i,SY2999: $i] :
~ ( c_ListOrder_Ostep1 @ SY2998 @ ( c_List_Olist_OCons @ SV421 @ SV998 @ SY2999 ) @ ( c_List_Olist_OCons @ SV9 @ SV753 @ SY2999 ) @ SY2999 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(2950,plain,
! [SV1167: $i,SV999: $i,SV755: $i,SV423: $i,SV12: $i] :
( ( ( c_ListOrder_Ostep1 @ SV12 @ ( c_List_Oappend @ SV423 @ SV755 @ SV999 ) @ ( c_List_Oappend @ SV423 @ SV1167 @ SV999 ) @ SV999 )
| ~ ( c_ListOrder_Ostep1 @ SV12 @ SV755 @ SV1167 @ SV999 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(2951,plain,
! [SV1000: $i,SV756: $i,SV424: $i,SV13: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV13 @ SV424 @ SV756 @ SV1000 ) )
= $true )
| ( ( ! [SY3001: $i] : ( c_ListOrder_Ostep1 @ SV13 @ ( c_List_Oappend @ SV424 @ SY3001 @ SV1000 ) @ ( c_List_Oappend @ SV756 @ SY3001 @ SV1000 ) @ SV1000 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(2952,plain,
! [SV15: $i,SV1168: $i,SV426: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV426 @ SV1168 @ SV15 )
| ! [SY3120: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3120 @ SV1168 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV426 @ SY3120 @ SV15 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(2953,plain,
! [SV16: $i,SV1169: $i,SV427: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1169 @ SV16 )
| ! [SY3121: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV427 @ SY3121 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SY3121 @ SV1169 @ SV16 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(2954,plain,
! [SV429: $i,SV22: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV22 @ SV429 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV22 )
= SV429 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV22 ) @ SV429 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2955,plain,
! [SV1001: $i,SV759: $i,SV431: $i,SV24: $i] :
( ( ( SV24 = SV431 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ SV431 ) @ SV24 ) )
| ! [SY3002: $i,SY3003: $i] :
~ ( c_ListOrder_Ostep1 @ SV759 @ ( c_List_Olist_OCons @ SV431 @ SV1001 @ SY3002 ) @ ( c_List_Olist_OCons @ SV24 @ SY3003 @ SY3002 ) @ SY3002 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2956,plain,
! [SV31: $i,SV436: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV436 @ ( c_Suc @ SV31 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV31 @ SV436 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2957,plain,
! [SV1170: $i,SV1004: $i,SV764: $i,SV438: $i,SV33: $i] :
( ( ( ( c_List_Oreplicate @ SV33 @ SV438 @ SV764 )
!= ( c_List_Oreplicate @ SV1004 @ SV1170 @ SV764 ) )
| ( SV438 = SV1170 )
| ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(2958,plain,
! [SV1171: $i,SV1006: $i,SV768: $i,SV448: $i,SV46: $i] :
( ( ( c_List_Omap @ SV46 @ ( c_List_Oreplicate @ SV448 @ SV768 @ SV1006 ) @ SV1006 @ SV1171 )
= ( c_List_Oreplicate @ SV448 @ ( hAPP @ SV46 @ SV768 ) @ SV1171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(2959,plain,
! [SV1007: $i,SV770: $i,SV452: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV452 ) @ SV770 ) @ SV1007 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV770 ) @ SV1007 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2960,plain,
! [SV1172: $i,SV771: $i,SV453: $i,SV51: $i] :
( ( ( ( c_List_Ofilter @ SV51 @ ( c_List_Oreplicate @ SV453 @ SV771 @ SV1172 ) @ SV1172 )
= ( c_List_Oreplicate @ SV453 @ SV771 @ SV1172 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV51 @ SV771 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(2961,plain,
! [SV1173: $i,SV1008: $i,SV772: $i,SV454: $i,SV52: $i] :
( ( ( ( c_List_Omap @ SV52 @ SV454 @ SV772 @ SV1008 )
!= ( c_List_Omap @ SV52 @ SV1173 @ SV772 @ SV1008 ) )
| ( ( c_Nat_Osize__class_Osize @ SV454 @ ( tc_List_Olist @ SV772 ) )
= ( c_Nat_Osize__class_Osize @ SV1173 @ ( tc_List_Olist @ SV772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(2962,plain,
! [SV455: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SV455 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV54 @ SV455 @ tc_nat )
= $true )
| ( ( SV54 = SV455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2963,plain,
! [SV55: $i,SV456: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV456 @ ( c_Suc @ SV55 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV456 @ SV55 @ tc_nat )
= $true )
| ( ( SV55 = SV456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2964,plain,
! [SV457: $i,SV56: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV56 @ ( c_Suc @ SV457 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV56 @ SV457 @ tc_nat )
= $true )
| ( ( SV56 = SV457 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2965,plain,
! [SV1009: $i,SV773: $i,SV458: $i,SV57: $i] :
( ( ( ! [SY3007: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV57 @ SV458 @ SV773 ) @ SV1009 @ SY3007 @ SV773 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV57 @ SV1009 @ SY3007 @ SV773 ) @ SV458 @ SV773 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_Nat_Osize__class_Osize @ SV57 @ ( tc_List_Olist @ SV773 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2966,plain,
! [SV1010: $i,SV774: $i,SV459: $i,SV58: $i] :
( ( ( ! [SY3008: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV58 @ SV459 @ SV774 ) @ SV1010 @ SY3008 @ SV774 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV58 @ SV1010 @ SY3008 @ SV774 ) @ SV459 @ SV774 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1010 @ ( c_Nat_Osize__class_Osize @ SV58 @ ( tc_List_Olist @ SV774 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2677]) ).
thf(2967,plain,
! [SV64: $i,SV1011: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1011 @ SV1011 @ SV64 )
= $false )
| ( ( class_Orderings_Oorder @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2968,plain,
! [SV65: $i,SV1012: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1012 @ SV1012 @ SV65 )
= $false )
| ( ( class_Orderings_Olinorder @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2969,plain,
! [SV66: $i,SV1013: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1013 @ SV1013 @ SV66 )
= $false )
| ( ( class_Orderings_Opreorder @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(2970,plain,
! [SV1014: $i,SV776: $i,SV463: $i,SV67: $i] :
( ( ( c_ListOrder_Ostep1 @ SV67 @ SV463 @ SV776 @ SV1014 )
= $true )
| ( ( ( SV776 = SV463 )
| ! [SY3009: $i,SY3010: $i] :
~ ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SY3009 @ SV463 @ SV1014 ) @ ( c_List_Olist_OCons @ SY3010 @ SV776 @ SV1014 ) @ SV1014 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(2971,plain,
! [SV68: $i,SV1174: $i,SV1015: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1174 @ SV68 )
| ( SV1174 = SV1015 )
| ( c_HOL_Oord__class_Oless @ SV1174 @ SV1015 @ SV68 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(2972,plain,
! [SV69: $i,SV1175: $i,SV1016: $i] :
( ( ( ( SV1016 = SV1175 )
| ( c_HOL_Oord__class_Oless @ SV1175 @ SV1016 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV1016 @ SV1175 @ SV69 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(2973,plain,
! [SV71: $i,SV777: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV465 @ SV777 @ tc_nat )
= $true )
| ( ( ( SV777 = SV465 )
| ( c_HOL_Oord__class_Oless @ SV777 @ SV465 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV465 ) @ SV777 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2685]) ).
thf(2974,plain,
! [SV73: $i,SV1176: $i,SV1017: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1017 @ SV1176 @ SV73 )
| ( SV1176 = SV1017 )
| ( c_HOL_Oord__class_Oless @ SV1176 @ SV1017 @ SV73 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(2975,plain,
! [SV75: $i,SV1177: $i,SV1019: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1019 @ SV1177 @ SV75 )
| ( SV1177 = SV1019 )
| ( c_HOL_Oord__class_Oless @ SV1177 @ SV1019 @ SV75 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(2976,plain,
! [SV76: $i,SV1178: $i,SV1020: $i] :
( ( ( ( SV1020 = SV1178 )
| ( c_HOL_Oord__class_Oless @ SV1020 @ SV1178 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV1178 @ SV1020 @ SV76 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(2977,plain,
! [SV77: $i,SV1179: $i,SV468: $i] :
( ( ( ! [SY3122: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV468 @ SV1179 @ SV77 ) @ SY3122 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV1179 @ SY3122 @ SV77 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(2978,plain,
! [SV78: $i,SV1180: $i,SV469: $i] :
( ( ( ! [SY3123: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV469 @ SV1180 @ SV78 ) @ SY3123 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SY3123 @ SV78 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(2979,plain,
! [SV83: $i,SV470: $i,SV1021: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1021 @ SV470 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV83 @ SV1021 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV83 ) @ SV470 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2693]) ).
thf(2980,plain,
! [SV1022: $i,SV779: $i,SV84: $i] :
( ( ( ( c_List_Oreplicate @ SV84 @ SV779 @ SV1022 )
= ( c_List_Olist_ONil @ SV1022 ) )
= $false )
| ( ( SV84
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2981,plain,
! [SV1023: $i,SV473: $i,SV88: $i] :
( ( ( ( c_List_Olist_ONil @ SV88 )
= ( c_List_Oreplicate @ SV473 @ SV1023 @ SV88 ) )
= $false )
| ( ( SV473
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2982,plain,
! [SV1024: $i,SV781: $i,SV475: $i,SV92: $i] :
( ( ( c_ListOrder_Ostep1 @ SV92 @ SV475 @ SV781 @ SV1024 )
= $true )
| ( ( ! [SY3016: $i,SY3017: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY3016 ) @ SY3017 ) )
| ~ ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SY3016 @ SV475 @ SV1024 ) @ ( c_List_Olist_OCons @ SY3017 @ SV781 @ SV1024 ) @ SV1024 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2697]) ).
thf(2983,plain,
! [SV1181: $i,SV1025: $i,SV782: $i,SV476: $i,SV93: $i] :
( ( ( c_ListOrder_Ostep1 @ SV93 @ ( c_List_Olist_OCons @ SV476 @ SV782 @ SV1025 ) @ ( c_List_Olist_OCons @ SV476 @ SV1181 @ SV1025 ) @ SV1025 )
| ~ ( c_ListOrder_Ostep1 @ SV93 @ SV782 @ SV1181 @ SV1025 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(2984,plain,
! [SV98: $i,SV1182: $i,SV1026: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1026 @ SV1182 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SV1026 @ SV98 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(2985,plain,
! [SV1027: $i,SV784: $i,SV481: $i,SV99: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV784 ) @ SV1027 ) )
= $true )
| ( ( ! [SY3020: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SY3020 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SV784 ) @ SY3020 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(2986,plain,
! [SV1028: $i,SV785: $i,SV482: $i,SV100: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1028 ) )
= $true )
| ( ( ! [SY3021: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SY3021 ) @ SV1028 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SY3021 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(2987,plain,
! [SV101: $i,SV1183: $i,SV1029: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SV1183 @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1029 @ SV101 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(2988,plain,
! [SV102: $i,SV1184: $i,SV1030: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1030 @ SV1184 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SV1184 @ SV1030 @ SV102 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(2989,plain,
! [SV103: $i,SV1185: $i,SV1031: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1031 @ SV1185 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SV1185 @ SV1031 @ SV103 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(2990,plain,
! [SV786: $i,SV484: $i,SV105: $i] :
( ( ( SV105
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 ) @ SV786 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV105 ) @ SV484 ) @ ( c_List_Oappend @ SV786 @ ( c_List_Olist_OCons @ SV484 @ ( 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)],[2707]) ).
thf(2991,plain,
! [SV1186: $i,SV1033: $i,SV791: $i,SV491: $i,SV113: $i] :
( ( ( ( c_List_Oappend @ SV113 @ SV491 @ SV791 )
!= ( c_List_Olist_OCons @ SV1033 @ SV1186 @ SV791 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1033 @ SV1186 @ SV113 @ SV491 @ SV791 ) @ SV491 @ SV791 )
= SV1186 )
| ( SV491
= ( c_List_Olist_OCons @ SV1033 @ SV1186 @ SV791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(2992,plain,
! [SV1187: $i,SV1034: $i,SV792: $i,SV492: $i,SV114: $i] :
( ( ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
!= ( c_List_Oappend @ SV1034 @ SV1187 @ SV792 ) )
| ( ( c_List_Olist_OCons @ SV114 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV114 @ SV492 @ SV1034 @ SV1187 @ SV792 ) @ SV792 )
= SV1034 )
| ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
= SV1187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(2993,plain,
! [SV1188: $i,SV1035: $i,SV793: $i,SV493: $i,SV115: $i] :
( ( ( ( c_List_Oappend @ SV115 @ SV493 @ SV793 )
!= ( c_List_Olist_OCons @ SV1035 @ SV1188 @ SV793 ) )
| ( SV115
= ( c_List_Olist_OCons @ SV1035 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1035 @ SV1188 @ SV115 @ SV493 @ SV793 ) @ SV793 ) )
| ( SV493
= ( c_List_Olist_OCons @ SV1035 @ SV1188 @ SV793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(2994,plain,
! [SV1189: $i,SV1036: $i,SV794: $i,SV494: $i,SV116: $i] :
( ( ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
!= ( c_List_Oappend @ SV1036 @ SV1189 @ SV794 ) )
| ( SV494
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV116 @ SV494 @ SV1036 @ SV1189 @ SV794 ) @ SV1189 @ SV794 ) )
| ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
= SV1189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(2995,plain,
! [SV1038: $i,SV798: $i,SV500: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV500 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV798 ) @ SV1038 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV500 ) @ SV1038 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV798 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(2996,plain,
! [SV501: $i,SV799: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV123 ) @ SV799 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV123 ) @ SV501 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV799 ) @ SV501 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2997,plain,
! [SV124: $i,SV800: $i,SV502: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV502 ) @ SV800 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV502 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV124 ) @ SV800 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2998,plain,
! [SV1190: $i,SV801: $i,SV504: $i,SV126: $i] :
( ( ( ( c_List_Ofilter @ SV126 @ ( c_List_Oreplicate @ SV504 @ SV801 @ SV1190 ) @ SV1190 )
= ( c_List_Olist_ONil @ SV1190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV126 @ SV801 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(2999,plain,
! [SV1039: $i,SV802: $i,SV505: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV127 @ SV505 @ SV802 ) ) @ ( c_Lambda_Osubst @ SV127 @ SV1039 @ SV802 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV505 ) @ SV1039 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2723]) ).
thf(3000,plain,
! [SV1040: $i,SV803: $i,SV506: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV128 @ SV506 @ SV803 ) ) @ ( c_Lambda_Osubst @ SV1040 @ SV506 @ SV803 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SV1040 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(3001,plain,
! [SV1041: $i,SV804: $i,SV507: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV507 @ SV804 ) ) @ ( c_Lambda_Osubst @ SV129 @ SV1041 @ SV804 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV507 ) @ SV1041 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(3002,plain,
! [SV805: $i,SV130: $i,SV508: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV508 ) @ SV130 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV805 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV130 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV508 @ SV130 @ SV805 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(3003,plain,
! [SV1191: $i,SV1043: $i,SV807: $i,SV510: $i,SV132: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV132 @ SV510 @ SV807 ) @ ( c_Suc @ SV1043 ) @ SV1191 @ SV807 )
= ( c_List_Olist_OCons @ SV132 @ ( c_List_Olist__update @ SV510 @ SV1043 @ SV1191 @ SV807 ) @ SV807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3004,plain,
! [SV511: $i,SV809: $i,SV134: $i] :
( ( ( SV134 = SV809 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV809 @ SV134 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV134 ) @ SV511 @ SV809 )
= ( c_Lambda_OdB_OVar @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(3005,plain,
! [SV512: $i,SV810: $i,SV135: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV135 @ SV810 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV135 ) @ SV512 @ SV810 )
= ( c_Lambda_OdB_OVar @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(3006,plain,
! [SV513: $i,SV811: $i,SV1192: $i,SV136: $i] :
( ( ( ~ ( c_Type_Otyping @ SV136 @ SV1192 @ SV811 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1192 ) @ SV513 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV136 @ SV513 @ SV811 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3007,plain,
! [SV514: $i,SV812: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV137 ) @ SV812 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV137 @ SV514 ) ) @ ( c_Lambda_Olift @ SV812 @ SV514 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(3008,plain,
! [SV1044: $i,SV813: $i,SV515: $i,SV138: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV138 @ ( tc_List_Olist @ SV515 ) )
!= ( c_Nat_Osize__class_Osize @ SV813 @ ( tc_List_Olist @ SV1044 ) ) )
= $true )
| ( ( ! [SY3030: $i,SY3031: $i] :
( ( c_Map_Omap__upds @ SY3030 @ ( c_List_Oappend @ SV138 @ SY3031 @ SV515 ) @ SV813 @ SV515 @ SV1044 )
= ( c_Map_Omap__upds @ SY3030 @ SV138 @ SV813 @ SV515 @ SV1044 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(3009,plain,
! [SV1045: $i,SV814: $i,SV516: $i,SV139: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV139 @ ( tc_List_Olist @ SV516 ) )
!= ( c_Nat_Osize__class_Osize @ SV814 @ ( tc_List_Olist @ SV1045 ) ) )
= $true )
| ( ( ! [SY3032: $i,SY3033: $i] :
( ( c_Map_Omap__upds @ SY3032 @ SV139 @ ( c_List_Oappend @ SV814 @ SY3033 @ SV1045 ) @ SV516 @ SV1045 )
= ( c_Map_Omap__upds @ SY3032 @ SV139 @ SV814 @ SV516 @ SV1045 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2734]) ).
thf(3010,plain,
! [SV141: $i,SV815: $i,SV518: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV518 @ SV815 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Oliftn @ SV141 @ ( c_Lambda_OdB_OVar @ SV518 ) @ SV815 )
= ( c_Lambda_OdB_OVar @ SV518 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(3011,plain,
! [SV519: $i,SV1193: $i,SV1046: $i,SV142: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV142 @ SV1046 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV519 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV142 @ SV519 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3012,plain,
! [SV1194: $i,SV1048: $i,SV817: $i,SV522: $i,SV146: $i] :
( ( ! [SY3124: $i] :
( ( c_List_Ofoldl @ SV146 @ SV522 @ ( c_List_Oappend @ SV817 @ SV1048 @ SV1194 ) @ SY3124 @ SV1194 )
= ( c_List_Ofoldl @ SV146 @ ( c_List_Ofoldl @ SV146 @ SV522 @ SV817 @ SY3124 @ SV1194 ) @ SV1048 @ SY3124 @ SV1194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3013,plain,
! [SV1195: $i,SV819: $i,SV524: $i,SV149: $i] :
( ( ( ( c_List_Omap @ SV149 @ SV524 @ SV819 @ SV1195 )
!= ( c_List_Olist_ONil @ SV1195 ) )
= $true )
| ( ( SV524
= ( c_List_Olist_ONil @ SV819 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3014,plain,
! [SV820: $i,SV526: $i,SV153: $i] :
( ( ( SV153
= ( c_List_Oappend @ SV526 @ SV153 @ SV820 ) )
= $false )
| ( ( SV526
= ( c_List_Olist_ONil @ SV820 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(3015,plain,
! [SV821: $i,SV527: $i,SV154: $i] :
( ( ( ( c_List_Oappend @ SV154 @ SV527 @ SV821 )
= SV527 )
= $false )
| ( ( SV154
= ( c_List_Olist_ONil @ SV821 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(3016,plain,
! [SV822: $i,SV528: $i,SV155: $i] :
( ( ( SV155
= ( c_List_Oappend @ SV155 @ SV528 @ SV822 ) )
= $false )
| ( ( SV528
= ( c_List_Olist_ONil @ SV822 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(3017,plain,
! [SV823: $i,SV529: $i,SV156: $i] :
( ( ( ( c_List_Oappend @ SV156 @ SV529 @ SV823 )
= SV156 )
= $false )
| ( ( SV529
= ( c_List_Olist_ONil @ SV823 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(3018,plain,
! [SV824: $i,SV531: $i,SV158: $i] :
( ( ( ( c_List_Orotate @ SV158 @ SV531 @ SV824 )
= ( c_List_Olist_ONil @ SV824 ) )
= $false )
| ( ( SV531
= ( c_List_Olist_ONil @ SV824 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(3019,plain,
! [SV826: $i,SV534: $i,SV161: $i] :
( ( ( ( c_List_Oappend @ SV161 @ SV534 @ SV826 )
= ( c_List_Olist_ONil @ SV826 ) )
= $false )
| ( ( SV534
= ( c_List_Olist_ONil @ SV826 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(3020,plain,
! [SV827: $i,SV535: $i,SV162: $i] :
( ( ( ( c_List_Oappend @ SV162 @ SV535 @ SV827 )
= ( c_List_Olist_ONil @ SV827 ) )
= $false )
| ( ( SV162
= ( c_List_Olist_ONil @ SV827 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(3021,plain,
! [SV828: $i,SV536: $i,SV163: $i] :
( ( ( ( c_List_Olist_ONil @ SV163 )
= ( c_List_Oappend @ SV536 @ SV828 @ SV163 ) )
= $false )
| ( ( SV828
= ( c_List_Olist_ONil @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(3022,plain,
! [SV1050: $i,SV537: $i,SV164: $i] :
( ( ( ( c_List_Olist_ONil @ SV164 )
= ( c_List_Oappend @ SV537 @ SV1050 @ SV164 ) )
= $false )
| ( ( SV537
= ( c_List_Olist_ONil @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(3023,plain,
! [SV1052: $i,SV830: $i,SV539: $i,SV167: $i] :
( ( ( ( c_List_Olist_ONil @ SV167 )
!= ( c_List_Omap @ SV539 @ SV830 @ SV1052 @ SV167 ) )
= $true )
| ( ( SV830
= ( c_List_Olist_ONil @ SV1052 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2757]) ).
thf(3024,plain,
! [SV831: $i,SV173: $i,SV545: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV545 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV173 @ SV545 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV831 @ 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 @ SV173 ) ) @ SV545 ) @ SV831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2758]) ).
thf(3025,plain,
! [SV174: $i,SV832: $i,SV546: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV546 ) @ SV832 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV174 ) )
= $false )
| ( ( SV174
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV546 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV546 @ SV832 @ SV174 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(3026,plain,
! [SV833: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV176 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV176 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV176 @ SV833 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(3027,plain,
! [SV834: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV177 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV177 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV177 @ SV834 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(3028,plain,
! [SV835: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV178 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV178 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV178 @ SV835 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(3029,plain,
! [SV836: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV179 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV179 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV179 @ SV836 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(3030,plain,
! [SV837: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV180 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV180 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV180 @ SV837 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(3031,plain,
! [SV838: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV181 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV181 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV181 @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(3032,plain,
! [SV839: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV182 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV182 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV182 @ SV839 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(3033,plain,
! [SV840: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV183 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV183 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV183 @ SV840 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(3034,plain,
! [SV841: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV184 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV184 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV184 @ SV841 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(3035,plain,
! [SV1196: $i,SV1053: $i,SV843: $i,SV549: $i,SV186: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SV549 @ SV843 @ SV1053 ) @ SV1053 ) @ ( c_Nat_Osize__class_Osize @ SV186 @ ( tc_List_Olist @ SV1053 ) ) @ SV1196 @ SV1053 )
= ( c_List_Oappend @ SV186 @ ( c_List_Olist_OCons @ SV1196 @ SV843 @ SV1053 ) @ SV1053 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3036,plain,
! [SV550: $i,SV844: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV187 ) @ SV844 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV187 @ SV550 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV844 @ SV550 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(3037,plain,
! [SV188: $i,SV845: $i,SV551: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV551 @ SV845 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV551 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV188 @ SV845 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(3038,plain,
! [SV846: $i,SV552: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ SV189 @ SV552 ) )
= $false )
| ( ( ! [SY2831: $i] :
( ! [SY2832: $i] :
( ( c_List_Olist_OCons @ SV552 @ ( c_List_Ofilter @ SV189 @ SY2832 @ SY2831 ) @ SY2831 )
= ( c_List_Ofilter @ SV189 @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV552 @ SY2832 @ SY2831 ) @ SY2831 ) @ SY2831 ) )
| ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ SV189 @ SV846 @ SY2831 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(3039,plain,
! [SV847: $i,SV553: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ SV190 @ SV553 ) )
= $false )
| ( ( ! [SY2833: $i] :
( ! [SY2834: $i] :
( ( c_List_Ofilter @ SV190 @ ( c_List_Oappend @ SV847 @ ( c_List_Olist_OCons @ SV553 @ SY2834 @ SY2833 ) @ SY2833 ) @ SY2833 )
= ( c_List_Olist_OCons @ SV553 @ ( c_List_Ofilter @ SV190 @ SY2834 @ SY2833 ) @ SY2833 ) )
| ( hBOOL @ ( hAPP @ SV190 @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ SV190 @ SV847 @ SY2833 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(3040,plain,
! [SV1197: $i,SV1054: $i,SV848: $i,SV554: $i,SV191: $i] :
( ( ( ( c_List_Olist_OCons @ SV191 @ SV554 @ SV848 )
!= ( c_List_Oappend @ SV1054 @ SV1197 @ SV848 ) )
| ( SV554
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV191 @ SV554 @ SV1054 @ SV1197 @ SV848 ) @ SV1197 @ SV848 ) )
| ( SV1054
= ( c_List_Olist_ONil @ SV848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(3041,plain,
! [SV1198: $i,SV1055: $i,SV849: $i,SV555: $i,SV192: $i] :
( ( ( ( c_List_Oappend @ SV192 @ SV555 @ SV849 )
!= ( c_List_Olist_OCons @ SV1055 @ SV1198 @ SV849 ) )
| ( SV192
= ( c_List_Olist_OCons @ SV1055 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1055 @ SV1198 @ SV192 @ SV555 @ SV849 ) @ SV849 ) )
| ( SV192
= ( c_List_Olist_ONil @ SV849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3042,plain,
! [SV1056: $i,SV852: $i,SV558: $i,SV195: $i] :
( ( ( SV195 = SV558 )
= $true )
| ( ( ( SV852 = SV1056 )
| ! [SY3040: $i,SY3041: $i] :
~ ( c_ListOrder_Ostep1 @ SY3040 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SV852 @ ( c_List_Olist_ONil @ SY3041 ) @ SY3041 ) @ SY3041 ) @ ( c_List_Oappend @ SV558 @ ( c_List_Olist_OCons @ SV1056 @ ( c_List_Olist_ONil @ SY3041 ) @ SY3041 ) @ SY3041 ) @ SY3041 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(3043,plain,
! [SV1057: $i,SV853: $i,SV559: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SV559 ) @ SV853 ) )
= $true )
| ( ( ( SV559 = SV853 )
| ! [SY3042: $i,SY3043: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SV1057 @ ( c_List_Olist_OCons @ SV559 @ ( c_List_Olist_ONil @ SY3042 ) @ SY3042 ) @ SY3042 ) @ ( c_List_Oappend @ SY3043 @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_ONil @ SY3042 ) @ SY3042 ) @ SY3042 ) @ SY3042 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(3044,plain,
! [SV1199: $i,SV1058: $i,SV854: $i,SV560: $i,SV197: $i] :
( ( ( ( c_List_Oappend @ SV197 @ SV560 @ SV854 )
!= ( c_List_Olist_OCons @ SV1058 @ SV1199 @ SV854 ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1058 @ SV1199 @ SV197 @ SV560 @ SV854 ) @ SV560 @ SV854 )
= SV1199 )
| ( SV197
= ( c_List_Olist_ONil @ SV854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3045,plain,
! [SV1200: $i,SV1059: $i,SV855: $i,SV561: $i,SV198: $i] :
( ( ( ( c_List_Olist_OCons @ SV198 @ SV561 @ SV855 )
!= ( c_List_Oappend @ SV1059 @ SV1200 @ SV855 ) )
| ( ( c_List_Olist_OCons @ SV198 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV198 @ SV561 @ SV1059 @ SV1200 @ SV855 ) @ SV855 )
= SV1059 )
| ( SV1059
= ( c_List_Olist_ONil @ SV855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3046,plain,
! [SV1060: $i,SV856: $i,SV562: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SV562 ) @ SV856 ) )
= $true )
| ( ( ! [SY3046: $i,SY3047: $i] :
( ( c_ListOrder_Ostep1 @ SV199 @ SV1060 @ SY3046 @ SY3047 )
| ~ ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SV1060 @ ( c_List_Olist_OCons @ SV562 @ ( c_List_Olist_ONil @ SY3047 ) @ SY3047 ) @ SY3047 ) @ ( c_List_Oappend @ SY3046 @ ( c_List_Olist_OCons @ SV856 @ ( c_List_Olist_ONil @ SY3047 ) @ SY3047 ) @ SY3047 ) @ SY3047 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2780]) ).
thf(3047,plain,
! [SV1061: $i,SV858: $i,SV564: $i,SV201: $i] :
( ( ( SV201 = SV564 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV858 @ SV201 @ SV564 @ SV1061 )
| ! [SY3048: $i,SY3049: $i] :
~ ( c_ListOrder_Ostep1 @ SV858 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SY3048 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ ( c_List_Oappend @ SV564 @ ( c_List_Olist_OCons @ SY3049 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ SV1061 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(3048,plain,
! [SV1062: $i,SV860: $i,SV566: $i,SV203: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV203 ) @ SV566 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV860 @ SV1062 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV1062
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV203 @ SV566 @ SV860 @ SV1062 ) @ ( c_List_Olist_OCons @ SV566 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1062
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(3049,plain,
! [SV568: $i,SV862: $i,SV205: $i] :
( ( ( SV205 = SV862 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV862 @ SV205 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV205 ) @ SV568 @ SV862 )
= ( c_Lambda_OdB_OVar @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(3050,plain,
! [SV570: $i,SV1201: $i,SV207: $i,SV1063: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1063 @ SV207 @ ( tc_fun @ SV1201 @ tc_bool ) ) @ SV570 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV207 @ SV570 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3051,plain,
! [SV1202: $i,SV1064: $i,SV863: $i,SV571: $i,SV208: $i] :
( ( ( c_List_Ofoldl @ SV208 @ SV571 @ SV863 @ SV1064 @ SV1202 )
= ( c_List_Ofoldr @ ( c_COMBC @ SV208 @ SV1064 @ SV1202 @ SV1064 ) @ ( c_List_Orev @ SV863 @ SV1202 ) @ SV571 @ SV1202 @ SV1064 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3052,plain,
! [SV1203: $i,SV1065: $i,SV864: $i,SV573: $i,SV210: $i] :
( ( ! [SY3125: $i] :
( ( c_List_Omap @ SV210 @ ( c_List_Olist__update @ SV573 @ SV864 @ SV1065 @ SV1203 ) @ SV1203 @ SY3125 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV210 @ SV573 @ SV1203 @ SY3125 ) @ SV864 @ ( hAPP @ SV210 @ SV1065 ) @ SY3125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3053,plain,
! [SV577: $i,SV868: $i,SV214: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV214 ) @ SV868 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV214 @ SV577 ) ) @ ( c_Lambda_Olift @ SV868 @ SV577 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3054,plain,
! [SV578: $i,SV1066: $i,SV215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1066 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1066 @ SV215 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1066 @ SV578 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV215 @ SV578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2790]) ).
thf(3055,plain,
! [SV580: $i,SV1067: $i,SV217: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1067 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1067 @ SV217 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1067 @ SV580 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV217 @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2791]) ).
thf(3056,plain,
! [SV219: $i,SV1068: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1068 @ SV219 )
= $true )
| ( ( ! [SY3054: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY3054 @ SV1068 @ SV219 ) @ SV219 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2792]) ).
thf(3057,plain,
! [SV1204: $i,SV1071: $i,SV874: $i,SV585: $i,SV223: $i] :
( ( ! [SY3126: $i] :
( ( c_List_Olist_Olist__case @ SV223 @ SV585 @ ( c_List_Olist_OCons @ SV874 @ SV1071 @ SV1204 ) @ SY3126 @ SV1204 )
= ( hAPP @ ( hAPP @ SV585 @ SV874 ) @ SV1071 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3058,plain,
! [SV1205: $i,SV1072: $i,SV875: $i,SV586: $i,SV224: $i] :
( ( ( c_List_Omap @ SV224 @ ( c_List_Olist_OCons @ SV586 @ SV875 @ SV1072 ) @ SV1072 @ SV1205 )
= ( c_List_Olist_OCons @ ( hAPP @ SV224 @ SV586 ) @ ( c_List_Omap @ SV224 @ SV875 @ SV1072 @ SV1205 ) @ SV1205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3059,plain,
! [SV1206: $i,SV1073: $i,SV876: $i,SV587: $i,SV225: $i] :
( ( ( c_List_Olist_OCons @ ( hAPP @ SV225 @ SV587 ) @ ( c_List_Omap @ SV225 @ SV876 @ SV1073 @ SV1206 ) @ SV1206 )
= ( c_List_Omap @ SV225 @ ( c_List_Olist_OCons @ SV587 @ SV876 @ SV1073 ) @ SV1073 @ SV1206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3060,plain,
! [SV1207: $i,SV1074: $i,SV877: $i,SV588: $i,SV226: $i] :
( ( ( c_List_Omap @ SV226 @ ( c_List_Olist_OCons @ SV588 @ SV877 @ SV1074 ) @ SV1074 @ SV1207 )
= ( c_List_Olist_OCons @ ( hAPP @ SV226 @ SV588 ) @ ( c_List_Omap @ SV226 @ SV877 @ SV1074 @ SV1207 ) @ SV1207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3061,plain,
! [SV1077: $i,SV591: $i,SV229: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV229 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV591 @ SV1077 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV229 )
= SV591 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(3062,plain,
! [SV230: $i,SV1208: $i,SV592: $i] :
( ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV592 @ SV1208 @ SV230 ) @ SV230 )
| ! [SY3127: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY3127 @ ( c_List_Olist_OCons @ SV592 @ SV1208 @ SV230 ) @ SV230 ) @ SV230 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3063,plain,
! [SV231: $i,SV1209: $i,SV1078: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1078 @ SV1209 @ SV231 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1209 @ SV1078 @ SV231 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3064,plain,
! [SV232: $i,SV1210: $i,SV1079: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1079 @ SV1210 @ SV232 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1210 @ SV1079 @ SV232 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3065,plain,
! [SV1080: $i,SV881: $i,SV594: $i,SV234: $i] :
( ( ( ( c_List_Orev @ SV234 @ SV594 )
!= ( c_List_Olist_OCons @ SV881 @ SV1080 @ SV594 ) )
= $true )
| ( ( SV234
= ( c_List_Oappend @ ( c_List_Orev @ SV1080 @ SV594 ) @ ( c_List_Olist_OCons @ SV881 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(3066,plain,
! [SV1211: $i,SV1081: $i,SV882: $i,SV596: $i,SV236: $i] :
( ( ! [SY3128: $i] :
( ( c_List_Ofoldl @ SV236 @ SV596 @ ( c_List_Olist_OCons @ SV882 @ SV1081 @ SV1211 ) @ SY3128 @ SV1211 )
= ( c_List_Ofoldl @ SV236 @ ( hAPP @ ( hAPP @ SV236 @ SV596 ) @ SV882 ) @ SV1081 @ SY3128 @ SV1211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3067,plain,
! [SV1082: $i,SV884: $i,SV598: $i,SV238: $i] :
( ( ( ! [SY3064: $i] :
( ( c_List_Olist_OCons @ SV238 @ SV598 @ SV884 )
!= ( c_List_Ofilter @ SV1082 @ SY3064 @ SV884 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1082 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(3068,plain,
! [SV1212: $i,SV1083: $i,SV600: $i,SV240: $i] :
( ( ( ( c_List_Ofilter @ SV240 @ ( c_List_Olist_OCons @ SV600 @ SV1083 @ SV1212 ) @ SV1212 )
= ( c_List_Olist_OCons @ SV600 @ ( c_List_Ofilter @ SV240 @ SV1083 @ SV1212 ) @ SV1212 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV240 @ SV600 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3069,plain,
! [SV886: $i,SV601: $i,SV241: $i] :
( ( ( ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SV601 ) @ SV601 )
= ( c_List_Orev @ SV886 @ SV601 ) )
= $false )
| ( ( SV886
= ( c_List_Olist_OCons @ SV241 @ ( c_List_Olist_ONil @ SV601 ) @ SV601 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(3070,plain,
! [SV1213: $i,SV1084: $i,SV887: $i,SV602: $i,SV242: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV242 @ SV602 @ SV887 @ ( c_Lambda_OdB_OAbs @ SV1084 ) @ SV1213 )
= ( hAPP @ SV887 @ SV1084 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3071,plain,
! [SV1085: $i,SV888: $i,SV603: $i,SV243: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV243 @ SV603 @ SV888 ) ) @ ( c_Lambda_Osubst @ SV1085 @ SV603 @ SV888 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV243 ) @ SV1085 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(3072,plain,
! [SV1087: $i,SV890: $i,SV605: $i,SV245: $i] :
( ( ( ( c_List_Oappend @ SV245 @ SV605 @ SV890 )
!= ( c_List_Oappend @ SV1087 @ SV605 @ SV890 ) )
= $true )
| ( ( SV245 = SV1087 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2813]) ).
thf(3073,plain,
! [SV1088: $i,SV891: $i,SV606: $i,SV246: $i] :
( ( ( ( c_List_Oappend @ SV246 @ SV606 @ SV891 )
!= ( c_List_Oappend @ SV246 @ SV1088 @ SV891 ) )
= $true )
| ( ( SV606 = SV1088 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2814]) ).
thf(3074,plain,
! [SV1089: $i,SV892: $i,SV607: $i,SV247: $i] :
( ( ( ! [SY3067: $i] :
( ( c_List_Ofilter @ SV247 @ SV607 @ SV892 )
!= ( c_List_Olist_OCons @ SV1089 @ SY3067 @ SV892 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV247 @ SV1089 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(3075,plain,
! [SV1214: $i,SV1090: $i,SV893: $i,SV608: $i,SV248: $i] :
( ( ( c_List_Orotate @ SV248 @ ( c_List_Omap @ SV608 @ SV893 @ SV1090 @ SV1214 ) @ SV1214 )
= ( c_List_Omap @ SV608 @ ( c_List_Orotate @ SV248 @ SV893 @ SV1090 ) @ SV1090 @ SV1214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3076,plain,
! [SV1215: $i,SV1091: $i,SV894: $i,SV612: $i,SV252: $i] :
( ( ! [SY3129: $i] :
( ( c_List_Ofoldr @ SV252 @ ( c_List_Oappend @ SV612 @ SV894 @ SV1091 ) @ SV1215 @ SV1091 @ SY3129 )
= ( c_List_Ofoldr @ SV252 @ SV612 @ ( c_List_Ofoldr @ SV252 @ SV894 @ SV1215 @ SV1091 @ SY3129 ) @ SV1091 @ SY3129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3077,plain,
! [SV1216: $i,SV1092: $i,SV613: $i,SV253: $i] :
( ( ( c_List_Olist__ex @ SV253 @ ( c_List_Olist_OCons @ SV613 @ SV1092 @ SV1216 ) @ SV1216 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV253 @ SV613 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3078,plain,
! [SV895: $i,SV614: $i,SV254: $i] :
( ( ( ( c_List_Orev @ SV254 @ SV614 )
= ( c_List_Olist_OCons @ SV895 @ ( c_List_Olist_ONil @ SV614 ) @ SV614 ) )
= $false )
| ( ( SV254
= ( c_List_Olist_OCons @ SV895 @ ( c_List_Olist_ONil @ SV614 ) @ SV614 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(3079,plain,
! [SV1093: $i,SV896: $i,SV615: $i,SV255: $i] :
( ( ( c_List_Olist__ex @ SV255 @ ( c_List_Olist_OCons @ SV615 @ SV896 @ SV1093 ) @ SV1093 )
= $true )
| ( ( ~ ( c_List_Olist__ex @ SV255 @ SV896 @ SV1093 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(3080,plain,
! [SV897: $i,SV616: $i,SV1217: $i,SV256: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV256 @ SV1217 ) )
| ~ ( c_List_Olist__ex @ SV256 @ ( c_List_Olist_OCons @ SV1217 @ SV616 @ SV897 ) @ SV897 ) )
= $true )
| ( ( c_List_Olist__ex @ SV256 @ SV616 @ SV897 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3081,plain,
! [SV1218: $i,SV1094: $i,SV898: $i,SV617: $i,SV257: $i] :
( ( ! [SY3130: $i] :
( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SV898 @ SV1094 ) @ ( c_List_Olist_OCons @ SV1218 @ SY3130 @ SV1094 ) @ SV1094 )
| ~ ( c_List_Olistrelp @ SV257 @ SV898 @ SY3130 @ SV1094 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SV1218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3082,plain,
! [SV258: $i,SV1219: $i,SV618: $i] :
( ( ( ! [SY3131: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ SV1219 @ SV258 ) @ SY3131 @ SV258 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1219 @ SY3131 @ SV258 ) @ SV258 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV258 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3083,plain,
! [SV259: $i,SV1220: $i,SV619: $i] :
( ( ( ! [SY3132: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1220 @ SY3132 @ SV259 ) @ SV259 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1220 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ SY3132 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV259 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3084,plain,
! [SV260: $i,SV1221: $i,SV620: $i] :
( ( ( ! [SY3133: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1221 @ SY3133 @ SV260 ) @ SV260 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1221 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ SY3133 @ SV260 ) @ SV260 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV260 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3085,plain,
! [SV261: $i,SV1222: $i,SV621: $i] :
( ( ( ! [SY3134: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ SV1222 @ SV261 ) @ SY3134 @ SV261 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1222 @ SY3134 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3086,plain,
! [SV1223: $i,SV1097: $i,SV625: $i,SV265: $i] :
( ( ( ( c_List_Oremove1 @ SV265 @ ( c_List_Olist_OCons @ SV625 @ SV1097 @ SV1223 ) @ SV1223 )
= ( c_List_Olist_OCons @ SV625 @ ( c_List_Oremove1 @ SV265 @ SV1097 @ SV1223 ) @ SV1223 ) )
= $true )
| ( ( SV265 = SV625 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3087,plain,
! [SV626: $i,SV901: $i,SV266: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV266 ) @ SV901 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV266 @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV901 @ SV626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(3088,plain,
! [SV1224: $i,SV1098: $i,SV902: $i,SV627: $i,SV267: $i] :
( ( ( c_List_Omap @ SV267 @ ( c_List_Oappend @ SV627 @ SV902 @ SV1098 ) @ SV1098 @ SV1224 )
= ( c_List_Oappend @ ( c_List_Omap @ SV267 @ SV627 @ SV1098 @ SV1224 ) @ ( c_List_Omap @ SV267 @ SV902 @ SV1098 @ SV1224 ) @ SV1224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3089,plain,
! [SV268: $i,SV628: $i] :
( ( ( c_List_Olistsp @ SV628 @ SV268 @ t_a )
= $false )
| ( ( SV268
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( SV268
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SV628 @ SV268 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SV628 @ SV268 ) @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(3090,plain,
! [SV1099: $i,SV903: $i,SV629: $i,SV269: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV269 ) @ SV629 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV903 ) @ SV1099 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV629 = SV1099 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(3091,plain,
! [SV1225: $i,SV904: $i,SV630: $i,SV270: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV270 ) @ SV630 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV904 ) @ SV1225 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV270 = SV904 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3092,plain,
! [SV905: $i,SV631: $i,SV271: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV271 @ SV631 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV905 ) )
= $false )
| ( ( SV271
= ( c_Lambda_OdB_OAbs @ SV905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(3093,plain,
! [SV1226: $i,SV1100: $i,SV632: $i,SV272: $i] :
( ( ( ( c_List_Oremove1 @ SV272 @ ( c_List_Ofilter @ SV632 @ SV1100 @ SV1226 ) @ SV1226 )
= ( c_List_Ofilter @ SV632 @ SV1100 @ SV1226 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV632 @ SV272 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3094,plain,
! [SV1227: $i,SV1101: $i,SV906: $i,SV633: $i,SV273: $i] :
( ( ! [SY3135: $i] :
( ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ ( c_List_Olist_OCons @ SV906 @ SV1101 @ SV1227 ) @ SY3135 @ SV1227 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV633 @ SV906 ) @ SV1101 ) @ ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ SV1101 @ SY3135 @ SV1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3095,plain,
! [SV907: $i,SV634: $i,SV274: $i] :
( ( ( ( c_List_Orev @ SV274 @ SV634 )
= ( c_List_Orev @ SV907 @ SV634 ) )
= $false )
| ( ( SV274 = SV907 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(3096,plain,
! [SV1228: $i,SV1102: $i,SV908: $i,SV635: $i,SV275: $i] :
( ( ( c_List_Ofoldr @ SV275 @ SV635 @ SV908 @ SV1102 @ SV1228 )
= ( c_List_Ofoldl @ ( c_COMBC @ SV275 @ SV1102 @ SV1228 @ SV1228 ) @ SV908 @ ( c_List_Orev @ SV635 @ SV1102 ) @ SV1228 @ SV1102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3097,plain,
! [SV1229: $i,SV1103: $i,SV909: $i,SV636: $i,SV276: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV276 @ SV636 @ SV909 @ ( c_Lambda_OdB_OAbs @ SV1103 ) @ SV1229 )
= ( hAPP @ ( hAPP @ SV909 @ SV1103 ) @ ( c_Lambda_OdB_OdB__rec @ SV276 @ SV636 @ SV909 @ SV1103 @ SV1229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3098,plain,
! [SV278: $i,SV1230: $i,SV1104: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1104 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1104 @ SV1230 @ SV278 ) @ SV278 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1104 @ SV1230 @ SV278 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3099,plain,
! [SV279: $i,SV1231: $i,SV1105: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1105 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1105 @ SV1231 @ SV279 ) @ SV279 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1105 @ SV1231 @ SV279 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3100,plain,
! [SV1232: $i,SV1106: $i,SV912: $i,SV639: $i,SV281: $i] :
( ( ! [SY3136: $i] :
( ( c_List_Ofoldr @ SV281 @ ( c_List_Olist_OCons @ SV639 @ SV912 @ SV1106 ) @ SV1232 @ SV1106 @ SY3136 )
= ( hAPP @ ( hAPP @ SV281 @ SV639 ) @ ( c_List_Ofoldr @ SV281 @ SV912 @ SV1232 @ SV1106 @ SY3136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3101,plain,
! [SV1233: $i,SV1107: $i,SV913: $i,SV640: $i,SV282: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV282 @ ( c_Lambda_OdB_OdB__case @ SV640 @ SV913 @ SV1107 @ ( c_Lambda_OdB_OAbs @ SV1233 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ SV1107 @ SV1233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3102,plain,
! [SV1234: $i,SV1108: $i,SV914: $i,SV641: $i,SV283: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV283 @ ( c_Lambda_OdB_OdB__case @ SV641 @ SV914 @ SV1108 @ ( c_Lambda_OdB_OAbs @ SV1234 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ SV1108 @ SV1234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3103,plain,
! [SV1110: $i,SV916: $i,SV644: $i,SV287: $i] :
( ( ( ! [SY3087: $i] :
( ( c_List_Olist_OCons @ SV287 @ SV644 @ SV916 )
!= ( c_List_Olist_OCons @ SV1110 @ SY3087 @ SV916 ) ) )
= $true )
| ( ( SV287 = SV1110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(3104,plain,
! [SV1235: $i,SV1111: $i,SV917: $i,SV645: $i,SV288: $i] :
( ( ( ( c_List_Olist_OCons @ SV288 @ SV645 @ SV917 )
!= ( c_List_Olist_OCons @ SV1111 @ SV1235 @ SV917 ) )
| ( SV645 = SV1235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3105,plain,
! [SV918: $i,SV289: $i,SV646: $i,SV1236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1236 ) @ SV646 ) )
| ~ ( c_Type_Otyping @ SV289 @ SV1236 @ SV918 ) )
= $true )
| ( ( c_Type_Otyping @ SV289 @ SV646 @ SV918 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3106,plain,
! [SV290: $i,SV1112: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1112 @ SV290 )
= $true )
| ( ( ! [SY3089: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1112 @ SY3089 @ SV290 ) @ SV290 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(3107,plain,
! [SV291: $i,SV1113: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1113 @ SV291 )
= $true )
| ( ( ! [SY3090: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY3090 @ SV1113 @ SV291 ) @ SV291 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(3108,plain,
! [SV1237: $i,SV1114: $i,SV919: $i,SV647: $i,SV292: $i] :
( ( ! [SY3137: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV647 @ SV919 @ SV1114 ) @ SV1237 @ SY3137 @ SV1114 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV1237 @ SY3137 @ SV1114 ) @ SV647 @ SV919 @ SV1114 ) )
| ( SV647 = SV1237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3109,plain,
! [SV293: $i,SV1115: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SV1115 @ SV293 ) @ SV293 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV1115 @ SV293 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(3110,plain,
! [SV1238: $i,SV1116: $i,SV648: $i,SV294: $i] :
( ( ( ( c_List_Ofilter @ SV294 @ ( c_List_Olist_OCons @ SV648 @ SV1116 @ SV1238 ) @ SV1238 )
= ( c_List_Ofilter @ SV294 @ SV1116 @ SV1238 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV294 @ SV648 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3111,plain,
! [SV1117: $i,SV920: $i,SV649: $i,SV295: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV295 @ SV649 @ ( tc_fun @ SV920 @ tc_bool ) ) @ SV1117 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV649 @ SV1117 ) )
| ~ ( hBOOL @ ( hAPP @ SV295 @ SV1117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3112,plain,
! [SV1118: $i,SV922: $i,SV651: $i,SV297: $i] :
( ( ( ! [SY3094: $i] :
( ( c_List_Oappend @ SV297 @ ( c_List_Olist_OCons @ SV651 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 )
!= ( c_List_Oappend @ SV1118 @ ( c_List_Olist_OCons @ SY3094 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 ) ) )
= $true )
| ( ( SV297 = SV1118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(3113,plain,
! [SV1239: $i,SV1119: $i,SV923: $i,SV652: $i,SV298: $i] :
( ( ( ( c_List_Oappend @ SV298 @ ( c_List_Olist_OCons @ SV652 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 )
!= ( c_List_Oappend @ SV1119 @ ( c_List_Olist_OCons @ SV1239 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 ) )
| ( SV652 = SV1239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3114,plain,
! [SV1240: $i,SV1120: $i,SV924: $i,SV653: $i,SV299: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV299 @ ( c_List_Olist_Olist__case @ SV653 @ SV924 @ ( c_List_Olist_OCons @ SV1120 @ SV1240 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV299 @ ( hAPP @ ( hAPP @ SV924 @ SV1120 ) @ SV1240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3115,plain,
! [SV1241: $i,SV1121: $i,SV925: $i,SV654: $i,SV300: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV300 @ ( c_List_Olist_Olist__case @ SV654 @ SV925 @ ( c_List_Olist_OCons @ SV1121 @ SV1241 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV300 @ ( hAPP @ ( hAPP @ SV925 @ SV1121 ) @ SV1241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3116,plain,
! [SV1242: $i,SV1122: $i,SV926: $i,SV655: $i,SV301: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV301 @ SV655 @ SV926 @ SV1122 ) @ SV655 @ SV1242 @ SV1122 )
= ( c_List_Olist__update @ SV301 @ SV655 @ SV1242 @ SV1122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3117,plain,
! [SV306: $i,SV1243: $i,SV1127: $i] :
( ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV1127 @ SV1243 @ SV306 ) @ SV306 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1243 @ SV306 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV306 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3118,plain,
! [SV1128: $i,SV661: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ SV309 @ ( c_List_Olist_Olist__case @ SV661 @ SV1128 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV309 @ SV661 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(3119,plain,
! [SV932: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ ( v_sko__List__Xzip__Xinduct__2 @ SV311 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV932 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(3120,plain,
! [SV934: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV314 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV314 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV934 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(3121,plain,
! [SV936: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ SV316 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV316 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV316 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV316 @ SV936 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(3122,plain,
! [SV937: $i,SV317: $i] :
( ( ( hBOOL @ ( hAPP @ SV317 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV317 @ ( v_sko__List__Xtake__Xinduct__2 @ SV317 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV317 @ SV937 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3123,plain,
! [SV942: $i,SV325: $i] :
( ( ( hBOOL @ ( hAPP @ SV325 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV325 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV325 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV325 @ SV942 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(3124,plain,
! [SV945: $i,SV329: $i] :
( ( ( hBOOL @ ( hAPP @ SV329 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV329 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV329 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV329 @ SV945 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(3125,plain,
! [SV948: $i,SV332: $i] :
( ( ( hBOOL @ ( hAPP @ SV332 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV332 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV332 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV332 @ SV948 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(3126,plain,
! [SV950: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ SV336 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV336 @ ( v_sko__List__Xlist__Xinduct__2 @ SV336 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV336 @ SV950 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(3127,plain,
! [SV952: $i,SV340: $i] :
( ( ( hBOOL @ ( hAPP @ SV340 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV340 @ ( v_sko__List__Xmap__Xinduct__2 @ SV340 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV340 @ SV952 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(3128,plain,
! [SV1134: $i,SV953: $i,SV682: $i,SV342: $i] :
( ( ( ( c_List_Olist__update @ SV342 @ SV682 @ SV953 @ SV1134 )
!= ( c_List_Olist_ONil @ SV1134 ) )
= $true )
| ( ( SV342
= ( c_List_Olist_ONil @ SV1134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(3129,plain,
! [SV1244: $i,SV1136: $i,SV957: $i,SV686: $i,SV346: $i] :
( ( ! [SY3138: $i] :
( ~ ( hBOOL @ ( hAPP @ SV346 @ ( c_Lambda_OdB_OdB__case @ SV686 @ SV957 @ SV1136 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1244 ) @ SY3138 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ SV957 @ SV1244 ) @ SY3138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3130,plain,
! [SV1245: $i,SV1137: $i,SV958: $i,SV687: $i,SV347: $i] :
( ( ! [SY3139: $i] :
( ~ ( hBOOL @ ( hAPP @ SV347 @ ( c_Lambda_OdB_OdB__case @ SV687 @ SV958 @ SV1137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1245 ) @ SY3139 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV347 @ ( hAPP @ ( hAPP @ SV958 @ SV1245 ) @ SY3139 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3131,plain,
! [SV1246: $i,SV1138: $i,SV960: $i,SV689: $i,SV349: $i] :
( ( ! [SY3140: $i] :
( ( c_Lambda_OdB_OdB__case @ SV349 @ SV689 @ SV960 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1138 ) @ SV1246 ) @ SY3140 )
= ( hAPP @ ( hAPP @ SV689 @ SV1138 ) @ SV1246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3132,plain,
! [SV1247: $i,SV1139: $i,SV961: $i,SV690: $i,SV350: $i] :
( ( ! [SY3141: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1139 ) @ SV1247 ) @ SY3141 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV690 @ SV1139 ) @ SV1247 ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ SV1139 @ SY3141 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ SV1247 @ SY3141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3133,plain,
! [SV962: $i,SV691: $i,SV351: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV351 @ SV691 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV962 @ SV691 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV351 = SV962 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(3134,plain,
! [SV352: $i,SV963: $i,SV692: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV692 ) @ SV963 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV692 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV352 ) @ SV963 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(3135,plain,
! [SV693: $i,SV964: $i,SV353: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV353 ) @ SV964 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV353 ) @ SV693 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV964 ) @ SV693 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(3136,plain,
! [SV356: $i,SV696: $i,SV1248: $i,SV967: $i] :
( ( ( ! [SY3142: $i] :
( ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SY3142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV696 )
| ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SY3142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 ) ) )
= $true )
| ( ( SV356 = SV696 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3137,plain,
! [SV1142: $i,SV968: $i,SV697: $i,SV357: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV357 ) @ SV697 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV968 ) @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(3138,plain,
! [SV1143: $i,SV969: $i,SV698: $i,SV358: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV358 ) ) @ SV698 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV969 ) @ SV1143 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(3139,plain,
! [SV1249: $i,SV1144: $i,SV970: $i,SV700: $i,SV360: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV360 @ ( c_Lambda_OdB_OdB__case @ SV700 @ SV970 @ SV1144 @ ( c_Lambda_OdB_OVar @ SV1249 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV360 @ ( hAPP @ SV700 @ SV1249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3140,plain,
! [SV1250: $i,SV1145: $i,SV971: $i,SV701: $i,SV361: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Lambda_OdB_OdB__case @ SV701 @ SV971 @ SV1145 @ ( c_Lambda_OdB_OVar @ SV1250 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV361 @ ( hAPP @ SV701 @ SV1250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3141,plain,
! [SV1251: $i,SV1146: $i,SV972: $i,SV704: $i,SV364: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV364 @ SV704 @ SV972 @ ( c_Lambda_OdB_OVar @ SV1146 ) @ SV1251 )
= ( hAPP @ SV364 @ SV1146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3142,plain,
! [SV973: $i,SV706: $i,SV366: $i] :
( ( ( c_Type_Otyping @ SV366 @ ( c_Lambda_OdB_OVar @ SV706 ) @ SV973 )
= $false )
| ( ( ( hAPP @ SV366 @ SV706 )
= SV973 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(3143,plain,
! [SV1252: $i,SV1147: $i,SV974: $i,SV707: $i,SV367: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV367 @ SV707 @ SV974 @ ( c_Lambda_OdB_OVar @ SV1147 ) @ SV1252 )
= ( hAPP @ SV367 @ SV1147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3144,plain,
! [SV975: $i,SV709: $i,SV369: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV369 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV709 @ SV975 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV975
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(3145,plain,
! [SV1148: $i,SV976: $i,SV710: $i,SV371: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV371 ) @ SV710 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ SV1148 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV371
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV371 @ SV710 @ SV976 @ SV1148 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1148
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(3146,plain,
! [SV1149: $i,SV711: $i,SV372: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV372 @ SV711 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV1149 ) )
= $false )
| ( ( SV711
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(3147,plain,
! [SV1150: $i,SV977: $i,SV712: $i,SV374: $i] :
( ( ( c_List_Olistsp @ SV374 @ ( c_List_Oappend @ SV712 @ SV977 @ SV1150 ) @ SV1150 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV374 @ SV977 @ SV1150 )
| ~ ( c_List_Olistsp @ SV374 @ SV712 @ SV1150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(3148,plain,
! [SV978: $i,SV713: $i,SV375: $i] :
( ( ( hBOOL @ ( hAPP @ SV375 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV375 @ SV713 @ SV978 ) ) )
= $false )
| ( ( c_List_Olistsp @ SV375 @ SV713 @ SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(3149,plain,
! [SV1151: $i,SV979: $i,SV714: $i,SV376: $i] :
( ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV714 @ ( tc_fun @ SV979 @ tc_bool ) ) @ SV1151 @ SV979 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV714 @ SV1151 @ SV979 )
| ~ ( c_List_Olistsp @ SV376 @ SV1151 @ SV979 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(3150,plain,
! [SV980: $i,SV715: $i,SV1253: $i,SV377: $i] :
( ( ( ~ ( c_List_Olistsp @ SV377 @ ( c_List_Oappend @ SV1253 @ SV715 @ SV980 ) @ SV980 ) )
= $true )
| ( ( c_List_Olistsp @ SV377 @ SV715 @ SV980 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3151,plain,
! [SV981: $i,SV1254: $i,SV716: $i,SV378: $i] :
( ( ( ~ ( c_List_Olistsp @ SV378 @ ( c_List_Oappend @ SV716 @ SV1254 @ SV981 ) @ SV981 ) )
= $true )
| ( ( c_List_Olistsp @ SV378 @ SV716 @ SV981 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3152,plain,
! [SV1255: $i,SV983: $i,SV717: $i,SV381: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV381 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV983 ) @ SV1255 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV381 = SV983 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3153,plain,
! [SV1152: $i,SV984: $i,SV718: $i,SV382: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV382 ) @ SV718 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV984 ) @ SV1152 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV718 = SV1152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2918]) ).
thf(3154,plain,
! [SV1153: $i,SV719: $i,SV383: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV383 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV719 @ SV1153 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV383 )
= SV719 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3155,plain,
! [SV720: $i,SV384: $i,SV1154: $i] :
( ( ( hBOOL @ ( hAPP @ SV1154 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1154 @ SV384 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1154 @ SV720 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV384 @ SV720 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(3156,plain,
! [SV721: $i,SV1155: $i,SV385: $i] :
( ( ( hBOOL @ ( hAPP @ SV385 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1155 @ SV385 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV385 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1155 @ SV721 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ SV721 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(3157,plain,
! [SV722: $i,SV386: $i,SV1156: $i] :
( ( ( hBOOL @ ( hAPP @ SV1156 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1156 @ SV386 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1156 @ SV722 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV386 @ SV722 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3158,plain,
! [SV723: $i,SV1157: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ SV387 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1157 @ SV387 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1157 @ SV723 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ SV723 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2923]) ).
thf(3159,plain,
! [SV724: $i,SV388: $i] :
( ( ( c_List_Olistsp @ SV388 @ SV724 @ t_a )
= $false )
| ( ( SV724
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV388 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV388 @ SV724 ) @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(3160,plain,
! [SV725: $i,SV389: $i] :
( ( ( c_List_Olistsp @ SV389 @ SV725 @ t_a )
= $false )
| ( ( SV725
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV389 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV389 @ SV725 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(3161,plain,
! [SV726: $i,SV390: $i,SV1158: $i] :
( ( ( c_List_Olistsp @ SV1158 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1158 @ SV390 ) @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV390 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1158 @ SV726 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV390 @ SV726 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(3162,plain,
! [SV727: $i,SV391: $i,SV1159: $i] :
( ( ( c_List_Olistsp @ SV1159 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1159 @ SV391 ) @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1159 @ SV727 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV391 @ SV727 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2927]) ).
thf(3163,plain,
! [SV985: $i,SV729: $i,SV393: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV729 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV985 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV729 )
= SV985 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3164,plain,
! [SV1160: $i,SV986: $i,SV394: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV394 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV394 @ ( c_Lambda_OdB_OVar @ SV986 ) @ SV1160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3165,plain,
! [SV987: $i,SV730: $i,SV396: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV396 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV730 @ SV987 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV987
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3166,plain,
! [SV1256: $i,SV988: $i,SV733: $i,SV399: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV399 ) @ SV733 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV988 ) @ SV1256 ) )
= $true )
| ( ( SV399 = SV988 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3167,plain,
! [SV1161: $i,SV989: $i,SV734: $i,SV400: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV400 ) @ SV734 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV989 ) @ SV1161 ) )
= $true )
| ( ( SV734 = SV1161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3168,plain,
! [SV1257: $i,SV1162: $i,SV991: $i,SV737: $i,SV404: $i] :
( ( ! [SY3143: $i] :
( ( hAPP @ ( c_COMBB @ SV404 @ SV737 @ SV991 @ SV1162 @ SV1257 ) @ SY3143 )
= ( hAPP @ SV404 @ ( hAPP @ SV737 @ SY3143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3169,plain,
! [SV1258: $i,SV1163: $i,SV992: $i,SV738: $i,SV405: $i] :
( ( ! [SY3144: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV405 @ SV738 @ SV992 @ SV1163 ) @ SV1258 ) @ SY3144 )
= ( hAPP @ ( hAPP @ SV405 @ SY3144 ) @ SV1258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3170,plain,
! [SV1259: $i,SV1164: $i,SV994: $i,SV744: $i,SV411: $i] :
( ( ! [SY3145: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV411 @ SV744 @ SV994 @ SV1164 ) @ SV1259 ) @ SY3145 )
= ( hAPP @ ( hAPP @ SV411 @ SY3145 ) @ SV1259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3171,plain,
! [SV1260: $i,SV1165: $i,SV995: $i,SV745: $i,SV412: $i] :
( ( ! [SY3146: $i] :
( ( hAPP @ ( c_COMBB @ SV412 @ SV745 @ SV995 @ SV1165 @ SV1260 ) @ SY3146 )
= ( hAPP @ SV412 @ ( hAPP @ SV745 @ SY3146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3172,plain,
! [SV1166: $i,SV747: $i,SV414: $i] :
( ( ( c_fequal @ SV414 @ SV747 @ SV1166 )
= $false )
| ( ( SV414 = SV747 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3173,plain,
! [SV748: $i,SV996: $i,SV1261: $i,SV416: $i,SV4: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV1261 ) @ SV996 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV1261 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV996 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3174,plain,
! [SV1262: $i,SV997: $i,SV751: $i,SV419: $i,SV7: $i] :
( ( ( ( c_List_Oreplicate @ SV7 @ SV419 @ SV751 )
!= ( c_List_Oreplicate @ SV997 @ SV1262 @ SV751 ) )
= $true )
| ( ( SV7 = SV997 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3175,plain,
! [SV752: $i,SV1263: $i,SV420: $i,SV8: $i] :
( ( ( ! [SY3147: $i] : ( c_ListOrder_Ostep1 @ SV8 @ ( c_List_Olist_OCons @ SV420 @ SV1263 @ SY3147 ) @ ( c_List_Olist_OCons @ SV752 @ SV1263 @ SY3147 ) @ SY3147 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV8 @ SV420 ) @ SV752 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3176,plain,
! [SV9: $i,SV421: $i,SV998: $i,SV753: $i] :
( ( ( SV753 = SV998 )
= $true )
| ( ( ! [SY2998: $i,SY2999: $i] :
~ ( c_ListOrder_Ostep1 @ SY2998 @ ( c_List_Olist_OCons @ SV421 @ SV998 @ SY2999 ) @ ( c_List_Olist_OCons @ SV9 @ SV753 @ SY2999 ) @ SY2999 ) )
= $true )
| ( ( SV9 = SV421 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3177,plain,
! [SV1167: $i,SV999: $i,SV755: $i,SV423: $i,SV12: $i] :
( ( ( c_ListOrder_Ostep1 @ SV12 @ ( c_List_Oappend @ SV423 @ SV755 @ SV999 ) @ ( c_List_Oappend @ SV423 @ SV1167 @ SV999 ) @ SV999 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV12 @ SV755 @ SV1167 @ SV999 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3178,plain,
! [SV1000: $i,SV756: $i,SV424: $i,SV13: $i] :
( ( ( c_ListOrder_Ostep1 @ SV13 @ SV424 @ SV756 @ SV1000 )
= $false )
| ( ( ! [SY3001: $i] : ( c_ListOrder_Ostep1 @ SV13 @ ( c_List_Oappend @ SV424 @ SY3001 @ SV1000 ) @ ( c_List_Oappend @ SV756 @ SY3001 @ SV1000 ) @ SV1000 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(3179,plain,
! [SV15: $i,SV1168: $i,SV426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV426 @ SV1168 @ SV15 )
= $true )
| ( ( ! [SY3120: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3120 @ SV1168 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV426 @ SY3120 @ SV15 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2952]) ).
thf(3180,plain,
! [SV16: $i,SV1169: $i,SV427: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1169 @ SV16 )
= $true )
| ( ( ! [SY3121: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV427 @ SY3121 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SY3121 @ SV1169 @ SV16 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3181,plain,
! [SV1001: $i,SV24: $i,SV431: $i,SV759: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ SV431 ) @ SV24 ) )
= $true )
| ( ( ! [SY3002: $i,SY3003: $i] :
~ ( c_ListOrder_Ostep1 @ SV759 @ ( c_List_Olist_OCons @ SV431 @ SV1001 @ SY3002 ) @ ( c_List_Olist_OCons @ SV24 @ SY3003 @ SY3002 ) @ SY3002 ) )
= $true )
| ( ( SV24 = SV431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2955]) ).
thf(3182,plain,
! [SV1170: $i,SV1004: $i,SV764: $i,SV438: $i,SV33: $i] :
( ( ( ( c_List_Oreplicate @ SV33 @ SV438 @ SV764 )
!= ( c_List_Oreplicate @ SV1004 @ SV1170 @ SV764 ) )
= $true )
| ( ( ( SV438 = SV1170 )
| ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2957]) ).
thf(3183,plain,
! [SV452: $i,SV1007: $i,SV770: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV770 ) @ SV1007 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV452 ) @ SV770 ) @ SV1007 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(3184,plain,
! [SV1172: $i,SV453: $i,SV771: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ SV51 @ SV771 ) )
= $false )
| ( ( ( c_List_Ofilter @ SV51 @ ( c_List_Oreplicate @ SV453 @ SV771 @ SV1172 ) @ SV1172 )
= ( c_List_Oreplicate @ SV453 @ SV771 @ SV1172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3185,plain,
! [SV1173: $i,SV1008: $i,SV772: $i,SV454: $i,SV52: $i] :
( ( ( ( c_List_Omap @ SV52 @ SV454 @ SV772 @ SV1008 )
!= ( c_List_Omap @ SV52 @ SV1173 @ SV772 @ SV1008 ) )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ SV454 @ ( tc_List_Olist @ SV772 ) )
= ( c_Nat_Osize__class_Osize @ SV1173 @ ( tc_List_Olist @ SV772 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2961]) ).
thf(3186,plain,
! [SV1264: $i,SV1009: $i,SV773: $i,SV458: $i,SV57: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV57 @ SV458 @ SV773 ) @ SV1009 @ SV1264 @ SV773 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV57 @ SV1009 @ SV1264 @ SV773 ) @ SV458 @ SV773 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_Nat_Osize__class_Osize @ SV57 @ ( tc_List_Olist @ SV773 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3187,plain,
! [SV1265: $i,SV1010: $i,SV774: $i,SV459: $i,SV58: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV58 @ SV459 @ SV774 ) @ SV1010 @ SV1265 @ SV774 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV58 @ SV1010 @ SV1265 @ SV774 ) @ SV459 @ SV774 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1010 @ ( c_Nat_Osize__class_Osize @ SV58 @ ( tc_List_Olist @ SV774 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(3188,plain,
! [SV1014: $i,SV67: $i,SV463: $i,SV776: $i] :
( ( ( SV776 = SV463 )
= $true )
| ( ( ! [SY3009: $i,SY3010: $i] :
~ ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SY3009 @ SV463 @ SV1014 ) @ ( c_List_Olist_OCons @ SY3010 @ SV776 @ SV1014 ) @ SV1014 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV67 @ SV463 @ SV776 @ SV1014 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2970]) ).
thf(3189,plain,
! [SV68: $i,SV1174: $i,SV1015: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1174 @ SV68 )
= $true )
| ( ( ( SV1174 = SV1015 )
| ( c_HOL_Oord__class_Oless @ SV1174 @ SV1015 @ SV68 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2971]) ).
thf(3190,plain,
! [SV69: $i,SV1175: $i,SV1016: $i] :
( ( ( SV1016 = SV1175 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1175 @ SV1016 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV1016 @ SV1175 @ SV69 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2972]) ).
thf(3191,plain,
! [SV71: $i,SV465: $i,SV777: $i] :
( ( ( SV777 = SV465 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV777 @ SV465 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV465 @ SV777 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV71 @ SV465 ) @ SV777 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3192,plain,
! [SV73: $i,SV1176: $i,SV1017: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1017 @ SV1176 @ SV73 )
= $true )
| ( ( ( SV1176 = SV1017 )
| ( c_HOL_Oord__class_Oless @ SV1176 @ SV1017 @ SV73 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(3193,plain,
! [SV75: $i,SV1177: $i,SV1019: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1019 @ SV1177 @ SV75 )
= $true )
| ( ( ( SV1177 = SV1019 )
| ( c_HOL_Oord__class_Oless @ SV1177 @ SV1019 @ SV75 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3194,plain,
! [SV76: $i,SV1178: $i,SV1020: $i] :
( ( ( SV1020 = SV1178 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1020 @ SV1178 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV1178 @ SV1020 @ SV76 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3195,plain,
! [SV1266: $i,SV77: $i,SV1179: $i,SV468: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV468 @ SV1179 @ SV77 ) @ SV1266 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV1179 @ SV1266 @ SV77 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3196,plain,
! [SV1267: $i,SV78: $i,SV1180: $i,SV469: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV469 @ SV1180 @ SV78 ) @ SV1267 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SV1267 @ SV78 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3197,plain,
! [SV83: $i,SV470: $i,SV1021: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1021 @ SV470 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV83 @ SV1021 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV83 ) @ SV470 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3198,plain,
! [SV781: $i,SV1024: $i,SV475: $i,SV1268: $i,SV92: $i] :
( ( ( ! [SY3148: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV1268 ) @ SY3148 ) )
| ~ ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SV1268 @ SV475 @ SV1024 ) @ ( c_List_Olist_OCons @ SY3148 @ SV781 @ SV1024 ) @ SV1024 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV92 @ SV475 @ SV781 @ SV1024 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3199,plain,
! [SV1181: $i,SV1025: $i,SV782: $i,SV476: $i,SV93: $i] :
( ( ( c_ListOrder_Ostep1 @ SV93 @ ( c_List_Olist_OCons @ SV476 @ SV782 @ SV1025 ) @ ( c_List_Olist_OCons @ SV476 @ SV1181 @ SV1025 ) @ SV1025 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV93 @ SV782 @ SV1181 @ SV1025 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3200,plain,
! [SV98: $i,SV1182: $i,SV1026: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1026 @ SV1182 @ SV98 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SV1026 @ SV98 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2984]) ).
thf(3201,plain,
! [SV784: $i,SV1027: $i,SV1269: $i,SV481: $i,SV99: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV1269 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SV784 ) @ SV1269 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV784 ) @ SV1027 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3202,plain,
! [SV785: $i,SV482: $i,SV1028: $i,SV1270: $i,SV100: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SV1270 ) @ SV1028 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1028 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3203,plain,
! [SV101: $i,SV1183: $i,SV1029: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SV1183 @ SV101 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1029 @ SV101 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2987]) ).
thf(3204,plain,
! [SV102: $i,SV1184: $i,SV1030: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1030 @ SV1184 @ SV102 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1184 @ SV1030 @ SV102 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2988]) ).
thf(3205,plain,
! [SV103: $i,SV1185: $i,SV1031: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1031 @ SV1185 @ SV103 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1185 @ SV1031 @ SV103 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2989]) ).
thf(3206,plain,
! [SV1186: $i,SV1033: $i,SV791: $i,SV491: $i,SV113: $i] :
( ( ( ( c_List_Oappend @ SV113 @ SV491 @ SV791 )
!= ( c_List_Olist_OCons @ SV1033 @ SV1186 @ SV791 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1033 @ SV1186 @ SV113 @ SV491 @ SV791 ) @ SV491 @ SV791 )
= SV1186 )
| ( SV491
= ( c_List_Olist_OCons @ SV1033 @ SV1186 @ SV791 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2991]) ).
thf(3207,plain,
! [SV1187: $i,SV1034: $i,SV792: $i,SV492: $i,SV114: $i] :
( ( ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
!= ( c_List_Oappend @ SV1034 @ SV1187 @ SV792 ) )
= $true )
| ( ( ( ( c_List_Olist_OCons @ SV114 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV114 @ SV492 @ SV1034 @ SV1187 @ SV792 ) @ SV792 )
= SV1034 )
| ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
= SV1187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3208,plain,
! [SV1188: $i,SV1035: $i,SV793: $i,SV493: $i,SV115: $i] :
( ( ( ( c_List_Oappend @ SV115 @ SV493 @ SV793 )
!= ( c_List_Olist_OCons @ SV1035 @ SV1188 @ SV793 ) )
= $true )
| ( ( ( SV115
= ( c_List_Olist_OCons @ SV1035 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1035 @ SV1188 @ SV115 @ SV493 @ SV793 ) @ SV793 ) )
| ( SV493
= ( c_List_Olist_OCons @ SV1035 @ SV1188 @ SV793 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2993]) ).
thf(3209,plain,
! [SV1189: $i,SV1036: $i,SV794: $i,SV494: $i,SV116: $i] :
( ( ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
!= ( c_List_Oappend @ SV1036 @ SV1189 @ SV794 ) )
= $true )
| ( ( ( SV494
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV116 @ SV494 @ SV1036 @ SV1189 @ SV794 ) @ SV1189 @ SV794 ) )
| ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
= SV1189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2994]) ).
thf(3210,plain,
! [SV798: $i,SV122: $i,SV1038: $i,SV500: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV500 ) @ SV1038 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV798 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV500 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV798 ) @ SV1038 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3211,plain,
! [SV802: $i,SV127: $i,SV1039: $i,SV505: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV505 ) @ SV1039 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV127 @ SV505 @ SV802 ) ) @ ( c_Lambda_Osubst @ SV127 @ SV1039 @ SV802 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3212,plain,
! [SV803: $i,SV506: $i,SV1040: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV128 ) @ SV1040 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV128 @ SV506 @ SV803 ) ) @ ( c_Lambda_Osubst @ SV1040 @ SV506 @ SV803 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3213,plain,
! [SV804: $i,SV129: $i,SV1041: $i,SV507: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV507 ) @ SV1041 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV129 @ SV507 @ SV804 ) ) @ ( c_Lambda_Osubst @ SV129 @ SV1041 @ SV804 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3214,plain,
! [SV513: $i,SV811: $i,SV1192: $i,SV136: $i] :
( ( ( ~ ( c_Type_Otyping @ SV136 @ SV1192 @ SV811 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1192 ) @ SV513 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV136 @ SV513 @ SV811 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3215,plain,
! [SV1044: $i,SV813: $i,SV515: $i,SV138: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV138 @ ( tc_List_Olist @ SV515 ) )
= ( c_Nat_Osize__class_Osize @ SV813 @ ( tc_List_Olist @ SV1044 ) ) )
= $false )
| ( ( ! [SY3030: $i,SY3031: $i] :
( ( c_Map_Omap__upds @ SY3030 @ ( c_List_Oappend @ SV138 @ SY3031 @ SV515 ) @ SV813 @ SV515 @ SV1044 )
= ( c_Map_Omap__upds @ SY3030 @ SV138 @ SV813 @ SV515 @ SV1044 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3216,plain,
! [SV1045: $i,SV814: $i,SV516: $i,SV139: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV139 @ ( tc_List_Olist @ SV516 ) )
= ( c_Nat_Osize__class_Osize @ SV814 @ ( tc_List_Olist @ SV1045 ) ) )
= $false )
| ( ( ! [SY3032: $i,SY3033: $i] :
( ( c_Map_Omap__upds @ SY3032 @ SV139 @ ( c_List_Oappend @ SV814 @ SY3033 @ SV1045 ) @ SV516 @ SV1045 )
= ( c_Map_Omap__upds @ SY3032 @ SV139 @ SV814 @ SV516 @ SV1045 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3217,plain,
! [SV519: $i,SV1193: $i,SV1046: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV142 @ SV1046 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV519 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV142 @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3218,plain,
! [SV1271: $i,SV1194: $i,SV1048: $i,SV817: $i,SV522: $i,SV146: $i] :
( ( ( c_List_Ofoldl @ SV146 @ SV522 @ ( c_List_Oappend @ SV817 @ SV1048 @ SV1194 ) @ SV1271 @ SV1194 )
= ( c_List_Ofoldl @ SV146 @ ( c_List_Ofoldl @ SV146 @ SV522 @ SV817 @ SV1271 @ SV1194 ) @ SV1048 @ SV1271 @ SV1194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3219,plain,
! [SV1195: $i,SV819: $i,SV524: $i,SV149: $i] :
( ( ( ( c_List_Omap @ SV149 @ SV524 @ SV819 @ SV1195 )
= ( c_List_Olist_ONil @ SV1195 ) )
= $false )
| ( ( SV524
= ( c_List_Olist_ONil @ SV819 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3220,plain,
! [SV1052: $i,SV830: $i,SV539: $i,SV167: $i] :
( ( ( ( c_List_Olist_ONil @ SV167 )
= ( c_List_Omap @ SV539 @ SV830 @ SV1052 @ SV167 ) )
= $false )
| ( ( SV830
= ( c_List_Olist_ONil @ SV1052 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3221,plain,
! [SV831: $i,SV173: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV545 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV173 @ SV545 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV831 @ 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 @ SV173 ) ) @ SV545 ) @ SV831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3222,plain,
! [SV833: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV176 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV176 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV176 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV176 @ SV833 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3223,plain,
! [SV834: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV177 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV177 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV177 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV177 @ SV834 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3224,plain,
! [SV835: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV178 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV178 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV178 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV178 @ SV835 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3225,plain,
! [SV836: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV179 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV179 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV179 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV179 @ SV836 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3226,plain,
! [SV837: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV180 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV180 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV180 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV180 @ SV837 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3030]) ).
thf(3227,plain,
! [SV838: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV181 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV181 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV181 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV181 @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3228,plain,
! [SV839: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV182 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV182 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV182 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV182 @ SV839 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3229,plain,
! [SV840: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV183 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV183 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV183 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV183 @ SV840 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3033]) ).
thf(3230,plain,
! [SV841: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV184 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV184 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV184 @ SV841 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3231,plain,
! [SV846: $i,SV1272: $i,SV189: $i,SV552: $i] :
( ( ( ! [SY3149: $i] :
( ( c_List_Olist_OCons @ SV552 @ ( c_List_Ofilter @ SV189 @ SY3149 @ SV1272 ) @ SV1272 )
= ( c_List_Ofilter @ SV189 @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV552 @ SY3149 @ SV1272 ) @ SV1272 ) @ SV1272 ) )
| ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ SV189 @ SV846 @ SV1272 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV189 @ SV552 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3232,plain,
! [SV1273: $i,SV553: $i,SV847: $i,SV190: $i] :
( ( ( ! [SY3150: $i] :
( ( c_List_Ofilter @ SV190 @ ( c_List_Oappend @ SV847 @ ( c_List_Olist_OCons @ SV553 @ SY3150 @ SV1273 ) @ SV1273 ) @ SV1273 )
= ( c_List_Olist_OCons @ SV553 @ ( c_List_Ofilter @ SV190 @ SY3150 @ SV1273 ) @ SV1273 ) )
| ( hBOOL @ ( hAPP @ SV190 @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ SV190 @ SV847 @ SV1273 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV190 @ SV553 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3233,plain,
! [SV1197: $i,SV1054: $i,SV848: $i,SV554: $i,SV191: $i] :
( ( ( ( c_List_Olist_OCons @ SV191 @ SV554 @ SV848 )
!= ( c_List_Oappend @ SV1054 @ SV1197 @ SV848 ) )
= $true )
| ( ( ( SV554
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV191 @ SV554 @ SV1054 @ SV1197 @ SV848 ) @ SV1197 @ SV848 ) )
| ( SV1054
= ( c_List_Olist_ONil @ SV848 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3040]) ).
thf(3234,plain,
! [SV1198: $i,SV1055: $i,SV849: $i,SV555: $i,SV192: $i] :
( ( ( ( c_List_Oappend @ SV192 @ SV555 @ SV849 )
!= ( c_List_Olist_OCons @ SV1055 @ SV1198 @ SV849 ) )
= $true )
| ( ( ( SV192
= ( c_List_Olist_OCons @ SV1055 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1055 @ SV1198 @ SV192 @ SV555 @ SV849 ) @ SV849 ) )
| ( SV192
= ( c_List_Olist_ONil @ SV849 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3041]) ).
thf(3235,plain,
! [SV558: $i,SV195: $i,SV1056: $i,SV852: $i] :
( ( ( SV852 = SV1056 )
= $true )
| ( ( ! [SY3040: $i,SY3041: $i] :
~ ( c_ListOrder_Ostep1 @ SY3040 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SV852 @ ( c_List_Olist_ONil @ SY3041 ) @ SY3041 ) @ SY3041 ) @ ( c_List_Oappend @ SV558 @ ( c_List_Olist_OCons @ SV1056 @ ( c_List_Olist_ONil @ SY3041 ) @ SY3041 ) @ SY3041 ) @ SY3041 ) )
= $true )
| ( ( SV195 = SV558 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3236,plain,
! [SV1057: $i,SV196: $i,SV853: $i,SV559: $i] :
( ( ( SV559 = SV853 )
= $true )
| ( ( ! [SY3042: $i,SY3043: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SV1057 @ ( c_List_Olist_OCons @ SV559 @ ( c_List_Olist_ONil @ SY3042 ) @ SY3042 ) @ SY3042 ) @ ( c_List_Oappend @ SY3043 @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_ONil @ SY3042 ) @ SY3042 ) @ SY3042 ) @ SY3042 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SV559 ) @ SV853 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3237,plain,
! [SV1199: $i,SV1058: $i,SV854: $i,SV560: $i,SV197: $i] :
( ( ( ( c_List_Oappend @ SV197 @ SV560 @ SV854 )
!= ( c_List_Olist_OCons @ SV1058 @ SV1199 @ SV854 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1058 @ SV1199 @ SV197 @ SV560 @ SV854 ) @ SV560 @ SV854 )
= SV1199 )
| ( SV197
= ( c_List_Olist_ONil @ SV854 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3238,plain,
! [SV1200: $i,SV1059: $i,SV855: $i,SV561: $i,SV198: $i] :
( ( ( ( c_List_Olist_OCons @ SV198 @ SV561 @ SV855 )
!= ( c_List_Oappend @ SV1059 @ SV1200 @ SV855 ) )
= $true )
| ( ( ( ( c_List_Olist_OCons @ SV198 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV198 @ SV561 @ SV1059 @ SV1200 @ SV855 ) @ SV855 )
= SV1059 )
| ( SV1059
= ( c_List_Olist_ONil @ SV855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3045]) ).
thf(3239,plain,
! [SV856: $i,SV562: $i,SV1274: $i,SV1060: $i,SV199: $i] :
( ( ( ! [SY3151: $i] :
( ( c_ListOrder_Ostep1 @ SV199 @ SV1060 @ SV1274 @ SY3151 )
| ~ ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SV1060 @ ( c_List_Olist_OCons @ SV562 @ ( c_List_Olist_ONil @ SY3151 ) @ SY3151 ) @ SY3151 ) @ ( c_List_Oappend @ SV1274 @ ( c_List_Olist_OCons @ SV856 @ ( c_List_Olist_ONil @ SY3151 ) @ SY3151 ) @ SY3151 ) @ SY3151 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SV562 ) @ SV856 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3240,plain,
! [SV1061: $i,SV564: $i,SV201: $i,SV858: $i] :
( ( ( c_ListOrder_Ostep1 @ SV858 @ SV201 @ SV564 @ SV1061 )
= $true )
| ( ( ! [SY3048: $i,SY3049: $i] :
~ ( c_ListOrder_Ostep1 @ SV858 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SY3048 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ ( c_List_Oappend @ SV564 @ ( c_List_Olist_OCons @ SY3049 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ SV1061 ) )
= $true )
| ( ( SV201 = SV564 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3241,plain,
! [SV1062: $i,SV860: $i,SV566: $i,SV203: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV203 ) @ SV566 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV860 @ SV1062 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV1062
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV203 @ SV566 @ SV860 @ SV1062 ) @ ( c_List_Olist_OCons @ SV566 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1062
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3242,plain,
! [SV570: $i,SV1201: $i,SV207: $i,SV1063: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1063 @ SV207 @ ( tc_fun @ SV1201 @ tc_bool ) ) @ SV570 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV207 @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3243,plain,
! [SV1275: $i,SV1203: $i,SV1065: $i,SV864: $i,SV573: $i,SV210: $i] :
( ( ( c_List_Omap @ SV210 @ ( c_List_Olist__update @ SV573 @ SV864 @ SV1065 @ SV1203 ) @ SV1203 @ SV1275 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV210 @ SV573 @ SV1203 @ SV1275 ) @ SV864 @ ( hAPP @ SV210 @ SV1065 ) @ SV1275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3244,plain,
! [SV578: $i,SV1066: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1066 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1066 @ SV215 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1066 @ SV578 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV215 @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3245,plain,
! [SV580: $i,SV1067: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1067 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1067 @ SV217 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV1067 @ SV580 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV217 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3246,plain,
! [SV219: $i,SV1068: $i,SV1276: $i] :
( ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1276 @ SV1068 @ SV219 ) @ SV219 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ SV1068 @ SV219 )
= $true )
| ( ( class_Orderings_Olinorder @ SV219 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3247,plain,
! [SV1277: $i,SV1204: $i,SV1071: $i,SV874: $i,SV585: $i,SV223: $i] :
( ( ( c_List_Olist_Olist__case @ SV223 @ SV585 @ ( c_List_Olist_OCons @ SV874 @ SV1071 @ SV1204 ) @ SV1277 @ SV1204 )
= ( hAPP @ ( hAPP @ SV585 @ SV874 ) @ SV1071 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3248,plain,
! [SV230: $i,SV1208: $i,SV592: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV592 @ SV1208 @ SV230 ) @ SV230 )
= $true )
| ( ( ! [SY3127: $i] :
~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY3127 @ ( c_List_Olist_OCons @ SV592 @ SV1208 @ SV230 ) @ SV230 ) @ SV230 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3249,plain,
! [SV1080: $i,SV881: $i,SV594: $i,SV234: $i] :
( ( ( ( c_List_Orev @ SV234 @ SV594 )
= ( c_List_Olist_OCons @ SV881 @ SV1080 @ SV594 ) )
= $false )
| ( ( SV234
= ( c_List_Oappend @ ( c_List_Orev @ SV1080 @ SV594 ) @ ( c_List_Olist_OCons @ SV881 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3250,plain,
! [SV1278: $i,SV1211: $i,SV1081: $i,SV882: $i,SV596: $i,SV236: $i] :
( ( ( c_List_Ofoldl @ SV236 @ SV596 @ ( c_List_Olist_OCons @ SV882 @ SV1081 @ SV1211 ) @ SV1278 @ SV1211 )
= ( c_List_Ofoldl @ SV236 @ ( hAPP @ ( hAPP @ SV236 @ SV596 ) @ SV882 ) @ SV1081 @ SV1278 @ SV1211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3251,plain,
! [SV1279: $i,SV1082: $i,SV884: $i,SV598: $i,SV238: $i] :
( ( ( ( c_List_Olist_OCons @ SV238 @ SV598 @ SV884 )
!= ( c_List_Ofilter @ SV1082 @ SV1279 @ SV884 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1082 @ SV238 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3252,plain,
! [SV1212: $i,SV1083: $i,SV600: $i,SV240: $i] :
( ( ( hBOOL @ ( hAPP @ SV240 @ SV600 ) )
= $false )
| ( ( ( c_List_Ofilter @ SV240 @ ( c_List_Olist_OCons @ SV600 @ SV1083 @ SV1212 ) @ SV1212 )
= ( c_List_Olist_OCons @ SV600 @ ( c_List_Ofilter @ SV240 @ SV1083 @ SV1212 ) @ SV1212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3253,plain,
! [SV888: $i,SV603: $i,SV1085: $i,SV243: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV243 ) @ SV1085 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV243 @ SV603 @ SV888 ) ) @ ( c_Lambda_Osubst @ SV1085 @ SV603 @ SV888 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3071]) ).
thf(3254,plain,
! [SV1087: $i,SV890: $i,SV605: $i,SV245: $i] :
( ( ( ( c_List_Oappend @ SV245 @ SV605 @ SV890 )
= ( c_List_Oappend @ SV1087 @ SV605 @ SV890 ) )
= $false )
| ( ( SV245 = SV1087 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3255,plain,
! [SV1088: $i,SV891: $i,SV606: $i,SV246: $i] :
( ( ( ( c_List_Oappend @ SV246 @ SV606 @ SV891 )
= ( c_List_Oappend @ SV246 @ SV1088 @ SV891 ) )
= $false )
| ( ( SV606 = SV1088 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3256,plain,
! [SV1280: $i,SV1089: $i,SV892: $i,SV607: $i,SV247: $i] :
( ( ( ( c_List_Ofilter @ SV247 @ SV607 @ SV892 )
!= ( c_List_Olist_OCons @ SV1089 @ SV1280 @ SV892 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV247 @ SV1089 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3257,plain,
! [SV1281: $i,SV1215: $i,SV1091: $i,SV894: $i,SV612: $i,SV252: $i] :
( ( ( c_List_Ofoldr @ SV252 @ ( c_List_Oappend @ SV612 @ SV894 @ SV1091 ) @ SV1215 @ SV1091 @ SV1281 )
= ( c_List_Ofoldr @ SV252 @ SV612 @ ( c_List_Ofoldr @ SV252 @ SV894 @ SV1215 @ SV1091 @ SV1281 ) @ SV1091 @ SV1281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3258,plain,
! [SV1216: $i,SV1092: $i,SV613: $i,SV253: $i] :
( ( ( hBOOL @ ( hAPP @ SV253 @ SV613 ) )
= $false )
| ( ( c_List_Olist__ex @ SV253 @ ( c_List_Olist_OCons @ SV613 @ SV1092 @ SV1216 ) @ SV1216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3259,plain,
! [SV615: $i,SV1093: $i,SV896: $i,SV255: $i] :
( ( ( c_List_Olist__ex @ SV255 @ SV896 @ SV1093 )
= $false )
| ( ( c_List_Olist__ex @ SV255 @ ( c_List_Olist_OCons @ SV615 @ SV896 @ SV1093 ) @ SV1093 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3260,plain,
! [SV897: $i,SV616: $i,SV1217: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ SV256 @ SV1217 ) )
= $true )
| ( ( ~ ( c_List_Olist__ex @ SV256 @ ( c_List_Olist_OCons @ SV1217 @ SV616 @ SV897 ) @ SV897 ) )
= $true )
| ( ( c_List_Olist__ex @ SV256 @ SV616 @ SV897 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3261,plain,
! [SV1282: $i,SV1218: $i,SV1094: $i,SV898: $i,SV617: $i,SV257: $i] :
( ( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SV898 @ SV1094 ) @ ( c_List_Olist_OCons @ SV1218 @ SV1282 @ SV1094 ) @ SV1094 )
| ~ ( c_List_Olistrelp @ SV257 @ SV898 @ SV1282 @ SV1094 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SV1218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3262,plain,
! [SV1283: $i,SV258: $i,SV1219: $i,SV618: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ SV1219 @ SV258 ) @ SV1283 @ SV258 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV618 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1219 @ SV1283 @ SV258 ) @ SV258 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV258 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3263,plain,
! [SV259: $i,SV1284: $i,SV1220: $i,SV619: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1220 @ SV1284 @ SV259 ) @ SV259 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1220 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV619 @ SV1284 @ SV259 ) @ SV259 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV259 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3264,plain,
! [SV260: $i,SV1285: $i,SV1221: $i,SV620: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1221 @ SV1285 @ SV260 ) @ SV260 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1221 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV620 @ SV1285 @ SV260 ) @ SV260 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV260 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3265,plain,
! [SV1286: $i,SV261: $i,SV1222: $i,SV621: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ SV1222 @ SV261 ) @ SV1286 @ SV261 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV621 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1222 @ SV1286 @ SV261 ) @ SV261 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV261 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3266,plain,
! [SV1099: $i,SV903: $i,SV629: $i,SV269: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV269 ) @ SV629 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV903 ) @ SV1099 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV629 = SV1099 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3267,plain,
! [SV1225: $i,SV904: $i,SV630: $i,SV270: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV270 ) @ SV630 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV904 ) @ SV1225 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV270 = SV904 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3268,plain,
! [SV1287: $i,SV1227: $i,SV1101: $i,SV906: $i,SV633: $i,SV273: $i] :
( ( ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ ( c_List_Olist_OCons @ SV906 @ SV1101 @ SV1227 ) @ SV1287 @ SV1227 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV633 @ SV906 ) @ SV1101 ) @ ( c_List_Olist_Olist__rec @ SV273 @ SV633 @ SV1101 @ SV1287 @ SV1227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3269,plain,
! [SV1288: $i,SV1232: $i,SV1106: $i,SV912: $i,SV639: $i,SV281: $i] :
( ( ( c_List_Ofoldr @ SV281 @ ( c_List_Olist_OCons @ SV639 @ SV912 @ SV1106 ) @ SV1232 @ SV1106 @ SV1288 )
= ( hAPP @ ( hAPP @ SV281 @ SV639 ) @ ( c_List_Ofoldr @ SV281 @ SV912 @ SV1232 @ SV1106 @ SV1288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3270,plain,
! [SV1233: $i,SV1107: $i,SV913: $i,SV640: $i,SV282: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV282 @ ( c_Lambda_OdB_OdB__case @ SV640 @ SV913 @ SV1107 @ ( c_Lambda_OdB_OAbs @ SV1233 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ SV1107 @ SV1233 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3101]) ).
thf(3271,plain,
! [SV1234: $i,SV1108: $i,SV914: $i,SV641: $i,SV283: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV283 @ ( c_Lambda_OdB_OdB__case @ SV641 @ SV914 @ SV1108 @ ( c_Lambda_OdB_OAbs @ SV1234 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ SV1108 @ SV1234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3272,plain,
! [SV1289: $i,SV1110: $i,SV916: $i,SV644: $i,SV287: $i] :
( ( ( ( c_List_Olist_OCons @ SV287 @ SV644 @ SV916 )
!= ( c_List_Olist_OCons @ SV1110 @ SV1289 @ SV916 ) )
= $true )
| ( ( SV287 = SV1110 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3273,plain,
! [SV1235: $i,SV1111: $i,SV917: $i,SV645: $i,SV288: $i] :
( ( ( ( c_List_Olist_OCons @ SV288 @ SV645 @ SV917 )
!= ( c_List_Olist_OCons @ SV1111 @ SV1235 @ SV917 ) )
= $true )
| ( ( SV645 = SV1235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3274,plain,
! [SV918: $i,SV289: $i,SV646: $i,SV1236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1236 ) @ SV646 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV289 @ SV1236 @ SV918 ) )
= $true )
| ( ( c_Type_Otyping @ SV289 @ SV646 @ SV918 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3275,plain,
! [SV290: $i,SV1290: $i,SV1112: $i] :
( ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1112 @ SV1290 @ SV290 ) @ SV290 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ SV1112 @ SV290 )
= $true )
| ( ( class_Orderings_Olinorder @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3276,plain,
! [SV291: $i,SV1113: $i,SV1291: $i] :
( ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1291 @ SV1113 @ SV291 ) @ SV291 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ SV1113 @ SV291 )
= $true )
| ( ( class_Orderings_Olinorder @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3277,plain,
! [SV1237: $i,SV1114: $i,SV919: $i,SV647: $i,SV292: $i] :
( ( ( ! [SY3137: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV647 @ SV919 @ SV1114 ) @ SV1237 @ SY3137 @ SV1114 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV1237 @ SY3137 @ SV1114 ) @ SV647 @ SV919 @ SV1114 ) ) )
= $true )
| ( ( SV647 = SV1237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3278,plain,
! [SV293: $i,SV1115: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1115 @ SV293 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SV1115 @ SV293 ) @ SV293 )
= $true )
| ( ( class_Orderings_Olinorder @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3279,plain,
! [SV920: $i,SV295: $i,SV1117: $i,SV649: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV649 @ SV1117 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV295 @ SV1117 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV295 @ SV649 @ ( tc_fun @ SV920 @ tc_bool ) ) @ SV1117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3111]) ).
thf(3280,plain,
! [SV1292: $i,SV1118: $i,SV922: $i,SV651: $i,SV297: $i] :
( ( ( ( c_List_Oappend @ SV297 @ ( c_List_Olist_OCons @ SV651 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 )
!= ( c_List_Oappend @ SV1118 @ ( c_List_Olist_OCons @ SV1292 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 ) )
= $true )
| ( ( SV297 = SV1118 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3281,plain,
! [SV1239: $i,SV1119: $i,SV923: $i,SV652: $i,SV298: $i] :
( ( ( ( c_List_Oappend @ SV298 @ ( c_List_Olist_OCons @ SV652 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 )
!= ( c_List_Oappend @ SV1119 @ ( c_List_Olist_OCons @ SV1239 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 ) )
= $true )
| ( ( SV652 = SV1239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3282,plain,
! [SV1240: $i,SV1120: $i,SV924: $i,SV653: $i,SV299: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV299 @ ( c_List_Olist_Olist__case @ SV653 @ SV924 @ ( c_List_Olist_OCons @ SV1120 @ SV1240 @ t_b ) @ t_a @ t_b ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV299 @ ( hAPP @ ( hAPP @ SV924 @ SV1120 ) @ SV1240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3283,plain,
! [SV1241: $i,SV1121: $i,SV925: $i,SV654: $i,SV300: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV300 @ ( c_List_Olist_Olist__case @ SV654 @ SV925 @ ( c_List_Olist_OCons @ SV1121 @ SV1241 @ t_b ) @ t_a @ t_b ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV300 @ ( hAPP @ ( hAPP @ SV925 @ SV1121 ) @ SV1241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3284,plain,
! [SV306: $i,SV1243: $i,SV1127: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV1127 @ SV1243 @ SV306 ) @ SV306 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV1243 @ SV306 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3117]) ).
thf(3285,plain,
! [SV1134: $i,SV953: $i,SV682: $i,SV342: $i] :
( ( ( ( c_List_Olist__update @ SV342 @ SV682 @ SV953 @ SV1134 )
= ( c_List_Olist_ONil @ SV1134 ) )
= $false )
| ( ( SV342
= ( c_List_Olist_ONil @ SV1134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3286,plain,
! [SV1293: $i,SV1244: $i,SV1136: $i,SV957: $i,SV686: $i,SV346: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV346 @ ( c_Lambda_OdB_OdB__case @ SV686 @ SV957 @ SV1136 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1244 ) @ SV1293 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ SV957 @ SV1244 ) @ SV1293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3287,plain,
! [SV1294: $i,SV1245: $i,SV1137: $i,SV958: $i,SV687: $i,SV347: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV347 @ ( c_Lambda_OdB_OdB__case @ SV687 @ SV958 @ SV1137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1245 ) @ SV1294 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV347 @ ( hAPP @ ( hAPP @ SV958 @ SV1245 ) @ SV1294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3288,plain,
! [SV1295: $i,SV1246: $i,SV1138: $i,SV960: $i,SV689: $i,SV349: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV349 @ SV689 @ SV960 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1138 ) @ SV1246 ) @ SV1295 )
= ( hAPP @ ( hAPP @ SV689 @ SV1138 ) @ SV1246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3289,plain,
! [SV1296: $i,SV1247: $i,SV1139: $i,SV961: $i,SV690: $i,SV350: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1139 ) @ SV1247 ) @ SV1296 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV690 @ SV1139 ) @ SV1247 ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ SV1139 @ SV1296 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV350 @ SV690 @ SV961 @ SV1247 @ SV1296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3290,plain,
! [SV356: $i,SV696: $i,SV1297: $i,SV1248: $i,SV967: $i] :
( ( ( ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SV1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV696 )
| ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SV1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 ) )
= $true )
| ( ( SV356 = SV696 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3291,plain,
! [SV1249: $i,SV1144: $i,SV970: $i,SV700: $i,SV360: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV360 @ ( c_Lambda_OdB_OdB__case @ SV700 @ SV970 @ SV1144 @ ( c_Lambda_OdB_OVar @ SV1249 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV360 @ ( hAPP @ SV700 @ SV1249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3292,plain,
! [SV1250: $i,SV1145: $i,SV971: $i,SV701: $i,SV361: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV361 @ ( c_Lambda_OdB_OdB__case @ SV701 @ SV971 @ SV1145 @ ( c_Lambda_OdB_OVar @ SV1250 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( hAPP @ SV701 @ SV1250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3140]) ).
thf(3293,plain,
! [SV1148: $i,SV976: $i,SV710: $i,SV371: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV371 ) @ SV710 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ SV1148 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV371
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV371 @ SV710 @ SV976 @ SV1148 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1148
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3294,plain,
! [SV712: $i,SV1150: $i,SV977: $i,SV374: $i] :
( ( ( ~ ( c_List_Olistsp @ SV374 @ SV977 @ SV1150 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV374 @ SV712 @ SV1150 ) )
= $true )
| ( ( c_List_Olistsp @ SV374 @ ( c_List_Oappend @ SV712 @ SV977 @ SV1150 ) @ SV1150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3295,plain,
! [SV376: $i,SV979: $i,SV1151: $i,SV714: $i] :
( ( ( ~ ( c_List_Olistsp @ SV714 @ SV1151 @ SV979 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV376 @ SV1151 @ SV979 ) )
= $true )
| ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV714 @ ( tc_fun @ SV979 @ tc_bool ) ) @ SV1151 @ SV979 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3296,plain,
! [SV980: $i,SV715: $i,SV1253: $i,SV377: $i] :
( ( ( c_List_Olistsp @ SV377 @ ( c_List_Oappend @ SV1253 @ SV715 @ SV980 ) @ SV980 )
= $false )
| ( ( c_List_Olistsp @ SV377 @ SV715 @ SV980 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3297,plain,
! [SV981: $i,SV1254: $i,SV716: $i,SV378: $i] :
( ( ( c_List_Olistsp @ SV378 @ ( c_List_Oappend @ SV716 @ SV1254 @ SV981 ) @ SV981 )
= $false )
| ( ( c_List_Olistsp @ SV378 @ SV716 @ SV981 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3151]) ).
thf(3298,plain,
! [SV1255: $i,SV983: $i,SV717: $i,SV381: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV381 ) @ SV717 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV983 ) @ SV1255 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV381 = SV983 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3299,plain,
! [SV1152: $i,SV984: $i,SV718: $i,SV382: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV382 ) @ SV718 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV984 ) @ SV1152 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV718 = SV1152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3300,plain,
! [SV720: $i,SV1154: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV1154 @ SV720 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1154 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1154 @ SV384 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV384 @ SV720 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3301,plain,
! [SV721: $i,SV1155: $i,SV385: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV385 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV1155 @ SV721 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1155 @ SV385 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ SV721 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3156]) ).
thf(3302,plain,
! [SV722: $i,SV1156: $i,SV386: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV1156 @ SV722 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1156 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1156 @ SV386 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV386 @ SV722 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3157]) ).
thf(3303,plain,
! [SV723: $i,SV1157: $i,SV387: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV1157 @ SV723 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1157 @ SV387 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ SV723 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3158]) ).
thf(3304,plain,
! [SV726: $i,SV1158: $i,SV390: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV390 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV1158 @ SV726 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV1158 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1158 @ SV390 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV390 @ SV726 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3161]) ).
thf(3305,plain,
! [SV727: $i,SV1159: $i,SV391: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV1159 @ SV727 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV1159 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1159 @ SV391 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV391 @ SV727 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3306,plain,
! [SV1256: $i,SV988: $i,SV733: $i,SV399: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV399 ) @ SV733 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV988 ) @ SV1256 ) )
= $false )
| ( ( SV399 = SV988 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3307,plain,
! [SV1161: $i,SV989: $i,SV734: $i,SV400: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV400 ) @ SV734 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV989 ) @ SV1161 ) )
= $false )
| ( ( SV734 = SV1161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3308,plain,
! [SV1298: $i,SV1257: $i,SV1162: $i,SV991: $i,SV737: $i,SV404: $i] :
( ( ( hAPP @ ( c_COMBB @ SV404 @ SV737 @ SV991 @ SV1162 @ SV1257 ) @ SV1298 )
= ( hAPP @ SV404 @ ( hAPP @ SV737 @ SV1298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3309,plain,
! [SV1299: $i,SV1258: $i,SV1163: $i,SV992: $i,SV738: $i,SV405: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV405 @ SV738 @ SV992 @ SV1163 ) @ SV1258 ) @ SV1299 )
= ( hAPP @ ( hAPP @ SV405 @ SV1299 ) @ SV1258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3310,plain,
! [SV1300: $i,SV1259: $i,SV1164: $i,SV994: $i,SV744: $i,SV411: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV411 @ SV744 @ SV994 @ SV1164 ) @ SV1259 ) @ SV1300 )
= ( hAPP @ ( hAPP @ SV411 @ SV1300 ) @ SV1259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3311,plain,
! [SV1301: $i,SV1260: $i,SV1165: $i,SV995: $i,SV745: $i,SV412: $i] :
( ( ( hAPP @ ( c_COMBB @ SV412 @ SV745 @ SV995 @ SV1165 @ SV1260 ) @ SV1301 )
= ( hAPP @ SV412 @ ( hAPP @ SV745 @ SV1301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3312,plain,
! [SV748: $i,SV996: $i,SV1261: $i,SV416: $i,SV4: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV1261 ) @ SV996 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV1261 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV996 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3313,plain,
! [SV1262: $i,SV997: $i,SV751: $i,SV419: $i,SV7: $i] :
( ( ( ( c_List_Oreplicate @ SV7 @ SV419 @ SV751 )
= ( c_List_Oreplicate @ SV997 @ SV1262 @ SV751 ) )
= $false )
| ( ( SV7 = SV997 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3314,plain,
! [SV752: $i,SV1302: $i,SV1263: $i,SV420: $i,SV8: $i] :
( ( ( c_ListOrder_Ostep1 @ SV8 @ ( c_List_Olist_OCons @ SV420 @ SV1263 @ SV1302 ) @ ( c_List_Olist_OCons @ SV752 @ SV1263 @ SV1302 ) @ SV1302 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV8 @ SV420 ) @ SV752 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3315,plain,
! [SV753: $i,SV9: $i,SV998: $i,SV421: $i,SV1303: $i] :
( ( ( ! [SY3152: $i] :
~ ( c_ListOrder_Ostep1 @ SV1303 @ ( c_List_Olist_OCons @ SV421 @ SV998 @ SY3152 ) @ ( c_List_Olist_OCons @ SV9 @ SV753 @ SY3152 ) @ SY3152 ) )
= $true )
| ( ( SV753 = SV998 )
= $true )
| ( ( SV9 = SV421 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3316,plain,
! [SV423: $i,SV999: $i,SV1167: $i,SV755: $i,SV12: $i] :
( ( ( c_ListOrder_Ostep1 @ SV12 @ SV755 @ SV1167 @ SV999 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV12 @ ( c_List_Oappend @ SV423 @ SV755 @ SV999 ) @ ( c_List_Oappend @ SV423 @ SV1167 @ SV999 ) @ SV999 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3317,plain,
! [SV756: $i,SV1000: $i,SV1304: $i,SV424: $i,SV13: $i] :
( ( ( c_ListOrder_Ostep1 @ SV13 @ ( c_List_Oappend @ SV424 @ SV1304 @ SV1000 ) @ ( c_List_Oappend @ SV756 @ SV1304 @ SV1000 ) @ SV1000 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV13 @ SV424 @ SV756 @ SV1000 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3318,plain,
! [SV426: $i,SV15: $i,SV1168: $i,SV1305: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1305 @ SV1168 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV426 @ SV1305 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV426 @ SV1168 @ SV15 )
= $true )
| ( ( class_Orderings_Opreorder @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3319,plain,
! [SV1169: $i,SV16: $i,SV1306: $i,SV427: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV427 @ SV1306 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV1306 @ SV1169 @ SV16 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1169 @ SV16 )
= $true )
| ( ( class_Orderings_Oorder @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3320,plain,
! [SV24: $i,SV1307: $i,SV1001: $i,SV431: $i,SV759: $i] :
( ( ( ! [SY3153: $i] :
~ ( c_ListOrder_Ostep1 @ SV759 @ ( c_List_Olist_OCons @ SV431 @ SV1001 @ SV1307 ) @ ( c_List_Olist_OCons @ SV24 @ SY3153 @ SV1307 ) @ SV1307 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ SV431 ) @ SV24 ) )
= $true )
| ( ( SV24 = SV431 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3321,plain,
! [SV1170: $i,SV1004: $i,SV764: $i,SV438: $i,SV33: $i] :
( ( ( ( c_List_Oreplicate @ SV33 @ SV438 @ SV764 )
= ( c_List_Oreplicate @ SV1004 @ SV1170 @ SV764 ) )
= $false )
| ( ( ( SV438 = SV1170 )
| ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3322,plain,
! [SV1173: $i,SV1008: $i,SV772: $i,SV454: $i,SV52: $i] :
( ( ( ( c_List_Omap @ SV52 @ SV454 @ SV772 @ SV1008 )
= ( c_List_Omap @ SV52 @ SV1173 @ SV772 @ SV1008 ) )
= $false )
| ( ( ( c_Nat_Osize__class_Osize @ SV454 @ ( tc_List_Olist @ SV772 ) )
= ( c_Nat_Osize__class_Osize @ SV1173 @ ( tc_List_Olist @ SV772 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3323,plain,
! [SV1264: $i,SV458: $i,SV773: $i,SV57: $i,SV1009: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_Nat_Osize__class_Osize @ SV57 @ ( tc_List_Olist @ SV773 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV57 @ SV458 @ SV773 ) @ SV1009 @ SV1264 @ SV773 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV57 @ SV1009 @ SV1264 @ SV773 ) @ SV458 @ SV773 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3324,plain,
! [SV1265: $i,SV459: $i,SV774: $i,SV58: $i,SV1010: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1010 @ ( c_Nat_Osize__class_Osize @ SV58 @ ( tc_List_Olist @ SV774 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV58 @ SV459 @ SV774 ) @ SV1010 @ SV1265 @ SV774 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV58 @ SV1010 @ SV1265 @ SV774 ) @ SV459 @ SV774 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3325,plain,
! [SV776: $i,SV1014: $i,SV463: $i,SV1308: $i,SV67: $i] :
( ( ( ! [SY3154: $i] :
~ ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SV1308 @ SV463 @ SV1014 ) @ ( c_List_Olist_OCons @ SY3154 @ SV776 @ SV1014 ) @ SV1014 ) )
= $true )
| ( ( SV776 = SV463 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV67 @ SV463 @ SV776 @ SV1014 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3326,plain,
! [SV68: $i,SV1015: $i,SV1174: $i] :
( ( ( SV1174 = SV1015 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1174 @ SV1015 @ SV68 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1174 @ SV68 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3327,plain,
! [SV69: $i,SV1016: $i,SV1175: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1175 @ SV1016 @ SV69 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1016 @ SV1175 @ SV69 )
= $true )
| ( ( SV1016 = SV1175 )
= $true )
| ( ( class_Orderings_Olinorder @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3190]) ).
thf(3328,plain,
! [SV73: $i,SV1017: $i,SV1176: $i] :
( ( ( SV1176 = SV1017 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1176 @ SV1017 @ SV73 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1017 @ SV1176 @ SV73 )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3192]) ).
thf(3329,plain,
! [SV75: $i,SV1019: $i,SV1177: $i] :
( ( ( SV1177 = SV1019 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1177 @ SV1019 @ SV75 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1019 @ SV1177 @ SV75 )
= $true )
| ( ( class_Orderings_Olinorder @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3193]) ).
thf(3330,plain,
! [SV76: $i,SV1178: $i,SV1020: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1020 @ SV1178 @ SV76 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1178 @ SV1020 @ SV76 )
= $true )
| ( ( SV1020 = SV1178 )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3331,plain,
! [SV1266: $i,SV77: $i,SV1179: $i,SV468: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV468 @ SV1179 @ SV77 ) @ SV1266 @ SV77 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1179 @ SV1266 @ SV77 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3332,plain,
! [SV1267: $i,SV78: $i,SV1180: $i,SV469: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV469 @ SV1180 @ SV78 ) @ SV1267 @ SV78 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV469 @ SV1267 @ SV78 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3333,plain,
! [SV470: $i,SV1021: $i,SV83: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV83 @ SV1021 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1021 @ SV470 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV83 ) @ SV470 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3334,plain,
! [SV781: $i,SV1024: $i,SV475: $i,SV1309: $i,SV1268: $i,SV92: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV1268 ) @ SV1309 ) )
| ~ ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SV1268 @ SV475 @ SV1024 ) @ ( c_List_Olist_OCons @ SV1309 @ SV781 @ SV1024 ) @ SV1024 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV92 @ SV475 @ SV781 @ SV1024 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3335,plain,
! [SV476: $i,SV1025: $i,SV1181: $i,SV782: $i,SV93: $i] :
( ( ( c_ListOrder_Ostep1 @ SV93 @ SV782 @ SV1181 @ SV1025 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV93 @ ( c_List_Olist_OCons @ SV476 @ SV782 @ SV1025 ) @ ( c_List_Olist_OCons @ SV476 @ SV1181 @ SV1025 ) @ SV1025 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3336,plain,
! [SV98: $i,SV1182: $i,SV1026: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1026 @ SV1182 @ SV98 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SV1026 @ SV98 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3337,plain,
! [SV784: $i,SV1027: $i,SV1269: $i,SV481: $i,SV99: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV1269 ) @ SV1027 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SV784 ) @ SV1269 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV784 ) @ SV1027 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3338,plain,
! [SV785: $i,SV482: $i,SV1028: $i,SV1270: $i,SV100: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SV1270 ) @ SV1028 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1028 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3339,plain,
! [SV101: $i,SV1183: $i,SV1029: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1029 @ SV1183 @ SV101 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1029 @ SV101 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3340,plain,
! [SV102: $i,SV1184: $i,SV1030: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1030 @ SV1184 @ SV102 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1184 @ SV1030 @ SV102 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3341,plain,
! [SV103: $i,SV1185: $i,SV1031: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1031 @ SV1185 @ SV103 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1185 @ SV1031 @ SV103 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3342,plain,
! [SV1186: $i,SV1033: $i,SV791: $i,SV491: $i,SV113: $i] :
( ( ( ( c_List_Oappend @ SV113 @ SV491 @ SV791 )
= ( c_List_Olist_OCons @ SV1033 @ SV1186 @ SV791 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1033 @ SV1186 @ SV113 @ SV491 @ SV791 ) @ SV491 @ SV791 )
= SV1186 )
| ( SV491
= ( c_List_Olist_OCons @ SV1033 @ SV1186 @ SV791 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3206]) ).
thf(3343,plain,
! [SV1187: $i,SV1034: $i,SV792: $i,SV492: $i,SV114: $i] :
( ( ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
= ( c_List_Oappend @ SV1034 @ SV1187 @ SV792 ) )
= $false )
| ( ( ( ( c_List_Olist_OCons @ SV114 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV114 @ SV492 @ SV1034 @ SV1187 @ SV792 ) @ SV792 )
= SV1034 )
| ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
= SV1187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3344,plain,
! [SV1188: $i,SV1035: $i,SV793: $i,SV493: $i,SV115: $i] :
( ( ( ( c_List_Oappend @ SV115 @ SV493 @ SV793 )
= ( c_List_Olist_OCons @ SV1035 @ SV1188 @ SV793 ) )
= $false )
| ( ( ( SV115
= ( c_List_Olist_OCons @ SV1035 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1035 @ SV1188 @ SV115 @ SV493 @ SV793 ) @ SV793 ) )
| ( SV493
= ( c_List_Olist_OCons @ SV1035 @ SV1188 @ SV793 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3345,plain,
! [SV1189: $i,SV1036: $i,SV794: $i,SV494: $i,SV116: $i] :
( ( ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
= ( c_List_Oappend @ SV1036 @ SV1189 @ SV794 ) )
= $false )
| ( ( ( SV494
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV116 @ SV494 @ SV1036 @ SV1189 @ SV794 ) @ SV1189 @ SV794 ) )
| ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
= SV1189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3209]) ).
thf(3346,plain,
! [SV798: $i,SV122: $i,SV1038: $i,SV500: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV500 ) @ SV1038 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV798 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV500 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV798 ) @ SV1038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3210]) ).
thf(3347,plain,
! [SV513: $i,SV811: $i,SV1192: $i,SV136: $i] :
( ( ( c_Type_Otyping @ SV136 @ SV1192 @ SV811 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1192 ) @ SV513 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV136 @ SV513 @ SV811 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3348,plain,
! [SV1044: $i,SV813: $i,SV515: $i,SV138: $i,SV1310: $i] :
( ( ( ! [SY3155: $i] :
( ( c_Map_Omap__upds @ SV1310 @ ( c_List_Oappend @ SV138 @ SY3155 @ SV515 ) @ SV813 @ SV515 @ SV1044 )
= ( c_Map_Omap__upds @ SV1310 @ SV138 @ SV813 @ SV515 @ SV1044 ) ) )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ SV138 @ ( tc_List_Olist @ SV515 ) )
= ( c_Nat_Osize__class_Osize @ SV813 @ ( tc_List_Olist @ SV1044 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3349,plain,
! [SV516: $i,SV1045: $i,SV814: $i,SV139: $i,SV1311: $i] :
( ( ( ! [SY3156: $i] :
( ( c_Map_Omap__upds @ SV1311 @ SV139 @ ( c_List_Oappend @ SV814 @ SY3156 @ SV1045 ) @ SV516 @ SV1045 )
= ( c_Map_Omap__upds @ SV1311 @ SV139 @ SV814 @ SV516 @ SV1045 ) ) )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ SV139 @ ( tc_List_Olist @ SV516 ) )
= ( c_Nat_Osize__class_Osize @ SV814 @ ( tc_List_Olist @ SV1045 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3350,plain,
! [SV831: $i,SV545: $i,SV173: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV173 @ SV545 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV545 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV173 ) ) @ SV545 ) @ SV831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3351,plain,
! [SV846: $i,SV1272: $i,SV189: $i,SV552: $i] :
( ( ( ! [SY3149: $i] :
( ( c_List_Olist_OCons @ SV552 @ ( c_List_Ofilter @ SV189 @ SY3149 @ SV1272 ) @ SV1272 )
= ( c_List_Ofilter @ SV189 @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV552 @ SY3149 @ SV1272 ) @ SV1272 ) @ SV1272 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ SV189 @ SV846 @ SV1272 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV189 @ SV552 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3231]) ).
thf(3352,plain,
! [SV1273: $i,SV553: $i,SV847: $i,SV190: $i] :
( ( ( ! [SY3150: $i] :
( ( c_List_Ofilter @ SV190 @ ( c_List_Oappend @ SV847 @ ( c_List_Olist_OCons @ SV553 @ SY3150 @ SV1273 ) @ SV1273 ) @ SV1273 )
= ( c_List_Olist_OCons @ SV553 @ ( c_List_Ofilter @ SV190 @ SY3150 @ SV1273 ) @ SV1273 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV190 @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ SV190 @ SV847 @ SV1273 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV190 @ SV553 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3232]) ).
thf(3353,plain,
! [SV1197: $i,SV1054: $i,SV848: $i,SV554: $i,SV191: $i] :
( ( ( ( c_List_Olist_OCons @ SV191 @ SV554 @ SV848 )
= ( c_List_Oappend @ SV1054 @ SV1197 @ SV848 ) )
= $false )
| ( ( ( SV554
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV191 @ SV554 @ SV1054 @ SV1197 @ SV848 ) @ SV1197 @ SV848 ) )
| ( SV1054
= ( c_List_Olist_ONil @ SV848 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3354,plain,
! [SV1198: $i,SV1055: $i,SV849: $i,SV555: $i,SV192: $i] :
( ( ( ( c_List_Oappend @ SV192 @ SV555 @ SV849 )
= ( c_List_Olist_OCons @ SV1055 @ SV1198 @ SV849 ) )
= $false )
| ( ( ( SV192
= ( c_List_Olist_OCons @ SV1055 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1055 @ SV1198 @ SV192 @ SV555 @ SV849 ) @ SV849 ) )
| ( SV192
= ( c_List_Olist_ONil @ SV849 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3355,plain,
! [SV1056: $i,SV558: $i,SV852: $i,SV195: $i,SV1312: $i] :
( ( ( ! [SY3157: $i] :
~ ( c_ListOrder_Ostep1 @ SV1312 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SV852 @ ( c_List_Olist_ONil @ SY3157 ) @ SY3157 ) @ SY3157 ) @ ( c_List_Oappend @ SV558 @ ( c_List_Olist_OCons @ SV1056 @ ( c_List_Olist_ONil @ SY3157 ) @ SY3157 ) @ SY3157 ) @ SY3157 ) )
= $true )
| ( ( SV852 = SV1056 )
= $true )
| ( ( SV195 = SV558 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3356,plain,
! [SV853: $i,SV1313: $i,SV559: $i,SV1057: $i,SV196: $i] :
( ( ( ! [SY3158: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SV1057 @ ( c_List_Olist_OCons @ SV559 @ ( c_List_Olist_ONil @ SV1313 ) @ SV1313 ) @ SV1313 ) @ ( c_List_Oappend @ SY3158 @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_ONil @ SV1313 ) @ SV1313 ) @ SV1313 ) @ SV1313 ) )
= $true )
| ( ( SV559 = SV853 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SV559 ) @ SV853 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3357,plain,
! [SV1199: $i,SV1058: $i,SV854: $i,SV560: $i,SV197: $i] :
( ( ( ( c_List_Oappend @ SV197 @ SV560 @ SV854 )
= ( c_List_Olist_OCons @ SV1058 @ SV1199 @ SV854 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1058 @ SV1199 @ SV197 @ SV560 @ SV854 ) @ SV560 @ SV854 )
= SV1199 )
| ( SV197
= ( c_List_Olist_ONil @ SV854 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3358,plain,
! [SV1200: $i,SV1059: $i,SV855: $i,SV561: $i,SV198: $i] :
( ( ( ( c_List_Olist_OCons @ SV198 @ SV561 @ SV855 )
= ( c_List_Oappend @ SV1059 @ SV1200 @ SV855 ) )
= $false )
| ( ( ( ( c_List_Olist_OCons @ SV198 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV198 @ SV561 @ SV1059 @ SV1200 @ SV855 ) @ SV855 )
= SV1059 )
| ( SV1059
= ( c_List_Olist_ONil @ SV855 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3359,plain,
! [SV856: $i,SV562: $i,SV1314: $i,SV1274: $i,SV1060: $i,SV199: $i] :
( ( ( ( c_ListOrder_Ostep1 @ SV199 @ SV1060 @ SV1274 @ SV1314 )
| ~ ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SV1060 @ ( c_List_Olist_OCons @ SV562 @ ( c_List_Olist_ONil @ SV1314 ) @ SV1314 ) @ SV1314 ) @ ( c_List_Oappend @ SV1274 @ ( c_List_Olist_OCons @ SV856 @ ( c_List_Olist_ONil @ SV1314 ) @ SV1314 ) @ SV1314 ) @ SV1314 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SV562 ) @ SV856 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3360,plain,
! [SV564: $i,SV1061: $i,SV1315: $i,SV201: $i,SV858: $i] :
( ( ( ! [SY3159: $i] :
~ ( c_ListOrder_Ostep1 @ SV858 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SV1315 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ ( c_List_Oappend @ SV564 @ ( c_List_Olist_OCons @ SY3159 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ SV1061 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV858 @ SV201 @ SV564 @ SV1061 )
= $true )
| ( ( SV201 = SV564 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3361,plain,
! [SV860: $i,SV566: $i,SV203: $i,SV1062: $i] :
( ( ( SV1062
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV203 @ SV566 @ SV860 @ SV1062 ) @ ( c_List_Olist_OCons @ SV566 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1062
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV203 ) @ SV566 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV860 @ SV1062 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3241]) ).
thf(3362,plain,
! [SV578: $i,SV1066: $i,SV215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV1066 @ SV578 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1066 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1066 @ SV215 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV215 @ SV578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3244]) ).
thf(3363,plain,
! [SV580: $i,SV1067: $i,SV217: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV1067 @ SV580 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1067 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1067 @ SV217 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV217 @ SV580 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3245]) ).
thf(3364,plain,
! [SV219: $i,SV1068: $i,SV1276: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1276 @ SV1068 @ SV219 ) @ SV219 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV1068 @ SV219 )
= $true )
| ( ( class_Orderings_Olinorder @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3365,plain,
! [SV230: $i,SV1208: $i,SV592: $i,SV1316: $i] :
( ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1316 @ ( c_List_Olist_OCons @ SV592 @ SV1208 @ SV230 ) @ SV230 ) @ SV230 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV592 @ SV1208 @ SV230 ) @ SV230 )
= $true )
| ( ( class_Orderings_Olinorder @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3366,plain,
! [SV1279: $i,SV1082: $i,SV884: $i,SV598: $i,SV238: $i] :
( ( ( ( c_List_Olist_OCons @ SV238 @ SV598 @ SV884 )
= ( c_List_Ofilter @ SV1082 @ SV1279 @ SV884 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1082 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3367,plain,
! [SV1280: $i,SV1089: $i,SV892: $i,SV607: $i,SV247: $i] :
( ( ( ( c_List_Ofilter @ SV247 @ SV607 @ SV892 )
= ( c_List_Olist_OCons @ SV1089 @ SV1280 @ SV892 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV247 @ SV1089 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3256]) ).
thf(3368,plain,
! [SV897: $i,SV616: $i,SV1217: $i,SV256: $i] :
( ( ( c_List_Olist__ex @ SV256 @ ( c_List_Olist_OCons @ SV1217 @ SV616 @ SV897 ) @ SV897 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV256 @ SV1217 ) )
= $true )
| ( ( c_List_Olist__ex @ SV256 @ SV616 @ SV897 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3369,plain,
! [SV1282: $i,SV1218: $i,SV1094: $i,SV898: $i,SV617: $i,SV257: $i] :
( ( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SV898 @ SV1094 ) @ ( c_List_Olist_OCons @ SV1218 @ SV1282 @ SV1094 ) @ SV1094 )
= $true )
| ( ( ~ ( c_List_Olistrelp @ SV257 @ SV898 @ SV1282 @ SV1094 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SV1218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3261]) ).
thf(3370,plain,
! [SV1233: $i,SV1107: $i,SV913: $i,SV640: $i,SV282: $i] :
( ( ( hBOOL @ ( hAPP @ SV282 @ ( c_Lambda_OdB_OdB__case @ SV640 @ SV913 @ SV1107 @ ( c_Lambda_OdB_OAbs @ SV1233 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ SV1107 @ SV1233 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3270]) ).
thf(3371,plain,
! [SV1234: $i,SV1108: $i,SV914: $i,SV641: $i,SV283: $i] :
( ( ( hBOOL @ ( hAPP @ SV283 @ ( c_Lambda_OdB_OdB__case @ SV641 @ SV914 @ SV1108 @ ( c_Lambda_OdB_OAbs @ SV1234 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ SV1108 @ SV1234 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3271]) ).
thf(3372,plain,
! [SV1289: $i,SV1110: $i,SV916: $i,SV644: $i,SV287: $i] :
( ( ( ( c_List_Olist_OCons @ SV287 @ SV644 @ SV916 )
= ( c_List_Olist_OCons @ SV1110 @ SV1289 @ SV916 ) )
= $false )
| ( ( SV287 = SV1110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3272]) ).
thf(3373,plain,
! [SV1235: $i,SV1111: $i,SV917: $i,SV645: $i,SV288: $i] :
( ( ( ( c_List_Olist_OCons @ SV288 @ SV645 @ SV917 )
= ( c_List_Olist_OCons @ SV1111 @ SV1235 @ SV917 ) )
= $false )
| ( ( SV645 = SV1235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3374,plain,
! [SV918: $i,SV289: $i,SV646: $i,SV1236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1236 ) @ SV646 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV289 @ SV1236 @ SV918 ) )
= $true )
| ( ( c_Type_Otyping @ SV289 @ SV646 @ SV918 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3274]) ).
thf(3375,plain,
! [SV290: $i,SV1290: $i,SV1112: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1112 @ SV1290 @ SV290 ) @ SV290 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV1112 @ SV290 )
= $true )
| ( ( class_Orderings_Olinorder @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3376,plain,
! [SV291: $i,SV1113: $i,SV1291: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1291 @ SV1113 @ SV291 ) @ SV291 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV1113 @ SV291 )
= $true )
| ( ( class_Orderings_Olinorder @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3377,plain,
! [SV1317: $i,SV1237: $i,SV1114: $i,SV919: $i,SV647: $i,SV292: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV647 @ SV919 @ SV1114 ) @ SV1237 @ SV1317 @ SV1114 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV292 @ SV1237 @ SV1317 @ SV1114 ) @ SV647 @ SV919 @ SV1114 ) )
= $true )
| ( ( SV647 = SV1237 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3378,plain,
! [SV920: $i,SV295: $i,SV1117: $i,SV649: $i] :
( ( ( hBOOL @ ( hAPP @ SV649 @ SV1117 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV295 @ SV1117 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV295 @ SV649 @ ( tc_fun @ SV920 @ tc_bool ) ) @ SV1117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3379,plain,
! [SV1292: $i,SV1118: $i,SV922: $i,SV651: $i,SV297: $i] :
( ( ( ( c_List_Oappend @ SV297 @ ( c_List_Olist_OCons @ SV651 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 )
= ( c_List_Oappend @ SV1118 @ ( c_List_Olist_OCons @ SV1292 @ ( c_List_Olist_ONil @ SV922 ) @ SV922 ) @ SV922 ) )
= $false )
| ( ( SV297 = SV1118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3380,plain,
! [SV1239: $i,SV1119: $i,SV923: $i,SV652: $i,SV298: $i] :
( ( ( ( c_List_Oappend @ SV298 @ ( c_List_Olist_OCons @ SV652 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 )
= ( c_List_Oappend @ SV1119 @ ( c_List_Olist_OCons @ SV1239 @ ( c_List_Olist_ONil @ SV923 ) @ SV923 ) @ SV923 ) )
= $false )
| ( ( SV652 = SV1239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3281]) ).
thf(3381,plain,
! [SV1240: $i,SV1120: $i,SV924: $i,SV653: $i,SV299: $i] :
( ( ( hBOOL @ ( hAPP @ SV299 @ ( c_List_Olist_Olist__case @ SV653 @ SV924 @ ( c_List_Olist_OCons @ SV1120 @ SV1240 @ t_b ) @ t_a @ t_b ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV299 @ ( hAPP @ ( hAPP @ SV924 @ SV1120 ) @ SV1240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3382,plain,
! [SV1241: $i,SV1121: $i,SV925: $i,SV654: $i,SV300: $i] :
( ( ( hBOOL @ ( hAPP @ SV300 @ ( c_List_Olist_Olist__case @ SV654 @ SV925 @ ( c_List_Olist_OCons @ SV1121 @ SV1241 @ t_b ) @ t_a @ t_b ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV300 @ ( hAPP @ ( hAPP @ SV925 @ SV1121 ) @ SV1241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3383,plain,
! [SV1127: $i,SV306: $i,SV1243: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1243 @ SV306 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV1127 @ SV1243 @ SV306 ) @ SV306 )
= $true )
| ( ( class_Orderings_Olinorder @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3284]) ).
thf(3384,plain,
! [SV1293: $i,SV1244: $i,SV1136: $i,SV957: $i,SV686: $i,SV346: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV346 @ ( c_Lambda_OdB_OdB__case @ SV686 @ SV957 @ SV1136 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1244 ) @ SV1293 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ SV957 @ SV1244 ) @ SV1293 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3385,plain,
! [SV1294: $i,SV1245: $i,SV1137: $i,SV958: $i,SV687: $i,SV347: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV347 @ ( c_Lambda_OdB_OdB__case @ SV687 @ SV958 @ SV1137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1245 ) @ SV1294 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV347 @ ( hAPP @ ( hAPP @ SV958 @ SV1245 ) @ SV1294 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3386,plain,
! [SV356: $i,SV696: $i,SV1297: $i,SV1248: $i,SV967: $i] :
( ( ( ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SV1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV696 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SV1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 ) )
= $true )
| ( ( SV356 = SV696 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3387,plain,
! [SV1249: $i,SV1144: $i,SV970: $i,SV700: $i,SV360: $i] :
( ( ( hBOOL @ ( hAPP @ SV360 @ ( c_Lambda_OdB_OdB__case @ SV700 @ SV970 @ SV1144 @ ( c_Lambda_OdB_OVar @ SV1249 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV360 @ ( hAPP @ SV700 @ SV1249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3388,plain,
! [SV1250: $i,SV1145: $i,SV971: $i,SV701: $i,SV361: $i] :
( ( ( hBOOL @ ( hAPP @ SV361 @ ( c_Lambda_OdB_OdB__case @ SV701 @ SV971 @ SV1145 @ ( c_Lambda_OdB_OVar @ SV1250 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV361 @ ( hAPP @ SV701 @ SV1250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3389,plain,
! [SV1148: $i,SV710: $i,SV976: $i,SV371: $i] :
( ( ( SV371
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV371 @ SV710 @ SV976 @ SV1148 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1148
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV371 ) @ SV710 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV976 @ SV1148 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3390,plain,
! [SV712: $i,SV1150: $i,SV977: $i,SV374: $i] :
( ( ( c_List_Olistsp @ SV374 @ SV977 @ SV1150 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV374 @ SV712 @ SV1150 ) )
= $true )
| ( ( c_List_Olistsp @ SV374 @ ( c_List_Oappend @ SV712 @ SV977 @ SV1150 ) @ SV1150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3294]) ).
thf(3391,plain,
! [SV376: $i,SV979: $i,SV1151: $i,SV714: $i] :
( ( ( c_List_Olistsp @ SV714 @ SV1151 @ SV979 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV376 @ SV1151 @ SV979 ) )
= $true )
| ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV714 @ ( tc_fun @ SV979 @ tc_bool ) ) @ SV1151 @ SV979 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3392,plain,
! [SV720: $i,SV1154: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP @ SV384 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV1154 @ SV720 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1154 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1154 @ SV384 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV384 @ SV720 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3300]) ).
thf(3393,plain,
! [SV721: $i,SV1155: $i,SV385: $i] :
( ( ( hBOOL @ ( hAPP @ SV385 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV1155 @ SV721 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1155 @ SV385 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ SV721 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3301]) ).
thf(3394,plain,
! [SV722: $i,SV1156: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP @ SV386 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV1156 @ SV722 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1156 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1156 @ SV386 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV386 @ SV722 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3302]) ).
thf(3395,plain,
! [SV723: $i,SV1157: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ SV387 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV1157 @ SV723 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1157 @ SV387 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3396,plain,
! [SV726: $i,SV1158: $i,SV390: $i] :
( ( ( hBOOL @ ( hAPP @ SV390 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV1158 @ SV726 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV1158 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1158 @ SV390 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV390 @ SV726 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3397,plain,
! [SV727: $i,SV1159: $i,SV391: $i] :
( ( ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV1159 @ SV727 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV1159 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1159 @ SV391 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV391 @ SV727 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3398,plain,
! [SV748: $i,SV996: $i,SV1261: $i,SV416: $i,SV4: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV1261 ) @ SV996 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV1261 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV996 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3399,plain,
! [SV753: $i,SV9: $i,SV1318: $i,SV998: $i,SV421: $i,SV1303: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV1303 @ ( c_List_Olist_OCons @ SV421 @ SV998 @ SV1318 ) @ ( c_List_Olist_OCons @ SV9 @ SV753 @ SV1318 ) @ SV1318 ) )
= $true )
| ( ( SV753 = SV998 )
= $true )
| ( ( SV9 = SV421 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3400,plain,
! [SV426: $i,SV15: $i,SV1168: $i,SV1305: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1305 @ SV1168 @ SV15 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV426 @ SV1305 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV426 @ SV1168 @ SV15 )
= $true )
| ( ( class_Orderings_Opreorder @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3401,plain,
! [SV1169: $i,SV16: $i,SV1306: $i,SV427: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV427 @ SV1306 @ SV16 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1306 @ SV1169 @ SV16 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1169 @ SV16 )
= $true )
| ( ( class_Orderings_Oorder @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3319]) ).
thf(3402,plain,
! [SV1319: $i,SV24: $i,SV1307: $i,SV1001: $i,SV431: $i,SV759: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV759 @ ( c_List_Olist_OCons @ SV431 @ SV1001 @ SV1307 ) @ ( c_List_Olist_OCons @ SV24 @ SV1319 @ SV1307 ) @ SV1307 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ SV431 ) @ SV24 ) )
= $true )
| ( ( SV24 = SV431 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(3403,plain,
! [SV1004: $i,SV764: $i,SV33: $i,SV1170: $i,SV438: $i] :
( ( ( SV438 = SV1170 )
= $true )
| ( ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Oreplicate @ SV33 @ SV438 @ SV764 )
= ( c_List_Oreplicate @ SV1004 @ SV1170 @ SV764 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3321]) ).
thf(3404,plain,
! [SV776: $i,SV1320: $i,SV1014: $i,SV463: $i,SV1308: $i,SV67: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SV1308 @ SV463 @ SV1014 ) @ ( c_List_Olist_OCons @ SV1320 @ SV776 @ SV1014 ) @ SV1014 ) )
= $true )
| ( ( SV776 = SV463 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV67 @ SV463 @ SV776 @ SV1014 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3405,plain,
! [SV468: $i,SV77: $i,SV1266: $i,SV1179: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1179 @ SV1266 @ SV77 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV468 @ SV1179 @ SV77 ) @ SV1266 @ SV77 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3406,plain,
! [SV1180: $i,SV78: $i,SV1267: $i,SV469: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV469 @ SV1267 @ SV78 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV469 @ SV1180 @ SV78 ) @ SV1267 @ SV78 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3407,plain,
! [SV781: $i,SV1024: $i,SV475: $i,SV1309: $i,SV1268: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV1268 ) @ SV1309 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SV1268 @ SV475 @ SV1024 ) @ ( c_List_Olist_OCons @ SV1309 @ SV781 @ SV1024 ) @ SV1024 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV92 @ SV475 @ SV781 @ SV1024 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3334]) ).
thf(3408,plain,
! [SV98: $i,SV1026: $i,SV1182: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1182 @ SV1026 @ SV98 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1026 @ SV1182 @ SV98 )
= $false )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3336]) ).
thf(3409,plain,
! [SV784: $i,SV1027: $i,SV1269: $i,SV481: $i,SV99: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV1269 ) @ SV1027 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SV784 ) @ SV1269 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV784 ) @ SV1027 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3410,plain,
! [SV785: $i,SV482: $i,SV1028: $i,SV1270: $i,SV100: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SV1270 ) @ SV1028 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1028 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3411,plain,
! [SV101: $i,SV1029: $i,SV1183: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1183 @ SV1029 @ SV101 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1029 @ SV1183 @ SV101 )
= $false )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3412,plain,
! [SV102: $i,SV1030: $i,SV1184: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1184 @ SV1030 @ SV102 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1030 @ SV1184 @ SV102 )
= $false )
| ( ( class_Orderings_Opreorder @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3413,plain,
! [SV103: $i,SV1031: $i,SV1185: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1185 @ SV1031 @ SV103 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1031 @ SV1185 @ SV103 )
= $false )
| ( ( class_Orderings_Opreorder @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3414,plain,
! [SV791: $i,SV491: $i,SV113: $i,SV1186: $i,SV1033: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1033 @ SV1186 @ SV113 @ SV491 @ SV791 ) @ SV491 @ SV791 )
= SV1186 )
= $true )
| ( ( SV491
= ( c_List_Olist_OCons @ SV1033 @ SV1186 @ SV791 ) )
= $true )
| ( ( ( c_List_Oappend @ SV113 @ SV491 @ SV791 )
= ( c_List_Olist_OCons @ SV1033 @ SV1186 @ SV791 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3415,plain,
! [SV792: $i,SV1187: $i,SV1034: $i,SV492: $i,SV114: $i] :
( ( ( ( c_List_Olist_OCons @ SV114 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV114 @ SV492 @ SV1034 @ SV1187 @ SV792 ) @ SV792 )
= SV1034 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
= SV1187 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV114 @ SV492 @ SV792 )
= ( c_List_Oappend @ SV1034 @ SV1187 @ SV792 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3343]) ).
thf(3416,plain,
! [SV793: $i,SV493: $i,SV1188: $i,SV1035: $i,SV115: $i] :
( ( ( SV115
= ( c_List_Olist_OCons @ SV1035 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1035 @ SV1188 @ SV115 @ SV493 @ SV793 ) @ SV793 ) )
= $true )
| ( ( SV493
= ( c_List_Olist_OCons @ SV1035 @ SV1188 @ SV793 ) )
= $true )
| ( ( ( c_List_Oappend @ SV115 @ SV493 @ SV793 )
= ( c_List_Olist_OCons @ SV1035 @ SV1188 @ SV793 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3344]) ).
thf(3417,plain,
! [SV794: $i,SV1189: $i,SV1036: $i,SV116: $i,SV494: $i] :
( ( ( SV494
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV116 @ SV494 @ SV1036 @ SV1189 @ SV794 ) @ SV1189 @ SV794 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
= SV1189 )
= $true )
| ( ( ( c_List_Olist_OCons @ SV116 @ SV494 @ SV794 )
= ( c_List_Oappend @ SV1036 @ SV1189 @ SV794 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3345]) ).
thf(3418,plain,
! [SV1038: $i,SV500: $i,SV798: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV122 ) @ SV798 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV500 ) @ SV1038 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV122 ) @ SV500 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV798 ) @ SV1038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3419,plain,
! [SV811: $i,SV136: $i,SV513: $i,SV1192: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1192 ) @ SV513 ) )
= $false )
| ( ( c_Type_Otyping @ SV136 @ SV1192 @ SV811 )
= $false )
| ( ( c_Type_Otyping @ SV136 @ SV513 @ SV811 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3420,plain,
! [SV1044: $i,SV813: $i,SV515: $i,SV1321: $i,SV138: $i,SV1310: $i] :
( ( ( ( c_Map_Omap__upds @ SV1310 @ ( c_List_Oappend @ SV138 @ SV1321 @ SV515 ) @ SV813 @ SV515 @ SV1044 )
= ( c_Map_Omap__upds @ SV1310 @ SV138 @ SV813 @ SV515 @ SV1044 ) )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ SV138 @ ( tc_List_Olist @ SV515 ) )
= ( c_Nat_Osize__class_Osize @ SV813 @ ( tc_List_Olist @ SV1044 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3421,plain,
! [SV516: $i,SV1045: $i,SV1322: $i,SV814: $i,SV139: $i,SV1311: $i] :
( ( ( ( c_Map_Omap__upds @ SV1311 @ SV139 @ ( c_List_Oappend @ SV814 @ SV1322 @ SV1045 ) @ SV516 @ SV1045 )
= ( c_Map_Omap__upds @ SV1311 @ SV139 @ SV814 @ SV516 @ SV1045 ) )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ SV139 @ ( tc_List_Olist @ SV516 ) )
= ( c_Nat_Osize__class_Osize @ SV814 @ ( tc_List_Olist @ SV1045 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3422,plain,
! [SV846: $i,SV1272: $i,SV1323: $i,SV189: $i,SV552: $i] :
( ( ( ( c_List_Olist_OCons @ SV552 @ ( c_List_Ofilter @ SV189 @ SV1323 @ SV1272 ) @ SV1272 )
= ( c_List_Ofilter @ SV189 @ ( c_List_Oappend @ SV846 @ ( c_List_Olist_OCons @ SV552 @ SV1323 @ SV1272 ) @ SV1272 ) @ SV1272 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV189 @ ( c_List_Osko__List__XCons__eq__filter__iff__1__3 @ SV189 @ SV846 @ SV1272 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV189 @ SV552 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3423,plain,
! [SV1273: $i,SV1324: $i,SV553: $i,SV847: $i,SV190: $i] :
( ( ( ( c_List_Ofilter @ SV190 @ ( c_List_Oappend @ SV847 @ ( c_List_Olist_OCons @ SV553 @ SV1324 @ SV1273 ) @ SV1273 ) @ SV1273 )
= ( c_List_Olist_OCons @ SV553 @ ( c_List_Ofilter @ SV190 @ SV1324 @ SV1273 ) @ SV1273 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV190 @ ( c_List_Osko__List__Xfilter__eq__Cons__iff__1__3 @ SV190 @ SV847 @ SV1273 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV190 @ SV553 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3424,plain,
! [SV848: $i,SV1197: $i,SV1054: $i,SV191: $i,SV554: $i] :
( ( ( SV554
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV191 @ SV554 @ SV1054 @ SV1197 @ SV848 ) @ SV1197 @ SV848 ) )
= $true )
| ( ( SV1054
= ( c_List_Olist_ONil @ SV848 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV191 @ SV554 @ SV848 )
= ( c_List_Oappend @ SV1054 @ SV1197 @ SV848 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3425,plain,
! [SV849: $i,SV555: $i,SV1198: $i,SV1055: $i,SV192: $i] :
( ( ( SV192
= ( c_List_Olist_OCons @ SV1055 @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1055 @ SV1198 @ SV192 @ SV555 @ SV849 ) @ SV849 ) )
= $true )
| ( ( SV192
= ( c_List_Olist_ONil @ SV849 ) )
= $true )
| ( ( ( c_List_Oappend @ SV192 @ SV555 @ SV849 )
= ( c_List_Olist_OCons @ SV1055 @ SV1198 @ SV849 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3426,plain,
! [SV1056: $i,SV558: $i,SV1325: $i,SV852: $i,SV195: $i,SV1312: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV1312 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SV852 @ ( c_List_Olist_ONil @ SV1325 ) @ SV1325 ) @ SV1325 ) @ ( c_List_Oappend @ SV558 @ ( c_List_Olist_OCons @ SV1056 @ ( c_List_Olist_ONil @ SV1325 ) @ SV1325 ) @ SV1325 ) @ SV1325 ) )
= $true )
| ( ( SV852 = SV1056 )
= $true )
| ( ( SV195 = SV558 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(3427,plain,
! [SV853: $i,SV1326: $i,SV1313: $i,SV559: $i,SV1057: $i,SV196: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SV1057 @ ( c_List_Olist_OCons @ SV559 @ ( c_List_Olist_ONil @ SV1313 ) @ SV1313 ) @ SV1313 ) @ ( c_List_Oappend @ SV1326 @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_ONil @ SV1313 ) @ SV1313 ) @ SV1313 ) @ SV1313 ) )
= $true )
| ( ( SV559 = SV853 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SV559 ) @ SV853 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3428,plain,
! [SV854: $i,SV560: $i,SV197: $i,SV1199: $i,SV1058: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ SV1058 @ SV1199 @ SV197 @ SV560 @ SV854 ) @ SV560 @ SV854 )
= SV1199 )
= $true )
| ( ( SV197
= ( c_List_Olist_ONil @ SV854 ) )
= $true )
| ( ( ( c_List_Oappend @ SV197 @ SV560 @ SV854 )
= ( c_List_Olist_OCons @ SV1058 @ SV1199 @ SV854 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3357]) ).
thf(3429,plain,
! [SV855: $i,SV1200: $i,SV1059: $i,SV561: $i,SV198: $i] :
( ( ( ( c_List_Olist_OCons @ SV198 @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ SV198 @ SV561 @ SV1059 @ SV1200 @ SV855 ) @ SV855 )
= SV1059 )
= $true )
| ( ( SV1059
= ( c_List_Olist_ONil @ SV855 ) )
= $true )
| ( ( ( c_List_Olist_OCons @ SV198 @ SV561 @ SV855 )
= ( c_List_Oappend @ SV1059 @ SV1200 @ SV855 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3358]) ).
thf(3430,plain,
! [SV856: $i,SV562: $i,SV1314: $i,SV1274: $i,SV1060: $i,SV199: $i] :
( ( ( c_ListOrder_Ostep1 @ SV199 @ SV1060 @ SV1274 @ SV1314 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SV1060 @ ( c_List_Olist_OCons @ SV562 @ ( c_List_Olist_ONil @ SV1314 ) @ SV1314 ) @ SV1314 ) @ ( c_List_Oappend @ SV1274 @ ( c_List_Olist_OCons @ SV856 @ ( c_List_Olist_ONil @ SV1314 ) @ SV1314 ) @ SV1314 ) @ SV1314 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SV562 ) @ SV856 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3359]) ).
thf(3431,plain,
! [SV1327: $i,SV564: $i,SV1061: $i,SV1315: $i,SV201: $i,SV858: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV858 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SV1315 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ ( c_List_Oappend @ SV564 @ ( c_List_Olist_OCons @ SV1327 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ SV1061 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV858 @ SV201 @ SV564 @ SV1061 )
= $true )
| ( ( SV201 = SV564 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3432,plain,
! [SV578: $i,SV1066: $i,SV215: $i] :
( ( ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV1066 @ SV578 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1066 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1066 @ SV215 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV215 @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3362]) ).
thf(3433,plain,
! [SV580: $i,SV1067: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV1067 @ SV580 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1067 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1067 @ SV217 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV217 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3363]) ).
thf(3434,plain,
! [SV230: $i,SV1208: $i,SV592: $i,SV1316: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1316 @ ( c_List_Olist_OCons @ SV592 @ SV1208 @ SV230 ) @ SV230 ) @ SV230 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV592 @ SV1208 @ SV230 ) @ SV230 )
= $true )
| ( ( class_Orderings_Olinorder @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3365]) ).
thf(3435,plain,
! [SV1218: $i,SV617: $i,SV1094: $i,SV1282: $i,SV898: $i,SV257: $i] :
( ( ( ~ ( c_List_Olistrelp @ SV257 @ SV898 @ SV1282 @ SV1094 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SV1218 ) ) )
= $true )
| ( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SV898 @ SV1094 ) @ ( c_List_Olist_OCons @ SV1218 @ SV1282 @ SV1094 ) @ SV1094 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3369]) ).
thf(3436,plain,
! [SV646: $i,SV918: $i,SV1236: $i,SV289: $i] :
( ( ( c_Type_Otyping @ SV289 @ SV1236 @ SV918 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1236 ) @ SV646 ) )
= $false )
| ( ( c_Type_Otyping @ SV289 @ SV646 @ SV918 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3374]) ).
thf(3437,plain,
! [SV920: $i,SV649: $i,SV1117: $i,SV295: $i] :
( ( ( hBOOL @ ( hAPP @ SV295 @ SV1117 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV649 @ SV1117 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV295 @ SV649 @ ( tc_fun @ SV920 @ tc_bool ) ) @ SV1117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3378]) ).
thf(3438,plain,
! [SV1293: $i,SV1244: $i,SV1136: $i,SV957: $i,SV686: $i,SV346: $i] :
( ( ( hBOOL @ ( hAPP @ SV346 @ ( c_Lambda_OdB_OdB__case @ SV686 @ SV957 @ SV1136 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1244 ) @ SV1293 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV346 @ ( hAPP @ ( hAPP @ SV957 @ SV1244 ) @ SV1293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3439,plain,
! [SV1294: $i,SV1245: $i,SV1137: $i,SV958: $i,SV687: $i,SV347: $i] :
( ( ( hBOOL @ ( hAPP @ SV347 @ ( c_Lambda_OdB_OdB__case @ SV687 @ SV958 @ SV1137 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1245 ) @ SV1294 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV347 @ ( hAPP @ ( hAPP @ SV958 @ SV1245 ) @ SV1294 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3440,plain,
! [SV356: $i,SV696: $i,SV1297: $i,SV1248: $i,SV967: $i] :
( ( ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SV1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV696 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SV1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 ) )
= $true )
| ( ( SV356 = SV696 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3441,plain,
! [SV977: $i,SV1150: $i,SV712: $i,SV374: $i] :
( ( ( c_List_Olistsp @ SV374 @ SV712 @ SV1150 )
= $false )
| ( ( c_List_Olistsp @ SV374 @ SV977 @ SV1150 )
= $false )
| ( ( c_List_Olistsp @ SV374 @ ( c_List_Oappend @ SV712 @ SV977 @ SV1150 ) @ SV1150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3442,plain,
! [SV714: $i,SV979: $i,SV1151: $i,SV376: $i] :
( ( ( c_List_Olistsp @ SV376 @ SV1151 @ SV979 )
= $false )
| ( ( c_List_Olistsp @ SV714 @ SV1151 @ SV979 )
= $false )
| ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV714 @ ( tc_fun @ SV979 @ tc_bool ) ) @ SV1151 @ SV979 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3443,plain,
! [SV384: $i,SV720: $i,SV1154: $i] :
( ( ( c_List_Olistsp @ SV1154 @ SV720 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV384 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1154 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1154 @ SV384 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV384 @ SV720 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3392]) ).
thf(3444,plain,
! [SV385: $i,SV721: $i,SV1155: $i] :
( ( ( c_List_Olistsp @ SV1155 @ SV721 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV385 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV385 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1155 @ SV385 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV385 @ SV721 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3445,plain,
! [SV386: $i,SV722: $i,SV1156: $i] :
( ( ( c_List_Olistsp @ SV1156 @ SV722 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV386 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1156 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1156 @ SV386 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV386 @ SV722 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3394]) ).
thf(3446,plain,
! [SV387: $i,SV723: $i,SV1157: $i] :
( ( ( c_List_Olistsp @ SV1157 @ SV723 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV387 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV387 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1157 @ SV387 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3447,plain,
! [SV390: $i,SV726: $i,SV1158: $i] :
( ( ( c_List_Olistsp @ SV1158 @ SV726 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV390 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( c_List_Olistsp @ SV1158 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1158 @ SV390 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV390 @ SV726 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3448,plain,
! [SV391: $i,SV727: $i,SV1159: $i] :
( ( ( c_List_Olistsp @ SV1159 @ SV727 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( c_List_Olistsp @ SV1159 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1159 @ SV391 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV391 @ SV727 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3449,plain,
! [SV996: $i,SV1261: $i,SV748: $i,SV416: $i,SV4: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV1261 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV1261 ) @ SV996 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV4 @ SV416 ) @ SV748 ) @ SV996 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3450,plain,
! [SV753: $i,SV9: $i,SV1318: $i,SV998: $i,SV421: $i,SV1303: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1303 @ ( c_List_Olist_OCons @ SV421 @ SV998 @ SV1318 ) @ ( c_List_Olist_OCons @ SV9 @ SV753 @ SV1318 ) @ SV1318 )
= $false )
| ( ( SV753 = SV998 )
= $true )
| ( ( SV9 = SV421 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3451,plain,
! [SV426: $i,SV15: $i,SV1168: $i,SV1305: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1305 @ SV1168 @ SV15 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV426 @ SV1305 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV426 @ SV1168 @ SV15 )
= $true )
| ( ( class_Orderings_Opreorder @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3400]) ).
thf(3452,plain,
! [SV1169: $i,SV16: $i,SV1306: $i,SV427: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1306 @ SV16 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1306 @ SV1169 @ SV16 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1169 @ SV16 )
= $true )
| ( ( class_Orderings_Oorder @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3401]) ).
thf(3453,plain,
! [SV1319: $i,SV24: $i,SV1307: $i,SV1001: $i,SV431: $i,SV759: $i] :
( ( ( c_ListOrder_Ostep1 @ SV759 @ ( c_List_Olist_OCons @ SV431 @ SV1001 @ SV1307 ) @ ( c_List_Olist_OCons @ SV24 @ SV1319 @ SV1307 ) @ SV1307 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ SV431 ) @ SV24 ) )
= $true )
| ( ( SV24 = SV431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3402]) ).
thf(3454,plain,
! [SV776: $i,SV1320: $i,SV1014: $i,SV463: $i,SV1308: $i,SV67: $i] :
( ( ( c_ListOrder_Ostep1 @ SV67 @ ( c_List_Olist_OCons @ SV1308 @ SV463 @ SV1014 ) @ ( c_List_Olist_OCons @ SV1320 @ SV776 @ SV1014 ) @ SV1014 )
= $false )
| ( ( SV776 = SV463 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV67 @ SV463 @ SV776 @ SV1014 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3404]) ).
thf(3455,plain,
! [SV781: $i,SV1309: $i,SV1024: $i,SV475: $i,SV1268: $i,SV92: $i] :
( ( ( c_ListOrder_Ostep1 @ SV92 @ ( c_List_Olist_OCons @ SV1268 @ SV475 @ SV1024 ) @ ( c_List_Olist_OCons @ SV1309 @ SV781 @ SV1024 ) @ SV1024 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV1268 ) @ SV1309 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV92 @ SV475 @ SV781 @ SV1024 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3456,plain,
! [SV1027: $i,SV481: $i,SV1269: $i,SV784: $i,SV99: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV99 @ SV784 ) @ SV1269 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV1269 ) @ SV1027 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV99 @ SV481 ) @ SV784 ) @ SV1027 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3457,plain,
! [SV1028: $i,SV1270: $i,SV785: $i,SV482: $i,SV100: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1270 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV100 @ SV1270 ) @ SV1028 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV100 @ SV482 ) @ SV785 ) @ SV1028 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3458,plain,
! [SV1056: $i,SV558: $i,SV1325: $i,SV852: $i,SV195: $i,SV1312: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1312 @ ( c_List_Oappend @ SV195 @ ( c_List_Olist_OCons @ SV852 @ ( c_List_Olist_ONil @ SV1325 ) @ SV1325 ) @ SV1325 ) @ ( c_List_Oappend @ SV558 @ ( c_List_Olist_OCons @ SV1056 @ ( c_List_Olist_ONil @ SV1325 ) @ SV1325 ) @ SV1325 ) @ SV1325 )
= $false )
| ( ( SV852 = SV1056 )
= $true )
| ( ( SV195 = SV558 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3459,plain,
! [SV853: $i,SV1326: $i,SV1313: $i,SV559: $i,SV1057: $i,SV196: $i] :
( ( ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Oappend @ SV1057 @ ( c_List_Olist_OCons @ SV559 @ ( c_List_Olist_ONil @ SV1313 ) @ SV1313 ) @ SV1313 ) @ ( c_List_Oappend @ SV1326 @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_ONil @ SV1313 ) @ SV1313 ) @ SV1313 ) @ SV1313 )
= $false )
| ( ( SV559 = SV853 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV196 @ SV559 ) @ SV853 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3460,plain,
! [SV856: $i,SV1274: $i,SV1314: $i,SV562: $i,SV1060: $i,SV199: $i] :
( ( ( c_ListOrder_Ostep1 @ SV199 @ ( c_List_Oappend @ SV1060 @ ( c_List_Olist_OCons @ SV562 @ ( c_List_Olist_ONil @ SV1314 ) @ SV1314 ) @ SV1314 ) @ ( c_List_Oappend @ SV1274 @ ( c_List_Olist_OCons @ SV856 @ ( c_List_Olist_ONil @ SV1314 ) @ SV1314 ) @ SV1314 ) @ SV1314 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV199 @ SV1060 @ SV1274 @ SV1314 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV199 @ SV562 ) @ SV856 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3430]) ).
thf(3461,plain,
! [SV1327: $i,SV564: $i,SV1061: $i,SV1315: $i,SV201: $i,SV858: $i] :
( ( ( c_ListOrder_Ostep1 @ SV858 @ ( c_List_Oappend @ SV201 @ ( c_List_Olist_OCons @ SV1315 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ ( c_List_Oappend @ SV564 @ ( c_List_Olist_OCons @ SV1327 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 ) @ SV1061 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV858 @ SV201 @ SV564 @ SV1061 )
= $true )
| ( ( SV201 = SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3462,plain,
! [SV215: $i,SV578: $i,SV1066: $i] :
( ( ( c_List_Olistsp @ SV1066 @ SV578 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV215 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV1066 @ SV215 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV1066 @ SV215 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV215 @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3432]) ).
thf(3463,plain,
! [SV217: $i,SV580: $i,SV1067: $i] :
( ( ( c_List_Olistsp @ SV1067 @ SV580 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV1067 @ SV217 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV1067 @ SV217 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV217 @ SV580 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3464,plain,
! [SV1218: $i,SV617: $i,SV1094: $i,SV1282: $i,SV898: $i,SV257: $i] :
( ( ( c_List_Olistrelp @ SV257 @ SV898 @ SV1282 @ SV1094 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SV1218 ) ) )
= $true )
| ( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SV898 @ SV1094 ) @ ( c_List_Olist_OCons @ SV1218 @ SV1282 @ SV1094 ) @ SV1094 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3435]) ).
thf(3465,plain,
! [SV696: $i,SV356: $i,SV1297: $i,SV1248: $i,SV967: $i] :
( ( ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SV1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV356 )
= $false )
| ( ( c_Type_Otyping @ SV967 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1248 ) @ SV1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV696 )
= $false )
| ( ( SV356 = SV696 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3466,plain,
! [SV1168: $i,SV15: $i,SV1305: $i,SV426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV426 @ SV1305 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1305 @ SV1168 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV426 @ SV1168 @ SV15 )
= $true )
| ( ( class_Orderings_Opreorder @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3467,plain,
! [SV427: $i,SV16: $i,SV1169: $i,SV1306: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1306 @ SV1169 @ SV16 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1306 @ SV16 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1169 @ SV16 )
= $true )
| ( ( class_Orderings_Oorder @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3468,plain,
! [SV1094: $i,SV1282: $i,SV898: $i,SV1218: $i,SV617: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV257 @ SV617 ) @ SV1218 ) )
= $false )
| ( ( c_List_Olistrelp @ SV257 @ SV898 @ SV1282 @ SV1094 )
= $false )
| ( ( c_List_Olistrelp @ SV257 @ ( c_List_Olist_OCons @ SV617 @ SV898 @ SV1094 ) @ ( c_List_Olist_OCons @ SV1218 @ SV1282 @ SV1094 ) @ SV1094 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3469,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1052,3468,3467,3466,3465,3463,3462,3461,3460,3459,3458,3457,3456,3455,3454,3453,3450,3449,3448,3447,3446,3445,3444,3443,3442,3441,3439,3438,3437,3436,3434,3429,3428,3425,3424,3423,3422,3421,3420,3419,3418,3417,3416,3415,3414,3413,3412,3411,3408,3406,3405,3403,3389,3388,3387,3383,3382,3381,3380,3379,3377,3376,3375,3373,3372,3371,3370,3368,3367,3366,3364,3361,3350,3335,3333,3330,3329,3328,3327,3326,3324,3323,3322,3317,3316,3314,3313,3311,3310,3309,3308,3307,3306,3299,3298,3297,3296,3289,3288,3285,3278,3269,3268,3267,3266,3265,3264,3263,3262,3259,3258,3257,3255,3254,3253,3252,3250,3249,3247,3243,3242,3230,3229,3228,3227,3226,3225,3224,3223,3222,3220,3219,3218,3217,3213,3212,3211,3191,3184,3183,3172,3165,3164,3163,3160,3159,3154,3148,3146,3144,3143,3142,3141,3138,3137,3135,3134,3133,3127,3126,3125,3124,3123,3122,3121,3120,3119,3118,3116,3110,3099,3098,3097,3096,3095,3093,3092,3089,3088,3087,3086,3078,3075,3070,3069,3064,3063,3061,3060,3059,3058,3053,3051,3049,3037,3036,3035,3025,3022,3021,3020,3019,3018,3017,3016,3015,3014,3010,3007,3005,3004,3003,3002,2998,2997,2996,2990,2981,2980,2969,2968,2967,2964,2963,2962,2958,2956,2954,2942,2941,2940,2939,2938,2935,2932,2931,2916,2899,2898,2890,2889,2888,2884,2883,2881,2880,2878,2877,2875,2872,2869,2866,2865,2864,2863,2848,2842,2829,2828,2827,2812,2800,2799,2794,2793,2788,2787,2756,2751,2750,2748,2743,2741,2739,2738,2735,2727,2721,2717,2716,2715,2710,2709,2708,2700,2699,2696,2688,2686,2684,2669,2668,2666,2665,2664,2663,2662,2661,2660,2659,2656,2655,2644,2614,2602,2600,2597,2586,2578,2567,2566,2565,2563,2562,2557,2553,2542,2531,2527,2489,2487,2484,2473,2469,2467,2462,2457,2455,2453,2447,2446,2438,2408,2396,2375,2373,2371,2364,2357,2339,2328,2317,2314,2312,2310,2308,2305,2302,2301,2297,2296,2292,2282,2273,2251,2245,2223,2220,2213,2206,2198,2172,2137,2136,2135,2121,2095,2092,2061,2058,2057,2056,2055,2054,2010,2008,2001,2000,1986,1981,1980,1976,1975,1972,1971,1955,1954,1953,1952,1930,1929,1925,1923,1915,1914,1900,1899,1897,1884,1877,1855,1852,1823,1820,1790,1648,1634,1633,1630,1568,1563,1562,1534,1524,1520,1502,1501,1481,1475,1474,1473,1472,1471,1470,1469,1468,1467,1105,1053]) ).
thf(3470,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL771-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23 % Computer : n004.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Oct 6 12:33:24 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.24 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.24/7.97 ...
% 45.24/7.97
% 45.24/7.97 No.of.Axioms: 428
% 45.24/7.97
% 45.24/7.97 Length.of.Defs: 0
% 45.24/7.97
% 45.24/7.97 Contains.Choice.Funs: false
% 45.24/7.97 ...........................................................................................................................................................................................
% 45.24/7.97
% 45.24/7.97 ********************************
% 45.24/7.97 * All subproblems solved! *
% 45.24/7.97 ********************************
% 45.24/7.97 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:428,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3469,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 45.24/7.97
% 45.24/7.97 %**** Beginning of derivation protocol ****
% 45.24/7.97 % SZS output start CNFRefutation
% See solution above
% 45.24/7.98
% 45.24/7.98 %**** End of derivation protocol ****
% 45.24/7.98 %**** no. of clauses in derivation: 3470 ****
% 45.24/7.98 %**** clause counter: 3469 ****
% 45.24/7.98
% 45.24/7.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:428,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3469,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------