%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL764-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 10:30:21 AM UTC 2026
% Result : Unsatisfiable 18.37s 3.24s
% Output : CNFRefutation 18.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 330
% Syntax : Number of formulae : 2642 (1883 unt; 0 typ; 0 def)
% Number of atoms : 11729 (4793 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 33117 (2137 ~;2845 |; 0 &;28135 @)
% ( 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 : 112 ( 109 usr; 8 con; 0-5 aty)
% Number of variables : 8987 ( 0 ^;8987 !; 0 ?;8987 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
thf(tp_c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tp_c_Lambda_Olift,type,
c_Lambda_Olift: $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_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_Oconcat__map,type,
c_List_Oconcat__map: $i > $i > $i > $i > $i ).
thf(tp_c_List_Odistinct,type,
c_List_Odistinct: $i > $i > $o ).
thf(tp_c_List_Odrop,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(tp_c_List_OdropWhile,type,
c_List_OdropWhile: $i > $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_Ohd,type,
c_List_Ohd: $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osort__key,type,
c_List_Olinorder__class_Osort__key: $i > $i > $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__all,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(tp_c_List_Olist__all2,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(tp_c_List_Olist__ex,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(tp_c_List_Olist__inter,type,
c_List_Olist__inter: $i > $i > $i > $i ).
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_Omember,type,
c_List_Omember: $i > $i > $i > $o ).
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_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__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_Osko__List__Xrev__induct__1__1,type,
c_List_Osko__List__Xrev__induct__1__1: $i > $i > $i ).
thf(tp_c_List_Osko__List__Xrev__induct__1__2,type,
c_List_Osko__List__Xrev__induct__1__2: $i > $i > $i ).
thf(tp_c_List_Osplice,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(tp_c_List_Osublist,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(tp_c_List_Otake,type,
c_List_Otake: $i > $i > $i > $i ).
thf(tp_c_List_Otl,type,
c_List_Otl: $i > $i > $i ).
thf(tp_c_Map_Omap__upds,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
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_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_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_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__Xdrop__Xinduct__1,type,
v_sko__List__Xdrop__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xdrop__Xinduct__2,type,
v_sko__List__Xdrop__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xfoldl__Xinduct__1,type,
v_sko__List__Xfoldl__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xfoldl__Xinduct__2,type,
v_sko__List__Xfoldl__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xhd__Xinduct__1,type,
v_sko__List__Xhd__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xhd__Xinduct__2,type,
v_sko__List__Xhd__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xlast__Xinduct__1,type,
v_sko__List__Xlast__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xlast__Xinduct__2,type,
v_sko__List__Xlast__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__Xlist__Xinducts__1,type,
v_sko__List__Xlist__Xinducts__1: $i > $i ).
thf(tp_v_sko__List__Xlist__Xinducts__2,type,
v_sko__List__Xlist__Xinducts__2: $i > $i ).
thf(tp_v_sko__List__Xlist__update__Xinduct__1,type,
v_sko__List__Xlist__update__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xlist__update__Xinduct__2,type,
v_sko__List__Xlist__update__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__Xlistsum__Xinduct__1,type,
v_sko__List__Xlistsum__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xlistsum__Xinduct__2,type,
v_sko__List__Xlistsum__Xinduct__2: $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__Xremdups__Xinduct__1,type,
v_sko__List__Xremdups__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xremdups__Xinduct__2,type,
v_sko__List__Xremdups__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__XremoveAll__Xinduct__1,type,
v_sko__List__XremoveAll__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__XremoveAll__Xinduct__2,type,
v_sko__List__XremoveAll__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xrev__Xinduct__1,type,
v_sko__List__Xrev__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xrev__Xinduct__2,type,
v_sko__List__Xrev__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xset__Xinduct__1,type,
v_sko__List__Xset__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xset__Xinduct__2,type,
v_sko__List__Xset__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__Xsplice__Xinduct__1,type,
v_sko__List__Xsplice__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xsplice__Xinduct__2,type,
v_sko__List__Xsplice__Xinduct__2: $i > $i ).
thf(tp_v_sko__List__XtakeWhile__Xinduct__1,type,
v_sko__List__XtakeWhile__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__XtakeWhile__Xinduct__2,type,
v_sko__List__XtakeWhile__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__Xtl__Xinduct__1,type,
v_sko__List__Xtl__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xtl__Xinduct__2,type,
v_sko__List__Xtl__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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(4,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(5,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(6,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(7,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(8,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(10,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinduct_1) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinducts_1) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Ocases_1) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Ocases_2) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinduct_2) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinduct_0) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinducts_2) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinducts_0) ).
thf(19,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(20,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(21,axiom,
! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(22,axiom,
! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',cls_listsp__infI_0) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).
thf(25,axiom,
! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(27,axiom,
! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).
thf(30,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(34,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(41,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(42,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',cls_take_Oinduct_0) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_0) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_list_Orecs_I1_J_0) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',cls_listset_Oinduct_0) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',cls_sublist__nil_0) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',cls_zip_Oinduct_0) ).
thf(58,axiom,
! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_0) ).
thf(60,axiom,
! [T_a: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_0) ).
thf(61,axiom,
! [V_P: $i,T_a: $i] :
~ ( c_List_Olist__ex @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I1_J_0) ).
thf(62,axiom,
! [T_a: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(63,axiom,
! [V_P: $i,T_a: $i] : ( c_List_Olist__all @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I1_J_0) ).
thf(64,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xfoldl__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl_Oinduct_0) ).
thf(65,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__update__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Oinduct_0) ).
thf(66,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XtakeWhile__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_0) ).
thf(67,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(68,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlast__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Oinduct_0) ).
thf(69,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(70,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(71,axiom,
! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(72,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(73,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(74,axiom,
! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(75,axiom,
! [V_P: $i,T_a: $i] :
( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).
thf(76,axiom,
! [T_a: $i,V_bs: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ T_a ) @ V_bs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(77,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XremoveAll__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Oinduct_0) ).
thf(78,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(79,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(80,axiom,
! [T_a: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(81,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(82,axiom,
! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(83,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsum__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Oinduct_0) ).
thf(84,axiom,
! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(85,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(86,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(87,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(88,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(89,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xdrop__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop_Oinduct_0) ).
thf(90,axiom,
! [T_b: $i,V_f: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Osort__key @ V_f @ ( c_List_Olist_ONil @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sort__key_Osimps_I1_J_0) ).
thf(91,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xs ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xrev__induct__1__2 @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__induct_0) ).
thf(92,axiom,
! [V_x: $i,T_a: $i] :
~ ( c_List_Omember @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I1_J_0) ).
thf(93,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xremdups__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups_Oinduct_0) ).
thf(94,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat__map_Osimps_I1_J_0) ).
thf(95,axiom,
! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(96,axiom,
! [T_a: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(97,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xhd__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Oinduct_0) ).
thf(98,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__Xinducts__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinducts_0) ).
thf(99,axiom,
! [V_ys: $i,T_b: $i,V_P: $i,T_a: $i] :
( ( V_ys
= ( c_List_Olist_ONil @ T_b ) )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).
thf(100,axiom,
! [V_xs: $i,T_a: $i,V_P: $i,T_b: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).
thf(101,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xtl__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Oinduct_0) ).
thf(102,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xset__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set_Oinduct_0) ).
thf(103,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xsplice__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Oinduct_0) ).
thf(104,axiom,
! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(105,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xrev__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Oinduct_0) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(107,axiom,
! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(108,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(109,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(111,axiom,
! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(112,axiom,
! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(113,axiom,
! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(114,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(116,axiom,
! [T_a: $i,V_P: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_1) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
thf(120,axiom,
! [V_P: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olist__all @ V_P @ V_ys @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_1) ).
thf(121,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_0) ).
thf(122,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(123,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(124,axiom,
! [T_a: $i,V_x: $i] : ( c_List_Olist__all2 @ ( c_fequal @ T_a ) @ V_x @ V_x @ T_a @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',cls_rev__filter_0) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(128,axiom,
! [V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Omember @ V_x @ V_ys @ T_a )
| ( V_x = V_y )
| ~ ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_0) ).
thf(129,axiom,
! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__map_0) ).
thf(130,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__rev_1) ).
thf(131,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__rev_0) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(134,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(137,axiom,
! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(138,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(139,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(140,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(143,axiom,
! [V_xs: $i,T_a: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(144,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(145,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
thf(150,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).
thf(151,axiom,
! [V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).
thf(152,axiom,
! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(153,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(154,axiom,
! [V_xs: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_b )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_0) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_list_Orecs_I2_J_0) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(157,axiom,
! [V_P: $i,V_n: $i,V_as: $i,T_a: $i,V_bs: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Odrop @ V_n @ V_as @ T_a ) @ ( c_List_Odrop @ V_n @ V_bs @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_as @ V_bs @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__dropI_0) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Ocases_0) ).
thf(159,axiom,
! [V_x: $i,V_ys: $i,T_a: $i] : ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_1) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(161,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(162,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(163,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(164,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).
thf(165,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).
thf(166,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
thf(167,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(168,axiom,
! [V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Omember @ V_x @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_2) ).
thf(169,axiom,
! [V_xs: $i,V_I: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__sublistI_0) ).
thf(170,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(172,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(174,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/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(176,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/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).
thf(182,axiom,
! [V_P: $i,V_x: $i,V_xa: $i,T_a: $i,V_y: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xa @ V_ys @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).
thf(183,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i,V_xa: $i,V_xb: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_xb @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_xa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).
thf(184,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).
thf(185,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).
thf(186,axiom,
! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(187,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).
thf(189,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(190,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( hAPP @ V_f @ V_x ) @ ( c_List_Oconcat__map @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat__map_Osimps_I2_J_0) ).
thf(191,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev_1) ).
thf(192,axiom,
! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev_0) ).
thf(193,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).
thf(194,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(195,axiom,
! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(196,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(197,axiom,
! [V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Odistinct @ V_ys @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(198,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_rotate__map_0) ).
thf(200,axiom,
! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(202,axiom,
! [T_b: $i,V_f: $i,V_xs: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_a @ T_b ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__sort_1) ).
thf(203,axiom,
! [T_b: $i,V_xs: $i,T_a: $i,V_f: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_a @ T_b ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__sort_0) ).
thf(204,axiom,
! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__take_0) ).
thf(205,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(206,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',cls_rev__map_0) ).
thf(208,axiom,
! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(209,axiom,
! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(210,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(211,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(212,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(213,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(214,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(215,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(216,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_empty__null_1) ).
thf(218,axiom,
! [V_P: $i,T_a: $i,T_b: $i] : ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(220,axiom,
! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(221,axiom,
! [V_P: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev1_0) ).
thf(222,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev1_1) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(224,axiom,
! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(225,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(226,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(227,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__take_0) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(229,axiom,
! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_ys @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_2) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(232,axiom,
! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(233,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(234,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/sandbox2/benchmark/theBenchmark.p',cls_map__update_0) ).
thf(235,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(236,axiom,
! [V_x: $i,V_xs: $i,T_b: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_b ) @ T_b ) @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(237,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(238,axiom,
! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinducts_3) ).
thf(240,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',cls_listsp_Oinduct_3) ).
thf(242,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
= V_xs )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(243,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
!= V_xs )
| ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(244,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).
thf(245,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(246,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(247,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__drop_0) ).
thf(248,axiom,
! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(249,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/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(250,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(251,axiom,
! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(252,axiom,
! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(253,axiom,
! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(254,axiom,
! [V_P: $i,V_x: $i,V_y: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).
thf(255,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/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(258,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(260,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__filter_0) ).
thf(261,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
thf(262,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
thf(263,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(264,axiom,
! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(265,axiom,
! [V_P: $i,V_a: $i,V_c: $i,T_a: $i,V_b: $i,V_d: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Oappend @ V_a @ V_c @ T_a ) @ ( c_List_Oappend @ V_b @ V_d @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_c @ V_d @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_a @ V_b @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).
thf(266,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/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(268,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/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(270,axiom,
! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(271,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(272,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__drop_0) ).
thf(273,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(274,axiom,
! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(275,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs = V_ys )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ T_a ) @ V_xs @ V_ys @ T_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).
thf(276,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(278,axiom,
! [V_P: $i,V_n: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__takeI_0) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',cls_remdups__filter_0) ).
thf(280,axiom,
! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__map_0) ).
thf(281,axiom,
! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__drop_0) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(283,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(284,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(285,axiom,
! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(286,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__tl_0) ).
thf(287,axiom,
! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__sort__key_0) ).
thf(288,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(289,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xs ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ V_P @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ V_P @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__induct_1) ).
thf(290,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
thf(291,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ V_P ) @ ( v_sko__List__Xtl__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Oinduct_1) ).
thf(292,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlast__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Oinduct_1) ).
thf(293,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Oinduct_1) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).
thf(295,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ V_P ) @ ( v_sko__List__Xsplice__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Oinduct_1) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).
thf(297,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/sandbox2/benchmark/theBenchmark.p',cls_listset_Oinduct_1) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',cls_zip_Oinduct_1) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_1) ).
thf(300,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ V_P ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_1) ).
thf(301,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ V_P ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Oinduct_1) ).
thf(302,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ V_P ) @ ( v_sko__List__Xremdups__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups_Oinduct_1) ).
thf(303,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__update__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Oinduct_1) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).
thf(305,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__Xinducts__1 @ V_P ) @ ( v_sko__List__Xlist__Xinducts__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinducts_1) ).
thf(306,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/sandbox2/benchmark/theBenchmark.p',cls_map_Oinduct_1) ).
thf(307,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ V_P ) @ ( v_sko__List__Xset__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set_Oinduct_1) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_take_Oinduct_1) ).
thf(309,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ V_P ) @ ( v_sko__List__Xhd__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Oinduct_1) ).
thf(310,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ohd @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a ) ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).
thf(311,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Suc_0) ).
thf(312,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(313,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(314,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',cls_concat_Oinduct_1) ).
thf(316,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ V_P ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl_Oinduct_1) ).
thf(317,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ V_P ) @ ( v_sko__List__Xrev__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Oinduct_1) ).
thf(318,axiom,
! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ V_P ) @ ( v_sko__List__Xdrop__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop_Oinduct_1) ).
thf(319,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/sandbox2/benchmark/theBenchmark.p',cls_rotate__Suc_0) ).
thf(320,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(321,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/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(322,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(323,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(324,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
thf(325,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(327,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__tl_0) ).
thf(328,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc_0) ).
thf(329,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(330,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[329]) ).
thf(331,negated_conjecture,
~ ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(332,plain,
$false = $false,
inference(unfold_def,[status(thm)],[330]) ).
thf(333,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(334,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(335,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(336,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(337,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(338,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(339,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(340,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)],[8]) ).
thf(341,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)],[9]) ).
thf(342,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)],[10]) ).
thf(343,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)],[11]) ).
thf(344,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)],[12]) ).
thf(345,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)],[13]) ).
thf(346,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)],[14]) ).
thf(347,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)],[15]) ).
thf(348,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)],[16]) ).
thf(349,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)],[17]) ).
thf(350,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)],[18]) ).
thf(351,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)],[19]) ).
thf(352,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)],[20]) ).
thf(353,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)],[21]) ).
thf(354,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)],[22]) ).
thf(355,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)],[23]) ).
thf(356,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)],[24]) ).
thf(357,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)],[25]) ).
thf(358,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)],[26]) ).
thf(359,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)],[27]) ).
thf(360,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)],[28]) ).
thf(361,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)],[29]) ).
thf(362,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)],[30]) ).
thf(363,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)],[31]) ).
thf(364,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)],[32]) ).
thf(365,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)],[33]) ).
thf(366,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)],[34]) ).
thf(367,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)],[35]) ).
thf(368,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)],[36]) ).
thf(369,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)],[37]) ).
thf(370,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)],[38]) ).
thf(371,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)],[39]) ).
thf(372,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)],[40]) ).
thf(373,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)],[41]) ).
thf(374,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)],[42]) ).
thf(375,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)],[43]) ).
thf(376,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)],[44]) ).
thf(377,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)],[45]) ).
thf(378,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)],[46]) ).
thf(379,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)],[47]) ).
thf(380,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)],[48]) ).
thf(381,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)],[49]) ).
thf(382,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)],[50]) ).
thf(383,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)],[51]) ).
thf(384,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)],[52]) ).
thf(385,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)],[53]) ).
thf(386,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)],[54]) ).
thf(387,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)],[55]) ).
thf(388,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)],[56]) ).
thf(389,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)],[57]) ).
thf(390,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)],[58]) ).
thf(391,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)],[59]) ).
thf(392,plain,
( ( ! [T_a: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(393,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)],[61]) ).
thf(394,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)],[62]) ).
thf(395,plain,
( ( ! [V_P: $i,T_a: $i] : ( c_List_Olist__all @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(396,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xfoldl__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(397,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__update__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(398,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XtakeWhile__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(399,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(400,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlast__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(401,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)],[69]) ).
thf(402,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)],[70]) ).
thf(403,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)],[71]) ).
thf(404,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)],[72]) ).
thf(405,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)],[73]) ).
thf(406,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)],[74]) ).
thf(407,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(408,plain,
( ( ! [T_a: $i,V_bs: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ T_a ) @ V_bs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(409,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XremoveAll__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(410,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)],[78]) ).
thf(411,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(412,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)],[80]) ).
thf(413,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)],[81]) ).
thf(414,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)],[82]) ).
thf(415,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsum__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(416,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)],[84]) ).
thf(417,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)],[85]) ).
thf(418,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)],[86]) ).
thf(419,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)],[87]) ).
thf(420,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)],[88]) ).
thf(421,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xdrop__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(422,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Osort__key @ V_f @ ( c_List_Olist_ONil @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(423,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xs ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xrev__induct__1__2 @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(424,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( c_List_Omember @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(425,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xremdups__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(426,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(427,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)],[95]) ).
thf(428,plain,
( ( ! [T_a: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(429,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xhd__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(430,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__Xinducts__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(431,plain,
( ( ! [V_ys: $i,T_b: $i,V_P: $i,T_a: $i] :
( ( V_ys
= ( c_List_Olist_ONil @ T_b ) )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(432,plain,
( ( ! [V_xs: $i,T_a: $i,V_P: $i,T_b: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(433,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xtl__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(434,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xset__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(435,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xsplice__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(436,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)],[104]) ).
thf(437,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xrev__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(438,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)],[106]) ).
thf(439,plain,
( ( ! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(440,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(441,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(442,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)],[110]) ).
thf(443,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)],[111]) ).
thf(444,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)],[112]) ).
thf(445,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)],[113]) ).
thf(446,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)],[114]) ).
thf(447,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)],[115]) ).
thf(448,plain,
( ( ! [T_a: $i,V_P: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(449,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)],[117]) ).
thf(450,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)],[118]) ).
thf(451,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)],[119]) ).
thf(452,plain,
( ( ! [V_P: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olist__all @ V_P @ V_ys @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(453,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(454,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)],[122]) ).
thf(455,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)],[123]) ).
thf(456,plain,
( ( ! [T_a: $i,V_x: $i] : ( c_List_Olist__all2 @ ( c_fequal @ T_a ) @ V_x @ V_x @ T_a @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(457,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)],[125]) ).
thf(458,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)],[126]) ).
thf(459,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)],[127]) ).
thf(460,plain,
( ( ! [V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Omember @ V_x @ V_ys @ T_a )
| ( V_x = V_y )
| ~ ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(461,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(462,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(463,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(464,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)],[132]) ).
thf(465,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)],[133]) ).
thf(466,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(467,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)],[135]) ).
thf(468,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)],[136]) ).
thf(469,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)],[137]) ).
thf(470,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)],[138]) ).
thf(471,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)],[139]) ).
thf(472,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)],[140]) ).
thf(473,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)],[141]) ).
thf(474,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)],[142]) ).
thf(475,plain,
( ( ! [V_xs: $i,T_a: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(476,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)],[144]) ).
thf(477,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)],[145]) ).
thf(478,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)],[146]) ).
thf(479,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)],[147]) ).
thf(480,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)],[148]) ).
thf(481,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)],[149]) ).
thf(482,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(483,plain,
( ( ! [V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(484,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)],[152]) ).
thf(485,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)],[153]) ).
thf(486,plain,
( ( ! [V_xs: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_b )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(487,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)],[155]) ).
thf(488,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)],[156]) ).
thf(489,plain,
( ( ! [V_P: $i,V_n: $i,V_as: $i,T_a: $i,V_bs: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Odrop @ V_n @ V_as @ T_a ) @ ( c_List_Odrop @ V_n @ V_bs @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_as @ V_bs @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(490,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)],[158]) ).
thf(491,plain,
( ( ! [V_x: $i,V_ys: $i,T_a: $i] : ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(492,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)],[160]) ).
thf(493,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(494,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(495,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)],[163]) ).
thf(496,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(497,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(498,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(499,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(500,plain,
( ( ! [V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Omember @ V_x @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(501,plain,
( ( ! [V_xs: $i,V_I: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(502,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(503,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)],[171]) ).
thf(504,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)],[172]) ).
thf(505,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)],[173]) ).
thf(506,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)],[174]) ).
thf(507,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)],[175]) ).
thf(508,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)],[176]) ).
thf(509,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)],[177]) ).
thf(510,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)],[178]) ).
thf(511,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)],[179]) ).
thf(512,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)],[180]) ).
thf(513,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)],[181]) ).
thf(514,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i,T_a: $i,V_y: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xa @ V_ys @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(515,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i,V_xa: $i,V_xb: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_xb @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_xa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(516,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(517,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(518,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)],[186]) ).
thf(519,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)],[187]) ).
thf(520,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)],[188]) ).
thf(521,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)],[189]) ).
thf(522,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( hAPP @ V_f @ V_x ) @ ( c_List_Oconcat__map @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(523,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(524,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(525,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(526,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)],[194]) ).
thf(527,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)],[195]) ).
thf(528,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)],[196]) ).
thf(529,plain,
( ( ! [V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Odistinct @ V_ys @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(530,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(531,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)],[199]) ).
thf(532,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(533,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)],[201]) ).
thf(534,plain,
( ( ! [T_b: $i,V_f: $i,V_xs: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_a @ T_b ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(535,plain,
( ( ! [T_b: $i,V_xs: $i,T_a: $i,V_f: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(536,plain,
( ( ! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(537,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)],[205]) ).
thf(538,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)],[206]) ).
thf(539,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)],[207]) ).
thf(540,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(541,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(542,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)],[210]) ).
thf(543,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)],[211]) ).
thf(544,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)],[212]) ).
thf(545,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)],[213]) ).
thf(546,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)],[214]) ).
thf(547,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)],[215]) ).
thf(548,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)],[216]) ).
thf(549,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)],[217]) ).
thf(550,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i] : ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(551,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)],[219]) ).
thf(552,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)],[220]) ).
thf(553,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(554,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(555,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)],[223]) ).
thf(556,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(557,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)],[225]) ).
thf(558,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)],[226]) ).
thf(559,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(560,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)],[228]) ).
thf(561,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_ys @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(562,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)],[230]) ).
thf(563,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)],[231]) ).
thf(564,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)],[232]) ).
thf(565,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)],[233]) ).
thf(566,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)],[234]) ).
thf(567,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)],[235]) ).
thf(568,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)],[236]) ).
thf(569,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)],[237]) ).
thf(570,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)],[238]) ).
thf(571,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)],[239]) ).
thf(572,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(573,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)],[241]) ).
thf(574,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
= V_xs )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(575,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
!= V_xs )
| ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(576,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(577,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(578,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(579,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(580,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)],[248]) ).
thf(581,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)],[249]) ).
thf(582,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(583,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)],[251]) ).
thf(584,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)],[252]) ).
thf(585,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)],[253]) ).
thf(586,plain,
( ( ! [V_P: $i,V_x: $i,V_y: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(587,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)],[255]) ).
thf(588,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)],[256]) ).
thf(589,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)],[257]) ).
thf(590,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)],[258]) ).
thf(591,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)],[259]) ).
thf(592,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(593,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(594,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(595,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)],[263]) ).
thf(596,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)],[264]) ).
thf(597,plain,
( ( ! [V_P: $i,V_a: $i,V_c: $i,T_a: $i,V_b: $i,V_d: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Oappend @ V_a @ V_c @ T_a ) @ ( c_List_Oappend @ V_b @ V_d @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_c @ V_d @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_a @ V_b @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(598,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)],[266]) ).
thf(599,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)],[267]) ).
thf(600,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)],[268]) ).
thf(601,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)],[269]) ).
thf(602,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)],[270]) ).
thf(603,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)],[271]) ).
thf(604,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(605,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)],[273]) ).
thf(606,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)],[274]) ).
thf(607,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs = V_ys )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ T_a ) @ V_xs @ V_ys @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(608,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)],[276]) ).
thf(609,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)],[277]) ).
thf(610,plain,
( ( ! [V_P: $i,V_n: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(611,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)],[279]) ).
thf(612,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(613,plain,
( ( ! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(614,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)],[282]) ).
thf(615,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)],[283]) ).
thf(616,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)],[284]) ).
thf(617,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)],[285]) ).
thf(618,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(619,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(620,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(621,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xs ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ V_P @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ V_P @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(622,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(623,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ V_P ) @ ( v_sko__List__Xtl__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(624,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlast__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(625,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(626,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)],[294]) ).
thf(627,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ V_P ) @ ( v_sko__List__Xsplice__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(628,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)],[296]) ).
thf(629,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)],[297]) ).
thf(630,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)],[298]) ).
thf(631,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)],[299]) ).
thf(632,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ V_P ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(633,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ V_P ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(634,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ V_P ) @ ( v_sko__List__Xremdups__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(635,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__update__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(636,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)],[304]) ).
thf(637,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__Xinducts__1 @ V_P ) @ ( v_sko__List__Xlist__Xinducts__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(638,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)],[306]) ).
thf(639,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ V_P ) @ ( v_sko__List__Xset__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(640,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)],[308]) ).
thf(641,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ V_P ) @ ( v_sko__List__Xhd__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(642,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ohd @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a ) ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(643,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(644,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(645,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(646,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(647,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)],[315]) ).
thf(648,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ V_P ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(649,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ V_P ) @ ( v_sko__List__Xrev__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(650,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ V_P ) @ ( v_sko__List__Xdrop__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(651,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)],[319]) ).
thf(652,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)],[320]) ).
thf(653,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)],[321]) ).
thf(654,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(655,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(656,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(657,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(658,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)],[326]) ).
thf(659,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(660,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(661,plain,
( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(662,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[332]) ).
thf(663,plain,
( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(664,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(665,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(666,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)],[658]) ).
thf(667,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(668,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(669,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(670,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(671,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)],[653]) ).
thf(672,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(673,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)],[651]) ).
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__Xdrop__Xinduct__1 @ V_P ) @ ( v_sko__List__Xdrop__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
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__Xrev__Xinduct__1 @ V_P ) @ ( v_sko__List__Xrev__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
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__Xfoldl__Xinduct__1 @ V_P ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
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__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)],[647]) ).
thf(678,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(679,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(680,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(681,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(682,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ohd @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a ) ) )
| ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(683,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ V_P ) @ ( v_sko__List__Xhd__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(684,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)],[640]) ).
thf(685,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ V_P ) @ ( v_sko__List__Xset__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(686,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)],[638]) ).
thf(687,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__Xinducts__1 @ V_P ) @ ( v_sko__List__Xlist__Xinducts__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(688,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)],[636]) ).
thf(689,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__update__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(690,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ V_P ) @ ( v_sko__List__Xremdups__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(691,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ V_P ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(692,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ V_P ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(693,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)],[631]) ).
thf(694,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)],[630]) ).
thf(695,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)],[629]) ).
thf(696,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)],[628]) ).
thf(697,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ V_P ) @ ( v_sko__List__Xsplice__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(698,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)],[626]) ).
thf(699,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(700,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ V_P ) @ ( v_sko__List__Xlast__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(701,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ V_P ) @ ( v_sko__List__Xtl__Xinduct__2 @ V_P ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(702,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_ys @ T_a ) @ ( c_List_Osplice @ V_xs @ ( c_List_Otl @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(703,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xs ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ V_P @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ V_P @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(704,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orotate1 @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(705,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(706,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a )
= ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(707,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)],[617]) ).
thf(708,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(709,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)],[615]) ).
thf(710,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)],[614]) ).
thf(711,plain,
( ( ! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(712,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(713,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)],[611]) ).
thf(714,plain,
( ( ! [V_P: $i,V_n: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ V_n @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(715,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)],[609]) ).
thf(716,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)],[608]) ).
thf(717,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs = V_ys )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ T_a ) @ V_xs @ V_ys @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(718,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)],[606]) ).
thf(719,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(720,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Otl @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(721,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)],[603]) ).
thf(722,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)],[602]) ).
thf(723,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)],[601]) ).
thf(724,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(copy,[status(thm)],[600]) ).
thf(725,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(copy,[status(thm)],[599]) ).
thf(726,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(copy,[status(thm)],[598]) ).
thf(727,plain,
( ( ! [V_P: $i,V_a: $i,V_c: $i,T_a: $i,V_b: $i,V_d: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Oappend @ V_a @ V_c @ T_a ) @ ( c_List_Oappend @ V_b @ V_d @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_c @ V_d @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_a @ V_b @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(728,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)],[596]) ).
thf(729,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)],[595]) ).
thf(730,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(731,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(732,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(733,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)],[591]) ).
thf(734,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)],[590]) ).
thf(735,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)],[589]) ).
thf(736,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)],[588]) ).
thf(737,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)],[587]) ).
thf(738,plain,
( ( ! [V_P: $i,V_x: $i,V_y: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(739,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)],[585]) ).
thf(740,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)],[584]) ).
thf(741,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(742,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(743,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(copy,[status(thm)],[581]) ).
thf(744,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)],[580]) ).
thf(745,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(746,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(747,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(748,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(749,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
!= V_xs )
| ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(750,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oremdups @ V_xs @ T_a )
= V_xs )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(751,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(copy,[status(thm)],[573]) ).
thf(752,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(753,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(copy,[status(thm)],[571]) ).
thf(754,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)],[570]) ).
thf(755,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)],[569]) ).
thf(756,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)],[568]) ).
thf(757,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)],[567]) ).
thf(758,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)],[566]) ).
thf(759,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)],[565]) ).
thf(760,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(761,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(copy,[status(thm)],[563]) ).
thf(762,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(copy,[status(thm)],[562]) ).
thf(763,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_ys @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(764,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(copy,[status(thm)],[560]) ).
thf(765,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(766,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)],[558]) ).
thf(767,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)],[557]) ).
thf(768,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(769,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)],[555]) ).
thf(770,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(771,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(772,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)],[552]) ).
thf(773,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)],[551]) ).
thf(774,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i] : ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(775,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)],[549]) ).
thf(776,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)],[548]) ).
thf(777,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)],[547]) ).
thf(778,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)],[546]) ).
thf(779,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)],[545]) ).
thf(780,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)],[544]) ).
thf(781,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)],[543]) ).
thf(782,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)],[542]) ).
thf(783,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(784,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(785,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)],[539]) ).
thf(786,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)],[538]) ).
thf(787,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)],[537]) ).
thf(788,plain,
( ( ! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(789,plain,
( ( ! [T_b: $i,V_xs: $i,T_a: $i,V_f: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(790,plain,
( ( ! [T_b: $i,V_f: $i,V_xs: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ V_f @ V_xs @ T_a @ T_b ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(791,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)],[533]) ).
thf(792,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(793,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)],[531]) ).
thf(794,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(795,plain,
( ( ! [V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Odistinct @ V_ys @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(796,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)],[528]) ).
thf(797,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)],[527]) ).
thf(798,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)],[526]) ).
thf(799,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(800,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(801,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Orev @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(802,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( hAPP @ V_f @ V_x ) @ ( c_List_Oconcat__map @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(803,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)],[521]) ).
thf(804,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)],[520]) ).
thf(805,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(806,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)],[518]) ).
thf(807,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_OdropWhile @ V_P @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(808,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_ys @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(809,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i,V_xa: $i,V_xb: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ V_xb @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_xa ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(810,plain,
( ( ! [V_P: $i,V_x: $i,V_xa: $i,T_a: $i,V_y: $i,V_ys: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_xa @ V_ys @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(811,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)],[513]) ).
thf(812,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(copy,[status(thm)],[512]) ).
thf(813,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)],[511]) ).
thf(814,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(copy,[status(thm)],[510]) ).
thf(815,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(copy,[status(thm)],[509]) ).
thf(816,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(copy,[status(thm)],[508]) ).
thf(817,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(copy,[status(thm)],[507]) ).
thf(818,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)],[506]) ).
thf(819,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)],[505]) ).
thf(820,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)],[504]) ).
thf(821,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)],[503]) ).
thf(822,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(823,plain,
( ( ! [V_xs: $i,V_I: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(824,plain,
( ( ! [V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Omember @ V_x @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(825,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otl @ V_xs @ T_a ) @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(826,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(827,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(828,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(829,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(830,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(831,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(832,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)],[492]) ).
thf(833,plain,
( ( ! [V_x: $i,V_ys: $i,T_a: $i] : ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(834,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)],[490]) ).
thf(835,plain,
( ( ! [V_P: $i,V_n: $i,V_as: $i,T_a: $i,V_bs: $i,T_b: $i] :
( ( c_List_Olist__all2 @ V_P @ ( c_List_Odrop @ V_n @ V_as @ T_a ) @ ( c_List_Odrop @ V_n @ V_bs @ T_b ) @ T_a @ T_b )
| ~ ( c_List_Olist__all2 @ V_P @ V_as @ V_bs @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(836,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)],[488]) ).
thf(837,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)],[487]) ).
thf(838,plain,
( ( ! [V_xs: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_List_Odistinct @ V_xs @ T_b )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(839,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)],[485]) ).
thf(840,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(841,plain,
( ( ! [V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Odistinct @ V_xs @ T_a )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(842,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Odistinct @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(843,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)],[481]) ).
thf(844,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(copy,[status(thm)],[480]) ).
thf(845,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(copy,[status(thm)],[479]) ).
thf(846,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)],[478]) ).
thf(847,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)],[477]) ).
thf(848,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)],[476]) ).
thf(849,plain,
( ( ! [V_xs: $i,T_a: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ V_xs @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(850,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(copy,[status(thm)],[474]) ).
thf(851,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)],[473]) ).
thf(852,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)],[472]) ).
thf(853,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)],[471]) ).
thf(854,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(855,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)],[469]) ).
thf(856,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(copy,[status(thm)],[468]) ).
thf(857,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(copy,[status(thm)],[467]) ).
thf(858,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(859,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)],[465]) ).
thf(860,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(copy,[status(thm)],[464]) ).
thf(861,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(862,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist__all @ V_P @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olist__all @ V_P @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(863,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(864,plain,
( ( ! [V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Omember @ V_x @ V_ys @ T_a )
| ( V_x = V_y )
| ~ ( c_List_Omember @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(865,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)],[459]) ).
thf(866,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)],[458]) ).
thf(867,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)],[457]) ).
thf(868,plain,
( ( ! [T_a: $i,V_x: $i] : ( c_List_Olist__all2 @ ( c_fequal @ T_a ) @ V_x @ V_x @ T_a @ T_a ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(869,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)],[455]) ).
thf(870,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)],[454]) ).
thf(871,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olist__all @ V_P @ V_xs @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(872,plain,
( ( ! [V_P: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olist__all @ V_P @ V_ys @ T_a )
| ~ ( c_List_Olist__all @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(873,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)],[451]) ).
thf(874,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)],[450]) ).
thf(875,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)],[449]) ).
thf(876,plain,
( ( ! [T_a: $i,V_P: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(877,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)],[447]) ).
thf(878,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)],[446]) ).
thf(879,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)],[445]) ).
thf(880,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)],[444]) ).
thf(881,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)],[443]) ).
thf(882,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(copy,[status(thm)],[442]) ).
thf(883,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(884,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(885,plain,
( ( ! [T_a: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(886,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)],[438]) ).
thf(887,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xrev__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(888,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)],[436]) ).
thf(889,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xsplice__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(890,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xset__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(891,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xtl__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(892,plain,
( ( ! [V_xs: $i,T_a: $i,V_P: $i,T_b: $i] :
( ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_List_Olist__all2 @ V_P @ V_xs @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(893,plain,
( ( ! [V_ys: $i,T_b: $i,V_P: $i,T_a: $i] :
( ( V_ys
= ( c_List_Olist_ONil @ T_b ) )
| ~ ( c_List_Olist__all2 @ V_P @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(894,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__Xinducts__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(895,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xhd__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(896,plain,
( ( ! [T_a: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(897,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)],[427]) ).
thf(898,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Oconcat__map @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(899,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xremdups__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(900,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( c_List_Omember @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(901,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xs ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__List__Xrev__induct__1__2 @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(902,plain,
( ( ! [T_b: $i,V_f: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Osort__key @ V_f @ ( c_List_Olist_ONil @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(903,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xdrop__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(904,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)],[420]) ).
thf(905,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)],[419]) ).
thf(906,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)],[418]) ).
thf(907,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)],[417]) ).
thf(908,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)],[416]) ).
thf(909,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlistsum__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(910,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)],[414]) ).
thf(911,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)],[413]) ).
thf(912,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)],[412]) ).
thf(913,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(914,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)],[410]) ).
thf(915,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XremoveAll__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(916,plain,
( ( ! [T_a: $i,V_bs: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ T_a ) @ V_bs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(917,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_OdropWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(918,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)],[406]) ).
thf(919,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)],[405]) ).
thf(920,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)],[404]) ).
thf(921,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)],[403]) ).
thf(922,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)],[402]) ).
thf(923,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)],[401]) ).
thf(924,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlast__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(925,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(926,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__XtakeWhile__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(927,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xlist__update__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(928,plain,
( ( ! [V_P: $i,V_list: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_list ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xfoldl__Xinduct__2 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(929,plain,
( ( ! [V_P: $i,T_a: $i] : ( c_List_Olist__all @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(930,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)],[394]) ).
thf(931,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)],[393]) ).
thf(932,plain,
( ( ! [T_a: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(933,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)],[391]) ).
thf(934,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)],[390]) ).
thf(935,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)],[389]) ).
thf(936,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)],[388]) ).
thf(937,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)],[387]) ).
thf(938,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)],[386]) ).
thf(939,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)],[385]) ).
thf(940,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)],[384]) ).
thf(941,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)],[383]) ).
thf(942,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)],[382]) ).
thf(943,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)],[381]) ).
thf(944,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)],[380]) ).
thf(945,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)],[379]) ).
thf(946,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)],[378]) ).
thf(947,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)],[377]) ).
thf(948,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)],[376]) ).
thf(949,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)],[375]) ).
thf(950,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)],[374]) ).
thf(951,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)],[373]) ).
thf(952,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)],[372]) ).
thf(953,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)],[371]) ).
thf(954,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)],[370]) ).
thf(955,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)],[369]) ).
thf(956,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)],[368]) ).
thf(957,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)],[367]) ).
thf(958,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)],[366]) ).
thf(959,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)],[365]) ).
thf(960,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)],[364]) ).
thf(961,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)],[363]) ).
thf(962,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)],[362]) ).
thf(963,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)],[361]) ).
thf(964,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)],[360]) ).
thf(965,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)],[359]) ).
thf(966,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)],[358]) ).
thf(967,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)],[357]) ).
thf(968,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)],[356]) ).
thf(969,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)],[355]) ).
thf(970,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(971,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(972,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)],[352]) ).
thf(973,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)],[351]) ).
thf(974,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(copy,[status(thm)],[350]) ).
thf(975,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(copy,[status(thm)],[349]) ).
thf(976,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(copy,[status(thm)],[348]) ).
thf(977,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(copy,[status(thm)],[347]) ).
thf(978,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)],[346]) ).
thf(979,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)],[345]) ).
thf(980,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(copy,[status(thm)],[344]) ).
thf(981,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(copy,[status(thm)],[343]) ).
thf(982,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)],[342]) ).
thf(983,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)],[341]) ).
thf(984,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)],[340]) ).
thf(985,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(986,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(987,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(988,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(989,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(990,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(991,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(992,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[662]) ).
thf(993,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ SX3 @ SX1 ) )
| ( SX0
= ( c_List_Oappend @ ( c_List_Orev @ SX3 @ SX1 ) @ ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(994,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX2
= ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(995,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(996,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(997,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 )
!= ( c_List_Oappend @ SX3 @ ( c_List_Olist_OCons @ SX4 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[870]) ).
thf(998,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(999,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 )
!= ( c_List_Oappend @ SX3 @ ( c_List_Olist_OCons @ SX4 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[869]) ).
thf(1000,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orotate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[886]) ).
thf(1001,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Olist_OCons @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(1002,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1003,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Oremdups @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[782]) ).
thf(1004,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= SX1 )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(1005,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(1006,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(1007,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Ofilter @ SX3 @ SX4 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[715]) ).
thf(1008,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[853]) ).
thf(1009,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oappend @ SX1 @ SX2 @ SX0 ) )
| ( SX2
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(1010,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[754]) ).
thf(1011,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oremdups @ SX1 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[944]) ).
thf(1012,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[786]) ).
thf(1013,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Oappend @ SX1 @ SX0 @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[778]) ).
thf(1014,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[820]) ).
thf(1015,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Omap @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Olist_ONil @ SX3 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[773]) ).
thf(1016,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[852]) ).
thf(1017,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Orev @ SX1 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[888]) ).
thf(1018,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[839]) ).
thf(1019,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Olist__update @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Olist_ONil @ SX3 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[966]) ).
thf(1020,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Omap @ SX1 @ SX2 @ SX3 @ SX0 ) )
| ( SX2
= ( c_List_Olist_ONil @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[914]) ).
thf(1021,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Oremdups @ SX0 @ SX1 )
!= SX0 )
| ( c_List_Odistinct @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[749]) ).
thf(1022,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[806]) ).
thf(1023,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oappend @ SX1 @ SX2 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(1024,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[958]) ).
thf(1025,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(1026,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_OdropWhile @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[807]) ).
thf(1027,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(1028,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(1029,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX0 @ SX3 @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(1030,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orotate1 @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[923]) ).
thf(1031,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= SX0 )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(1032,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Ofilter @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[791]) ).
thf(1033,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Oappend @ SX0 @ SX1 @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(1034,plain,
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(1035,plain,
! [SV1: $i] :
( ( ! [SY1039: $i,SY1040: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV1 ) @ SY1039 @ SY1040 )
= ( c_List_Odrop @ SV1 @ ( c_List_Otl @ SY1039 @ SY1040 ) @ SY1040 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(1036,plain,
! [SV2: $i] :
( ( ! [SY1041: $i,SY1042: $i] :
( ( c_List_Otake @ SV2 @ ( c_List_Otl @ SY1041 @ SY1042 ) @ SY1042 )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ SV2 ) @ SY1041 @ SY1042 ) @ SY1042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(1037,plain,
! [SV3: $i] :
( ( ! [SY1043: $i,SY1044: $i,SY1045: $i,SY1046: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV3 @ SY1043 @ SY1044 ) @ ( c_Suc @ SY1045 ) @ SY1046 @ SY1044 )
= ( c_List_Olist_OCons @ SV3 @ ( c_List_Olist__update @ SY1043 @ SY1045 @ SY1046 @ SY1044 ) @ SY1044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(1038,plain,
! [SV4: $i] :
( ( ! [SY1047: $i,SY1048: $i,SY1049: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV4 ) @ ( c_List_Olist_OCons @ SY1047 @ SY1048 @ SY1049 ) @ SY1049 )
= ( c_List_Odrop @ SV4 @ SY1048 @ SY1049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(1039,plain,
! [SV5: $i] :
( ( ! [SY1050: $i,SY1051: $i,SY1052: $i] :
( ( c_List_Otake @ ( c_Suc @ SV5 ) @ ( c_List_Olist_OCons @ SY1050 @ SY1051 @ SY1052 ) @ SY1052 )
= ( c_List_Olist_OCons @ SY1050 @ ( c_List_Otake @ SV5 @ SY1051 @ SY1052 ) @ SY1052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(1040,plain,
! [SV6: $i] :
( ( ! [SY1053: $i,SY1054: $i] :
( ( c_List_Orotate @ ( c_Suc @ SV6 ) @ SY1053 @ SY1054 )
= ( c_List_Orotate1 @ ( c_List_Orotate @ SV6 @ SY1053 @ SY1054 ) @ SY1054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(1041,plain,
! [SV7: $i] :
( ( ! [SY1055: $i] :
( ( hBOOL @ ( hAPP @ SV7 @ SY1055 ) )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ SV7 ) @ ( v_sko__List__Xdrop__Xinduct__2 @ SV7 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(1042,plain,
! [SV8: $i] :
( ( ! [SY1056: $i] :
( ( hBOOL @ ( hAPP @ SV8 @ SY1056 ) )
| ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ SV8 ) @ ( v_sko__List__Xrev__Xinduct__2 @ SV8 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(1043,plain,
! [SV9: $i] :
( ( ! [SY1057: $i] :
( ( hBOOL @ ( hAPP @ SV9 @ SY1057 ) )
| ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ SV9 ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV9 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(1044,plain,
! [SV10: $i] :
( ( ! [SY1058: $i] :
( ( hBOOL @ ( hAPP @ SV10 @ SY1058 ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV10 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV10 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(1045,plain,
! [SV11: $i] :
( ( ! [SY1059: $i,SY1060: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV11 @ SY1059 @ SY1060 ) @ SY1060 )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(1046,plain,
! [SV12: $i] :
( ( ! [SY1061: $i,SY1062: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ SV12 @ SY1061 @ SY1062 ) @ SY1062 )
= ( c_List_Ohd @ SV12 @ SY1062 ) )
| ( SV12
= ( c_List_Olist_ONil @ SY1062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(1047,plain,
! [SV13: $i] :
( ( ! [SY1063: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ SV13 ) @ SY1063 @ SV13 ) @ SV13 )
= ( c_List_Ohd @ SY1063 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(1048,plain,
! [SV14: $i] :
( ( ! [SY1064: $i,SY1065: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV14 ) @ SY1064 @ SY1065 )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ SY1064 @ SY1065 ) @ ( c_List_Otake @ SV14 @ ( c_List_Otl @ SY1064 @ SY1065 ) @ SY1065 ) @ SY1065 ) )
| ( SY1064
= ( c_List_Olist_ONil @ SY1065 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(1049,plain,
! [SV15: $i] :
( ( ! [SY1066: $i,SY1067: $i] :
( ~ ( hBOOL @ ( hAPP @ SV15 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV15 @ SY1066 @ SY1067 ) @ SY1067 ) ) )
| ( ( c_List_OdropWhile @ SV15 @ SY1066 @ SY1067 )
= ( c_List_Olist_ONil @ SY1067 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(1050,plain,
! [SV16: $i] :
( ( ! [SY1068: $i] :
( ( hBOOL @ ( hAPP @ SV16 @ SY1068 ) )
| ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ SV16 ) @ ( v_sko__List__Xhd__Xinduct__2 @ SV16 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(1051,plain,
! [SV17: $i] :
( ( ! [SY1069: $i] :
( ( hBOOL @ ( hAPP @ SV17 @ SY1069 ) )
| ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV17 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV17 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(1052,plain,
! [SV18: $i] :
( ( ! [SY1070: $i] :
( ( hBOOL @ ( hAPP @ SV18 @ SY1070 ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ SV18 ) @ ( v_sko__List__Xset__Xinduct__2 @ SV18 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(1053,plain,
! [SV19: $i] :
( ( ! [SY1071: $i] :
( ( hBOOL @ ( hAPP @ SV19 @ SY1071 ) )
| ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV19 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV19 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(1054,plain,
! [SV20: $i] :
( ( ! [SY1072: $i] :
( ( hBOOL @ ( hAPP @ SV20 @ SY1072 ) )
| ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinducts__1 @ SV20 ) @ ( v_sko__List__Xlist__Xinducts__2 @ SV20 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(1055,plain,
! [SV21: $i] :
( ( ! [SY1073: $i] :
( ( hBOOL @ ( hAPP @ SV21 @ SY1073 ) )
| ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV21 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV21 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(1056,plain,
! [SV22: $i] :
( ( ! [SY1074: $i] :
( ( hBOOL @ ( hAPP @ SV22 @ SY1074 ) )
| ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ SV22 ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV22 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(1057,plain,
! [SV23: $i] :
( ( ! [SY1075: $i] :
( ( hBOOL @ ( hAPP @ SV23 @ SY1075 ) )
| ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ SV23 ) @ ( v_sko__List__Xremdups__Xinduct__2 @ SV23 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(1058,plain,
! [SV24: $i] :
( ( ! [SY1076: $i] :
( ( hBOOL @ ( hAPP @ SV24 @ SY1076 ) )
| ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ SV24 ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV24 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(1059,plain,
! [SV25: $i] :
( ( ! [SY1077: $i] :
( ( hBOOL @ ( hAPP @ SV25 @ SY1077 ) )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ SV25 ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV25 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(1060,plain,
! [SV26: $i] :
( ( ! [SY1078: $i] :
( ( hBOOL @ ( hAPP @ SV26 @ SY1078 ) )
| ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV26 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV26 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(1061,plain,
! [SV27: $i] :
( ( ! [SY1079: $i] :
( ( hBOOL @ ( hAPP @ SV27 @ SY1079 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV27 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV27 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(1062,plain,
! [SV28: $i] :
( ( ! [SY1080: $i] :
( ( hBOOL @ ( hAPP @ SV28 @ SY1080 ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV28 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV28 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(1063,plain,
! [SV29: $i] :
( ( ! [SY1081: $i] :
( ( hBOOL @ ( hAPP @ SV29 @ SY1081 ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV29 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV29 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(1064,plain,
! [SV30: $i] :
( ( ! [SY1082: $i] :
( ( hBOOL @ ( hAPP @ SV30 @ SY1082 ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ SV30 ) @ ( v_sko__List__Xsplice__Xinduct__2 @ SV30 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(1065,plain,
! [SV31: $i] :
( ( ! [SY1083: $i] :
( ( hBOOL @ ( hAPP @ SV31 @ SY1083 ) )
| ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV31 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV31 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(1066,plain,
! [SV32: $i] :
( ( ! [SY1084: $i] :
( ( hBOOL @ ( hAPP @ SV32 @ SY1084 ) )
| ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ SV32 ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV32 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(1067,plain,
! [SV33: $i] :
( ( ! [SY1085: $i] :
( ( hBOOL @ ( hAPP @ SV33 @ SY1085 ) )
| ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ SV33 ) @ ( v_sko__List__Xlast__Xinduct__2 @ SV33 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(1068,plain,
! [SV34: $i] :
( ( ! [SY1086: $i] :
( ( hBOOL @ ( hAPP @ SV34 @ SY1086 ) )
| ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ SV34 ) @ ( v_sko__List__Xtl__Xinduct__2 @ SV34 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(1069,plain,
! [SV35: $i] :
( ( ! [SY1087: $i,SY1088: $i,SY1089: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV35 @ SY1087 @ SY1088 ) @ SY1089 @ SY1088 )
= ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY1089 @ SY1088 ) @ ( c_List_Osplice @ SY1087 @ ( c_List_Otl @ SY1089 @ SY1088 ) @ SY1088 ) @ SY1088 ) @ SY1088 ) )
| ( SY1089
= ( c_List_Olist_ONil @ SY1088 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(1070,plain,
! [SV36: $i] :
( ( ! [SY1090: $i,SY1091: $i] :
( ( hBOOL @ ( hAPP @ SV36 @ SY1090 ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV36 @ SY1091 ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ SV36 @ SY1091 ) @ ( c_List_Olist_ONil @ SY1091 ) @ SY1091 ) @ SY1091 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Olist_ONil @ SY1091 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(1071,plain,
! [SV37: $i] :
( ( ! [SY1092: $i] :
( ( ( c_List_Orotate1 @ SV37 @ SY1092 )
= ( c_List_Oappend @ ( c_List_Otl @ SV37 @ SY1092 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV37 @ SY1092 ) @ ( c_List_Olist_ONil @ SY1092 ) @ SY1092 ) @ SY1092 ) )
| ( SV37
= ( c_List_Olist_ONil @ SY1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(1072,plain,
! [SV38: $i] :
( ( ! [SY1093: $i,SY1094: $i,SY1095: $i] :
( ~ ( class_Orderings_Olinorder @ SV38 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SY1093 @ ( c_List_Olinorder__class_Osort__key @ SY1093 @ SY1094 @ SY1095 @ SV38 ) @ SY1095 @ SV38 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(1073,plain,
! [SV39: $i] :
( ( ! [SY1096: $i,SY1097: $i] :
( ( c_List_Odrop @ SV39 @ ( c_List_Otl @ SY1096 @ SY1097 ) @ SY1097 )
= ( c_List_Otl @ ( c_List_Odrop @ SV39 @ SY1096 @ SY1097 ) @ SY1097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(1074,plain,
! [SV40: $i] :
( ( ! [SY1098: $i,SY1099: $i,SY1100: $i,SY1101: $i] :
( ( c_ListOrder_Ostep1 @ SV40 @ ( c_List_Oappend @ SY1098 @ SY1099 @ SY1100 ) @ ( c_List_Oappend @ SY1098 @ SY1101 @ SY1100 ) @ SY1100 )
| ~ ( c_ListOrder_Ostep1 @ SV40 @ SY1099 @ SY1101 @ SY1100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(1075,plain,
! [SV41: $i] :
( ( ! [SY1102: $i,SY1103: $i,SY1104: $i,SY1105: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV41 @ SY1102 @ SY1103 @ SY1104 )
| ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Oappend @ SY1102 @ SY1105 @ SY1104 ) @ ( c_List_Oappend @ SY1103 @ SY1105 @ SY1104 ) @ SY1104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(1076,plain,
! [SV42: $i] :
( ( ! [SY1106: $i,SY1107: $i,SY1108: $i] :
( ( ( c_List_Ofilter @ SV42 @ ( c_List_Olist_OCons @ SY1106 @ SY1107 @ SY1108 ) @ SY1108 )
= ( c_List_Olist_OCons @ SY1106 @ ( c_List_Ofilter @ SV42 @ SY1107 @ SY1108 ) @ SY1108 ) )
| ~ ( hBOOL @ ( hAPP @ SV42 @ SY1106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(1077,plain,
! [SV43: $i] :
( ( ! [SY1109: $i,SY1110: $i] :
( ~ ( class_Orderings_Olinorder @ SV43 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SY1109 @ SY1110 @ SV43 ) @ SV43 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1110 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(1078,plain,
! [SV44: $i] :
( ( ! [SY1111: $i,SY1112: $i,SY1113: $i,SY1114: $i] :
( ( c_List_Otake @ SV44 @ ( c_List_Omap @ SY1111 @ SY1112 @ SY1113 @ SY1114 ) @ SY1114 )
= ( c_List_Omap @ SY1111 @ ( c_List_Otake @ SV44 @ SY1112 @ SY1113 ) @ SY1113 @ SY1114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(1079,plain,
! [SV45: $i] :
( ( ! [SY1115: $i,SY1116: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ SV45 @ SY1115 @ SY1116 ) @ SY1116 )
= ( c_List_Ofilter @ SV45 @ ( c_List_Oremdups @ SY1115 @ SY1116 ) @ SY1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(1080,plain,
! [SV46: $i] :
( ( ! [SY1117: $i,SY1118: $i,SY1119: $i,SY1120: $i,SY1121: $i] :
( ( c_List_Olist__all2 @ SV46 @ ( c_List_Otake @ SY1117 @ SY1118 @ SY1119 ) @ ( c_List_Otake @ SY1117 @ SY1120 @ SY1121 ) @ SY1119 @ SY1121 )
| ~ ( c_List_Olist__all2 @ SV46 @ SY1118 @ SY1120 @ SY1119 @ SY1121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(1081,plain,
! [SV47: $i] :
( ( ! [SY1122: $i,SY1123: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV47 @ SY1122 @ SY1123 ) @ SY1123 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1122 @ SY1123 ) @ ( c_List_Olist_OCons @ SV47 @ ( c_List_Olist_ONil @ SY1123 ) @ SY1123 ) @ SY1123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(1082,plain,
! [SV48: $i] :
( ( ! [SY1124: $i,SY1125: $i] :
( ( SV48 = SY1124 )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ SY1125 ) @ SV48 @ SY1124 @ SY1125 @ SY1125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(1083,plain,
! [SV49: $i] :
( ( ! [SY1126: $i,SY1127: $i,SY1128: $i,SY1129: $i,SY1130: $i] :
( ( c_List_Ofoldl @ SV49 @ SY1126 @ ( c_List_Olist_OCons @ SY1127 @ SY1128 @ SY1129 ) @ SY1130 @ SY1129 )
= ( c_List_Ofoldl @ SV49 @ ( hAPP @ ( hAPP @ SV49 @ SY1126 ) @ SY1127 ) @ SY1128 @ SY1130 @ SY1129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(1084,plain,
! [SV50: $i] :
( ( ! [SY1131: $i,SY1132: $i,SY1133: $i,SY1134: $i,SY1135: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY1131 ) @ SY1132 ) )
| ( c_ListOrder_Ostep1 @ SV50 @ SY1133 @ SY1134 @ SY1135 )
| ~ ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SY1133 @ ( c_List_Olist_OCons @ SY1131 @ ( c_List_Olist_ONil @ SY1135 ) @ SY1135 ) @ SY1135 ) @ ( c_List_Oappend @ SY1134 @ ( c_List_Olist_OCons @ SY1132 @ ( c_List_Olist_ONil @ SY1135 ) @ SY1135 ) @ SY1135 ) @ SY1135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(1085,plain,
! [SV51: $i] :
( ( ! [SY1136: $i,SY1137: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ SV51 @ SY1136 @ SY1137 ) @ SY1137 )
= ( c_List_Odrop @ SV51 @ ( c_List_Otl @ SY1136 @ SY1137 ) @ SY1137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(1086,plain,
! [SV52: $i] :
( ( ! [SY1138: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV52 @ ( c_List_Olist_ONil @ SY1138 ) @ SY1138 ) @ SY1138 )
= ( c_List_Olist_OCons @ SV52 @ ( c_List_Olist_ONil @ SY1138 ) @ SY1138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(1087,plain,
! [SV53: $i] :
( ( ! [SY1139: $i,SY1140: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SY1139 @ ( tc_fun @ SY1140 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1139 @ SV53 @ ( tc_fun @ SY1140 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(1088,plain,
! [SV54: $i] :
( ( ! [SY1141: $i,SY1142: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV54 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1141 @ SY1142 @ SV54 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1142 @ SY1141 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(1089,plain,
! [SV55: $i] :
( ( ! [SY1143: $i,SY1144: $i] :
( ~ ( class_Lattices_Olattice @ SV55 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1143 @ SY1144 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1144 @ SY1143 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(1090,plain,
! [SV56: $i] :
( ( ! [SY1145: $i,SY1146: $i,SY1147: $i] :
( ~ ( class_Orderings_Olinorder @ SV56 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1145 @ SY1146 @ SV56 ) @ SV56 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1147 @ ( c_List_Olist_OCons @ SY1145 @ SY1146 @ SV56 ) @ SV56 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(1091,plain,
! [SV57: $i] :
( ( ! [SY1148: $i,SY1149: $i,SY1150: $i,SY1151: $i,SY1152: $i,SY1153: $i] :
( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SY1148 @ SY1149 @ SY1150 ) @ ( c_List_Oappend @ SY1151 @ SY1152 @ SY1153 ) @ SY1150 @ SY1153 )
| ~ ( c_List_Olist__all2 @ SV57 @ SY1149 @ SY1152 @ SY1150 @ SY1153 )
| ~ ( c_List_Olist__all2 @ SV57 @ SY1148 @ SY1151 @ SY1150 @ SY1153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(1092,plain,
! [SV58: $i] :
( ( ! [SY1154: $i,SY1155: $i,SY1156: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV58 @ SY1154 @ SY1155 ) @ SY1156 @ SY1155 )
= ( c_List_Olist_OCons @ SV58 @ ( c_List_Oappend @ SY1154 @ SY1156 @ SY1155 ) @ SY1155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(1093,plain,
! [SV59: $i] :
( ( ! [SY1157: $i,SY1158: $i,SY1159: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV59 @ SY1157 @ SY1158 ) @ SY1159 @ SY1158 )
= ( c_List_Olist_OCons @ SV59 @ ( c_List_Oappend @ SY1157 @ SY1159 @ SY1158 ) @ SY1158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(1094,plain,
! [SV60: $i] :
( ( ! [SY1160: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate1 @ SV60 @ SY1160 ) @ SY1160 )
| ~ ( c_List_Odistinct @ SV60 @ SY1160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(1095,plain,
! [SV61: $i] :
( ( ! [SY1161: $i] :
( ( c_List_Odistinct @ SV61 @ SY1161 )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ SV61 @ SY1161 ) @ SY1161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(1096,plain,
! [SV62: $i] :
( ( ! [SY1162: $i,SY1163: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ SV62 @ SY1162 @ SY1163 ) @ SY1163 )
| ~ ( c_List_Odistinct @ SY1162 @ SY1163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(1097,plain,
! [SV63: $i] :
( ( ! [SY1164: $i,SY1165: $i,SY1166: $i,SY1167: $i] :
( ( c_List_Omap @ SV63 @ ( c_List_Olist_OCons @ SY1164 @ SY1165 @ SY1166 ) @ SY1166 @ SY1167 )
= ( c_List_Olist_OCons @ ( hAPP @ SV63 @ SY1164 ) @ ( c_List_Omap @ SV63 @ SY1165 @ SY1166 @ SY1167 ) @ SY1167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(1098,plain,
! [SV64: $i] :
( ( ! [SY1168: $i,SY1169: $i,SY1170: $i,SY1171: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV64 @ SY1168 ) @ ( c_List_Omap @ SV64 @ SY1169 @ SY1170 @ SY1171 ) @ SY1171 )
= ( c_List_Omap @ SV64 @ ( c_List_Olist_OCons @ SY1168 @ SY1169 @ SY1170 ) @ SY1170 @ SY1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(1099,plain,
! [SV65: $i] :
( ( ! [SY1172: $i,SY1173: $i,SY1174: $i,SY1175: $i] :
( ( c_List_Omap @ SV65 @ ( c_List_Olist_OCons @ SY1172 @ SY1173 @ SY1174 ) @ SY1174 @ SY1175 )
= ( c_List_Olist_OCons @ ( hAPP @ SV65 @ SY1172 ) @ ( c_List_Omap @ SV65 @ SY1173 @ SY1174 @ SY1175 ) @ SY1175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1100,plain,
! [SV66: $i] :
( ( ! [SY1176: $i,SY1177: $i,SY1178: $i,SY1179: $i,SY1180: $i] :
( ( c_List_Olist_Olist__case @ SV66 @ SY1176 @ ( c_List_Olist_OCons @ SY1177 @ SY1178 @ SY1179 ) @ SY1180 @ SY1179 )
= ( hAPP @ ( hAPP @ SY1176 @ SY1177 ) @ SY1178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1101,plain,
! [SV67: $i] :
( ( ! [SY1181: $i,SY1182: $i] :
( ( c_List_Oremove1 @ SV67 @ ( c_List_Olist_OCons @ SV67 @ SY1181 @ SY1182 ) @ SY1182 )
= SY1181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(1102,plain,
! [SV68: $i] :
( ( ! [SY1183: $i,SY1184: $i,SY1185: $i,SY1186: $i,SY1187: $i,SY1188: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SY1183 ) @ SY1184 ) )
| ~ ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SY1183 @ SY1185 @ SY1186 ) @ ( c_List_Olist_OCons @ SY1184 @ SY1187 @ SY1188 ) @ SY1186 @ SY1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1103,plain,
! [SV69: $i] :
( ( ! [SY1189: $i,SY1190: $i,SY1191: $i] :
( ( c_List_Olist_OCons @ SV69 @ ( c_List_Oappend @ SY1189 @ SY1190 @ SY1191 ) @ SY1191 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV69 @ SY1189 @ SY1191 ) @ SY1190 @ SY1191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(1104,plain,
! [SV70: $i] :
( ( ! [SY1192: $i,SY1193: $i,SY1194: $i] :
( ( c_List_Olist_OCons @ SV70 @ ( c_List_Oappend @ SY1192 @ SY1193 @ SY1194 ) @ SY1194 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV70 @ SY1192 @ SY1194 ) @ SY1193 @ SY1194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(1105,plain,
! [SV71: $i] :
( ( ! [SY1195: $i,SY1196: $i,SY1197: $i,SY1198: $i,SY1199: $i] :
( ( SV71 = SY1195 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1196 @ SY1195 ) @ SV71 ) )
| ~ ( c_ListOrder_Ostep1 @ SY1196 @ ( c_List_Olist_OCons @ SY1195 @ SY1197 @ SY1198 ) @ ( c_List_Olist_OCons @ SV71 @ SY1199 @ SY1198 ) @ SY1198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(1106,plain,
! [SV72: $i] :
( ( ! [SY1200: $i,SY1201: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ SV72 @ SY1200 @ SY1201 ) @ ( c_List_Odrop @ SV72 @ SY1200 @ SY1201 ) @ SY1201 )
= SY1200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(1107,plain,
! [SV73: $i] :
( ( ! [SY1202: $i,SY1203: $i] :
( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_List_Olinorder__class_Osorted @ SY1202 @ SV73 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1203 @ SY1202 @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1108,plain,
! [SV74: $i] :
( ( ! [SY1204: $i,SY1205: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV74 @ SY1204 ) @ ( c_List_Olist_OCons @ SY1205 @ ( c_List_Olist_ONil @ SY1204 ) @ SY1204 ) @ SY1204 ) @ SY1204 )
= ( c_List_Olist_OCons @ SY1205 @ SV74 @ SY1204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1109,plain,
! [SV75: $i] :
( ( ! [SY1206: $i,SY1207: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ SV75 @ SY1206 @ SY1207 ) @ SY1207 )
| ~ ( c_List_Odistinct @ SY1206 @ SY1207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1110,plain,
! [SV76: $i] :
( ( ! [SY1208: $i] :
( ( c_List_Odistinct @ ( c_List_Orev @ SV76 @ SY1208 ) @ SY1208 )
| ~ ( c_List_Odistinct @ SV76 @ SY1208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1111,plain,
! [SV77: $i] :
( ( ! [SY1209: $i] :
( ( c_List_Odistinct @ SV77 @ SY1209 )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ SV77 @ SY1209 ) @ SY1209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(1112,plain,
! [SV78: $i] :
( ( ! [SY1210: $i,SY1211: $i,SY1212: $i] :
( ( c_List_Olist__all @ SV78 @ SY1210 @ SY1211 )
| ~ ( c_List_Olist__all @ SV78 @ ( c_List_Olist_OCons @ SY1212 @ SY1210 @ SY1211 ) @ SY1211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(1113,plain,
! [SV79: $i] :
( ( ! [SY1213: $i] :
( ( ( c_List_Oremdups @ SV79 @ SY1213 )
= SV79 )
| ~ ( c_List_Odistinct @ SV79 @ SY1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1114,plain,
! [SV80: $i] :
( ( ! [SY1214: $i,SY1215: $i] :
( ( hBOOL @ ( hAPP @ SV80 @ SY1214 ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY1215 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY1215 @ SV80 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1215 @ SY1214 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1115,plain,
! [SV81: $i] :
( ( ! [SY1216: $i,SY1217: $i,SY1218: $i] :
( ( hBOOL @ ( hAPP @ SV81 @ SY1216 ) )
| ~ ( c_List_Olist__all @ SV81 @ ( c_List_Olist_OCons @ SY1216 @ SY1217 @ SY1218 ) @ SY1218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1116,plain,
! [SV82: $i] :
( ( ! [SY1219: $i,SY1220: $i] :
( ( hBOOL @ ( hAPP @ SV82 @ SY1219 ) )
| ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY1220 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY1220 @ SV82 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1220 @ SY1219 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1117,plain,
! [SV83: $i] :
( ( ! [SY1221: $i,SY1222: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV83 @ SY1221 @ SY1222 ) @ SY1222 )
= ( c_List_Oappend @ SY1221 @ ( c_List_Olist_OCons @ SV83 @ ( c_List_Olist_ONil @ SY1222 ) @ SY1222 ) @ SY1222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1118,plain,
! [SV84: $i] :
( ( ! [SY1223: $i,SY1224: $i] :
( ( c_List_Olist_OCons @ SV84 @ SY1223 @ SY1224 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1224 ) @ ( c_List_Olist_OCons @ SV84 @ SY1223 @ SY1224 ) @ SY1224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1119,plain,
! [SV85: $i] :
( ( ! [SY1225: $i,SY1226: $i,SY1227: $i,SY1228: $i,SY1229: $i] :
( ( c_List_Omap @ SV85 @ ( c_List_Olist__update @ SY1225 @ SY1226 @ SY1227 @ SY1228 ) @ SY1228 @ SY1229 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV85 @ SY1225 @ SY1228 @ SY1229 ) @ SY1226 @ ( hAPP @ SV85 @ SY1227 ) @ SY1229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1120,plain,
! [SV86: $i] :
( ( ! [SY1230: $i] :
( ( c_List_Olist_OCons @ SV86 @ ( c_List_Olist_ONil @ SY1230 ) @ SY1230 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV86 @ ( c_List_Olist_ONil @ SY1230 ) @ SY1230 ) @ SY1230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1121,plain,
! [SV87: $i] :
( ( ! [SY1231: $i,SY1232: $i,SY1233: $i,SY1234: $i,SY1235: $i] :
( ( SV87 = SY1231 )
| ( c_ListOrder_Ostep1 @ SY1232 @ SV87 @ SY1231 @ SY1233 )
| ~ ( c_ListOrder_Ostep1 @ SY1232 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SY1234 @ ( c_List_Olist_ONil @ SY1233 ) @ SY1233 ) @ SY1233 ) @ ( c_List_Oappend @ SY1231 @ ( c_List_Olist_OCons @ SY1235 @ ( c_List_Olist_ONil @ SY1233 ) @ SY1233 ) @ SY1233 ) @ SY1233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1122,plain,
! [SV88: $i] :
( ( ! [SY1236: $i,SY1237: $i,SY1238: $i] :
( ( hBOOL @ ( hAPP @ SV88 @ SY1236 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1237 @ SV88 @ ( tc_fun @ SY1238 @ tc_bool ) ) @ SY1236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1123,plain,
! [SV89: $i] :
( ( ! [SY1239: $i,SY1240: $i,SY1241: $i] :
( ( hBOOL @ ( hAPP @ SV89 @ SY1239 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SY1240 @ ( tc_fun @ SY1241 @ tc_bool ) ) @ SY1239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1124,plain,
! [SV90: $i] :
( ( ! [SY1242: $i,SY1243: $i,SY1244: $i] :
( ( c_List_Olist__all @ SV90 @ ( c_List_Oappend @ SY1242 @ SY1243 @ SY1244 ) @ SY1244 )
| ~ ( c_List_Olist__all @ SV90 @ SY1243 @ SY1244 )
| ~ ( c_List_Olist__all @ SV90 @ SY1242 @ SY1244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(1125,plain,
! [SV91: $i] :
( ( ! [SY1245: $i] :
( ~ ( class_Orderings_Olinorder @ SV91 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1245 @ ( c_List_Olist_ONil @ SV91 ) @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1126,plain,
! [SV92: $i] :
( ( ! [SY1246: $i,SY1247: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ SV92 @ SY1246 @ SY1247 ) @ SY1247 )
| ~ ( c_List_Odistinct @ SY1246 @ SY1247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1127,plain,
! [SV93: $i] :
( ( ! [SY1248: $i,SY1249: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV93 @ SY1248 @ SY1249 ) @ SY1249 )
= ( c_List_Oappend @ ( c_List_Orev @ SY1248 @ SY1249 ) @ ( c_List_Orev @ SV93 @ SY1249 ) @ SY1249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1128,plain,
! [SV94: $i] :
( ( ! [SY1250: $i,SY1251: $i,SY1252: $i,SY1253: $i,SY1254: $i] :
( ( c_List_Ofoldl @ SV94 @ SY1250 @ ( c_List_Oappend @ SY1251 @ SY1252 @ SY1253 ) @ SY1254 @ SY1253 )
= ( c_List_Ofoldl @ SV94 @ ( c_List_Ofoldl @ SV94 @ SY1250 @ SY1251 @ SY1254 @ SY1253 ) @ SY1252 @ SY1254 @ SY1253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1129,plain,
! [SV95: $i] :
( ( ! [SY1255: $i,SY1256: $i] :
( ( c_List_Odistinct @ SV95 @ SY1255 )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ SY1256 @ SV95 @ SY1255 ) @ SY1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1130,plain,
! [SV96: $i] :
( ( ! [SY1257: $i,SY1258: $i,SY1259: $i] :
( ( c_List_Ofilter @ SV96 @ ( c_List_Oappend @ SY1257 @ SY1258 @ SY1259 ) @ SY1259 )
= ( c_List_Oappend @ ( c_List_Ofilter @ SV96 @ SY1257 @ SY1259 ) @ ( c_List_Ofilter @ SV96 @ SY1258 @ SY1259 ) @ SY1259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1131,plain,
! [SV97: $i] :
( ( ! [SY1260: $i,SY1261: $i,SY1262: $i,SY1263: $i] :
( ( c_List_Olist__all2 @ SV97 @ ( c_List_Orev @ SY1260 @ SY1261 ) @ SY1262 @ SY1261 @ SY1263 )
| ~ ( c_List_Olist__all2 @ SV97 @ SY1260 @ ( c_List_Orev @ SY1262 @ SY1263 ) @ SY1261 @ SY1263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1132,plain,
! [SV98: $i] :
( ( ! [SY1264: $i,SY1265: $i,SY1266: $i,SY1267: $i] :
( ( c_List_Olist__all2 @ SV98 @ SY1264 @ ( c_List_Orev @ SY1265 @ SY1266 ) @ SY1267 @ SY1266 )
| ~ ( c_List_Olist__all2 @ SV98 @ ( c_List_Orev @ SY1264 @ SY1267 ) @ SY1265 @ SY1267 @ SY1266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1133,plain,
! [SV99: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV99 ) @ ( c_List_Olist_ONil @ SV99 ) @ SV99 )
= ( c_List_Olist_ONil @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1134,plain,
! [SV100: $i] :
( ( ! [SY1268: $i,SY1269: $i] : ( c_List_Olist__all2 @ SV100 @ ( c_List_Olist_ONil @ SY1268 ) @ ( c_List_Olist_ONil @ SY1269 ) @ SY1268 @ SY1269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1135,plain,
! [SV101: $i] :
( ( ! [SY1270: $i] :
( ( SV101
= ( c_List_Olist_ONil @ SY1270 ) )
| ~ ( c_List_Onull @ SV101 @ SY1270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1136,plain,
! [SV102: $i] :
( ( ( c_List_Olist_ONil @ SV102 )
= ( c_List_Orev @ ( c_List_Olist_ONil @ SV102 ) @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1137,plain,
! [SV103: $i] :
( ( ( c_List_Olist_ONil @ SV103 )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ SV103 ) @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1138,plain,
! [SV104: $i] :
( ( ! [SY1271: $i,SY1272: $i,SY1273: $i,SY1274: $i,SY1275: $i] :
( ( SV104 = SY1271 )
| ( SY1272 = SY1273 )
| ~ ( c_ListOrder_Ostep1 @ SY1274 @ ( c_List_Olist_OCons @ SY1271 @ SY1273 @ SY1275 ) @ ( c_List_Olist_OCons @ SV104 @ SY1272 @ SY1275 ) @ SY1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1139,plain,
! [SV105: $i] :
( ( ! [SY1276: $i,SY1277: $i,SY1278: $i,SY1279: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SY1276 ) @ SY1277 ) )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Olist_OCons @ SY1276 @ SY1278 @ SY1279 ) @ ( c_List_Olist_OCons @ SY1277 @ SY1278 @ SY1279 ) @ SY1279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1140,plain,
! [SV106: $i] :
( ( ! [SY1280: $i,SY1281: $i,SY1282: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV106 @ SY1280 @ SY1281 @ SY1282 ) @ SY1282 )
= ( c_List_Omap @ SV106 @ ( c_List_Orev @ SY1280 @ SY1281 ) @ SY1281 @ SY1282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1141,plain,
! [SV107: $i] :
( ( ! [SY1283: $i,SY1284: $i] :
( ~ ( class_Orderings_Olinorder @ SV107 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SY1283 @ SY1284 @ SV107 ) @ SV107 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1284 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1142,plain,
! [SV108: $i] :
( ( ! [SY1285: $i,SY1286: $i,SY1287: $i] :
( ~ ( class_Orderings_Olinorder @ SV108 )
| ( c_List_Odistinct @ SY1285 @ SY1286 )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SY1287 @ SY1285 @ SY1286 @ SV108 ) @ SY1286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1143,plain,
! [SV109: $i] :
( ( ! [SY1288: $i,SY1289: $i,SY1290: $i] :
( ~ ( class_Orderings_Olinorder @ SV109 )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SY1288 @ SY1289 @ SY1290 @ SV109 ) @ SY1290 )
| ~ ( c_List_Odistinct @ SY1289 @ SY1290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1144,plain,
! [SV110: $i] :
( ( ! [SY1291: $i,SY1292: $i,SY1293: $i,SY1294: $i,SY1295: $i,SY1296: $i] :
( ( c_List_Olist__all2 @ SV110 @ SY1291 @ SY1292 @ SY1293 @ SY1294 )
| ~ ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SY1295 @ SY1291 @ SY1293 ) @ ( c_List_Olist_OCons @ SY1296 @ SY1292 @ SY1294 ) @ SY1293 @ SY1294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1145,plain,
! [SV111: $i] :
( ( ! [SY1297: $i,SY1298: $i,SY1299: $i,SY1300: $i] :
( ( c_List_Orotate @ SV111 @ ( c_List_Omap @ SY1297 @ SY1298 @ SY1299 @ SY1300 ) @ SY1300 )
= ( c_List_Omap @ SY1297 @ ( c_List_Orotate @ SV111 @ SY1298 @ SY1299 ) @ SY1299 @ SY1300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1146,plain,
! [SV112: $i] :
( ( ! [SY1301: $i,SY1302: $i] :
( ( c_List_Odistinct @ SV112 @ SY1301 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV112 @ SY1302 @ SY1301 ) @ SY1301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1147,plain,
! [SV113: $i] :
( ( ! [SY1303: $i,SY1304: $i] :
( ( c_List_Odistinct @ SV113 @ SY1303 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SY1304 @ SV113 @ SY1303 ) @ SY1303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1148,plain,
! [SV114: $i] :
( ( ! [SY1305: $i] :
( SV114
= ( c_List_Orev @ ( c_List_Orev @ SV114 @ SY1305 ) @ SY1305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1149,plain,
! [SV115: $i] :
( ( ! [SY1306: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV115 @ SY1306 ) @ SY1306 )
= SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1150,plain,
! [SV116: $i] :
( ( ! [SY1307: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV116 @ SY1307 ) @ SY1307 )
= SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1151,plain,
! [SV117: $i] :
( ( ! [SY1308: $i,SY1309: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ SV117 @ SY1308 @ SY1309 ) @ SY1309 )
| ~ ( c_List_Odistinct @ SY1308 @ SY1309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1152,plain,
! [SV118: $i] :
( ( ! [SY1310: $i,SY1311: $i,SY1312: $i,SY1313: $i] :
( ( c_List_Olist__all2 @ SV118 @ SY1310 @ SY1311 @ SY1312 @ SY1313 )
| ~ ( c_List_Olist__all2 @ SV118 @ ( c_List_Orev @ SY1310 @ SY1312 ) @ ( c_List_Orev @ SY1311 @ SY1313 ) @ SY1312 @ SY1313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1153,plain,
! [SV119: $i] :
( ( ! [SY1314: $i,SY1315: $i,SY1316: $i,SY1317: $i] :
( ( c_List_Olist__all2 @ SV119 @ ( c_List_Orev @ SY1314 @ SY1315 ) @ ( c_List_Orev @ SY1316 @ SY1317 ) @ SY1315 @ SY1317 )
| ~ ( c_List_Olist__all2 @ SV119 @ SY1314 @ SY1316 @ SY1315 @ SY1317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1154,plain,
! [SV120: $i] :
( ( ! [SY1318: $i,SY1319: $i,SY1320: $i,SY1321: $i] :
( ( c_List_Oconcat__map @ SV120 @ ( c_List_Olist_OCons @ SY1318 @ SY1319 @ SY1320 ) @ SY1320 @ SY1321 )
= ( c_List_Oappend @ ( hAPP @ SV120 @ SY1318 ) @ ( c_List_Oconcat__map @ SV120 @ SY1319 @ SY1320 @ SY1321 ) @ SY1321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1155,plain,
! [SV121: $i] :
( ( ! [SY1322: $i,SY1323: $i,SY1324: $i,SY1325: $i,SY1326: $i] :
( ( c_List_Ofoldr @ SV121 @ ( c_List_Oappend @ SY1322 @ SY1323 @ SY1324 ) @ SY1325 @ SY1324 @ SY1326 )
= ( c_List_Ofoldr @ SV121 @ SY1322 @ ( c_List_Ofoldr @ SV121 @ SY1323 @ SY1325 @ SY1324 @ SY1326 ) @ SY1324 @ SY1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1156,plain,
! [SV122: $i] :
( ( ! [SY1327: $i,SY1328: $i,SY1329: $i] :
( ( c_List_Olist__ex @ SV122 @ ( c_List_Olist_OCons @ SY1327 @ SY1328 @ SY1329 ) @ SY1329 )
| ~ ( hBOOL @ ( hAPP @ SV122 @ SY1327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1157,plain,
! [SV123: $i] :
( ( ! [SY1330: $i,SY1331: $i,SY1332: $i,SY1333: $i,SY1334: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SY1330 ) @ SY1331 ) )
| ( SY1330 = SY1331 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SY1332 @ ( c_List_Olist_OCons @ SY1330 @ ( c_List_Olist_ONil @ SY1333 ) @ SY1333 ) @ SY1333 ) @ ( c_List_Oappend @ SY1334 @ ( c_List_Olist_OCons @ SY1331 @ ( c_List_Olist_ONil @ SY1333 ) @ SY1333 ) @ SY1333 ) @ SY1333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1158,plain,
! [SV124: $i] :
( ( ! [SY1335: $i,SY1336: $i,SY1337: $i,SY1338: $i,SY1339: $i,SY1340: $i] :
( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SY1335 @ SY1336 @ SY1337 ) @ ( c_List_Olist_OCons @ SY1338 @ SY1339 @ SY1340 ) @ SY1337 @ SY1340 )
| ~ ( c_List_Olist__all2 @ SV124 @ SY1336 @ SY1339 @ SY1337 @ SY1340 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SY1335 ) @ SY1338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1159,plain,
! [SV125: $i] :
( ( ! [SY1341: $i,SY1342: $i,SY1343: $i,SY1344: $i,SY1345: $i,SY1346: $i] :
( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SY1341 @ SY1342 @ SY1343 ) @ ( c_List_Olist_OCons @ SY1344 @ SY1345 @ SY1346 ) @ SY1343 @ SY1346 )
| ~ ( c_List_Olist__all2 @ SV125 @ SY1342 @ SY1345 @ SY1343 @ SY1346 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SY1341 ) @ SY1344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1160,plain,
! [SV126: $i] :
( ( ! [SY1347: $i,SY1348: $i,SY1349: $i,SY1350: $i,SY1351: $i,SY1352: $i] :
( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SY1347 @ SY1348 @ SY1349 ) @ ( c_List_Olist_OCons @ SY1350 @ SY1351 @ SY1352 ) @ SY1349 @ SY1352 )
| ~ ( c_List_Olist__all2 @ SV126 @ SY1348 @ SY1351 @ SY1349 @ SY1352 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SY1347 ) @ SY1350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1161,plain,
! [SV127: $i] :
( ( ! [SY1353: $i,SY1354: $i,SY1355: $i] :
( ( c_List_Olist__ex @ SV127 @ ( c_List_Olist_OCons @ SY1353 @ SY1354 @ SY1355 ) @ SY1355 )
| ~ ( c_List_Olist__ex @ SV127 @ SY1354 @ SY1355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1162,plain,
! [SV128: $i] :
( ( ! [SY1356: $i,SY1357: $i,SY1358: $i] :
( ( c_List_Olist__ex @ SV128 @ SY1356 @ SY1357 )
| ( hBOOL @ ( hAPP @ SV128 @ SY1358 ) )
| ~ ( c_List_Olist__ex @ SV128 @ ( c_List_Olist_OCons @ SY1358 @ SY1356 @ SY1357 ) @ SY1357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1163,plain,
! [SV129: $i] :
( ( ! [SY1359: $i,SY1360: $i,SY1361: $i,SY1362: $i,SY1363: $i] :
( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SY1359 @ SY1360 @ SY1361 ) @ ( c_List_Olist_OCons @ SY1362 @ SY1363 @ SY1361 ) @ SY1361 )
| ~ ( c_List_Olistrelp @ SV129 @ SY1360 @ SY1363 @ SY1361 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SY1359 ) @ SY1362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1164,plain,
! [SV130: $i] :
( ( ! [SY1364: $i,SY1365: $i,SY1366: $i] :
( ~ ( class_Lattices_Olattice @ SV130 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1364 @ SY1365 @ SV130 ) @ SY1366 @ SV130 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1364 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1365 @ SY1366 @ SV130 ) @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1165,plain,
! [SV131: $i] :
( ( ! [SY1367: $i,SY1368: $i,SY1369: $i] :
( ~ ( class_Lattices_Olattice @ SV131 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1367 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1368 @ SY1369 @ SV131 ) @ SV131 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1368 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1367 @ SY1369 @ SV131 ) @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1166,plain,
! [SV132: $i] :
( ( ! [SY1370: $i,SY1371: $i,SY1372: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV132 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1370 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1371 @ SY1372 @ SV132 ) @ SV132 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1371 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1370 @ SY1372 @ SV132 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1167,plain,
! [SV133: $i] :
( ( ! [SY1373: $i,SY1374: $i,SY1375: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV133 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1373 @ SY1374 @ SV133 ) @ SY1375 @ SV133 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1373 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1374 @ SY1375 @ SV133 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1168,plain,
! [SV134: $i] :
( ( ! [SY1376: $i,SY1377: $i,SY1378: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV134 @ SY1376 @ ( tc_fun @ SY1377 @ tc_bool ) ) @ SY1378 @ ( tc_fun @ SY1377 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV134 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1376 @ SY1378 @ ( tc_fun @ SY1377 @ tc_bool ) ) @ ( tc_fun @ SY1377 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1169,plain,
! [SV135: $i] :
( ( ! [SY1379: $i,SY1380: $i,SY1381: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV135 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1379 @ SY1380 @ ( tc_fun @ SY1381 @ tc_bool ) ) @ ( tc_fun @ SY1381 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1379 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV135 @ SY1380 @ ( tc_fun @ SY1381 @ tc_bool ) ) @ ( tc_fun @ SY1381 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1170,plain,
! [SV136: $i] :
( ( ! [SY1382: $i,SY1383: $i,SY1384: $i] :
( ( ( c_List_Oremove1 @ SV136 @ ( c_List_Olist_OCons @ SY1382 @ SY1383 @ SY1384 ) @ SY1384 )
= ( c_List_Olist_OCons @ SY1382 @ ( c_List_Oremove1 @ SV136 @ SY1383 @ SY1384 ) @ SY1384 ) )
| ( SV136 = SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1171,plain,
! [SV137: $i] :
( ( ! [SY1385: $i,SY1386: $i,SY1387: $i,SY1388: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV137 @ SY1385 @ SY1386 ) @ ( c_List_Olist_OCons @ SY1387 @ SY1388 @ SY1386 ) @ SY1386 )
= ( c_List_Olist_OCons @ SV137 @ ( c_List_Olist_OCons @ SY1387 @ ( c_List_Osplice @ SY1385 @ SY1388 @ SY1386 ) @ SY1386 ) @ SY1386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1172,plain,
! [SV138: $i] :
( ( ! [SY1389: $i,SY1390: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ SV138 @ SY1389 @ SY1390 ) @ SY1390 )
| ~ ( c_List_Odistinct @ SV138 @ SY1390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1173,plain,
! [SV139: $i] :
( ( ! [SY1391: $i,SY1392: $i,SY1393: $i] :
( ( c_List_Omember @ SV139 @ ( c_List_Olist_OCons @ SY1391 @ SY1392 @ SY1393 ) @ SY1393 )
| ~ ( c_List_Omember @ SV139 @ SY1392 @ SY1393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1174,plain,
! [SV140: $i] :
( ( ! [SY1394: $i,SY1395: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ SV140 @ SY1394 @ SY1395 ) @ SY1395 )
= ( c_List_Oappend @ ( c_List_Otl @ SV140 @ SY1395 ) @ SY1394 @ SY1395 ) )
| ( SV140
= ( c_List_Olist_ONil @ SY1395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1175,plain,
! [SV141: $i] :
( ( ! [SY1396: $i,SY1397: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ SV141 @ SY1396 @ SY1397 ) @ SY1397 )
| ~ ( c_List_Odistinct @ SY1396 @ SY1397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1176,plain,
! [SV142: $i] :
( ( ! [SY1398: $i,SY1399: $i,SY1400: $i] :
( ( ( c_List_OdropWhile @ SV142 @ ( c_List_Olist_OCons @ SY1398 @ SY1399 @ SY1400 ) @ SY1400 )
= ( c_List_OdropWhile @ SV142 @ SY1399 @ SY1400 ) )
| ~ ( hBOOL @ ( hAPP @ SV142 @ SY1398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1177,plain,
! [SV143: $i] :
( ( ! [SY1401: $i,SY1402: $i,SY1403: $i] :
( ( ( c_List_OdropWhile @ SV143 @ ( c_List_Olist_OCons @ SY1401 @ SY1402 @ SY1403 ) @ SY1403 )
= ( c_List_Olist_OCons @ SY1401 @ SY1402 @ SY1403 ) )
| ( hBOOL @ ( hAPP @ SV143 @ SY1401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1178,plain,
! [SV144: $i] :
( ( ! [SY1404: $i,SY1405: $i,SY1406: $i,SY1407: $i,SY1408: $i] :
( ( c_ListOrder_Ostep1 @ SV144 @ SY1404 @ SY1405 @ SY1406 )
| ( SY1405 = SY1404 )
| ~ ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SY1407 @ SY1404 @ SY1406 ) @ ( c_List_Olist_OCons @ SY1408 @ SY1405 @ SY1406 ) @ SY1406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1179,plain,
! [SV145: $i] :
( ( ! [SY1409: $i,SY1410: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ SV145 @ SY1409 @ SY1410 ) @ SY1410 )
= SY1409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1180,plain,
! [SV146: $i] :
( ( ! [SY1411: $i,SY1412: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV146 @ SY1411 @ SY1412 ) @ ( c_List_Olist_ONil @ SY1412 ) @ SY1412 )
= ( c_List_Olist_OCons @ SV146 @ SY1411 @ SY1412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1181,plain,
! [SV147: $i] :
( ( ! [SY1413: $i,SY1414: $i,SY1415: $i,SY1416: $i] :
( ( c_List_Omap @ SV147 @ ( c_List_Oappend @ SY1413 @ SY1414 @ SY1415 ) @ SY1415 @ SY1416 )
= ( c_List_Oappend @ ( c_List_Omap @ SV147 @ SY1413 @ SY1415 @ SY1416 ) @ ( c_List_Omap @ SV147 @ SY1414 @ SY1415 @ SY1416 ) @ SY1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1182,plain,
! [SV148: $i] :
( ( ! [SY1417: $i,SY1418: $i] : ( c_List_Omember @ SV148 @ ( c_List_Olist_OCons @ SV148 @ SY1417 @ SY1418 ) @ SY1418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1183,plain,
! [SV149: $i] :
( ( ! [SY1419: $i] :
( ( SV149
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SY1419 @ SV149 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SY1419 @ SV149 ) @ t_a ) )
| ( SV149
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SY1419 @ SV149 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1184,plain,
! [SV150: $i] :
( ( ! [SY1420: $i,SY1421: $i,SY1422: $i,SY1423: $i,SY1424: $i] :
( ( c_List_Olist__all2 @ SV150 @ ( c_List_Odrop @ SY1420 @ SY1421 @ SY1422 ) @ ( c_List_Odrop @ SY1420 @ SY1423 @ SY1424 ) @ SY1422 @ SY1424 )
| ~ ( c_List_Olist__all2 @ SV150 @ SY1421 @ SY1423 @ SY1422 @ SY1424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1185,plain,
! [SV151: $i] :
( ( ! [SY1425: $i,SY1426: $i,SY1427: $i] :
( ( ( c_List_Oremove1 @ SV151 @ ( c_List_Ofilter @ SY1425 @ SY1426 @ SY1427 ) @ SY1427 )
= ( c_List_Ofilter @ SY1425 @ SY1426 @ SY1427 ) )
| ( hBOOL @ ( hAPP @ SY1425 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1186,plain,
! [SV152: $i] :
( ( ! [SY1428: $i,SY1429: $i,SY1430: $i,SY1431: $i,SY1432: $i] :
( ( c_List_Olist_Olist__rec @ SV152 @ SY1428 @ ( c_List_Olist_OCons @ SY1429 @ SY1430 @ SY1431 ) @ SY1432 @ SY1431 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY1428 @ SY1429 ) @ SY1430 ) @ ( c_List_Olist_Olist__rec @ SV152 @ SY1428 @ SY1430 @ SY1432 @ SY1431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1187,plain,
! [SV153: $i] :
( ( ! [SY1433: $i,SY1434: $i,SY1435: $i] :
( ( c_List_Odistinct @ SV153 @ SY1433 )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ SY1434 @ SV153 @ SY1433 @ SY1435 ) @ SY1435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1188,plain,
! [SV154: $i] :
( ( ! [SY1436: $i,SY1437: $i,SY1438: $i,SY1439: $i,SY1440: $i] :
( ( SV154 = SY1436 )
| ( SY1437 = SY1438 )
| ~ ( c_ListOrder_Ostep1 @ SY1439 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SY1437 @ ( c_List_Olist_ONil @ SY1440 ) @ SY1440 ) @ SY1440 ) @ ( c_List_Oappend @ SY1436 @ ( c_List_Olist_OCons @ SY1438 @ ( c_List_Olist_ONil @ SY1440 ) @ SY1440 ) @ SY1440 ) @ SY1440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1189,plain,
! [SV155: $i] :
( ( ! [SY1441: $i,SY1442: $i] :
( ( c_List_Odistinct @ SV155 @ SY1441 )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ SY1442 @ SV155 @ SY1441 ) @ SY1441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1190,plain,
! [SV156: $i] :
( ( ! [SY1443: $i,SY1444: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ SV156 @ SY1443 @ SY1444 ) @ SY1444 )
| ~ ( c_List_Odistinct @ SY1443 @ SY1444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1191,plain,
! [SV157: $i] :
( ( ! [SY1445: $i,SY1446: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ SV157 @ SY1445 @ SY1446 ) @ SY1446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1192,plain,
! [SV158: $i] :
( ( ! [SY1447: $i,SY1448: $i] :
( ~ ( class_Lattices_Olattice @ SV158 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1447 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1447 @ SY1448 @ SV158 ) @ SV158 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1447 @ SY1448 @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1193,plain,
! [SV159: $i] :
( ( ! [SY1449: $i,SY1450: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV159 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1449 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1449 @ SY1450 @ SV159 ) @ SV159 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1449 @ SY1450 @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1194,plain,
! [SV160: $i] :
( ( ! [SY1451: $i,SY1452: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ SY1451 @ ( tc_fun @ SY1452 @ tc_bool ) ) @ ( tc_fun @ SY1452 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ SY1451 @ ( tc_fun @ SY1452 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1195,plain,
! [SV161: $i] :
( ( ! [SY1453: $i,SY1454: $i,SY1455: $i,SY1456: $i,SY1457: $i] :
( ( c_List_Ofoldr @ SV161 @ ( c_List_Olist_OCons @ SY1453 @ SY1454 @ SY1455 ) @ SY1456 @ SY1455 @ SY1457 )
= ( hAPP @ ( hAPP @ SV161 @ SY1453 ) @ ( c_List_Ofoldr @ SV161 @ SY1454 @ SY1456 @ SY1455 @ SY1457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1196,plain,
! [SV162: $i] :
( ( ! [SY1458: $i,SY1459: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV162 ) @ ( c_List_Olist_OCons @ SY1458 @ SY1459 @ SV162 ) @ SV162 )
= ( c_List_Olist_OCons @ SY1458 @ SY1459 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1197,plain,
! [SV163: $i] :
( ( ! [SY1460: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ SV163 @ SY1460 ) @ SY1460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1198,plain,
! [SV164: $i] :
( ( ! [SY1461: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV164 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1461 @ SY1461 @ SV164 )
= SY1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1199,plain,
! [SV165: $i] :
( ( ! [SY1462: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV165 @ ( tc_fun @ SY1462 @ tc_bool ) )
= SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1200,plain,
! [SV166: $i] :
( ( ! [SY1463: $i,SY1464: $i,SY1465: $i,SY1466: $i,SY1467: $i] :
( ( c_ListOrder_Ostep1 @ SV166 @ SY1463 @ SY1464 @ SY1465 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SY1466 ) @ SY1467 ) )
| ~ ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SY1466 @ SY1463 @ SY1465 ) @ ( c_List_Olist_OCons @ SY1467 @ SY1464 @ SY1465 ) @ SY1465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1201,plain,
! [SV167: $i] :
( ( ! [SY1468: $i,SY1469: $i,SY1470: $i,SY1471: $i] :
( ( c_ListOrder_Ostep1 @ SV167 @ ( c_List_Olist_OCons @ SY1468 @ SY1469 @ SY1470 ) @ ( c_List_Olist_OCons @ SY1468 @ SY1471 @ SY1470 ) @ SY1470 )
| ~ ( c_ListOrder_Ostep1 @ SV167 @ SY1469 @ SY1471 @ SY1470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1202,plain,
! [SV168: $i] :
( ( ! [SY1472: $i,SY1473: $i] :
( ~ ( class_Orderings_Olinorder @ SV168 )
| ( c_List_Olinorder__class_Osorted @ SY1472 @ SV168 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY1472 @ SY1473 @ SV168 ) @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1203,plain,
! [SV169: $i] :
( ( ! [SY1474: $i,SY1475: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( c_List_Olinorder__class_Osorted @ SY1474 @ SV169 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY1475 @ SY1474 @ SV169 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1204,plain,
! [SV170: $i] :
( ( ! [SY1476: $i,SY1477: $i,SY1478: $i] :
( ( c_List_Olist__all @ SV170 @ ( c_List_Olist_OCons @ SY1476 @ SY1477 @ SY1478 ) @ SY1478 )
| ~ ( c_List_Olist__all @ SV170 @ SY1477 @ SY1478 )
| ~ ( hBOOL @ ( hAPP @ SV170 @ SY1476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1205,plain,
! [SV171: $i] :
( ( ! [SY1479: $i,SY1480: $i,SY1481: $i,SY1482: $i,SY1483: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SY1479 @ SY1480 @ SY1481 ) @ SY1482 @ SY1483 @ SY1481 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SY1482 @ SY1483 @ SY1481 ) @ SY1479 @ SY1480 @ SY1481 ) )
| ( SY1479 = SY1482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1206,plain,
! [SV172: $i] :
( ( ! [SY1484: $i] :
( ~ ( class_Orderings_Olinorder @ SV172 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SY1484 @ SV172 ) @ SV172 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1484 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1207,plain,
! [SV173: $i] :
( ( ! [SY1485: $i,SY1486: $i] :
( ( c_List_Olist__all @ SV173 @ SY1485 @ SY1486 )
| ~ ( c_List_Olist__all @ SV173 @ ( c_List_Orev @ SY1485 @ SY1486 ) @ SY1486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1208,plain,
! [SV174: $i] :
( ( ! [SY1487: $i,SY1488: $i] :
( ( c_List_Olist__all @ SV174 @ ( c_List_Orev @ SY1487 @ SY1488 ) @ SY1488 )
| ~ ( c_List_Olist__all @ SV174 @ SY1487 @ SY1488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1209,plain,
! [SV175: $i] :
( ( ! [SY1489: $i,SY1490: $i,SY1491: $i,SY1492: $i] :
( ( c_List_Odrop @ SV175 @ ( c_List_Omap @ SY1489 @ SY1490 @ SY1491 @ SY1492 ) @ SY1492 )
= ( c_List_Omap @ SY1489 @ ( c_List_Odrop @ SV175 @ SY1490 @ SY1491 ) @ SY1491 @ SY1492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1210,plain,
! [SV176: $i] :
( ( ! [SY1493: $i,SY1494: $i,SY1495: $i] :
( ( c_List_Omember @ SV176 @ SY1493 @ SY1494 )
| ( SV176 = SY1495 )
| ~ ( c_List_Omember @ SV176 @ ( c_List_Olist_OCons @ SY1495 @ SY1493 @ SY1494 ) @ SY1494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1211,plain,
! [SV177: $i] :
( ( ! [SY1496: $i,SY1497: $i,SY1498: $i] :
( ( ( c_List_Ofilter @ SV177 @ ( c_List_Olist_OCons @ SY1496 @ SY1497 @ SY1498 ) @ SY1498 )
= ( c_List_Ofilter @ SV177 @ SY1497 @ SY1498 ) )
| ( hBOOL @ ( hAPP @ SV177 @ SY1496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1212,plain,
! [SV178: $i] :
( ( ! [SY1499: $i,SY1500: $i,SY1501: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV178 @ SY1499 @ ( tc_fun @ SY1500 @ tc_bool ) ) @ SY1501 ) )
| ~ ( hBOOL @ ( hAPP @ SY1499 @ SY1501 ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ SY1501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1213,plain,
! [SV179: $i] :
( ( ! [SY1502: $i,SY1503: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ SV179 @ SY1502 @ SY1503 ) @ SY1503 )
= ( c_List_Ofilter @ SV179 @ ( c_List_Orev @ SY1502 @ SY1503 ) @ SY1503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1214,plain,
! [SV180: $i] :
( ( ! [SY1504: $i] : ( c_List_Olist__all2 @ ( c_fequal @ SV180 ) @ SY1504 @ SY1504 @ SV180 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1215,plain,
! [SV181: $i] :
( ( ! [SY1505: $i,SY1506: $i,SY1507: $i] :
( ( c_List_Olist__all @ SV181 @ SY1505 @ SY1506 )
| ~ ( c_List_Olist__all @ SV181 @ ( c_List_Oappend @ SY1505 @ SY1507 @ SY1506 ) @ SY1506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1216,plain,
! [SV182: $i] :
( ( ! [SY1508: $i,SY1509: $i,SY1510: $i] :
( ( c_List_Olist__all @ SV182 @ SY1508 @ SY1509 )
| ~ ( c_List_Olist__all @ SV182 @ ( c_List_Oappend @ SY1510 @ SY1508 @ SY1509 ) @ SY1509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1217,plain,
! [SV183: $i] :
( ( ! [SY1511: $i,SY1512: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ SV183 @ SY1511 @ SY1512 ) @ SY1512 )
= ( c_List_Orotate @ SV183 @ ( c_List_Orotate1 @ SY1511 @ SY1512 ) @ SY1512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1218,plain,
! [SV184: $i] :
( ( ! [SY1513: $i,SY1514: $i,SY1515: $i,SY1516: $i] :
( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_Olist__case @ SY1513 @ SY1514 @ ( c_List_Olist_OCons @ SY1515 @ SY1516 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV184 @ ( hAPP @ ( hAPP @ SY1514 @ SY1515 ) @ SY1516 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1219,plain,
! [SV185: $i] :
( ( ! [SY1517: $i,SY1518: $i,SY1519: $i,SY1520: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_List_Olist_Olist__case @ SY1517 @ SY1518 @ ( c_List_Olist_OCons @ SY1519 @ SY1520 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV185 @ ( hAPP @ ( hAPP @ SY1518 @ SY1519 ) @ SY1520 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1220,plain,
! [SV186: $i] :
( ( ! [SY1521: $i,SY1522: $i] :
( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ SY1521 @ SY1522 @ SV186 ) @ SV186 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1522 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1221,plain,
! [SV187: $i] :
( ( ! [SY1523: $i,SY1524: $i,SY1525: $i,SY1526: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV187 @ SY1523 @ SY1524 @ SY1525 ) @ SY1523 @ SY1526 @ SY1525 )
= ( c_List_Olist__update @ SV187 @ SY1523 @ SY1526 @ SY1525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1222,plain,
! [SV188: $i] :
( ( ! [SY1527: $i,SY1528: $i,SY1529: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV188 @ SY1527 @ SY1528 ) @ SY1529 @ SY1528 )
= ( c_List_Oappend @ SV188 @ ( c_List_Oappend @ SY1527 @ SY1529 @ SY1528 ) @ SY1528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1223,plain,
! [SV189: $i] :
( ( ! [SY1530: $i,SY1531: $i,SY1532: $i] :
( ( c_List_Oappend @ SV189 @ ( c_List_Oappend @ SY1530 @ SY1531 @ SY1532 ) @ SY1532 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV189 @ SY1530 @ SY1532 ) @ SY1531 @ SY1532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1224,plain,
! [SV190: $i] :
( ( ! [SY1533: $i,SY1534: $i,SY1535: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV190 @ SY1533 @ SY1534 ) @ SY1535 @ SY1534 )
= ( c_List_Oappend @ SV190 @ ( c_List_Oappend @ SY1533 @ SY1535 @ SY1534 ) @ SY1534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1225,plain,
! [SV191: $i] :
( ( ! [SY1536: $i,SY1537: $i,SY1538: $i] :
( ( c_List_Oappend @ SV191 @ ( c_List_Oappend @ SY1536 @ SY1537 @ SY1538 ) @ SY1538 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV191 @ SY1536 @ SY1538 ) @ SY1537 @ SY1538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1226,plain,
! [SV192: $i] :
( ( ! [SY1539: $i,SY1540: $i] :
( ~ ( class_Orderings_Olinorder @ SV192 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SY1539 @ SY1540 @ SV192 ) @ SV192 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1540 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1227,plain,
! [SV193: $i] :
( ( ! [SY1541: $i] :
( ( c_List_Osplice @ SV193 @ ( c_List_Olist_ONil @ SY1541 ) @ SY1541 )
= SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1228,plain,
! [SV194: $i] :
( ( ! [SY1542: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ SV194 ) @ SY1542 @ SV194 )
= SY1542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1229,plain,
! [SV195: $i] :
( ( ( c_List_Otl @ ( c_List_Olist_ONil @ SV195 ) @ SV195 )
= ( c_List_Olist_ONil @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1230,plain,
! [SV196: $i] :
( ( ! [SY1543: $i] :
( ( hBOOL @ ( hAPP @ SV196 @ SY1543 ) )
| ( hBOOL @ ( hAPP @ SV196 @ ( v_sko__List__Xrev__Xinduct__2 @ SV196 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV196 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1231,plain,
! [SV197: $i] :
( ( ! [SY1544: $i] :
( ( hBOOL @ ( hAPP @ SV197 @ SY1544 ) )
| ( hBOOL @ ( hAPP @ SV197 @ ( v_sko__List__Xsplice__Xinduct__2 @ SV197 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV197 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1232,plain,
! [SV198: $i] :
( ( ! [SY1545: $i] :
( ( hBOOL @ ( hAPP @ SV198 @ SY1545 ) )
| ( hBOOL @ ( hAPP @ SV198 @ ( v_sko__List__Xset__Xinduct__2 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV198 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1233,plain,
! [SV199: $i] :
( ( ! [SY1546: $i] :
( ( hBOOL @ ( hAPP @ SV199 @ SY1546 ) )
| ( hBOOL @ ( hAPP @ SV199 @ ( v_sko__List__Xtl__Xinduct__2 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV199 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1234,plain,
! [SV200: $i] :
( ( ! [SY1547: $i,SY1548: $i,SY1549: $i] :
( ( SV200
= ( c_List_Olist_ONil @ SY1547 ) )
| ~ ( c_List_Olist__all2 @ SY1548 @ SV200 @ ( c_List_Olist_ONil @ SY1549 ) @ SY1547 @ SY1549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1235,plain,
! [SV201: $i] :
( ( ! [SY1550: $i,SY1551: $i,SY1552: $i] :
( ( SV201
= ( c_List_Olist_ONil @ SY1550 ) )
| ~ ( c_List_Olist__all2 @ SY1551 @ ( c_List_Olist_ONil @ SY1552 ) @ SV201 @ SY1552 @ SY1550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1236,plain,
! [SV202: $i] :
( ( ! [SY1553: $i] :
( ( hBOOL @ ( hAPP @ SV202 @ SY1553 ) )
| ( hBOOL @ ( hAPP @ SV202 @ ( v_sko__List__Xlist__Xinducts__2 @ SV202 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV202 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1237,plain,
! [SV203: $i] :
( ( ! [SY1554: $i] :
( ( hBOOL @ ( hAPP @ SV203 @ SY1554 ) )
| ( hBOOL @ ( hAPP @ SV203 @ ( v_sko__List__Xhd__Xinduct__2 @ SV203 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV203 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1238,plain,
! [SV204: $i] :
( ( c_List_Odistinct @ ( c_List_Olist_ONil @ SV204 ) @ SV204 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1239,plain,
! [SV205: $i] :
( ( ! [SY1555: $i,SY1556: $i] :
( ( c_List_Oconcat__map @ SV205 @ ( c_List_Olist_ONil @ SY1555 ) @ SY1555 @ SY1556 )
= ( c_List_Olist_ONil @ SY1556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1240,plain,
! [SV206: $i] :
( ( ! [SY1557: $i] :
( ( hBOOL @ ( hAPP @ SV206 @ SY1557 ) )
| ( hBOOL @ ( hAPP @ SV206 @ ( v_sko__List__Xremdups__Xinduct__2 @ SV206 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV206 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1241,plain,
! [SV207: $i] :
( ( ! [SY1558: $i] :
~ ( c_List_Omember @ SV207 @ ( c_List_Olist_ONil @ SY1558 ) @ SY1558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1242,plain,
! [SV208: $i] :
( ( ! [SY1559: $i,SY1560: $i] :
( ( hBOOL @ ( hAPP @ SV208 @ SY1559 ) )
| ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV208 @ SY1560 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Olist_ONil @ SY1560 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1243,plain,
! [SV209: $i] :
( ( ! [SY1561: $i,SY1562: $i] :
( ~ ( class_Orderings_Olinorder @ SV209 )
| ( ( c_List_Olinorder__class_Osort__key @ SY1561 @ ( c_List_Olist_ONil @ SY1562 ) @ SY1562 @ SV209 )
= ( c_List_Olist_ONil @ SY1562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1244,plain,
! [SV210: $i] :
( ( ! [SY1563: $i] :
( ( hBOOL @ ( hAPP @ SV210 @ SY1563 ) )
| ( hBOOL @ ( hAPP @ SV210 @ ( v_sko__List__Xdrop__Xinduct__2 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV210 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1245,plain,
! [SV211: $i] :
( ( ! [SY1564: $i,SY1565: $i,SY1566: $i] :
( ( c_List_Ofoldl @ SV211 @ SY1564 @ ( c_List_Olist_ONil @ SY1565 ) @ SY1566 @ SY1565 )
= SY1564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1246,plain,
! [SV212: $i] :
( ( ! [SY1567: $i] :
( ( hBOOL @ ( hAPP @ SV212 @ SY1567 ) )
| ( hBOOL @ ( hAPP @ SV212 @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV212 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV212 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1247,plain,
! [SV213: $i] :
( ( ! [SY1568: $i,SY1569: $i] :
~ ( c_ListOrder_Ostep1 @ SV213 @ SY1568 @ ( c_List_Olist_ONil @ SY1569 ) @ SY1569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1248,plain,
! [SV214: $i] :
( ( ! [SY1570: $i,SY1571: $i] :
~ ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_ONil @ SY1570 ) @ SY1571 @ SY1570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1249,plain,
! [SV215: $i] :
( ( ( c_List_Oremdups @ ( c_List_Olist_ONil @ SV215 ) @ SV215 )
= ( c_List_Olist_ONil @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1250,plain,
! [SV216: $i] :
( ( ! [SY1572: $i] :
( ( c_List_Odrop @ SV216 @ ( c_List_Olist_ONil @ SY1572 ) @ SY1572 )
= ( c_List_Olist_ONil @ SY1572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1251,plain,
! [SV217: $i] :
( ( ! [SY1573: $i] :
( ( hBOOL @ ( hAPP @ SV217 @ SY1573 ) )
| ( hBOOL @ ( hAPP @ SV217 @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV217 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1252,plain,
! [SV218: $i] :
( ( ! [SY1574: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ SV218 ) @ SY1574 @ SV218 )
= ( c_List_Olist_ONil @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1253,plain,
! [SV219: $i] :
( ( ! [SY1575: $i] :
( ( c_List_OdropWhile @ SV219 @ ( c_List_Olist_ONil @ SY1575 ) @ SY1575 )
= ( c_List_Olist_ONil @ SY1575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1254,plain,
! [SV220: $i] :
( ( ! [SY1576: $i] :
( SV220
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1576 ) @ SV220 @ SY1576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1255,plain,
! [SV221: $i] :
( ( ! [SY1577: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV221 ) @ SY1577 @ SV221 )
= SY1577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1256,plain,
! [SV222: $i] :
( ( ! [SY1578: $i] :
( SV222
= ( c_List_Oappend @ SV222 @ ( c_List_Olist_ONil @ SY1578 ) @ SY1578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1257,plain,
! [SV223: $i] :
( ( ! [SY1579: $i] :
( SV223
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1579 ) @ SV223 @ SY1579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1258,plain,
! [SV224: $i] :
( ( ! [SY1580: $i] :
( ( c_List_Oappend @ SV224 @ ( c_List_Olist_ONil @ SY1580 ) @ SY1580 )
= SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1259,plain,
! [SV225: $i] :
( ( ! [SY1581: $i] :
( ( hBOOL @ ( hAPP @ SV225 @ SY1581 ) )
| ( hBOOL @ ( hAPP @ SV225 @ ( v_sko__List__Xlast__Xinduct__2 @ SV225 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV225 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1260,plain,
! [SV226: $i] :
( ( ! [SY1582: $i] :
( ( c_List_Otake @ SV226 @ ( c_List_Olist_ONil @ SY1582 ) @ SY1582 )
= ( c_List_Olist_ONil @ SY1582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1261,plain,
! [SV227: $i] :
( ( ! [SY1583: $i] :
( ( hBOOL @ ( hAPP @ SV227 @ SY1583 ) )
| ( hBOOL @ ( hAPP @ SV227 @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV227 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV227 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1262,plain,
! [SV228: $i] :
( ( ! [SY1584: $i] :
( ( hBOOL @ ( hAPP @ SV228 @ SY1584 ) )
| ( hBOOL @ ( hAPP @ SV228 @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV228 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV228 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1263,plain,
! [SV229: $i] :
( ( ! [SY1585: $i] :
( ( hBOOL @ ( hAPP @ SV229 @ SY1585 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV229 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV229 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1264,plain,
! [SV230: $i] :
( ( ! [SY1586: $i] : ( c_List_Olist__all @ SV230 @ ( c_List_Olist_ONil @ SY1586 ) @ SY1586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1265,plain,
! [SV231: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ SV231 ) @ SV231 )
= ( c_List_Olist_ONil @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1266,plain,
! [SV232: $i] :
( ( ! [SY1587: $i] :
~ ( c_List_Olist__ex @ SV232 @ ( c_List_Olist_ONil @ SY1587 ) @ SY1587 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1267,plain,
! [SV233: $i] :
( ( c_List_Onull @ ( c_List_Olist_ONil @ SV233 ) @ SV233 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1268,plain,
! [SV234: $i] :
( ( ! [SY1588: $i,SY1589: $i] :
( ~ ( hBOOL @ ( hAPP @ SV234 @ ( c_List_Olist_Olist__case @ SY1588 @ SY1589 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV234 @ SY1588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1269,plain,
! [SV235: $i] :
( ( ! [SY1590: $i,SY1591: $i,SY1592: $i] :
( ( c_List_Ofoldr @ SV235 @ ( c_List_Olist_ONil @ SY1590 ) @ SY1591 @ SY1590 @ SY1592 )
= SY1591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1270,plain,
! [SV236: $i] :
( ( ! [SY1593: $i] :
( ( hBOOL @ ( hAPP @ SV236 @ SY1593 ) )
| ( hBOOL @ ( hAPP @ SV236 @ ( v_sko__List__Xzip__Xinduct__2 @ SV236 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1271,plain,
! [SV237: $i] :
( ( ! [SY1594: $i,SY1595: $i] :
( ( c_List_Omap @ SV237 @ ( c_List_Olist_ONil @ SY1594 ) @ SY1594 @ SY1595 )
= ( c_List_Olist_ONil @ SY1595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1272,plain,
! [SV238: $i] :
( ( ! [SY1596: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ SV238 ) @ SY1596 @ SV238 )
= ( c_List_Olist_ONil @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1273,plain,
! [SV239: $i] :
( ( ! [SY1597: $i] :
( ( hBOOL @ ( hAPP @ SV239 @ SY1597 ) )
| ( hBOOL @ ( hAPP @ SV239 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV239 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV239 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1274,plain,
! [SV240: $i] :
( ( ! [SY1598: $i,SY1599: $i,SY1600: $i] :
( ( c_List_Olist_Olist__rec @ SV240 @ SY1598 @ ( c_List_Olist_ONil @ SY1599 ) @ SY1600 @ SY1599 )
= SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1275,plain,
! [SV241: $i] :
( ( ! [SY1601: $i] :
( ( hBOOL @ ( hAPP @ SV241 @ SY1601 ) )
| ( hBOOL @ ( hAPP @ SV241 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV241 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1276,plain,
! [SV242: $i] :
( ( ! [SY1602: $i] :
( ( hBOOL @ ( hAPP @ SV242 @ SY1602 ) )
| ( hBOOL @ ( hAPP @ SV242 @ ( v_sko__List__Xtake__Xinduct__2 @ SV242 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV242 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1277,plain,
! [SV243: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV243 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV243 ) @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1278,plain,
! [SV244: $i] :
( ( ! [SY1603: $i,SY1604: $i] :
( ( c_List_Ofiltermap @ SV244 @ ( c_List_Olist_ONil @ SY1603 ) @ SY1603 @ SY1604 )
= ( c_List_Olist_ONil @ SY1604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1279,plain,
! [SV245: $i] :
( ( ! [SY1605: $i] :
( ( c_List_Ofilter @ SV245 @ ( c_List_Olist_ONil @ SY1605 ) @ SY1605 )
= ( c_List_Olist_ONil @ SY1605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1280,plain,
! [SV246: $i] :
( ( ! [SY1606: $i,SY1607: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV246 ) @ SY1606 @ SY1607 @ SV246 )
= ( c_List_Olist_ONil @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1281,plain,
! [SV247: $i] :
( ( ! [SY1608: $i,SY1609: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV247 ) @ SY1608 @ SY1609 @ SV247 )
= ( c_List_Olist_ONil @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1282,plain,
! [SV248: $i] :
( ( ! [SY1610: $i,SY1611: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV248 ) @ SY1610 @ SY1611 @ SV248 )
= ( c_List_Olist_ONil @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1283,plain,
! [SV249: $i] :
( ( ! [SY1612: $i] :
( ( hBOOL @ ( hAPP @ SV249 @ SY1612 ) )
| ( hBOOL @ ( hAPP @ SV249 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV249 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV249 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1284,plain,
! [SV250: $i] :
( ( ! [SY1613: $i] :
( ( c_List_Oremove1 @ SV250 @ ( c_List_Olist_ONil @ SY1613 ) @ SY1613 )
= ( c_List_Olist_ONil @ SY1613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1285,plain,
! [SV251: $i] :
( ( ! [SY1614: $i] :
( ( hBOOL @ ( hAPP @ SV251 @ SY1614 ) )
| ( hBOOL @ ( hAPP @ SV251 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV251 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1286,plain,
! [SV252: $i] :
( ( ! [SY1615: $i,SY1616: $i,SY1617: $i] :
( ( c_Map_Omap__upds @ SV252 @ SY1615 @ ( c_List_Olist_ONil @ SY1616 ) @ SY1617 @ SY1616 )
= SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1287,plain,
! [SV253: $i] :
( ( ! [SY1618: $i,SY1619: $i,SY1620: $i] :
( ( c_Map_Omap__upds @ SV253 @ ( c_List_Olist_ONil @ SY1618 ) @ SY1619 @ SY1618 @ SY1620 )
= SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1288,plain,
! [SV254: $i] :
( ( ! [SY1621: $i] :
( ( hBOOL @ ( hAPP @ SV254 @ SY1621 ) )
| ( hBOOL @ ( hAPP @ SV254 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV254 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV254 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1289,plain,
! [SV255: $i] :
( ( ! [SY1622: $i,SY1623: $i,SY1624: $i] :
( ( c_List_Olist_Olist__case @ SV255 @ SY1622 @ ( c_List_Olist_ONil @ SY1623 ) @ SY1624 @ SY1623 )
= SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1290,plain,
! [SV256: $i] :
( ( ! [SY1625: $i] :
( ( c_List_Orotate @ SV256 @ ( c_List_Olist_ONil @ SY1625 ) @ SY1625 )
= ( c_List_Olist_ONil @ SY1625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1291,plain,
! [SV257: $i] :
( ( ! [SY1626: $i] :
( ( hBOOL @ ( hAPP @ SV257 @ SY1626 ) )
| ( hBOOL @ ( hAPP @ SV257 @ ( v_sko__List__Xlist__Xinduct__2 @ SV257 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1292,plain,
! [SV258: $i] :
( ( ! [SY1627: $i,SY1628: $i] :
( ( c_List_Olist_ONil @ SV258 )
= ( c_List_Omap @ SY1627 @ ( c_List_Olist_ONil @ SY1628 ) @ SY1628 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1293,plain,
! [SV259: $i] :
( ( ( c_List_Olist_ONil @ SV259 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV259 ) @ ( c_List_Olist_ONil @ SV259 ) @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1294,plain,
! [SV260: $i] :
( ( ! [SY1629: $i] : ( c_List_Olistrelp @ SV260 @ ( c_List_Olist_ONil @ SY1629 ) @ ( c_List_Olist_ONil @ SY1629 ) @ SY1629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1295,plain,
! [SV261: $i] :
( ( ! [SY1630: $i] :
( ( hBOOL @ ( hAPP @ SV261 @ SY1630 ) )
| ( hBOOL @ ( hAPP @ SV261 @ ( v_sko__List__Xmap__Xinduct__2 @ SV261 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Olist_ONil @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1296,plain,
! [SV262: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_ONil @ SV262 ) @ SV262 )
= ( c_List_Olist_ONil @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1297,plain,
! [SV263: $i] :
( ( ! [SY1631: $i,SY1632: $i,SY1633: $i] :
( ( c_List_Olistsp @ SV263 @ ( c_List_Oappend @ SY1631 @ SY1632 @ SY1633 ) @ SY1633 )
| ~ ( c_List_Olistsp @ SV263 @ SY1632 @ SY1633 )
| ~ ( c_List_Olistsp @ SV263 @ SY1631 @ SY1633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1298,plain,
! [SV264: $i] :
( ( ! [SY1634: $i,SY1635: $i] :
( ( c_List_Olistsp @ SV264 @ SY1634 @ SY1635 )
| ~ ( hBOOL @ ( hAPP @ SV264 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV264 @ SY1634 @ SY1635 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1299,plain,
! [SV265: $i] :
( ( ! [SY1636: $i,SY1637: $i,SY1638: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV265 @ SY1636 @ ( tc_fun @ SY1637 @ tc_bool ) ) @ SY1638 @ SY1637 )
| ~ ( c_List_Olistsp @ SY1636 @ SY1638 @ SY1637 )
| ~ ( c_List_Olistsp @ SV265 @ SY1638 @ SY1637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1300,plain,
! [SV266: $i] :
( ( ! [SY1639: $i,SY1640: $i,SY1641: $i] :
( ( c_List_Olistsp @ SV266 @ SY1639 @ SY1640 )
| ~ ( c_List_Olistsp @ SV266 @ ( c_List_Oappend @ SY1641 @ SY1639 @ SY1640 ) @ SY1640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1301,plain,
! [SV267: $i] :
( ( ! [SY1642: $i,SY1643: $i,SY1644: $i] :
( ( c_List_Olistsp @ SV267 @ SY1642 @ SY1643 )
| ~ ( c_List_Olistsp @ SV267 @ ( c_List_Oappend @ SY1642 @ SY1644 @ SY1643 ) @ SY1643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1302,plain,
! [SV268: $i] :
( ( ! [SY1645: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV268 @ SY1645 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1303,plain,
! [SV269: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV269 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1304,plain,
! [SV270: $i] :
( ( ! [SY1646: $i,SY1647: $i] :
( ( hBOOL @ ( hAPP @ SV270 @ SY1646 ) )
| ( hBOOL @ ( hAPP @ SY1647 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY1647 @ SV270 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV270 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1647 @ SY1646 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1305,plain,
! [SV271: $i] :
( ( ! [SY1648: $i,SY1649: $i] :
( ( hBOOL @ ( hAPP @ SV271 @ SY1648 ) )
| ( hBOOL @ ( hAPP @ SV271 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY1649 @ SV271 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1649 @ SY1648 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1306,plain,
! [SV272: $i] :
( ( ! [SY1650: $i,SY1651: $i] :
( ( hBOOL @ ( hAPP @ SV272 @ SY1650 ) )
| ( hBOOL @ ( hAPP @ SY1651 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY1651 @ SV272 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1651 @ SY1650 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1307,plain,
! [SV273: $i] :
( ( ! [SY1652: $i,SY1653: $i] :
( ( hBOOL @ ( hAPP @ SV273 @ SY1652 ) )
| ( hBOOL @ ( hAPP @ SV273 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY1653 @ SV273 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV273 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1653 @ SY1652 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1308,plain,
! [SV274: $i] :
( ( ! [SY1654: $i] :
( ( c_List_Olistsp @ SV274 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV274 @ SY1654 ) @ t_a )
| ( SY1654
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV274 @ SY1654 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1309,plain,
! [SV275: $i] :
( ( ! [SY1655: $i] :
( ( hBOOL @ ( hAPP @ SV275 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV275 @ SY1655 ) ) )
| ( SY1655
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV275 @ SY1655 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1310,plain,
! [SV276: $i] :
( ( ! [SY1656: $i,SY1657: $i] :
( ( hBOOL @ ( hAPP @ SV276 @ SY1656 ) )
| ( c_List_Olistsp @ SY1657 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY1657 @ SV276 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV276 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1657 @ SY1656 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1311,plain,
! [SV277: $i] :
( ( ! [SY1658: $i,SY1659: $i] :
( ( hBOOL @ ( hAPP @ SV277 @ SY1658 ) )
| ( c_List_Olistsp @ SY1659 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY1659 @ SV277 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV277 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1659 @ SY1658 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1312,plain,
! [SV278: $i] :
( ( ! [SY1660: $i] : ( c_List_Olistsp @ SV278 @ ( c_List_Olist_ONil @ SY1660 ) @ SY1660 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1313,plain,
! [SV279: $i] :
( ( ! [SY1661: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV279 @ SY1661 ) )
| ~ ( class_Lattices_Olattice @ SY1661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1314,plain,
! [SV280: $i] :
( ( ! [SY1662: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV280 @ SY1662 ) )
| ~ ( class_Lattices_Olattice @ SY1662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1315,plain,
! [SV281: $i] :
( ( ! [SY1663: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV281 ) @ SY1663 ) @ SY1663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1316,plain,
! [SV282: $i] :
( ( ! [SY1664: $i,SY1665: $i] :
( ( SV282 = SY1664 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1665 ) @ SV282 ) @ SY1664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1317,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1318,plain,
! [SV283: $i] :
( ( ! [SY1666: $i,SY1667: $i,SY1668: $i] :
( ( ( c_List_Orev @ SV283 @ SY1666 )
!= ( c_List_Olist_OCons @ SY1667 @ SY1668 @ SY1666 ) )
| ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SY1668 @ SY1666 ) @ ( c_List_Olist_OCons @ SY1667 @ ( c_List_Olist_ONil @ SY1666 ) @ SY1666 ) @ SY1666 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1319,plain,
! [SV284: $i] :
( ( ! [SY1669: $i,SY1670: $i] :
( ( ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SY1669 ) @ SY1669 )
!= ( c_List_Orev @ SY1670 @ SY1669 ) )
| ( SY1670
= ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SY1669 ) @ SY1669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1320,plain,
! [SV285: $i] :
( ( ( c_Suc @ SV285 )
!= SV285 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1321,plain,
! [SV286: $i] :
( ( ! [SY1671: $i,SY1672: $i] :
( ( ( c_List_Oappend @ SV286 @ SY1671 @ SY1672 )
!= ( c_List_Olist_ONil @ SY1672 ) )
| ( SY1671
= ( c_List_Olist_ONil @ SY1672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1322,plain,
! [SV287: $i] :
( ( ! [SY1673: $i,SY1674: $i,SY1675: $i,SY1676: $i] :
( ( ( c_List_Oappend @ SV287 @ ( c_List_Olist_OCons @ SY1673 @ ( c_List_Olist_ONil @ SY1674 ) @ SY1674 ) @ SY1674 )
!= ( c_List_Oappend @ SY1675 @ ( c_List_Olist_OCons @ SY1676 @ ( c_List_Olist_ONil @ SY1674 ) @ SY1674 ) @ SY1674 ) )
| ( SY1673 = SY1676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1323,plain,
! [SV288: $i] :
( ( ! [SY1677: $i,SY1678: $i] :
( ( c_List_Olist_OCons @ SV288 @ SY1677 @ SY1678 )
!= ( c_List_Olist_ONil @ SY1678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1324,plain,
! [SV289: $i] :
( ( ! [SY1679: $i,SY1680: $i,SY1681: $i,SY1682: $i] :
( ( ( c_List_Oappend @ SV289 @ ( c_List_Olist_OCons @ SY1679 @ ( c_List_Olist_ONil @ SY1680 ) @ SY1680 ) @ SY1680 )
!= ( c_List_Oappend @ SY1681 @ ( c_List_Olist_OCons @ SY1682 @ ( c_List_Olist_ONil @ SY1680 ) @ SY1680 ) @ SY1680 ) )
| ( SV289 = SY1681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1325,plain,
! [SV290: $i] :
( ( ! [SY1683: $i,SY1684: $i] :
( ( ( c_List_Orotate @ SV290 @ SY1683 @ SY1684 )
!= ( c_List_Olist_ONil @ SY1684 ) )
| ( SY1683
= ( c_List_Olist_ONil @ SY1684 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1326,plain,
! [SV291: $i] :
( ( ! [SY1685: $i,SY1686: $i] :
( ( c_List_Olist_ONil @ SV291 )
!= ( c_List_Olist_OCons @ SY1685 @ SY1686 @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1327,plain,
! [SV292: $i] :
( ( ! [SY1687: $i,SY1688: $i] :
( ( ( c_List_Oappend @ SV292 @ SY1687 @ SY1688 )
!= ( c_List_Olist_ONil @ SY1688 ) )
| ( SV292
= ( c_List_Olist_ONil @ SY1688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1328,plain,
! [SV293: $i] :
( ( ! [SY1689: $i] :
( ( ( c_List_Oremdups @ SV293 @ SY1689 )
!= ( c_List_Olist_ONil @ SY1689 ) )
| ( SV293
= ( c_List_Olist_ONil @ SY1689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1329,plain,
! [SV294: $i] :
( ( ! [SY1690: $i,SY1691: $i] :
( ( ( c_List_Oappend @ SV294 @ SY1690 @ SY1691 )
!= SY1690 )
| ( SV294
= ( c_List_Olist_ONil @ SY1691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1330,plain,
! [SV295: $i] :
( ( SV295
!= ( c_Suc @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1331,plain,
! [SV296: $i] :
( ( ! [SY1692: $i] :
( ( ( c_Suc @ SV296 )
!= ( c_Suc @ SY1692 ) )
| ( SV296 = SY1692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1332,plain,
! [SV297: $i] :
( ( ! [SY1693: $i,SY1694: $i,SY1695: $i,SY1696: $i] :
( ( ( c_List_Olist_OCons @ SV297 @ SY1693 @ SY1694 )
!= ( c_List_Ofilter @ SY1695 @ SY1696 @ SY1694 ) )
| ( hBOOL @ ( hAPP @ SY1695 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1333,plain,
! [SV298: $i] :
( ( ! [SY1697: $i,SY1698: $i,SY1699: $i,SY1700: $i] :
( ( ( c_List_Olist_OCons @ SV298 @ SY1697 @ SY1698 )
!= ( c_List_Olist_OCons @ SY1699 @ SY1700 @ SY1698 ) )
| ( SY1697 = SY1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1334,plain,
! [SV299: $i] :
( ( ! [SY1701: $i,SY1702: $i] :
( ( ( c_List_Olist_ONil @ SV299 )
!= ( c_List_Oappend @ SY1701 @ SY1702 @ SV299 ) )
| ( SY1702
= ( c_List_Olist_ONil @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1335,plain,
! [SV300: $i] :
( ( ! [SY1703: $i,SY1704: $i] :
( ( c_List_Olist_OCons @ SV300 @ SY1703 @ SY1704 )
!= SY1703 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1336,plain,
! [SV301: $i] :
( ( ! [SY1705: $i] :
( ( ( c_List_Olist_ONil @ SV301 )
!= ( c_List_Oremdups @ SY1705 @ SV301 ) )
| ( SY1705
= ( c_List_Olist_ONil @ SV301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1337,plain,
! [SV302: $i] :
( ( ! [SY1706: $i,SY1707: $i,SY1708: $i] :
( ( ( c_List_Oappend @ SV302 @ SY1706 @ SY1707 )
!= ( c_List_Oappend @ SY1708 @ SY1706 @ SY1707 ) )
| ( SV302 = SY1708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1338,plain,
! [SV303: $i] :
( ( ! [SY1709: $i,SY1710: $i] :
( ( SV303
!= ( c_List_Oappend @ SY1709 @ SV303 @ SY1710 ) )
| ( SY1709
= ( c_List_Olist_ONil @ SY1710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1339,plain,
! [SV304: $i] :
( ( ! [SY1711: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV304 )
!= ( c_Lambda_OdB_OAbs @ SY1711 ) )
| ( SV304 = SY1711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1340,plain,
! [SV305: $i] :
( ( ! [SY1712: $i,SY1713: $i,SY1714: $i] :
( ( ( c_List_Omap @ SV305 @ SY1712 @ SY1713 @ SY1714 )
!= ( c_List_Olist_ONil @ SY1714 ) )
| ( SY1712
= ( c_List_Olist_ONil @ SY1713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1341,plain,
! [SV306: $i] :
( ( ! [SY1715: $i,SY1716: $i,SY1717: $i,SY1718: $i] :
( ( ( c_List_Olist_OCons @ SV306 @ SY1715 @ SY1716 )
!= ( c_List_Olist_OCons @ SY1717 @ SY1718 @ SY1716 ) )
| ( SV306 = SY1717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1342,plain,
! [SV307: $i] :
( ( ! [SY1719: $i] :
( ( ( c_List_Olist_ONil @ SV307 )
!= ( c_List_Orev @ SY1719 @ SV307 ) )
| ( SY1719
= ( c_List_Olist_ONil @ SV307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1343,plain,
! [SV308: $i] :
( ( ! [SY1720: $i,SY1721: $i] :
( ( ( c_List_Orev @ SV308 @ SY1720 )
!= ( c_List_Orev @ SY1721 @ SY1720 ) )
| ( SV308 = SY1721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1344,plain,
! [SV309: $i] :
( ( ! [SY1722: $i,SY1723: $i,SY1724: $i] :
( ( ( c_List_Olist__update @ SV309 @ SY1722 @ SY1723 @ SY1724 )
!= ( c_List_Olist_ONil @ SY1724 ) )
| ( SV309
= ( c_List_Olist_ONil @ SY1724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1345,plain,
! [SV310: $i] :
( ( ! [SY1725: $i,SY1726: $i,SY1727: $i] :
( ( ( c_List_Olist_ONil @ SV310 )
!= ( c_List_Omap @ SY1725 @ SY1726 @ SY1727 @ SV310 ) )
| ( SY1726
= ( c_List_Olist_ONil @ SY1727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1346,plain,
! [SV311: $i] :
( ( ! [SY1728: $i] :
( ( ( c_List_Oremdups @ SV311 @ SY1728 )
!= SV311 )
| ( c_List_Odistinct @ SV311 @ SY1728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1347,plain,
! [SV312: $i] :
( ( ! [SY1729: $i,SY1730: $i] :
( ( ( c_List_Orev @ SV312 @ SY1729 )
!= ( c_List_Olist_OCons @ SY1730 @ ( c_List_Olist_ONil @ SY1729 ) @ SY1729 ) )
| ( SV312
= ( c_List_Olist_OCons @ SY1730 @ ( c_List_Olist_ONil @ SY1729 ) @ SY1729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1348,plain,
! [SV313: $i] :
( ( ! [SY1731: $i,SY1732: $i] :
( ( ( c_List_Olist_ONil @ SV313 )
!= ( c_List_Oappend @ SY1731 @ SY1732 @ SV313 ) )
| ( SY1731
= ( c_List_Olist_ONil @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1349,plain,
! [SV314: $i] :
( ( ! [SY1733: $i] :
( ( ( c_List_Orev @ SV314 @ SY1733 )
!= ( c_List_Olist_ONil @ SY1733 ) )
| ( SV314
= ( c_List_Olist_ONil @ SY1733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1350,plain,
! [SV315: $i] :
( ( ! [SY1734: $i,SY1735: $i] :
( ( c_List_Olist_OCons @ SV315 @ SY1734 @ SY1735 )
!= ( c_List_Olist_ONil @ SY1735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1351,plain,
! [SV316: $i] :
( ( ! [SY1736: $i,SY1737: $i,SY1738: $i,SY1739: $i] :
( ( ( c_List_OdropWhile @ SV316 @ SY1736 @ SY1737 )
!= ( c_List_Olist_OCons @ SY1738 @ SY1739 @ SY1737 ) )
| ~ ( hBOOL @ ( hAPP @ SV316 @ SY1738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1352,plain,
! [SV317: $i] :
( ( ! [SY1740: $i] :
( ( ( c_Suc @ SV317 )
!= ( c_Suc @ SY1740 ) )
| ( SV317 = SY1740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1353,plain,
! [SV318: $i] :
( ( ! [SY1741: $i,SY1742: $i] :
( SV318
!= ( c_List_Olist_OCons @ SY1741 @ SV318 @ SY1742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1354,plain,
! [SV319: $i] :
( ( ! [SY1743: $i,SY1744: $i,SY1745: $i] :
( ( ( c_List_Oappend @ SV319 @ SY1743 @ SY1744 )
!= ( c_List_Oappend @ SV319 @ SY1745 @ SY1744 ) )
| ( SY1743 = SY1745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1355,plain,
! [SV320: $i] :
( ( ! [SY1746: $i] :
( ( ( c_List_Orotate1 @ SV320 @ SY1746 )
!= ( c_List_Olist_ONil @ SY1746 ) )
| ( SV320
= ( c_List_Olist_ONil @ SY1746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1356,plain,
! [SV321: $i] :
( ( ! [SY1747: $i,SY1748: $i] :
( ( ( c_List_Oappend @ SV321 @ SY1747 @ SY1748 )
!= SV321 )
| ( SY1747
= ( c_List_Olist_ONil @ SY1748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1357,plain,
! [SV322: $i] :
( ( ! [SY1749: $i,SY1750: $i,SY1751: $i,SY1752: $i] :
( ( ( c_List_Ofilter @ SV322 @ SY1749 @ SY1750 )
!= ( c_List_Olist_OCons @ SY1751 @ SY1752 @ SY1750 ) )
| ( hBOOL @ ( hAPP @ SV322 @ SY1751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1358,plain,
! [SV323: $i] :
( ( ! [SY1753: $i,SY1754: $i] :
( ( SV323
!= ( c_List_Oappend @ SV323 @ SY1753 @ SY1754 ) )
| ( SY1753
= ( c_List_Olist_ONil @ SY1754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1359,plain,
! [SV324: $i,SV1: $i] :
( ( ! [SY1755: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV1 ) @ SV324 @ SY1755 )
= ( c_List_Odrop @ SV1 @ ( c_List_Otl @ SV324 @ SY1755 ) @ SY1755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1360,plain,
! [SV325: $i,SV2: $i] :
( ( ! [SY1756: $i] :
( ( c_List_Otake @ SV2 @ ( c_List_Otl @ SV325 @ SY1756 ) @ SY1756 )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ SV2 ) @ SV325 @ SY1756 ) @ SY1756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1361,plain,
! [SV326: $i,SV3: $i] :
( ( ! [SY1757: $i,SY1758: $i,SY1759: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV3 @ SV326 @ SY1757 ) @ ( c_Suc @ SY1758 ) @ SY1759 @ SY1757 )
= ( c_List_Olist_OCons @ SV3 @ ( c_List_Olist__update @ SV326 @ SY1758 @ SY1759 @ SY1757 ) @ SY1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1362,plain,
! [SV327: $i,SV4: $i] :
( ( ! [SY1760: $i,SY1761: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV4 ) @ ( c_List_Olist_OCons @ SV327 @ SY1760 @ SY1761 ) @ SY1761 )
= ( c_List_Odrop @ SV4 @ SY1760 @ SY1761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1363,plain,
! [SV328: $i,SV5: $i] :
( ( ! [SY1762: $i,SY1763: $i] :
( ( c_List_Otake @ ( c_Suc @ SV5 ) @ ( c_List_Olist_OCons @ SV328 @ SY1762 @ SY1763 ) @ SY1763 )
= ( c_List_Olist_OCons @ SV328 @ ( c_List_Otake @ SV5 @ SY1762 @ SY1763 ) @ SY1763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1364,plain,
! [SV329: $i,SV6: $i] :
( ( ! [SY1764: $i] :
( ( c_List_Orotate @ ( c_Suc @ SV6 ) @ SV329 @ SY1764 )
= ( c_List_Orotate1 @ ( c_List_Orotate @ SV6 @ SV329 @ SY1764 ) @ SY1764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1365,plain,
! [SV330: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ SV7 @ SV330 ) )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ SV7 ) @ ( v_sko__List__Xdrop__Xinduct__2 @ SV7 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1366,plain,
! [SV331: $i,SV8: $i] :
( ( ( hBOOL @ ( hAPP @ SV8 @ SV331 ) )
| ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ SV8 ) @ ( v_sko__List__Xrev__Xinduct__2 @ SV8 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1367,plain,
! [SV332: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP @ SV9 @ SV332 ) )
| ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ SV9 ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV9 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1368,plain,
! [SV333: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ SV333 ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV10 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV10 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1369,plain,
! [SV334: $i,SV11: $i] :
( ( ! [SY1765: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV11 @ SV334 @ SY1765 ) @ SY1765 )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1370,plain,
! [SV335: $i,SV12: $i] :
( ( ! [SY1766: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ SV12 @ SV335 @ SY1766 ) @ SY1766 )
= ( c_List_Ohd @ SV12 @ SY1766 ) )
| ( SV12
= ( c_List_Olist_ONil @ SY1766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1371,plain,
! [SV336: $i,SV13: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ SV13 ) @ SV336 @ SV13 ) @ SV13 )
= ( c_List_Ohd @ SV336 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1372,plain,
! [SV337: $i,SV14: $i] :
( ( ! [SY1767: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV14 ) @ SV337 @ SY1767 )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ SV337 @ SY1767 ) @ ( c_List_Otake @ SV14 @ ( c_List_Otl @ SV337 @ SY1767 ) @ SY1767 ) @ SY1767 ) )
| ( SV337
= ( c_List_Olist_ONil @ SY1767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1373,plain,
! [SV338: $i,SV15: $i] :
( ( ! [SY1768: $i] :
( ~ ( hBOOL @ ( hAPP @ SV15 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV15 @ SV338 @ SY1768 ) @ SY1768 ) ) )
| ( ( c_List_OdropWhile @ SV15 @ SV338 @ SY1768 )
= ( c_List_Olist_ONil @ SY1768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1374,plain,
! [SV339: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ SV16 @ SV339 ) )
| ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ SV16 ) @ ( v_sko__List__Xhd__Xinduct__2 @ SV16 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1375,plain,
! [SV340: $i,SV17: $i] :
( ( ( hBOOL @ ( hAPP @ SV17 @ SV340 ) )
| ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV17 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV17 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1376,plain,
! [SV341: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ SV341 ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ SV18 ) @ ( v_sko__List__Xset__Xinduct__2 @ SV18 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1377,plain,
! [SV342: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ SV19 @ SV342 ) )
| ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV19 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV19 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1378,plain,
! [SV343: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ SV20 @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinducts__1 @ SV20 ) @ ( v_sko__List__Xlist__Xinducts__2 @ SV20 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1379,plain,
! [SV344: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ SV21 @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV21 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV21 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1380,plain,
! [SV345: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP @ SV22 @ SV345 ) )
| ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ SV22 ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV22 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1381,plain,
! [SV346: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ SV23 @ SV346 ) )
| ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ SV23 ) @ ( v_sko__List__Xremdups__Xinduct__2 @ SV23 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1382,plain,
! [SV347: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ SV24 @ SV347 ) )
| ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ SV24 ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV24 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1383,plain,
! [SV348: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ SV348 ) )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ SV25 ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV25 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1384,plain,
! [SV349: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ SV26 @ SV349 ) )
| ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV26 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV26 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1385,plain,
! [SV350: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ SV27 @ SV350 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV27 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV27 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1386,plain,
! [SV351: $i,SV28: $i] :
( ( ( hBOOL @ ( hAPP @ SV28 @ SV351 ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV28 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV28 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1387,plain,
! [SV352: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ SV352 ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV29 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV29 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1388,plain,
! [SV353: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ SV30 @ SV353 ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ SV30 ) @ ( v_sko__List__Xsplice__Xinduct__2 @ SV30 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1389,plain,
! [SV354: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ SV31 @ SV354 ) )
| ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV31 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV31 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1390,plain,
! [SV355: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ SV32 @ SV355 ) )
| ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ SV32 ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV32 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1391,plain,
! [SV356: $i,SV33: $i] :
( ( ( hBOOL @ ( hAPP @ SV33 @ SV356 ) )
| ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ SV33 ) @ ( v_sko__List__Xlast__Xinduct__2 @ SV33 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1392,plain,
! [SV357: $i,SV34: $i] :
( ( ( hBOOL @ ( hAPP @ SV34 @ SV357 ) )
| ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ SV34 ) @ ( v_sko__List__Xtl__Xinduct__2 @ SV34 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1393,plain,
! [SV358: $i,SV35: $i] :
( ( ! [SY1769: $i,SY1770: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV35 @ SV358 @ SY1769 ) @ SY1770 @ SY1769 )
= ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY1770 @ SY1769 ) @ ( c_List_Osplice @ SV358 @ ( c_List_Otl @ SY1770 @ SY1769 ) @ SY1769 ) @ SY1769 ) @ SY1769 ) )
| ( SY1770
= ( c_List_Olist_ONil @ SY1769 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1394,plain,
! [SV359: $i,SV36: $i] :
( ( ! [SY1771: $i] :
( ( hBOOL @ ( hAPP @ SV36 @ SV359 ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV36 @ SY1771 ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ SV36 @ SY1771 ) @ ( c_List_Olist_ONil @ SY1771 ) @ SY1771 ) @ SY1771 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Olist_ONil @ SY1771 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1395,plain,
! [SV360: $i,SV37: $i] :
( ( ( ( c_List_Orotate1 @ SV37 @ SV360 )
= ( c_List_Oappend @ ( c_List_Otl @ SV37 @ SV360 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV37 @ SV360 ) @ ( c_List_Olist_ONil @ SV360 ) @ SV360 ) @ SV360 ) )
| ( SV37
= ( c_List_Olist_ONil @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1396,plain,
! [SV361: $i,SV38: $i] :
( ( ! [SY1772: $i,SY1773: $i] :
( ~ ( class_Orderings_Olinorder @ SV38 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV361 @ ( c_List_Olinorder__class_Osort__key @ SV361 @ SY1772 @ SY1773 @ SV38 ) @ SY1773 @ SV38 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1397,plain,
! [SV362: $i,SV39: $i] :
( ( ! [SY1774: $i] :
( ( c_List_Odrop @ SV39 @ ( c_List_Otl @ SV362 @ SY1774 ) @ SY1774 )
= ( c_List_Otl @ ( c_List_Odrop @ SV39 @ SV362 @ SY1774 ) @ SY1774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1398,plain,
! [SV363: $i,SV40: $i] :
( ( ! [SY1775: $i,SY1776: $i,SY1777: $i] :
( ( c_ListOrder_Ostep1 @ SV40 @ ( c_List_Oappend @ SV363 @ SY1775 @ SY1776 ) @ ( c_List_Oappend @ SV363 @ SY1777 @ SY1776 ) @ SY1776 )
| ~ ( c_ListOrder_Ostep1 @ SV40 @ SY1775 @ SY1777 @ SY1776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1399,plain,
! [SV364: $i,SV41: $i] :
( ( ! [SY1778: $i,SY1779: $i,SY1780: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV41 @ SV364 @ SY1778 @ SY1779 )
| ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Oappend @ SV364 @ SY1780 @ SY1779 ) @ ( c_List_Oappend @ SY1778 @ SY1780 @ SY1779 ) @ SY1779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1400,plain,
! [SV365: $i,SV42: $i] :
( ( ! [SY1781: $i,SY1782: $i] :
( ( ( c_List_Ofilter @ SV42 @ ( c_List_Olist_OCons @ SV365 @ SY1781 @ SY1782 ) @ SY1782 )
= ( c_List_Olist_OCons @ SV365 @ ( c_List_Ofilter @ SV42 @ SY1781 @ SY1782 ) @ SY1782 ) )
| ~ ( hBOOL @ ( hAPP @ SV42 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1401,plain,
! [SV366: $i,SV43: $i] :
( ( ! [SY1783: $i] :
( ~ ( class_Orderings_Olinorder @ SV43 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV366 @ SY1783 @ SV43 ) @ SV43 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1783 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1402,plain,
! [SV367: $i,SV44: $i] :
( ( ! [SY1784: $i,SY1785: $i,SY1786: $i] :
( ( c_List_Otake @ SV44 @ ( c_List_Omap @ SV367 @ SY1784 @ SY1785 @ SY1786 ) @ SY1786 )
= ( c_List_Omap @ SV367 @ ( c_List_Otake @ SV44 @ SY1784 @ SY1785 ) @ SY1785 @ SY1786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1403,plain,
! [SV368: $i,SV45: $i] :
( ( ! [SY1787: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ SV45 @ SV368 @ SY1787 ) @ SY1787 )
= ( c_List_Ofilter @ SV45 @ ( c_List_Oremdups @ SV368 @ SY1787 ) @ SY1787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1404,plain,
! [SV369: $i,SV46: $i] :
( ( ! [SY1788: $i,SY1789: $i,SY1790: $i,SY1791: $i] :
( ( c_List_Olist__all2 @ SV46 @ ( c_List_Otake @ SV369 @ SY1788 @ SY1789 ) @ ( c_List_Otake @ SV369 @ SY1790 @ SY1791 ) @ SY1789 @ SY1791 )
| ~ ( c_List_Olist__all2 @ SV46 @ SY1788 @ SY1790 @ SY1789 @ SY1791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1405,plain,
! [SV370: $i,SV47: $i] :
( ( ! [SY1792: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV47 @ SV370 @ SY1792 ) @ SY1792 )
= ( c_List_Oappend @ ( c_List_Orev @ SV370 @ SY1792 ) @ ( c_List_Olist_OCons @ SV47 @ ( c_List_Olist_ONil @ SY1792 ) @ SY1792 ) @ SY1792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1406,plain,
! [SV371: $i,SV48: $i] :
( ( ! [SY1793: $i] :
( ( SV48 = SV371 )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ SY1793 ) @ SV48 @ SV371 @ SY1793 @ SY1793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1407,plain,
! [SV372: $i,SV49: $i] :
( ( ! [SY1794: $i,SY1795: $i,SY1796: $i,SY1797: $i] :
( ( c_List_Ofoldl @ SV49 @ SV372 @ ( c_List_Olist_OCons @ SY1794 @ SY1795 @ SY1796 ) @ SY1797 @ SY1796 )
= ( c_List_Ofoldl @ SV49 @ ( hAPP @ ( hAPP @ SV49 @ SV372 ) @ SY1794 ) @ SY1795 @ SY1797 @ SY1796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1408,plain,
! [SV373: $i,SV50: $i] :
( ( ! [SY1798: $i,SY1799: $i,SY1800: $i,SY1801: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV373 ) @ SY1798 ) )
| ( c_ListOrder_Ostep1 @ SV50 @ SY1799 @ SY1800 @ SY1801 )
| ~ ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SY1799 @ ( c_List_Olist_OCons @ SV373 @ ( c_List_Olist_ONil @ SY1801 ) @ SY1801 ) @ SY1801 ) @ ( c_List_Oappend @ SY1800 @ ( c_List_Olist_OCons @ SY1798 @ ( c_List_Olist_ONil @ SY1801 ) @ SY1801 ) @ SY1801 ) @ SY1801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1409,plain,
! [SV374: $i,SV51: $i] :
( ( ! [SY1802: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ SV51 @ SV374 @ SY1802 ) @ SY1802 )
= ( c_List_Odrop @ SV51 @ ( c_List_Otl @ SV374 @ SY1802 ) @ SY1802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1410,plain,
! [SV375: $i,SV52: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV52 @ ( c_List_Olist_ONil @ SV375 ) @ SV375 ) @ SV375 )
= ( c_List_Olist_OCons @ SV52 @ ( c_List_Olist_ONil @ SV375 ) @ SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1411,plain,
! [SV376: $i,SV53: $i] :
( ( ! [SY1803: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SV376 @ ( tc_fun @ SY1803 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV53 @ ( tc_fun @ SY1803 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1412,plain,
! [SV377: $i,SV54: $i] :
( ( ! [SY1804: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV54 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV377 @ SY1804 @ SV54 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1804 @ SV377 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1413,plain,
! [SV378: $i,SV55: $i] :
( ( ! [SY1805: $i] :
( ~ ( class_Lattices_Olattice @ SV55 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 @ SY1805 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1805 @ SV378 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1414,plain,
! [SV379: $i,SV56: $i] :
( ( ! [SY1806: $i,SY1807: $i] :
( ~ ( class_Orderings_Olinorder @ SV56 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV379 @ SY1806 @ SV56 ) @ SV56 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1807 @ ( c_List_Olist_OCons @ SV379 @ SY1806 @ SV56 ) @ SV56 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1415,plain,
! [SV380: $i,SV57: $i] :
( ( ! [SY1808: $i,SY1809: $i,SY1810: $i,SY1811: $i,SY1812: $i] :
( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SY1808 @ SY1809 ) @ ( c_List_Oappend @ SY1810 @ SY1811 @ SY1812 ) @ SY1809 @ SY1812 )
| ~ ( c_List_Olist__all2 @ SV57 @ SY1808 @ SY1811 @ SY1809 @ SY1812 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SY1810 @ SY1809 @ SY1812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1416,plain,
! [SV381: $i,SV58: $i] :
( ( ! [SY1813: $i,SY1814: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV58 @ SV381 @ SY1813 ) @ SY1814 @ SY1813 )
= ( c_List_Olist_OCons @ SV58 @ ( c_List_Oappend @ SV381 @ SY1814 @ SY1813 ) @ SY1813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1417,plain,
! [SV382: $i,SV59: $i] :
( ( ! [SY1815: $i,SY1816: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV59 @ SV382 @ SY1815 ) @ SY1816 @ SY1815 )
= ( c_List_Olist_OCons @ SV59 @ ( c_List_Oappend @ SV382 @ SY1816 @ SY1815 ) @ SY1815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1418,plain,
! [SV383: $i,SV60: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate1 @ SV60 @ SV383 ) @ SV383 )
| ~ ( c_List_Odistinct @ SV60 @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1419,plain,
! [SV384: $i,SV61: $i] :
( ( ( c_List_Odistinct @ SV61 @ SV384 )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ SV61 @ SV384 ) @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1420,plain,
! [SV385: $i,SV62: $i] :
( ( ! [SY1817: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ SV62 @ SV385 @ SY1817 ) @ SY1817 )
| ~ ( c_List_Odistinct @ SV385 @ SY1817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1421,plain,
! [SV386: $i,SV63: $i] :
( ( ! [SY1818: $i,SY1819: $i,SY1820: $i] :
( ( c_List_Omap @ SV63 @ ( c_List_Olist_OCons @ SV386 @ SY1818 @ SY1819 ) @ SY1819 @ SY1820 )
= ( c_List_Olist_OCons @ ( hAPP @ SV63 @ SV386 ) @ ( c_List_Omap @ SV63 @ SY1818 @ SY1819 @ SY1820 ) @ SY1820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1422,plain,
! [SV387: $i,SV64: $i] :
( ( ! [SY1821: $i,SY1822: $i,SY1823: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV64 @ SV387 ) @ ( c_List_Omap @ SV64 @ SY1821 @ SY1822 @ SY1823 ) @ SY1823 )
= ( c_List_Omap @ SV64 @ ( c_List_Olist_OCons @ SV387 @ SY1821 @ SY1822 ) @ SY1822 @ SY1823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1423,plain,
! [SV388: $i,SV65: $i] :
( ( ! [SY1824: $i,SY1825: $i,SY1826: $i] :
( ( c_List_Omap @ SV65 @ ( c_List_Olist_OCons @ SV388 @ SY1824 @ SY1825 ) @ SY1825 @ SY1826 )
= ( c_List_Olist_OCons @ ( hAPP @ SV65 @ SV388 ) @ ( c_List_Omap @ SV65 @ SY1824 @ SY1825 @ SY1826 ) @ SY1826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1424,plain,
! [SV389: $i,SV66: $i] :
( ( ! [SY1827: $i,SY1828: $i,SY1829: $i,SY1830: $i] :
( ( c_List_Olist_Olist__case @ SV66 @ SV389 @ ( c_List_Olist_OCons @ SY1827 @ SY1828 @ SY1829 ) @ SY1830 @ SY1829 )
= ( hAPP @ ( hAPP @ SV389 @ SY1827 ) @ SY1828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1425,plain,
! [SV390: $i,SV67: $i] :
( ( ! [SY1831: $i] :
( ( c_List_Oremove1 @ SV67 @ ( c_List_Olist_OCons @ SV67 @ SV390 @ SY1831 ) @ SY1831 )
= SV390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1426,plain,
! [SV391: $i,SV68: $i] :
( ( ! [SY1832: $i,SY1833: $i,SY1834: $i,SY1835: $i,SY1836: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV391 ) @ SY1832 ) )
| ~ ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SV391 @ SY1833 @ SY1834 ) @ ( c_List_Olist_OCons @ SY1832 @ SY1835 @ SY1836 ) @ SY1834 @ SY1836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1427,plain,
! [SV392: $i,SV69: $i] :
( ( ! [SY1837: $i,SY1838: $i] :
( ( c_List_Olist_OCons @ SV69 @ ( c_List_Oappend @ SV392 @ SY1837 @ SY1838 ) @ SY1838 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV69 @ SV392 @ SY1838 ) @ SY1837 @ SY1838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1428,plain,
! [SV393: $i,SV70: $i] :
( ( ! [SY1839: $i,SY1840: $i] :
( ( c_List_Olist_OCons @ SV70 @ ( c_List_Oappend @ SV393 @ SY1839 @ SY1840 ) @ SY1840 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV70 @ SV393 @ SY1840 ) @ SY1839 @ SY1840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1429,plain,
! [SV394: $i,SV71: $i] :
( ( ! [SY1841: $i,SY1842: $i,SY1843: $i,SY1844: $i] :
( ( SV71 = SV394 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1841 @ SV394 ) @ SV71 ) )
| ~ ( c_ListOrder_Ostep1 @ SY1841 @ ( c_List_Olist_OCons @ SV394 @ SY1842 @ SY1843 ) @ ( c_List_Olist_OCons @ SV71 @ SY1844 @ SY1843 ) @ SY1843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1430,plain,
! [SV395: $i,SV72: $i] :
( ( ! [SY1845: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ SV72 @ SV395 @ SY1845 ) @ ( c_List_Odrop @ SV72 @ SV395 @ SY1845 ) @ SY1845 )
= SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1431,plain,
! [SV396: $i,SV73: $i] :
( ( ! [SY1846: $i] :
( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_List_Olinorder__class_Osorted @ SV396 @ SV73 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY1846 @ SV396 @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1432,plain,
! [SV397: $i,SV74: $i] :
( ( ! [SY1847: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV74 @ SV397 ) @ ( c_List_Olist_OCons @ SY1847 @ ( c_List_Olist_ONil @ SV397 ) @ SV397 ) @ SV397 ) @ SV397 )
= ( c_List_Olist_OCons @ SY1847 @ SV74 @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1433,plain,
! [SV398: $i,SV75: $i] :
( ( ! [SY1848: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ SV75 @ SV398 @ SY1848 ) @ SY1848 )
| ~ ( c_List_Odistinct @ SV398 @ SY1848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1434,plain,
! [SV399: $i,SV76: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orev @ SV76 @ SV399 ) @ SV399 )
| ~ ( c_List_Odistinct @ SV76 @ SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1435,plain,
! [SV400: $i,SV77: $i] :
( ( ( c_List_Odistinct @ SV77 @ SV400 )
| ~ ( c_List_Odistinct @ ( c_List_Orev @ SV77 @ SV400 ) @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1436,plain,
! [SV401: $i,SV78: $i] :
( ( ! [SY1849: $i,SY1850: $i] :
( ( c_List_Olist__all @ SV78 @ SV401 @ SY1849 )
| ~ ( c_List_Olist__all @ SV78 @ ( c_List_Olist_OCons @ SY1850 @ SV401 @ SY1849 ) @ SY1849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1437,plain,
! [SV402: $i,SV79: $i] :
( ( ( ( c_List_Oremdups @ SV79 @ SV402 )
= SV79 )
| ~ ( c_List_Odistinct @ SV79 @ SV402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1438,plain,
! [SV403: $i,SV80: $i] :
( ( ! [SY1851: $i] :
( ( hBOOL @ ( hAPP @ SV80 @ SV403 ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY1851 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY1851 @ SV80 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1851 @ SV403 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1439,plain,
! [SV404: $i,SV81: $i] :
( ( ! [SY1852: $i,SY1853: $i] :
( ( hBOOL @ ( hAPP @ SV81 @ SV404 ) )
| ~ ( c_List_Olist__all @ SV81 @ ( c_List_Olist_OCons @ SV404 @ SY1852 @ SY1853 ) @ SY1853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1440,plain,
! [SV405: $i,SV82: $i] :
( ( ! [SY1854: $i] :
( ( hBOOL @ ( hAPP @ SV82 @ SV405 ) )
| ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY1854 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY1854 @ SV82 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY1854 @ SV405 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1441,plain,
! [SV406: $i,SV83: $i] :
( ( ! [SY1855: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV83 @ SV406 @ SY1855 ) @ SY1855 )
= ( c_List_Oappend @ SV406 @ ( c_List_Olist_OCons @ SV83 @ ( c_List_Olist_ONil @ SY1855 ) @ SY1855 ) @ SY1855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1442,plain,
! [SV407: $i,SV84: $i] :
( ( ! [SY1856: $i] :
( ( c_List_Olist_OCons @ SV84 @ SV407 @ SY1856 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY1856 ) @ ( c_List_Olist_OCons @ SV84 @ SV407 @ SY1856 ) @ SY1856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1443,plain,
! [SV408: $i,SV85: $i] :
( ( ! [SY1857: $i,SY1858: $i,SY1859: $i,SY1860: $i] :
( ( c_List_Omap @ SV85 @ ( c_List_Olist__update @ SV408 @ SY1857 @ SY1858 @ SY1859 ) @ SY1859 @ SY1860 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV85 @ SV408 @ SY1859 @ SY1860 ) @ SY1857 @ ( hAPP @ SV85 @ SY1858 ) @ SY1860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1444,plain,
! [SV409: $i,SV86: $i] :
( ( ( c_List_Olist_OCons @ SV86 @ ( c_List_Olist_ONil @ SV409 ) @ SV409 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV86 @ ( c_List_Olist_ONil @ SV409 ) @ SV409 ) @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1445,plain,
! [SV410: $i,SV87: $i] :
( ( ! [SY1861: $i,SY1862: $i,SY1863: $i,SY1864: $i] :
( ( SV87 = SV410 )
| ( c_ListOrder_Ostep1 @ SY1861 @ SV87 @ SV410 @ SY1862 )
| ~ ( c_ListOrder_Ostep1 @ SY1861 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SY1863 @ ( c_List_Olist_ONil @ SY1862 ) @ SY1862 ) @ SY1862 ) @ ( c_List_Oappend @ SV410 @ ( c_List_Olist_OCons @ SY1864 @ ( c_List_Olist_ONil @ SY1862 ) @ SY1862 ) @ SY1862 ) @ SY1862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1446,plain,
! [SV411: $i,SV88: $i] :
( ( ! [SY1865: $i,SY1866: $i] :
( ( hBOOL @ ( hAPP @ SV88 @ SV411 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1865 @ SV88 @ ( tc_fun @ SY1866 @ tc_bool ) ) @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1447,plain,
! [SV412: $i,SV89: $i] :
( ( ! [SY1867: $i,SY1868: $i] :
( ( hBOOL @ ( hAPP @ SV89 @ SV412 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SY1867 @ ( tc_fun @ SY1868 @ tc_bool ) ) @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1448,plain,
! [SV413: $i,SV90: $i] :
( ( ! [SY1869: $i,SY1870: $i] :
( ( c_List_Olist__all @ SV90 @ ( c_List_Oappend @ SV413 @ SY1869 @ SY1870 ) @ SY1870 )
| ~ ( c_List_Olist__all @ SV90 @ SY1869 @ SY1870 )
| ~ ( c_List_Olist__all @ SV90 @ SV413 @ SY1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1449,plain,
! [SV414: $i,SV91: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV91 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV414 @ ( c_List_Olist_ONil @ SV91 ) @ SV91 ) @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1450,plain,
! [SV415: $i,SV92: $i] :
( ( ! [SY1871: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ SV92 @ SV415 @ SY1871 ) @ SY1871 )
| ~ ( c_List_Odistinct @ SV415 @ SY1871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1451,plain,
! [SV416: $i,SV93: $i] :
( ( ! [SY1872: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV93 @ SV416 @ SY1872 ) @ SY1872 )
= ( c_List_Oappend @ ( c_List_Orev @ SV416 @ SY1872 ) @ ( c_List_Orev @ SV93 @ SY1872 ) @ SY1872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1452,plain,
! [SV417: $i,SV94: $i] :
( ( ! [SY1873: $i,SY1874: $i,SY1875: $i,SY1876: $i] :
( ( c_List_Ofoldl @ SV94 @ SV417 @ ( c_List_Oappend @ SY1873 @ SY1874 @ SY1875 ) @ SY1876 @ SY1875 )
= ( c_List_Ofoldl @ SV94 @ ( c_List_Ofoldl @ SV94 @ SV417 @ SY1873 @ SY1876 @ SY1875 ) @ SY1874 @ SY1876 @ SY1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1453,plain,
! [SV418: $i,SV95: $i] :
( ( ! [SY1877: $i] :
( ( c_List_Odistinct @ SV95 @ SV418 )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ SY1877 @ SV95 @ SV418 ) @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1454,plain,
! [SV419: $i,SV96: $i] :
( ( ! [SY1878: $i,SY1879: $i] :
( ( c_List_Ofilter @ SV96 @ ( c_List_Oappend @ SV419 @ SY1878 @ SY1879 ) @ SY1879 )
= ( c_List_Oappend @ ( c_List_Ofilter @ SV96 @ SV419 @ SY1879 ) @ ( c_List_Ofilter @ SV96 @ SY1878 @ SY1879 ) @ SY1879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1455,plain,
! [SV420: $i,SV97: $i] :
( ( ! [SY1880: $i,SY1881: $i,SY1882: $i] :
( ( c_List_Olist__all2 @ SV97 @ ( c_List_Orev @ SV420 @ SY1880 ) @ SY1881 @ SY1880 @ SY1882 )
| ~ ( c_List_Olist__all2 @ SV97 @ SV420 @ ( c_List_Orev @ SY1881 @ SY1882 ) @ SY1880 @ SY1882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1456,plain,
! [SV421: $i,SV98: $i] :
( ( ! [SY1883: $i,SY1884: $i,SY1885: $i] :
( ( c_List_Olist__all2 @ SV98 @ SV421 @ ( c_List_Orev @ SY1883 @ SY1884 ) @ SY1885 @ SY1884 )
| ~ ( c_List_Olist__all2 @ SV98 @ ( c_List_Orev @ SV421 @ SY1885 ) @ SY1883 @ SY1885 @ SY1884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1457,plain,
! [SV422: $i,SV100: $i] :
( ( ! [SY1886: $i] : ( c_List_Olist__all2 @ SV100 @ ( c_List_Olist_ONil @ SV422 ) @ ( c_List_Olist_ONil @ SY1886 ) @ SV422 @ SY1886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1458,plain,
! [SV423: $i,SV101: $i] :
( ( ( SV101
= ( c_List_Olist_ONil @ SV423 ) )
| ~ ( c_List_Onull @ SV101 @ SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1459,plain,
! [SV424: $i,SV104: $i] :
( ( ! [SY1887: $i,SY1888: $i,SY1889: $i,SY1890: $i] :
( ( SV104 = SV424 )
| ( SY1887 = SY1888 )
| ~ ( c_ListOrder_Ostep1 @ SY1889 @ ( c_List_Olist_OCons @ SV424 @ SY1888 @ SY1890 ) @ ( c_List_Olist_OCons @ SV104 @ SY1887 @ SY1890 ) @ SY1890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1460,plain,
! [SV425: $i,SV105: $i] :
( ( ! [SY1891: $i,SY1892: $i,SY1893: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV425 ) @ SY1891 ) )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Olist_OCons @ SV425 @ SY1892 @ SY1893 ) @ ( c_List_Olist_OCons @ SY1891 @ SY1892 @ SY1893 ) @ SY1893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1461,plain,
! [SV426: $i,SV106: $i] :
( ( ! [SY1894: $i,SY1895: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV106 @ SV426 @ SY1894 @ SY1895 ) @ SY1895 )
= ( c_List_Omap @ SV106 @ ( c_List_Orev @ SV426 @ SY1894 ) @ SY1894 @ SY1895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1462,plain,
! [SV427: $i,SV107: $i] :
( ( ! [SY1896: $i] :
( ~ ( class_Orderings_Olinorder @ SV107 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV427 @ SY1896 @ SV107 ) @ SV107 )
| ~ ( c_List_Olinorder__class_Osorted @ SY1896 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1463,plain,
! [SV428: $i,SV108: $i] :
( ( ! [SY1897: $i,SY1898: $i] :
( ~ ( class_Orderings_Olinorder @ SV108 )
| ( c_List_Odistinct @ SV428 @ SY1897 )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SY1898 @ SV428 @ SY1897 @ SV108 ) @ SY1897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1464,plain,
! [SV429: $i,SV109: $i] :
( ( ! [SY1899: $i,SY1900: $i] :
( ~ ( class_Orderings_Olinorder @ SV109 )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV429 @ SY1899 @ SY1900 @ SV109 ) @ SY1900 )
| ~ ( c_List_Odistinct @ SY1899 @ SY1900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1465,plain,
! [SV430: $i,SV110: $i] :
( ( ! [SY1901: $i,SY1902: $i,SY1903: $i,SY1904: $i,SY1905: $i] :
( ( c_List_Olist__all2 @ SV110 @ SV430 @ SY1901 @ SY1902 @ SY1903 )
| ~ ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SY1904 @ SV430 @ SY1902 ) @ ( c_List_Olist_OCons @ SY1905 @ SY1901 @ SY1903 ) @ SY1902 @ SY1903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1466,plain,
! [SV431: $i,SV111: $i] :
( ( ! [SY1906: $i,SY1907: $i,SY1908: $i] :
( ( c_List_Orotate @ SV111 @ ( c_List_Omap @ SV431 @ SY1906 @ SY1907 @ SY1908 ) @ SY1908 )
= ( c_List_Omap @ SV431 @ ( c_List_Orotate @ SV111 @ SY1906 @ SY1907 ) @ SY1907 @ SY1908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1467,plain,
! [SV432: $i,SV112: $i] :
( ( ! [SY1909: $i] :
( ( c_List_Odistinct @ SV112 @ SV432 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV112 @ SY1909 @ SV432 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1468,plain,
! [SV433: $i,SV113: $i] :
( ( ! [SY1910: $i] :
( ( c_List_Odistinct @ SV113 @ SV433 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SY1910 @ SV113 @ SV433 ) @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1469,plain,
! [SV434: $i,SV114: $i] :
( ( SV114
= ( c_List_Orev @ ( c_List_Orev @ SV114 @ SV434 ) @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1470,plain,
! [SV435: $i,SV115: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV115 @ SV435 ) @ SV435 )
= SV115 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1471,plain,
! [SV436: $i,SV116: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV116 @ SV436 ) @ SV436 )
= SV116 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1472,plain,
! [SV437: $i,SV117: $i] :
( ( ! [SY1911: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ SV117 @ SV437 @ SY1911 ) @ SY1911 )
| ~ ( c_List_Odistinct @ SV437 @ SY1911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1473,plain,
! [SV438: $i,SV118: $i] :
( ( ! [SY1912: $i,SY1913: $i,SY1914: $i] :
( ( c_List_Olist__all2 @ SV118 @ SV438 @ SY1912 @ SY1913 @ SY1914 )
| ~ ( c_List_Olist__all2 @ SV118 @ ( c_List_Orev @ SV438 @ SY1913 ) @ ( c_List_Orev @ SY1912 @ SY1914 ) @ SY1913 @ SY1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1474,plain,
! [SV439: $i,SV119: $i] :
( ( ! [SY1915: $i,SY1916: $i,SY1917: $i] :
( ( c_List_Olist__all2 @ SV119 @ ( c_List_Orev @ SV439 @ SY1915 ) @ ( c_List_Orev @ SY1916 @ SY1917 ) @ SY1915 @ SY1917 )
| ~ ( c_List_Olist__all2 @ SV119 @ SV439 @ SY1916 @ SY1915 @ SY1917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1475,plain,
! [SV440: $i,SV120: $i] :
( ( ! [SY1918: $i,SY1919: $i,SY1920: $i] :
( ( c_List_Oconcat__map @ SV120 @ ( c_List_Olist_OCons @ SV440 @ SY1918 @ SY1919 ) @ SY1919 @ SY1920 )
= ( c_List_Oappend @ ( hAPP @ SV120 @ SV440 ) @ ( c_List_Oconcat__map @ SV120 @ SY1918 @ SY1919 @ SY1920 ) @ SY1920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1476,plain,
! [SV441: $i,SV121: $i] :
( ( ! [SY1921: $i,SY1922: $i,SY1923: $i,SY1924: $i] :
( ( c_List_Ofoldr @ SV121 @ ( c_List_Oappend @ SV441 @ SY1921 @ SY1922 ) @ SY1923 @ SY1922 @ SY1924 )
= ( c_List_Ofoldr @ SV121 @ SV441 @ ( c_List_Ofoldr @ SV121 @ SY1921 @ SY1923 @ SY1922 @ SY1924 ) @ SY1922 @ SY1924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1477,plain,
! [SV442: $i,SV122: $i] :
( ( ! [SY1925: $i,SY1926: $i] :
( ( c_List_Olist__ex @ SV122 @ ( c_List_Olist_OCons @ SV442 @ SY1925 @ SY1926 ) @ SY1926 )
| ~ ( hBOOL @ ( hAPP @ SV122 @ SV442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1478,plain,
! [SV443: $i,SV123: $i] :
( ( ! [SY1927: $i,SY1928: $i,SY1929: $i,SY1930: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV443 ) @ SY1927 ) )
| ( SV443 = SY1927 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SY1928 @ ( c_List_Olist_OCons @ SV443 @ ( c_List_Olist_ONil @ SY1929 ) @ SY1929 ) @ SY1929 ) @ ( c_List_Oappend @ SY1930 @ ( c_List_Olist_OCons @ SY1927 @ ( c_List_Olist_ONil @ SY1929 ) @ SY1929 ) @ SY1929 ) @ SY1929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1479,plain,
! [SV444: $i,SV124: $i] :
( ( ! [SY1931: $i,SY1932: $i,SY1933: $i,SY1934: $i,SY1935: $i] :
( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SY1931 @ SY1932 ) @ ( c_List_Olist_OCons @ SY1933 @ SY1934 @ SY1935 ) @ SY1932 @ SY1935 )
| ~ ( c_List_Olist__all2 @ SV124 @ SY1931 @ SY1934 @ SY1932 @ SY1935 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SY1933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1480,plain,
! [SV445: $i,SV125: $i] :
( ( ! [SY1936: $i,SY1937: $i,SY1938: $i,SY1939: $i,SY1940: $i] :
( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SY1936 @ SY1937 ) @ ( c_List_Olist_OCons @ SY1938 @ SY1939 @ SY1940 ) @ SY1937 @ SY1940 )
| ~ ( c_List_Olist__all2 @ SV125 @ SY1936 @ SY1939 @ SY1937 @ SY1940 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SY1938 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1481,plain,
! [SV446: $i,SV126: $i] :
( ( ! [SY1941: $i,SY1942: $i,SY1943: $i,SY1944: $i,SY1945: $i] :
( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SY1941 @ SY1942 ) @ ( c_List_Olist_OCons @ SY1943 @ SY1944 @ SY1945 ) @ SY1942 @ SY1945 )
| ~ ( c_List_Olist__all2 @ SV126 @ SY1941 @ SY1944 @ SY1942 @ SY1945 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SY1943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1482,plain,
! [SV447: $i,SV127: $i] :
( ( ! [SY1946: $i,SY1947: $i] :
( ( c_List_Olist__ex @ SV127 @ ( c_List_Olist_OCons @ SV447 @ SY1946 @ SY1947 ) @ SY1947 )
| ~ ( c_List_Olist__ex @ SV127 @ SY1946 @ SY1947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1483,plain,
! [SV448: $i,SV128: $i] :
( ( ! [SY1948: $i,SY1949: $i] :
( ( c_List_Olist__ex @ SV128 @ SV448 @ SY1948 )
| ( hBOOL @ ( hAPP @ SV128 @ SY1949 ) )
| ~ ( c_List_Olist__ex @ SV128 @ ( c_List_Olist_OCons @ SY1949 @ SV448 @ SY1948 ) @ SY1948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1484,plain,
! [SV449: $i,SV129: $i] :
( ( ! [SY1950: $i,SY1951: $i,SY1952: $i,SY1953: $i] :
( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SY1950 @ SY1951 ) @ ( c_List_Olist_OCons @ SY1952 @ SY1953 @ SY1951 ) @ SY1951 )
| ~ ( c_List_Olistrelp @ SV129 @ SY1950 @ SY1953 @ SY1951 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SY1952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1485,plain,
! [SV450: $i,SV130: $i] :
( ( ! [SY1954: $i,SY1955: $i] :
( ~ ( class_Lattices_Olattice @ SV130 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ SY1954 @ SV130 ) @ SY1955 @ SV130 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1954 @ SY1955 @ SV130 ) @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1486,plain,
! [SV451: $i,SV131: $i] :
( ( ! [SY1956: $i,SY1957: $i] :
( ~ ( class_Lattices_Olattice @ SV131 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1956 @ SY1957 @ SV131 ) @ SV131 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1956 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ SY1957 @ SV131 ) @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1487,plain,
! [SV452: $i,SV132: $i] :
( ( ! [SY1958: $i,SY1959: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV132 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1958 @ SY1959 @ SV132 ) @ SV132 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1958 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ SY1959 @ SV132 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1488,plain,
! [SV453: $i,SV133: $i] :
( ( ! [SY1960: $i,SY1961: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV133 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ SY1960 @ SV133 ) @ SY1961 @ SV133 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1960 @ SY1961 @ SV133 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1489,plain,
! [SV454: $i,SV134: $i] :
( ( ! [SY1962: $i,SY1963: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV134 @ SV454 @ ( tc_fun @ SY1962 @ tc_bool ) ) @ SY1963 @ ( tc_fun @ SY1962 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV134 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV454 @ SY1963 @ ( tc_fun @ SY1962 @ tc_bool ) ) @ ( tc_fun @ SY1962 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1490,plain,
! [SV455: $i,SV135: $i] :
( ( ! [SY1964: $i,SY1965: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV135 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV455 @ SY1964 @ ( tc_fun @ SY1965 @ tc_bool ) ) @ ( tc_fun @ SY1965 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV455 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV135 @ SY1964 @ ( tc_fun @ SY1965 @ tc_bool ) ) @ ( tc_fun @ SY1965 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1491,plain,
! [SV456: $i,SV136: $i] :
( ( ! [SY1966: $i,SY1967: $i] :
( ( ( c_List_Oremove1 @ SV136 @ ( c_List_Olist_OCons @ SV456 @ SY1966 @ SY1967 ) @ SY1967 )
= ( c_List_Olist_OCons @ SV456 @ ( c_List_Oremove1 @ SV136 @ SY1966 @ SY1967 ) @ SY1967 ) )
| ( SV136 = SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1492,plain,
! [SV457: $i,SV137: $i] :
( ( ! [SY1968: $i,SY1969: $i,SY1970: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV137 @ SV457 @ SY1968 ) @ ( c_List_Olist_OCons @ SY1969 @ SY1970 @ SY1968 ) @ SY1968 )
= ( c_List_Olist_OCons @ SV137 @ ( c_List_Olist_OCons @ SY1969 @ ( c_List_Osplice @ SV457 @ SY1970 @ SY1968 ) @ SY1968 ) @ SY1968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1493,plain,
! [SV458: $i,SV138: $i] :
( ( ! [SY1971: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ SV138 @ SV458 @ SY1971 ) @ SY1971 )
| ~ ( c_List_Odistinct @ SV138 @ SY1971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1494,plain,
! [SV459: $i,SV139: $i] :
( ( ! [SY1972: $i,SY1973: $i] :
( ( c_List_Omember @ SV139 @ ( c_List_Olist_OCons @ SV459 @ SY1972 @ SY1973 ) @ SY1973 )
| ~ ( c_List_Omember @ SV139 @ SY1972 @ SY1973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1495,plain,
! [SV460: $i,SV140: $i] :
( ( ! [SY1974: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ SV140 @ SV460 @ SY1974 ) @ SY1974 )
= ( c_List_Oappend @ ( c_List_Otl @ SV140 @ SY1974 ) @ SV460 @ SY1974 ) )
| ( SV140
= ( c_List_Olist_ONil @ SY1974 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1496,plain,
! [SV461: $i,SV141: $i] :
( ( ! [SY1975: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ SV141 @ SV461 @ SY1975 ) @ SY1975 )
| ~ ( c_List_Odistinct @ SV461 @ SY1975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1497,plain,
! [SV462: $i,SV142: $i] :
( ( ! [SY1976: $i,SY1977: $i] :
( ( ( c_List_OdropWhile @ SV142 @ ( c_List_Olist_OCons @ SV462 @ SY1976 @ SY1977 ) @ SY1977 )
= ( c_List_OdropWhile @ SV142 @ SY1976 @ SY1977 ) )
| ~ ( hBOOL @ ( hAPP @ SV142 @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1498,plain,
! [SV463: $i,SV143: $i] :
( ( ! [SY1978: $i,SY1979: $i] :
( ( ( c_List_OdropWhile @ SV143 @ ( c_List_Olist_OCons @ SV463 @ SY1978 @ SY1979 ) @ SY1979 )
= ( c_List_Olist_OCons @ SV463 @ SY1978 @ SY1979 ) )
| ( hBOOL @ ( hAPP @ SV143 @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1499,plain,
! [SV464: $i,SV144: $i] :
( ( ! [SY1980: $i,SY1981: $i,SY1982: $i,SY1983: $i] :
( ( c_ListOrder_Ostep1 @ SV144 @ SV464 @ SY1980 @ SY1981 )
| ( SY1980 = SV464 )
| ~ ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SY1982 @ SV464 @ SY1981 ) @ ( c_List_Olist_OCons @ SY1983 @ SY1980 @ SY1981 ) @ SY1981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1500,plain,
! [SV465: $i,SV145: $i] :
( ( ! [SY1984: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ SV145 @ SV465 @ SY1984 ) @ SY1984 )
= SV465 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1501,plain,
! [SV466: $i,SV146: $i] :
( ( ! [SY1985: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV146 @ SV466 @ SY1985 ) @ ( c_List_Olist_ONil @ SY1985 ) @ SY1985 )
= ( c_List_Olist_OCons @ SV146 @ SV466 @ SY1985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1502,plain,
! [SV467: $i,SV147: $i] :
( ( ! [SY1986: $i,SY1987: $i,SY1988: $i] :
( ( c_List_Omap @ SV147 @ ( c_List_Oappend @ SV467 @ SY1986 @ SY1987 ) @ SY1987 @ SY1988 )
= ( c_List_Oappend @ ( c_List_Omap @ SV147 @ SV467 @ SY1987 @ SY1988 ) @ ( c_List_Omap @ SV147 @ SY1986 @ SY1987 @ SY1988 ) @ SY1988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1503,plain,
! [SV468: $i,SV148: $i] :
( ( ! [SY1989: $i] : ( c_List_Omember @ SV148 @ ( c_List_Olist_OCons @ SV148 @ SV468 @ SY1989 ) @ SY1989 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1504,plain,
! [SV469: $i,SV149: $i] :
( ( ( SV149
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SV469 @ SV149 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SV469 @ SV149 ) @ t_a ) )
| ( SV149
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV469 @ SV149 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1505,plain,
! [SV470: $i,SV150: $i] :
( ( ! [SY1990: $i,SY1991: $i,SY1992: $i,SY1993: $i] :
( ( c_List_Olist__all2 @ SV150 @ ( c_List_Odrop @ SV470 @ SY1990 @ SY1991 ) @ ( c_List_Odrop @ SV470 @ SY1992 @ SY1993 ) @ SY1991 @ SY1993 )
| ~ ( c_List_Olist__all2 @ SV150 @ SY1990 @ SY1992 @ SY1991 @ SY1993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1506,plain,
! [SV471: $i,SV151: $i] :
( ( ! [SY1994: $i,SY1995: $i] :
( ( ( c_List_Oremove1 @ SV151 @ ( c_List_Ofilter @ SV471 @ SY1994 @ SY1995 ) @ SY1995 )
= ( c_List_Ofilter @ SV471 @ SY1994 @ SY1995 ) )
| ( hBOOL @ ( hAPP @ SV471 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1507,plain,
! [SV472: $i,SV152: $i] :
( ( ! [SY1996: $i,SY1997: $i,SY1998: $i,SY1999: $i] :
( ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ ( c_List_Olist_OCons @ SY1996 @ SY1997 @ SY1998 ) @ SY1999 @ SY1998 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV472 @ SY1996 ) @ SY1997 ) @ ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ SY1997 @ SY1999 @ SY1998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1508,plain,
! [SV473: $i,SV153: $i] :
( ( ! [SY2000: $i,SY2001: $i] :
( ( c_List_Odistinct @ SV153 @ SV473 )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ SY2000 @ SV153 @ SV473 @ SY2001 ) @ SY2001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1509,plain,
! [SV474: $i,SV154: $i] :
( ( ! [SY2002: $i,SY2003: $i,SY2004: $i,SY2005: $i] :
( ( SV154 = SV474 )
| ( SY2002 = SY2003 )
| ~ ( c_ListOrder_Ostep1 @ SY2004 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SY2002 @ ( c_List_Olist_ONil @ SY2005 ) @ SY2005 ) @ SY2005 ) @ ( c_List_Oappend @ SV474 @ ( c_List_Olist_OCons @ SY2003 @ ( c_List_Olist_ONil @ SY2005 ) @ SY2005 ) @ SY2005 ) @ SY2005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1510,plain,
! [SV475: $i,SV155: $i] :
( ( ! [SY2006: $i] :
( ( c_List_Odistinct @ SV155 @ SV475 )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ SY2006 @ SV155 @ SV475 ) @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1511,plain,
! [SV476: $i,SV156: $i] :
( ( ! [SY2007: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ SV156 @ SV476 @ SY2007 ) @ SY2007 )
| ~ ( c_List_Odistinct @ SV476 @ SY2007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1512,plain,
! [SV477: $i,SV157: $i] :
( ( ! [SY2008: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ SV157 @ SV477 @ SY2008 ) @ SY2008 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1513,plain,
! [SV478: $i,SV158: $i] :
( ( ! [SY2009: $i] :
( ~ ( class_Lattices_Olattice @ SV158 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ SY2009 @ SV158 ) @ SV158 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ SY2009 @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1514,plain,
! [SV479: $i,SV159: $i] :
( ( ! [SY2010: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV159 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SY2010 @ SV159 ) @ SV159 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SY2010 @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1515,plain,
! [SV480: $i,SV160: $i] :
( ( ! [SY2011: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ SV480 @ ( tc_fun @ SY2011 @ tc_bool ) ) @ ( tc_fun @ SY2011 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ SV480 @ ( tc_fun @ SY2011 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1516,plain,
! [SV481: $i,SV161: $i] :
( ( ! [SY2012: $i,SY2013: $i,SY2014: $i,SY2015: $i] :
( ( c_List_Ofoldr @ SV161 @ ( c_List_Olist_OCons @ SV481 @ SY2012 @ SY2013 ) @ SY2014 @ SY2013 @ SY2015 )
= ( hAPP @ ( hAPP @ SV161 @ SV481 ) @ ( c_List_Ofoldr @ SV161 @ SY2012 @ SY2014 @ SY2013 @ SY2015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1517,plain,
! [SV482: $i,SV162: $i] :
( ( ! [SY2016: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV162 ) @ ( c_List_Olist_OCons @ SV482 @ SY2016 @ SV162 ) @ SV162 )
= ( c_List_Olist_OCons @ SV482 @ SY2016 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1518,plain,
! [SV483: $i,SV163: $i] :
( ( c_List_Odistinct @ ( c_List_Oremdups @ SV163 @ SV483 ) @ SV483 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1519,plain,
! [SV484: $i,SV164: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV164 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV484 @ SV484 @ SV164 )
= SV484 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1520,plain,
! [SV485: $i,SV165: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV165 @ ( tc_fun @ SV485 @ tc_bool ) )
= SV165 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1521,plain,
! [SV486: $i,SV166: $i] :
( ( ! [SY2017: $i,SY2018: $i,SY2019: $i,SY2020: $i] :
( ( c_ListOrder_Ostep1 @ SV166 @ SV486 @ SY2017 @ SY2018 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SY2019 ) @ SY2020 ) )
| ~ ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SY2019 @ SV486 @ SY2018 ) @ ( c_List_Olist_OCons @ SY2020 @ SY2017 @ SY2018 ) @ SY2018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1522,plain,
! [SV487: $i,SV167: $i] :
( ( ! [SY2021: $i,SY2022: $i,SY2023: $i] :
( ( c_ListOrder_Ostep1 @ SV167 @ ( c_List_Olist_OCons @ SV487 @ SY2021 @ SY2022 ) @ ( c_List_Olist_OCons @ SV487 @ SY2023 @ SY2022 ) @ SY2022 )
| ~ ( c_ListOrder_Ostep1 @ SV167 @ SY2021 @ SY2023 @ SY2022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1523,plain,
! [SV488: $i,SV168: $i] :
( ( ! [SY2024: $i] :
( ~ ( class_Orderings_Olinorder @ SV168 )
| ( c_List_Olinorder__class_Osorted @ SV488 @ SV168 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV488 @ SY2024 @ SV168 ) @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1524,plain,
! [SV489: $i,SV169: $i] :
( ( ! [SY2025: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( c_List_Olinorder__class_Osorted @ SV489 @ SV169 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY2025 @ SV489 @ SV169 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1525,plain,
! [SV490: $i,SV170: $i] :
( ( ! [SY2026: $i,SY2027: $i] :
( ( c_List_Olist__all @ SV170 @ ( c_List_Olist_OCons @ SV490 @ SY2026 @ SY2027 ) @ SY2027 )
| ~ ( c_List_Olist__all @ SV170 @ SY2026 @ SY2027 )
| ~ ( hBOOL @ ( hAPP @ SV170 @ SV490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1526,plain,
! [SV491: $i,SV171: $i] :
( ( ! [SY2028: $i,SY2029: $i,SY2030: $i,SY2031: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV491 @ SY2028 @ SY2029 ) @ SY2030 @ SY2031 @ SY2029 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SY2030 @ SY2031 @ SY2029 ) @ SV491 @ SY2028 @ SY2029 ) )
| ( SV491 = SY2030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1527,plain,
! [SV492: $i,SV172: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV172 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SV492 @ SV172 ) @ SV172 )
| ~ ( c_List_Olinorder__class_Osorted @ SV492 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1528,plain,
! [SV493: $i,SV173: $i] :
( ( ! [SY2032: $i] :
( ( c_List_Olist__all @ SV173 @ SV493 @ SY2032 )
| ~ ( c_List_Olist__all @ SV173 @ ( c_List_Orev @ SV493 @ SY2032 ) @ SY2032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1529,plain,
! [SV494: $i,SV174: $i] :
( ( ! [SY2033: $i] :
( ( c_List_Olist__all @ SV174 @ ( c_List_Orev @ SV494 @ SY2033 ) @ SY2033 )
| ~ ( c_List_Olist__all @ SV174 @ SV494 @ SY2033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1530,plain,
! [SV495: $i,SV175: $i] :
( ( ! [SY2034: $i,SY2035: $i,SY2036: $i] :
( ( c_List_Odrop @ SV175 @ ( c_List_Omap @ SV495 @ SY2034 @ SY2035 @ SY2036 ) @ SY2036 )
= ( c_List_Omap @ SV495 @ ( c_List_Odrop @ SV175 @ SY2034 @ SY2035 ) @ SY2035 @ SY2036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1531,plain,
! [SV496: $i,SV176: $i] :
( ( ! [SY2037: $i,SY2038: $i] :
( ( c_List_Omember @ SV176 @ SV496 @ SY2037 )
| ( SV176 = SY2038 )
| ~ ( c_List_Omember @ SV176 @ ( c_List_Olist_OCons @ SY2038 @ SV496 @ SY2037 ) @ SY2037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1532,plain,
! [SV497: $i,SV177: $i] :
( ( ! [SY2039: $i,SY2040: $i] :
( ( ( c_List_Ofilter @ SV177 @ ( c_List_Olist_OCons @ SV497 @ SY2039 @ SY2040 ) @ SY2040 )
= ( c_List_Ofilter @ SV177 @ SY2039 @ SY2040 ) )
| ( hBOOL @ ( hAPP @ SV177 @ SV497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1533,plain,
! [SV498: $i,SV178: $i] :
( ( ! [SY2041: $i,SY2042: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV178 @ SV498 @ ( tc_fun @ SY2041 @ tc_bool ) ) @ SY2042 ) )
| ~ ( hBOOL @ ( hAPP @ SV498 @ SY2042 ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ SY2042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1534,plain,
! [SV499: $i,SV179: $i] :
( ( ! [SY2043: $i] :
( ( c_List_Orev @ ( c_List_Ofilter @ SV179 @ SV499 @ SY2043 ) @ SY2043 )
= ( c_List_Ofilter @ SV179 @ ( c_List_Orev @ SV499 @ SY2043 ) @ SY2043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1535,plain,
! [SV500: $i,SV180: $i] :
( ( c_List_Olist__all2 @ ( c_fequal @ SV180 ) @ SV500 @ SV500 @ SV180 @ SV180 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1536,plain,
! [SV501: $i,SV181: $i] :
( ( ! [SY2044: $i,SY2045: $i] :
( ( c_List_Olist__all @ SV181 @ SV501 @ SY2044 )
| ~ ( c_List_Olist__all @ SV181 @ ( c_List_Oappend @ SV501 @ SY2045 @ SY2044 ) @ SY2044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1537,plain,
! [SV502: $i,SV182: $i] :
( ( ! [SY2046: $i,SY2047: $i] :
( ( c_List_Olist__all @ SV182 @ SV502 @ SY2046 )
| ~ ( c_List_Olist__all @ SV182 @ ( c_List_Oappend @ SY2047 @ SV502 @ SY2046 ) @ SY2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1538,plain,
! [SV503: $i,SV183: $i] :
( ( ! [SY2048: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ SV183 @ SV503 @ SY2048 ) @ SY2048 )
= ( c_List_Orotate @ SV183 @ ( c_List_Orotate1 @ SV503 @ SY2048 ) @ SY2048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1539,plain,
! [SV504: $i,SV184: $i] :
( ( ! [SY2049: $i,SY2050: $i,SY2051: $i] :
( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_Olist__case @ SV504 @ SY2049 @ ( c_List_Olist_OCons @ SY2050 @ SY2051 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV184 @ ( hAPP @ ( hAPP @ SY2049 @ SY2050 ) @ SY2051 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1540,plain,
! [SV505: $i,SV185: $i] :
( ( ! [SY2052: $i,SY2053: $i,SY2054: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_List_Olist_Olist__case @ SV505 @ SY2052 @ ( c_List_Olist_OCons @ SY2053 @ SY2054 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV185 @ ( hAPP @ ( hAPP @ SY2052 @ SY2053 ) @ SY2054 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1541,plain,
! [SV506: $i,SV186: $i] :
( ( ! [SY2055: $i] :
( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ SV506 @ SY2055 @ SV186 ) @ SV186 )
| ~ ( c_List_Olinorder__class_Osorted @ SY2055 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1542,plain,
! [SV507: $i,SV187: $i] :
( ( ! [SY2056: $i,SY2057: $i,SY2058: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV187 @ SV507 @ SY2056 @ SY2057 ) @ SV507 @ SY2058 @ SY2057 )
= ( c_List_Olist__update @ SV187 @ SV507 @ SY2058 @ SY2057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1543,plain,
! [SV508: $i,SV188: $i] :
( ( ! [SY2059: $i,SY2060: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV188 @ SV508 @ SY2059 ) @ SY2060 @ SY2059 )
= ( c_List_Oappend @ SV188 @ ( c_List_Oappend @ SV508 @ SY2060 @ SY2059 ) @ SY2059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1544,plain,
! [SV509: $i,SV189: $i] :
( ( ! [SY2061: $i,SY2062: $i] :
( ( c_List_Oappend @ SV189 @ ( c_List_Oappend @ SV509 @ SY2061 @ SY2062 ) @ SY2062 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV189 @ SV509 @ SY2062 ) @ SY2061 @ SY2062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1545,plain,
! [SV510: $i,SV190: $i] :
( ( ! [SY2063: $i,SY2064: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV190 @ SV510 @ SY2063 ) @ SY2064 @ SY2063 )
= ( c_List_Oappend @ SV190 @ ( c_List_Oappend @ SV510 @ SY2064 @ SY2063 ) @ SY2063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1546,plain,
! [SV511: $i,SV191: $i] :
( ( ! [SY2065: $i,SY2066: $i] :
( ( c_List_Oappend @ SV191 @ ( c_List_Oappend @ SV511 @ SY2065 @ SY2066 ) @ SY2066 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV191 @ SV511 @ SY2066 ) @ SY2065 @ SY2066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1547,plain,
! [SV512: $i,SV192: $i] :
( ( ! [SY2067: $i] :
( ~ ( class_Orderings_Olinorder @ SV192 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV512 @ SY2067 @ SV192 ) @ SV192 )
| ~ ( c_List_Olinorder__class_Osorted @ SY2067 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1548,plain,
! [SV513: $i,SV193: $i] :
( ( ( c_List_Osplice @ SV193 @ ( c_List_Olist_ONil @ SV513 ) @ SV513 )
= SV193 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1549,plain,
! [SV514: $i,SV194: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_ONil @ SV194 ) @ SV514 @ SV194 )
= SV514 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1550,plain,
! [SV515: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ SV196 @ SV515 ) )
| ( hBOOL @ ( hAPP @ SV196 @ ( v_sko__List__Xrev__Xinduct__2 @ SV196 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV196 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1551,plain,
! [SV516: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ SV197 @ SV516 ) )
| ( hBOOL @ ( hAPP @ SV197 @ ( v_sko__List__Xsplice__Xinduct__2 @ SV197 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV197 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1552,plain,
! [SV517: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ SV198 @ SV517 ) )
| ( hBOOL @ ( hAPP @ SV198 @ ( v_sko__List__Xset__Xinduct__2 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV198 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1553,plain,
! [SV518: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ SV199 @ SV518 ) )
| ( hBOOL @ ( hAPP @ SV199 @ ( v_sko__List__Xtl__Xinduct__2 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV199 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1554,plain,
! [SV519: $i,SV200: $i] :
( ( ! [SY2068: $i,SY2069: $i] :
( ( SV200
= ( c_List_Olist_ONil @ SV519 ) )
| ~ ( c_List_Olist__all2 @ SY2068 @ SV200 @ ( c_List_Olist_ONil @ SY2069 ) @ SV519 @ SY2069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1555,plain,
! [SV520: $i,SV201: $i] :
( ( ! [SY2070: $i,SY2071: $i] :
( ( SV201
= ( c_List_Olist_ONil @ SV520 ) )
| ~ ( c_List_Olist__all2 @ SY2070 @ ( c_List_Olist_ONil @ SY2071 ) @ SV201 @ SY2071 @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1556,plain,
! [SV521: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ SV202 @ SV521 ) )
| ( hBOOL @ ( hAPP @ SV202 @ ( v_sko__List__Xlist__Xinducts__2 @ SV202 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV202 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1557,plain,
! [SV522: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ SV203 @ SV522 ) )
| ( hBOOL @ ( hAPP @ SV203 @ ( v_sko__List__Xhd__Xinduct__2 @ SV203 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV203 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1558,plain,
! [SV523: $i,SV205: $i] :
( ( ! [SY2072: $i] :
( ( c_List_Oconcat__map @ SV205 @ ( c_List_Olist_ONil @ SV523 ) @ SV523 @ SY2072 )
= ( c_List_Olist_ONil @ SY2072 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1559,plain,
! [SV524: $i,SV206: $i] :
( ( ( hBOOL @ ( hAPP @ SV206 @ SV524 ) )
| ( hBOOL @ ( hAPP @ SV206 @ ( v_sko__List__Xremdups__Xinduct__2 @ SV206 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV206 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1560,plain,
! [SV525: $i,SV207: $i] :
( ( ~ ( c_List_Omember @ SV207 @ ( c_List_Olist_ONil @ SV525 ) @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1561,plain,
! [SV526: $i,SV208: $i] :
( ( ! [SY2073: $i] :
( ( hBOOL @ ( hAPP @ SV208 @ SV526 ) )
| ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV208 @ SY2073 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Olist_ONil @ SY2073 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1562,plain,
! [SV527: $i,SV209: $i] :
( ( ! [SY2074: $i] :
( ~ ( class_Orderings_Olinorder @ SV209 )
| ( ( c_List_Olinorder__class_Osort__key @ SV527 @ ( c_List_Olist_ONil @ SY2074 ) @ SY2074 @ SV209 )
= ( c_List_Olist_ONil @ SY2074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1563,plain,
! [SV528: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ SV210 @ SV528 ) )
| ( hBOOL @ ( hAPP @ SV210 @ ( v_sko__List__Xdrop__Xinduct__2 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV210 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1564,plain,
! [SV529: $i,SV211: $i] :
( ( ! [SY2075: $i,SY2076: $i] :
( ( c_List_Ofoldl @ SV211 @ SV529 @ ( c_List_Olist_ONil @ SY2075 ) @ SY2076 @ SY2075 )
= SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1565,plain,
! [SV530: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP @ SV212 @ SV530 ) )
| ( hBOOL @ ( hAPP @ SV212 @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV212 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV212 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1566,plain,
! [SV531: $i,SV213: $i] :
( ( ! [SY2077: $i] :
~ ( c_ListOrder_Ostep1 @ SV213 @ SV531 @ ( c_List_Olist_ONil @ SY2077 ) @ SY2077 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1567,plain,
! [SV532: $i,SV214: $i] :
( ( ! [SY2078: $i] :
~ ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_ONil @ SV532 ) @ SY2078 @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1568,plain,
! [SV533: $i,SV216: $i] :
( ( ( c_List_Odrop @ SV216 @ ( c_List_Olist_ONil @ SV533 ) @ SV533 )
= ( c_List_Olist_ONil @ SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1569,plain,
! [SV534: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ SV534 ) )
| ( hBOOL @ ( hAPP @ SV217 @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV217 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1570,plain,
! [SV535: $i,SV218: $i] :
( ( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ SV218 ) @ SV535 @ SV218 )
= ( c_List_Olist_ONil @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1571,plain,
! [SV536: $i,SV219: $i] :
( ( ( c_List_OdropWhile @ SV219 @ ( c_List_Olist_ONil @ SV536 ) @ SV536 )
= ( c_List_Olist_ONil @ SV536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1572,plain,
! [SV537: $i,SV220: $i] :
( ( SV220
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV537 ) @ SV220 @ SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1573,plain,
! [SV538: $i,SV221: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV221 ) @ SV538 @ SV221 )
= SV538 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1574,plain,
! [SV539: $i,SV222: $i] :
( ( SV222
= ( c_List_Oappend @ SV222 @ ( c_List_Olist_ONil @ SV539 ) @ SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1575,plain,
! [SV540: $i,SV223: $i] :
( ( SV223
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV540 ) @ SV223 @ SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1576,plain,
! [SV541: $i,SV224: $i] :
( ( ( c_List_Oappend @ SV224 @ ( c_List_Olist_ONil @ SV541 ) @ SV541 )
= SV224 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1577,plain,
! [SV542: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ SV225 @ SV542 ) )
| ( hBOOL @ ( hAPP @ SV225 @ ( v_sko__List__Xlast__Xinduct__2 @ SV225 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV225 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1578,plain,
! [SV543: $i,SV226: $i] :
( ( ( c_List_Otake @ SV226 @ ( c_List_Olist_ONil @ SV543 ) @ SV543 )
= ( c_List_Olist_ONil @ SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1579,plain,
! [SV544: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ SV227 @ SV544 ) )
| ( hBOOL @ ( hAPP @ SV227 @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV227 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV227 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1580,plain,
! [SV545: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP @ SV228 @ SV545 ) )
| ( hBOOL @ ( hAPP @ SV228 @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV228 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV228 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1581,plain,
! [SV546: $i,SV229: $i] :
( ( ( hBOOL @ ( hAPP @ SV229 @ SV546 ) )
| ( hBOOL @ ( hAPP @ SV229 @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV229 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV229 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1582,plain,
! [SV547: $i,SV230: $i] :
( ( c_List_Olist__all @ SV230 @ ( c_List_Olist_ONil @ SV547 ) @ SV547 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1583,plain,
! [SV548: $i,SV232: $i] :
( ( ~ ( c_List_Olist__ex @ SV232 @ ( c_List_Olist_ONil @ SV548 ) @ SV548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1584,plain,
! [SV549: $i,SV234: $i] :
( ( ! [SY2079: $i] :
( ~ ( hBOOL @ ( hAPP @ SV234 @ ( c_List_Olist_Olist__case @ SV549 @ SY2079 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV234 @ SV549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1585,plain,
! [SV550: $i,SV235: $i] :
( ( ! [SY2080: $i,SY2081: $i] :
( ( c_List_Ofoldr @ SV235 @ ( c_List_Olist_ONil @ SV550 ) @ SY2080 @ SV550 @ SY2081 )
= SY2080 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1586,plain,
! [SV551: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ SV236 @ SV551 ) )
| ( hBOOL @ ( hAPP @ SV236 @ ( v_sko__List__Xzip__Xinduct__2 @ SV236 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1587,plain,
! [SV552: $i,SV237: $i] :
( ( ! [SY2082: $i] :
( ( c_List_Omap @ SV237 @ ( c_List_Olist_ONil @ SV552 ) @ SV552 @ SY2082 )
= ( c_List_Olist_ONil @ SY2082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1588,plain,
! [SV553: $i,SV238: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_ONil @ SV238 ) @ SV553 @ SV238 )
= ( c_List_Olist_ONil @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1589,plain,
! [SV554: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ SV239 @ SV554 ) )
| ( hBOOL @ ( hAPP @ SV239 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV239 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV239 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1590,plain,
! [SV555: $i,SV240: $i] :
( ( ! [SY2083: $i,SY2084: $i] :
( ( c_List_Olist_Olist__rec @ SV240 @ SV555 @ ( c_List_Olist_ONil @ SY2083 ) @ SY2084 @ SY2083 )
= SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1591,plain,
! [SV556: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ SV556 ) )
| ( hBOOL @ ( hAPP @ SV241 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV241 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1592,plain,
! [SV557: $i,SV242: $i] :
( ( ( hBOOL @ ( hAPP @ SV242 @ SV557 ) )
| ( hBOOL @ ( hAPP @ SV242 @ ( v_sko__List__Xtake__Xinduct__2 @ SV242 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV242 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1593,plain,
! [SV243: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV243 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV243 ) @ SV243 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1277]) ).
thf(1594,plain,
! [SV558: $i,SV244: $i] :
( ( ! [SY2085: $i] :
( ( c_List_Ofiltermap @ SV244 @ ( c_List_Olist_ONil @ SV558 ) @ SV558 @ SY2085 )
= ( c_List_Olist_ONil @ SY2085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1595,plain,
! [SV559: $i,SV245: $i] :
( ( ( c_List_Ofilter @ SV245 @ ( c_List_Olist_ONil @ SV559 ) @ SV559 )
= ( c_List_Olist_ONil @ SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1596,plain,
! [SV560: $i,SV246: $i] :
( ( ! [SY2086: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV246 ) @ SV560 @ SY2086 @ SV246 )
= ( c_List_Olist_ONil @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1597,plain,
! [SV561: $i,SV247: $i] :
( ( ! [SY2087: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV247 ) @ SV561 @ SY2087 @ SV247 )
= ( c_List_Olist_ONil @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1598,plain,
! [SV562: $i,SV248: $i] :
( ( ! [SY2088: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV248 ) @ SV562 @ SY2088 @ SV248 )
= ( c_List_Olist_ONil @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1599,plain,
! [SV563: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP @ SV249 @ SV563 ) )
| ( hBOOL @ ( hAPP @ SV249 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV249 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV249 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1600,plain,
! [SV564: $i,SV250: $i] :
( ( ( c_List_Oremove1 @ SV250 @ ( c_List_Olist_ONil @ SV564 ) @ SV564 )
= ( c_List_Olist_ONil @ SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1601,plain,
! [SV565: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ SV251 @ SV565 ) )
| ( hBOOL @ ( hAPP @ SV251 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV251 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1602,plain,
! [SV566: $i,SV252: $i] :
( ( ! [SY2089: $i,SY2090: $i] :
( ( c_Map_Omap__upds @ SV252 @ SV566 @ ( c_List_Olist_ONil @ SY2089 ) @ SY2090 @ SY2089 )
= SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1603,plain,
! [SV567: $i,SV253: $i] :
( ( ! [SY2091: $i,SY2092: $i] :
( ( c_Map_Omap__upds @ SV253 @ ( c_List_Olist_ONil @ SV567 ) @ SY2091 @ SV567 @ SY2092 )
= SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1604,plain,
! [SV568: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ SV254 @ SV568 ) )
| ( hBOOL @ ( hAPP @ SV254 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV254 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV254 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1605,plain,
! [SV569: $i,SV255: $i] :
( ( ! [SY2093: $i,SY2094: $i] :
( ( c_List_Olist_Olist__case @ SV255 @ SV569 @ ( c_List_Olist_ONil @ SY2093 ) @ SY2094 @ SY2093 )
= SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1606,plain,
! [SV570: $i,SV256: $i] :
( ( ( c_List_Orotate @ SV256 @ ( c_List_Olist_ONil @ SV570 ) @ SV570 )
= ( c_List_Olist_ONil @ SV570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1607,plain,
! [SV571: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ SV257 @ SV571 ) )
| ( hBOOL @ ( hAPP @ SV257 @ ( v_sko__List__Xlist__Xinduct__2 @ SV257 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1608,plain,
! [SV572: $i,SV258: $i] :
( ( ! [SY2095: $i] :
( ( c_List_Olist_ONil @ SV258 )
= ( c_List_Omap @ SV572 @ ( c_List_Olist_ONil @ SY2095 ) @ SY2095 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1609,plain,
! [SV573: $i,SV260: $i] :
( ( c_List_Olistrelp @ SV260 @ ( c_List_Olist_ONil @ SV573 ) @ ( c_List_Olist_ONil @ SV573 ) @ SV573 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1610,plain,
! [SV574: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ SV574 ) )
| ( hBOOL @ ( hAPP @ SV261 @ ( v_sko__List__Xmap__Xinduct__2 @ SV261 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1611,plain,
! [SV575: $i,SV263: $i] :
( ( ! [SY2096: $i,SY2097: $i] :
( ( c_List_Olistsp @ SV263 @ ( c_List_Oappend @ SV575 @ SY2096 @ SY2097 ) @ SY2097 )
| ~ ( c_List_Olistsp @ SV263 @ SY2096 @ SY2097 )
| ~ ( c_List_Olistsp @ SV263 @ SV575 @ SY2097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1612,plain,
! [SV576: $i,SV264: $i] :
( ( ! [SY2098: $i] :
( ( c_List_Olistsp @ SV264 @ SV576 @ SY2098 )
| ~ ( hBOOL @ ( hAPP @ SV264 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV264 @ SV576 @ SY2098 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1613,plain,
! [SV577: $i,SV265: $i] :
( ( ! [SY2099: $i,SY2100: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV265 @ SV577 @ ( tc_fun @ SY2099 @ tc_bool ) ) @ SY2100 @ SY2099 )
| ~ ( c_List_Olistsp @ SV577 @ SY2100 @ SY2099 )
| ~ ( c_List_Olistsp @ SV265 @ SY2100 @ SY2099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1614,plain,
! [SV578: $i,SV266: $i] :
( ( ! [SY2101: $i,SY2102: $i] :
( ( c_List_Olistsp @ SV266 @ SV578 @ SY2101 )
| ~ ( c_List_Olistsp @ SV266 @ ( c_List_Oappend @ SY2102 @ SV578 @ SY2101 ) @ SY2101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1615,plain,
! [SV579: $i,SV267: $i] :
( ( ! [SY2103: $i,SY2104: $i] :
( ( c_List_Olistsp @ SV267 @ SV579 @ SY2103 )
| ~ ( c_List_Olistsp @ SV267 @ ( c_List_Oappend @ SV579 @ SY2104 @ SY2103 ) @ SY2103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1616,plain,
! [SV580: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV268 @ SV580 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1617,plain,
! [SV269: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV269 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1618,plain,
! [SV581: $i,SV270: $i] :
( ( ! [SY2105: $i] :
( ( hBOOL @ ( hAPP @ SV270 @ SV581 ) )
| ( hBOOL @ ( hAPP @ SY2105 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SY2105 @ SV270 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV270 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2105 @ SV581 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1619,plain,
! [SV582: $i,SV271: $i] :
( ( ! [SY2106: $i] :
( ( hBOOL @ ( hAPP @ SV271 @ SV582 ) )
| ( hBOOL @ ( hAPP @ SV271 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2106 @ SV271 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2106 @ SV582 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1620,plain,
! [SV583: $i,SV272: $i] :
( ( ! [SY2107: $i] :
( ( hBOOL @ ( hAPP @ SV272 @ SV583 ) )
| ( hBOOL @ ( hAPP @ SY2107 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SY2107 @ SV272 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2107 @ SV583 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1621,plain,
! [SV584: $i,SV273: $i] :
( ( ! [SY2108: $i] :
( ( hBOOL @ ( hAPP @ SV273 @ SV584 ) )
| ( hBOOL @ ( hAPP @ SV273 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2108 @ SV273 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV273 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2108 @ SV584 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1622,plain,
! [SV585: $i,SV274: $i] :
( ( ( c_List_Olistsp @ SV274 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV274 @ SV585 ) @ t_a )
| ( SV585
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV274 @ SV585 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1623,plain,
! [SV586: $i,SV275: $i] :
( ( ( hBOOL @ ( hAPP @ SV275 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV275 @ SV586 ) ) )
| ( SV586
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV275 @ SV586 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1624,plain,
! [SV587: $i,SV276: $i] :
( ( ! [SY2109: $i] :
( ( hBOOL @ ( hAPP @ SV276 @ SV587 ) )
| ( c_List_Olistsp @ SY2109 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SY2109 @ SV276 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV276 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2109 @ SV587 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1625,plain,
! [SV588: $i,SV277: $i] :
( ( ! [SY2110: $i] :
( ( hBOOL @ ( hAPP @ SV277 @ SV588 ) )
| ( c_List_Olistsp @ SY2110 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SY2110 @ SV277 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV277 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SY2110 @ SV588 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1626,plain,
! [SV589: $i,SV278: $i] :
( ( c_List_Olistsp @ SV278 @ ( c_List_Olist_ONil @ SV589 ) @ SV589 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1627,plain,
! [SV590: $i,SV279: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV279 @ SV590 ) )
| ~ ( class_Lattices_Olattice @ SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1628,plain,
! [SV591: $i,SV280: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV280 @ SV591 ) )
| ~ ( class_Lattices_Olattice @ SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1629,plain,
! [SV592: $i,SV281: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV281 ) @ SV592 ) @ SV592 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1630,plain,
! [SV593: $i,SV282: $i] :
( ( ! [SY2111: $i] :
( ( SV282 = SV593 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY2111 ) @ SV282 ) @ SV593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1631,plain,
! [SV594: $i,SV283: $i] :
( ( ! [SY2112: $i,SY2113: $i] :
( ( ( c_List_Orev @ SV283 @ SV594 )
!= ( c_List_Olist_OCons @ SY2112 @ SY2113 @ SV594 ) )
| ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SY2113 @ SV594 ) @ ( c_List_Olist_OCons @ SY2112 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1632,plain,
! [SV595: $i,SV284: $i] :
( ( ! [SY2114: $i] :
( ( ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 )
!= ( c_List_Orev @ SY2114 @ SV595 ) )
| ( SY2114
= ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1633,plain,
! [SV285: $i] :
( ( ( c_Suc @ SV285 )
= SV285 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1634,plain,
! [SV596: $i,SV286: $i] :
( ( ! [SY2115: $i] :
( ( ( c_List_Oappend @ SV286 @ SV596 @ SY2115 )
!= ( c_List_Olist_ONil @ SY2115 ) )
| ( SV596
= ( c_List_Olist_ONil @ SY2115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1635,plain,
! [SV597: $i,SV287: $i] :
( ( ! [SY2116: $i,SY2117: $i,SY2118: $i] :
( ( ( c_List_Oappend @ SV287 @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ SY2116 ) @ SY2116 ) @ SY2116 )
!= ( c_List_Oappend @ SY2117 @ ( c_List_Olist_OCons @ SY2118 @ ( c_List_Olist_ONil @ SY2116 ) @ SY2116 ) @ SY2116 ) )
| ( SV597 = SY2118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1636,plain,
! [SV598: $i,SV288: $i] :
( ( ! [SY2119: $i] :
( ( c_List_Olist_OCons @ SV288 @ SV598 @ SY2119 )
!= ( c_List_Olist_ONil @ SY2119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1637,plain,
! [SV599: $i,SV289: $i] :
( ( ! [SY2120: $i,SY2121: $i,SY2122: $i] :
( ( ( c_List_Oappend @ SV289 @ ( c_List_Olist_OCons @ SV599 @ ( c_List_Olist_ONil @ SY2120 ) @ SY2120 ) @ SY2120 )
!= ( c_List_Oappend @ SY2121 @ ( c_List_Olist_OCons @ SY2122 @ ( c_List_Olist_ONil @ SY2120 ) @ SY2120 ) @ SY2120 ) )
| ( SV289 = SY2121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1638,plain,
! [SV600: $i,SV290: $i] :
( ( ! [SY2123: $i] :
( ( ( c_List_Orotate @ SV290 @ SV600 @ SY2123 )
!= ( c_List_Olist_ONil @ SY2123 ) )
| ( SV600
= ( c_List_Olist_ONil @ SY2123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1639,plain,
! [SV601: $i,SV291: $i] :
( ( ! [SY2124: $i] :
( ( c_List_Olist_ONil @ SV291 )
!= ( c_List_Olist_OCons @ SV601 @ SY2124 @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1640,plain,
! [SV602: $i,SV292: $i] :
( ( ! [SY2125: $i] :
( ( ( c_List_Oappend @ SV292 @ SV602 @ SY2125 )
!= ( c_List_Olist_ONil @ SY2125 ) )
| ( SV292
= ( c_List_Olist_ONil @ SY2125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1641,plain,
! [SV603: $i,SV293: $i] :
( ( ( ( c_List_Oremdups @ SV293 @ SV603 )
!= ( c_List_Olist_ONil @ SV603 ) )
| ( SV293
= ( c_List_Olist_ONil @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1642,plain,
! [SV604: $i,SV294: $i] :
( ( ! [SY2126: $i] :
( ( ( c_List_Oappend @ SV294 @ SV604 @ SY2126 )
!= SV604 )
| ( SV294
= ( c_List_Olist_ONil @ SY2126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1643,plain,
! [SV295: $i] :
( ( SV295
= ( c_Suc @ SV295 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1644,plain,
! [SV605: $i,SV296: $i] :
( ( ( ( c_Suc @ SV296 )
!= ( c_Suc @ SV605 ) )
| ( SV296 = SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1645,plain,
! [SV606: $i,SV297: $i] :
( ( ! [SY2127: $i,SY2128: $i,SY2129: $i] :
( ( ( c_List_Olist_OCons @ SV297 @ SV606 @ SY2127 )
!= ( c_List_Ofilter @ SY2128 @ SY2129 @ SY2127 ) )
| ( hBOOL @ ( hAPP @ SY2128 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1646,plain,
! [SV607: $i,SV298: $i] :
( ( ! [SY2130: $i,SY2131: $i,SY2132: $i] :
( ( ( c_List_Olist_OCons @ SV298 @ SV607 @ SY2130 )
!= ( c_List_Olist_OCons @ SY2131 @ SY2132 @ SY2130 ) )
| ( SV607 = SY2132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1647,plain,
! [SV608: $i,SV299: $i] :
( ( ! [SY2133: $i] :
( ( ( c_List_Olist_ONil @ SV299 )
!= ( c_List_Oappend @ SV608 @ SY2133 @ SV299 ) )
| ( SY2133
= ( c_List_Olist_ONil @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1648,plain,
! [SV609: $i,SV300: $i] :
( ( ! [SY2134: $i] :
( ( c_List_Olist_OCons @ SV300 @ SV609 @ SY2134 )
!= SV609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1649,plain,
! [SV610: $i,SV301: $i] :
( ( ( ( c_List_Olist_ONil @ SV301 )
!= ( c_List_Oremdups @ SV610 @ SV301 ) )
| ( SV610
= ( c_List_Olist_ONil @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1650,plain,
! [SV611: $i,SV302: $i] :
( ( ! [SY2135: $i,SY2136: $i] :
( ( ( c_List_Oappend @ SV302 @ SV611 @ SY2135 )
!= ( c_List_Oappend @ SY2136 @ SV611 @ SY2135 ) )
| ( SV302 = SY2136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1651,plain,
! [SV612: $i,SV303: $i] :
( ( ! [SY2137: $i] :
( ( SV303
!= ( c_List_Oappend @ SV612 @ SV303 @ SY2137 ) )
| ( SV612
= ( c_List_Olist_ONil @ SY2137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1652,plain,
! [SV613: $i,SV304: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV304 )
!= ( c_Lambda_OdB_OAbs @ SV613 ) )
| ( SV304 = SV613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1653,plain,
! [SV614: $i,SV305: $i] :
( ( ! [SY2138: $i,SY2139: $i] :
( ( ( c_List_Omap @ SV305 @ SV614 @ SY2138 @ SY2139 )
!= ( c_List_Olist_ONil @ SY2139 ) )
| ( SV614
= ( c_List_Olist_ONil @ SY2138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1654,plain,
! [SV615: $i,SV306: $i] :
( ( ! [SY2140: $i,SY2141: $i,SY2142: $i] :
( ( ( c_List_Olist_OCons @ SV306 @ SV615 @ SY2140 )
!= ( c_List_Olist_OCons @ SY2141 @ SY2142 @ SY2140 ) )
| ( SV306 = SY2141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1655,plain,
! [SV616: $i,SV307: $i] :
( ( ( ( c_List_Olist_ONil @ SV307 )
!= ( c_List_Orev @ SV616 @ SV307 ) )
| ( SV616
= ( c_List_Olist_ONil @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1656,plain,
! [SV617: $i,SV308: $i] :
( ( ! [SY2143: $i] :
( ( ( c_List_Orev @ SV308 @ SV617 )
!= ( c_List_Orev @ SY2143 @ SV617 ) )
| ( SV308 = SY2143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1657,plain,
! [SV618: $i,SV309: $i] :
( ( ! [SY2144: $i,SY2145: $i] :
( ( ( c_List_Olist__update @ SV309 @ SV618 @ SY2144 @ SY2145 )
!= ( c_List_Olist_ONil @ SY2145 ) )
| ( SV309
= ( c_List_Olist_ONil @ SY2145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1658,plain,
! [SV619: $i,SV310: $i] :
( ( ! [SY2146: $i,SY2147: $i] :
( ( ( c_List_Olist_ONil @ SV310 )
!= ( c_List_Omap @ SV619 @ SY2146 @ SY2147 @ SV310 ) )
| ( SY2146
= ( c_List_Olist_ONil @ SY2147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1659,plain,
! [SV620: $i,SV311: $i] :
( ( ( ( c_List_Oremdups @ SV311 @ SV620 )
!= SV311 )
| ( c_List_Odistinct @ SV311 @ SV620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1660,plain,
! [SV621: $i,SV312: $i] :
( ( ! [SY2148: $i] :
( ( ( c_List_Orev @ SV312 @ SV621 )
!= ( c_List_Olist_OCons @ SY2148 @ ( c_List_Olist_ONil @ SV621 ) @ SV621 ) )
| ( SV312
= ( c_List_Olist_OCons @ SY2148 @ ( c_List_Olist_ONil @ SV621 ) @ SV621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1661,plain,
! [SV622: $i,SV313: $i] :
( ( ! [SY2149: $i] :
( ( ( c_List_Olist_ONil @ SV313 )
!= ( c_List_Oappend @ SV622 @ SY2149 @ SV313 ) )
| ( SV622
= ( c_List_Olist_ONil @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1662,plain,
! [SV623: $i,SV314: $i] :
( ( ( ( c_List_Orev @ SV314 @ SV623 )
!= ( c_List_Olist_ONil @ SV623 ) )
| ( SV314
= ( c_List_Olist_ONil @ SV623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1663,plain,
! [SV624: $i,SV315: $i] :
( ( ! [SY2150: $i] :
( ( c_List_Olist_OCons @ SV315 @ SV624 @ SY2150 )
!= ( c_List_Olist_ONil @ SY2150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1664,plain,
! [SV625: $i,SV316: $i] :
( ( ! [SY2151: $i,SY2152: $i,SY2153: $i] :
( ( ( c_List_OdropWhile @ SV316 @ SV625 @ SY2151 )
!= ( c_List_Olist_OCons @ SY2152 @ SY2153 @ SY2151 ) )
| ~ ( hBOOL @ ( hAPP @ SV316 @ SY2152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1665,plain,
! [SV626: $i,SV317: $i] :
( ( ( ( c_Suc @ SV317 )
!= ( c_Suc @ SV626 ) )
| ( SV317 = SV626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1666,plain,
! [SV627: $i,SV318: $i] :
( ( ! [SY2154: $i] :
( SV318
!= ( c_List_Olist_OCons @ SV627 @ SV318 @ SY2154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1667,plain,
! [SV628: $i,SV319: $i] :
( ( ! [SY2155: $i,SY2156: $i] :
( ( ( c_List_Oappend @ SV319 @ SV628 @ SY2155 )
!= ( c_List_Oappend @ SV319 @ SY2156 @ SY2155 ) )
| ( SV628 = SY2156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1668,plain,
! [SV629: $i,SV320: $i] :
( ( ( ( c_List_Orotate1 @ SV320 @ SV629 )
!= ( c_List_Olist_ONil @ SV629 ) )
| ( SV320
= ( c_List_Olist_ONil @ SV629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1669,plain,
! [SV630: $i,SV321: $i] :
( ( ! [SY2157: $i] :
( ( ( c_List_Oappend @ SV321 @ SV630 @ SY2157 )
!= SV321 )
| ( SV630
= ( c_List_Olist_ONil @ SY2157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1670,plain,
! [SV631: $i,SV322: $i] :
( ( ! [SY2158: $i,SY2159: $i,SY2160: $i] :
( ( ( c_List_Ofilter @ SV322 @ SV631 @ SY2158 )
!= ( c_List_Olist_OCons @ SY2159 @ SY2160 @ SY2158 ) )
| ( hBOOL @ ( hAPP @ SV322 @ SY2159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1671,plain,
! [SV632: $i,SV323: $i] :
( ( ! [SY2161: $i] :
( ( SV323
!= ( c_List_Oappend @ SV323 @ SV632 @ SY2161 ) )
| ( SV632
= ( c_List_Olist_ONil @ SY2161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1672,plain,
! [SV633: $i,SV324: $i,SV1: $i] :
( ( ( c_List_Odrop @ ( c_Suc @ SV1 ) @ SV324 @ SV633 )
= ( c_List_Odrop @ SV1 @ ( c_List_Otl @ SV324 @ SV633 ) @ SV633 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1673,plain,
! [SV634: $i,SV325: $i,SV2: $i] :
( ( ( c_List_Otake @ SV2 @ ( c_List_Otl @ SV325 @ SV634 ) @ SV634 )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ SV2 ) @ SV325 @ SV634 ) @ SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1674,plain,
! [SV635: $i,SV326: $i,SV3: $i] :
( ( ! [SY2162: $i,SY2163: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV3 @ SV326 @ SV635 ) @ ( c_Suc @ SY2162 ) @ SY2163 @ SV635 )
= ( c_List_Olist_OCons @ SV3 @ ( c_List_Olist__update @ SV326 @ SY2162 @ SY2163 @ SV635 ) @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1675,plain,
! [SV636: $i,SV327: $i,SV4: $i] :
( ( ! [SY2164: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV4 ) @ ( c_List_Olist_OCons @ SV327 @ SV636 @ SY2164 ) @ SY2164 )
= ( c_List_Odrop @ SV4 @ SV636 @ SY2164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1676,plain,
! [SV637: $i,SV328: $i,SV5: $i] :
( ( ! [SY2165: $i] :
( ( c_List_Otake @ ( c_Suc @ SV5 ) @ ( c_List_Olist_OCons @ SV328 @ SV637 @ SY2165 ) @ SY2165 )
= ( c_List_Olist_OCons @ SV328 @ ( c_List_Otake @ SV5 @ SV637 @ SY2165 ) @ SY2165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1677,plain,
! [SV638: $i,SV329: $i,SV6: $i] :
( ( ( c_List_Orotate @ ( c_Suc @ SV6 ) @ SV329 @ SV638 )
= ( c_List_Orotate1 @ ( c_List_Orotate @ SV6 @ SV329 @ SV638 ) @ SV638 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1678,plain,
! [SV330: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ SV7 @ SV330 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ SV7 ) @ ( v_sko__List__Xdrop__Xinduct__2 @ SV7 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1679,plain,
! [SV331: $i,SV8: $i] :
( ( ( hBOOL @ ( hAPP @ SV8 @ SV331 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ SV8 ) @ ( v_sko__List__Xrev__Xinduct__2 @ SV8 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1680,plain,
! [SV332: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP @ SV9 @ SV332 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ SV9 ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV9 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1681,plain,
! [SV333: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ SV333 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV10 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV10 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1682,plain,
! [SV639: $i,SV334: $i,SV11: $i] :
( ( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV11 @ SV334 @ SV639 ) @ SV639 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1683,plain,
! [SV640: $i,SV335: $i,SV12: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oappend @ SV12 @ SV335 @ SV640 ) @ SV640 )
= ( c_List_Ohd @ SV12 @ SV640 ) )
| ( SV12
= ( c_List_Olist_ONil @ SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1684,plain,
! [SV641: $i,SV337: $i,SV14: $i] :
( ( ( ( c_List_Otake @ ( c_Suc @ SV14 ) @ SV337 @ SV641 )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ SV337 @ SV641 ) @ ( c_List_Otake @ SV14 @ ( c_List_Otl @ SV337 @ SV641 ) @ SV641 ) @ SV641 ) )
| ( SV337
= ( c_List_Olist_ONil @ SV641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1685,plain,
! [SV642: $i,SV338: $i,SV15: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV15 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV15 @ SV338 @ SV642 ) @ SV642 ) ) )
| ( ( c_List_OdropWhile @ SV15 @ SV338 @ SV642 )
= ( c_List_Olist_ONil @ SV642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1686,plain,
! [SV339: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ SV16 @ SV339 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ SV16 ) @ ( v_sko__List__Xhd__Xinduct__2 @ SV16 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1687,plain,
! [SV340: $i,SV17: $i] :
( ( ( hBOOL @ ( hAPP @ SV17 @ SV340 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV17 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV17 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1688,plain,
! [SV341: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ SV341 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ SV18 ) @ ( v_sko__List__Xset__Xinduct__2 @ SV18 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1689,plain,
! [SV342: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ SV19 @ SV342 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV19 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV19 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1690,plain,
! [SV343: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ SV20 @ SV343 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinducts__1 @ SV20 ) @ ( v_sko__List__Xlist__Xinducts__2 @ SV20 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1691,plain,
! [SV344: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ SV21 @ SV344 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV21 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV21 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1692,plain,
! [SV345: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP @ SV22 @ SV345 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ SV22 ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV22 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1693,plain,
! [SV346: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ SV23 @ SV346 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ SV23 ) @ ( v_sko__List__Xremdups__Xinduct__2 @ SV23 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1694,plain,
! [SV347: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ SV24 @ SV347 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ SV24 ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV24 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1695,plain,
! [SV348: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ SV348 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ SV25 ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV25 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1696,plain,
! [SV349: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ SV26 @ SV349 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV26 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV26 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1697,plain,
! [SV350: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ SV27 @ SV350 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV27 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV27 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1698,plain,
! [SV351: $i,SV28: $i] :
( ( ( hBOOL @ ( hAPP @ SV28 @ SV351 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV28 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV28 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1699,plain,
! [SV352: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ SV352 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV29 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV29 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1700,plain,
! [SV353: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ SV30 @ SV353 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ SV30 ) @ ( v_sko__List__Xsplice__Xinduct__2 @ SV30 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1701,plain,
! [SV354: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ SV31 @ SV354 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV31 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV31 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1702,plain,
! [SV355: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ SV32 @ SV355 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ SV32 ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV32 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1703,plain,
! [SV356: $i,SV33: $i] :
( ( ( hBOOL @ ( hAPP @ SV33 @ SV356 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ SV33 ) @ ( v_sko__List__Xlast__Xinduct__2 @ SV33 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1704,plain,
! [SV357: $i,SV34: $i] :
( ( ( hBOOL @ ( hAPP @ SV34 @ SV357 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ SV34 ) @ ( v_sko__List__Xtl__Xinduct__2 @ SV34 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1705,plain,
! [SV643: $i,SV358: $i,SV35: $i] :
( ( ! [SY2166: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV35 @ SV358 @ SV643 ) @ SY2166 @ SV643 )
= ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SY2166 @ SV643 ) @ ( c_List_Osplice @ SV358 @ ( c_List_Otl @ SY2166 @ SV643 ) @ SV643 ) @ SV643 ) @ SV643 ) )
| ( SY2166
= ( c_List_Olist_ONil @ SV643 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1706,plain,
! [SV644: $i,SV359: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP @ SV36 @ SV359 ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV36 @ SV644 ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ SV36 @ SV644 ) @ ( c_List_Olist_ONil @ SV644 ) @ SV644 ) @ SV644 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Olist_ONil @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1707,plain,
! [SV360: $i,SV37: $i] :
( ( ( ( c_List_Orotate1 @ SV37 @ SV360 )
= ( c_List_Oappend @ ( c_List_Otl @ SV37 @ SV360 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV37 @ SV360 ) @ ( c_List_Olist_ONil @ SV360 ) @ SV360 ) @ SV360 ) )
= $true )
| ( ( SV37
= ( c_List_Olist_ONil @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1708,plain,
! [SV645: $i,SV361: $i,SV38: $i] :
( ( ! [SY2167: $i] :
( ~ ( class_Orderings_Olinorder @ SV38 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV361 @ ( c_List_Olinorder__class_Osort__key @ SV361 @ SV645 @ SY2167 @ SV38 ) @ SY2167 @ SV38 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1709,plain,
! [SV646: $i,SV362: $i,SV39: $i] :
( ( ( c_List_Odrop @ SV39 @ ( c_List_Otl @ SV362 @ SV646 ) @ SV646 )
= ( c_List_Otl @ ( c_List_Odrop @ SV39 @ SV362 @ SV646 ) @ SV646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1710,plain,
! [SV647: $i,SV363: $i,SV40: $i] :
( ( ! [SY2168: $i,SY2169: $i] :
( ( c_ListOrder_Ostep1 @ SV40 @ ( c_List_Oappend @ SV363 @ SV647 @ SY2168 ) @ ( c_List_Oappend @ SV363 @ SY2169 @ SY2168 ) @ SY2168 )
| ~ ( c_ListOrder_Ostep1 @ SV40 @ SV647 @ SY2169 @ SY2168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1711,plain,
! [SV648: $i,SV364: $i,SV41: $i] :
( ( ! [SY2170: $i,SY2171: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV41 @ SV364 @ SV648 @ SY2170 )
| ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Oappend @ SV364 @ SY2171 @ SY2170 ) @ ( c_List_Oappend @ SV648 @ SY2171 @ SY2170 ) @ SY2170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1712,plain,
! [SV649: $i,SV365: $i,SV42: $i] :
( ( ! [SY2172: $i] :
( ( ( c_List_Ofilter @ SV42 @ ( c_List_Olist_OCons @ SV365 @ SV649 @ SY2172 ) @ SY2172 )
= ( c_List_Olist_OCons @ SV365 @ ( c_List_Ofilter @ SV42 @ SV649 @ SY2172 ) @ SY2172 ) )
| ~ ( hBOOL @ ( hAPP @ SV42 @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1713,plain,
! [SV650: $i,SV366: $i,SV43: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV43 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV366 @ SV650 @ SV43 ) @ SV43 )
| ~ ( c_List_Olinorder__class_Osorted @ SV650 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1714,plain,
! [SV651: $i,SV367: $i,SV44: $i] :
( ( ! [SY2173: $i,SY2174: $i] :
( ( c_List_Otake @ SV44 @ ( c_List_Omap @ SV367 @ SV651 @ SY2173 @ SY2174 ) @ SY2174 )
= ( c_List_Omap @ SV367 @ ( c_List_Otake @ SV44 @ SV651 @ SY2173 ) @ SY2173 @ SY2174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1715,plain,
! [SV652: $i,SV368: $i,SV45: $i] :
( ( ( c_List_Oremdups @ ( c_List_Ofilter @ SV45 @ SV368 @ SV652 ) @ SV652 )
= ( c_List_Ofilter @ SV45 @ ( c_List_Oremdups @ SV368 @ SV652 ) @ SV652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1716,plain,
! [SV653: $i,SV369: $i,SV46: $i] :
( ( ! [SY2175: $i,SY2176: $i,SY2177: $i] :
( ( c_List_Olist__all2 @ SV46 @ ( c_List_Otake @ SV369 @ SV653 @ SY2175 ) @ ( c_List_Otake @ SV369 @ SY2176 @ SY2177 ) @ SY2175 @ SY2177 )
| ~ ( c_List_Olist__all2 @ SV46 @ SV653 @ SY2176 @ SY2175 @ SY2177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1717,plain,
! [SV654: $i,SV370: $i,SV47: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV47 @ SV370 @ SV654 ) @ SV654 )
= ( c_List_Oappend @ ( c_List_Orev @ SV370 @ SV654 ) @ ( c_List_Olist_OCons @ SV47 @ ( c_List_Olist_ONil @ SV654 ) @ SV654 ) @ SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1718,plain,
! [SV655: $i,SV371: $i,SV48: $i] :
( ( ( SV48 = SV371 )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ SV655 ) @ SV48 @ SV371 @ SV655 @ SV655 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1719,plain,
! [SV656: $i,SV372: $i,SV49: $i] :
( ( ! [SY2178: $i,SY2179: $i,SY2180: $i] :
( ( c_List_Ofoldl @ SV49 @ SV372 @ ( c_List_Olist_OCons @ SV656 @ SY2178 @ SY2179 ) @ SY2180 @ SY2179 )
= ( c_List_Ofoldl @ SV49 @ ( hAPP @ ( hAPP @ SV49 @ SV372 ) @ SV656 ) @ SY2178 @ SY2180 @ SY2179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1720,plain,
! [SV657: $i,SV373: $i,SV50: $i] :
( ( ! [SY2181: $i,SY2182: $i,SY2183: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV373 ) @ SV657 ) )
| ( c_ListOrder_Ostep1 @ SV50 @ SY2181 @ SY2182 @ SY2183 )
| ~ ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SY2181 @ ( c_List_Olist_OCons @ SV373 @ ( c_List_Olist_ONil @ SY2183 ) @ SY2183 ) @ SY2183 ) @ ( c_List_Oappend @ SY2182 @ ( c_List_Olist_OCons @ SV657 @ ( c_List_Olist_ONil @ SY2183 ) @ SY2183 ) @ SY2183 ) @ SY2183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1721,plain,
! [SV658: $i,SV374: $i,SV51: $i] :
( ( ( c_List_Otl @ ( c_List_Odrop @ SV51 @ SV374 @ SV658 ) @ SV658 )
= ( c_List_Odrop @ SV51 @ ( c_List_Otl @ SV374 @ SV658 ) @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1722,plain,
! [SV659: $i,SV376: $i,SV53: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SV376 @ ( tc_fun @ SV659 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV53 @ ( tc_fun @ SV659 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1723,plain,
! [SV660: $i,SV377: $i,SV54: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV54 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV377 @ SV660 @ SV54 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV660 @ SV377 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1724,plain,
! [SV661: $i,SV378: $i,SV55: $i] :
( ( ~ ( class_Lattices_Olattice @ SV55 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 @ SV661 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV661 @ SV378 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1725,plain,
! [SV662: $i,SV379: $i,SV56: $i] :
( ( ! [SY2184: $i] :
( ~ ( class_Orderings_Olinorder @ SV56 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2184 @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1726,plain,
! [SV663: $i,SV380: $i,SV57: $i] :
( ( ! [SY2185: $i,SY2186: $i,SY2187: $i,SY2188: $i] :
( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SY2185 ) @ ( c_List_Oappend @ SY2186 @ SY2187 @ SY2188 ) @ SY2185 @ SY2188 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV663 @ SY2187 @ SY2185 @ SY2188 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SY2186 @ SY2185 @ SY2188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1727,plain,
! [SV664: $i,SV381: $i,SV58: $i] :
( ( ! [SY2189: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV58 @ SV381 @ SV664 ) @ SY2189 @ SV664 )
= ( c_List_Olist_OCons @ SV58 @ ( c_List_Oappend @ SV381 @ SY2189 @ SV664 ) @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1728,plain,
! [SV665: $i,SV382: $i,SV59: $i] :
( ( ! [SY2190: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV59 @ SV382 @ SV665 ) @ SY2190 @ SV665 )
= ( c_List_Olist_OCons @ SV59 @ ( c_List_Oappend @ SV382 @ SY2190 @ SV665 ) @ SV665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1729,plain,
! [SV383: $i,SV60: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate1 @ SV60 @ SV383 ) @ SV383 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV60 @ SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1730,plain,
! [SV384: $i,SV61: $i] :
( ( ( c_List_Odistinct @ SV61 @ SV384 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ SV61 @ SV384 ) @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1731,plain,
! [SV666: $i,SV385: $i,SV62: $i] :
( ( ( c_List_Odistinct @ ( c_List_Ofilter @ SV62 @ SV385 @ SV666 ) @ SV666 )
| ~ ( c_List_Odistinct @ SV385 @ SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1732,plain,
! [SV667: $i,SV386: $i,SV63: $i] :
( ( ! [SY2191: $i,SY2192: $i] :
( ( c_List_Omap @ SV63 @ ( c_List_Olist_OCons @ SV386 @ SV667 @ SY2191 ) @ SY2191 @ SY2192 )
= ( c_List_Olist_OCons @ ( hAPP @ SV63 @ SV386 ) @ ( c_List_Omap @ SV63 @ SV667 @ SY2191 @ SY2192 ) @ SY2192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1733,plain,
! [SV668: $i,SV387: $i,SV64: $i] :
( ( ! [SY2193: $i,SY2194: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV64 @ SV387 ) @ ( c_List_Omap @ SV64 @ SV668 @ SY2193 @ SY2194 ) @ SY2194 )
= ( c_List_Omap @ SV64 @ ( c_List_Olist_OCons @ SV387 @ SV668 @ SY2193 ) @ SY2193 @ SY2194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1734,plain,
! [SV669: $i,SV388: $i,SV65: $i] :
( ( ! [SY2195: $i,SY2196: $i] :
( ( c_List_Omap @ SV65 @ ( c_List_Olist_OCons @ SV388 @ SV669 @ SY2195 ) @ SY2195 @ SY2196 )
= ( c_List_Olist_OCons @ ( hAPP @ SV65 @ SV388 ) @ ( c_List_Omap @ SV65 @ SV669 @ SY2195 @ SY2196 ) @ SY2196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1735,plain,
! [SV670: $i,SV389: $i,SV66: $i] :
( ( ! [SY2197: $i,SY2198: $i,SY2199: $i] :
( ( c_List_Olist_Olist__case @ SV66 @ SV389 @ ( c_List_Olist_OCons @ SV670 @ SY2197 @ SY2198 ) @ SY2199 @ SY2198 )
= ( hAPP @ ( hAPP @ SV389 @ SV670 ) @ SY2197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1736,plain,
! [SV671: $i,SV390: $i,SV67: $i] :
( ( ( c_List_Oremove1 @ SV67 @ ( c_List_Olist_OCons @ SV67 @ SV390 @ SV671 ) @ SV671 )
= SV390 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1737,plain,
! [SV672: $i,SV391: $i,SV68: $i] :
( ( ! [SY2200: $i,SY2201: $i,SY2202: $i,SY2203: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV391 ) @ SV672 ) )
| ~ ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SV391 @ SY2200 @ SY2201 ) @ ( c_List_Olist_OCons @ SV672 @ SY2202 @ SY2203 ) @ SY2201 @ SY2203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1738,plain,
! [SV673: $i,SV392: $i,SV69: $i] :
( ( ! [SY2204: $i] :
( ( c_List_Olist_OCons @ SV69 @ ( c_List_Oappend @ SV392 @ SV673 @ SY2204 ) @ SY2204 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV69 @ SV392 @ SY2204 ) @ SV673 @ SY2204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1739,plain,
! [SV674: $i,SV393: $i,SV70: $i] :
( ( ! [SY2205: $i] :
( ( c_List_Olist_OCons @ SV70 @ ( c_List_Oappend @ SV393 @ SV674 @ SY2205 ) @ SY2205 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV70 @ SV393 @ SY2205 ) @ SV674 @ SY2205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1740,plain,
! [SV675: $i,SV394: $i,SV71: $i] :
( ( ! [SY2206: $i,SY2207: $i,SY2208: $i] :
( ( SV71 = SV394 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV675 @ SV394 ) @ SV71 ) )
| ~ ( c_ListOrder_Ostep1 @ SV675 @ ( c_List_Olist_OCons @ SV394 @ SY2206 @ SY2207 ) @ ( c_List_Olist_OCons @ SV71 @ SY2208 @ SY2207 ) @ SY2207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1741,plain,
! [SV676: $i,SV395: $i,SV72: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ SV72 @ SV395 @ SV676 ) @ ( c_List_Odrop @ SV72 @ SV395 @ SV676 ) @ SV676 )
= SV395 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1742,plain,
! [SV677: $i,SV396: $i,SV73: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_List_Olinorder__class_Osorted @ SV396 @ SV73 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV677 @ SV396 @ SV73 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1743,plain,
! [SV678: $i,SV397: $i,SV74: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV74 @ SV397 ) @ ( c_List_Olist_OCons @ SV678 @ ( c_List_Olist_ONil @ SV397 ) @ SV397 ) @ SV397 ) @ SV397 )
= ( c_List_Olist_OCons @ SV678 @ SV74 @ SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1744,plain,
! [SV679: $i,SV398: $i,SV75: $i] :
( ( ( c_List_Odistinct @ ( c_List_Odrop @ SV75 @ SV398 @ SV679 ) @ SV679 )
| ~ ( c_List_Odistinct @ SV398 @ SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1745,plain,
! [SV399: $i,SV76: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orev @ SV76 @ SV399 ) @ SV399 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV76 @ SV399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1746,plain,
! [SV400: $i,SV77: $i] :
( ( ( c_List_Odistinct @ SV77 @ SV400 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Orev @ SV77 @ SV400 ) @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1747,plain,
! [SV680: $i,SV401: $i,SV78: $i] :
( ( ! [SY2209: $i] :
( ( c_List_Olist__all @ SV78 @ SV401 @ SV680 )
| ~ ( c_List_Olist__all @ SV78 @ ( c_List_Olist_OCons @ SY2209 @ SV401 @ SV680 ) @ SV680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1748,plain,
! [SV402: $i,SV79: $i] :
( ( ( ( c_List_Oremdups @ SV79 @ SV402 )
= SV79 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV79 @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1749,plain,
! [SV681: $i,SV403: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ SV80 @ SV403 ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV681 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV681 @ SV80 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV681 @ SV403 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1750,plain,
! [SV682: $i,SV404: $i,SV81: $i] :
( ( ! [SY2210: $i] :
( ( hBOOL @ ( hAPP @ SV81 @ SV404 ) )
| ~ ( c_List_Olist__all @ SV81 @ ( c_List_Olist_OCons @ SV404 @ SV682 @ SY2210 ) @ SY2210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1751,plain,
! [SV683: $i,SV405: $i,SV82: $i] :
( ( ( hBOOL @ ( hAPP @ SV82 @ SV405 ) )
| ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV683 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV683 @ SV82 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV683 @ SV405 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1752,plain,
! [SV684: $i,SV406: $i,SV83: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ SV83 @ SV406 @ SV684 ) @ SV684 )
= ( c_List_Oappend @ SV406 @ ( c_List_Olist_OCons @ SV83 @ ( c_List_Olist_ONil @ SV684 ) @ SV684 ) @ SV684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1753,plain,
! [SV685: $i,SV407: $i,SV84: $i] :
( ( ( c_List_Olist_OCons @ SV84 @ SV407 @ SV685 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV685 ) @ ( c_List_Olist_OCons @ SV84 @ SV407 @ SV685 ) @ SV685 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1754,plain,
! [SV686: $i,SV408: $i,SV85: $i] :
( ( ! [SY2211: $i,SY2212: $i,SY2213: $i] :
( ( c_List_Omap @ SV85 @ ( c_List_Olist__update @ SV408 @ SV686 @ SY2211 @ SY2212 ) @ SY2212 @ SY2213 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV85 @ SV408 @ SY2212 @ SY2213 ) @ SV686 @ ( hAPP @ SV85 @ SY2211 ) @ SY2213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1755,plain,
! [SV687: $i,SV410: $i,SV87: $i] :
( ( ! [SY2214: $i,SY2215: $i,SY2216: $i] :
( ( SV87 = SV410 )
| ( c_ListOrder_Ostep1 @ SV687 @ SV87 @ SV410 @ SY2214 )
| ~ ( c_ListOrder_Ostep1 @ SV687 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SY2215 @ ( c_List_Olist_ONil @ SY2214 ) @ SY2214 ) @ SY2214 ) @ ( c_List_Oappend @ SV410 @ ( c_List_Olist_OCons @ SY2216 @ ( c_List_Olist_ONil @ SY2214 ) @ SY2214 ) @ SY2214 ) @ SY2214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1756,plain,
! [SV688: $i,SV411: $i,SV88: $i] :
( ( ! [SY2217: $i] :
( ( hBOOL @ ( hAPP @ SV88 @ SV411 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV688 @ SV88 @ ( tc_fun @ SY2217 @ tc_bool ) ) @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1757,plain,
! [SV689: $i,SV412: $i,SV89: $i] :
( ( ! [SY2218: $i] :
( ( hBOOL @ ( hAPP @ SV89 @ SV412 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV689 @ ( tc_fun @ SY2218 @ tc_bool ) ) @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1758,plain,
! [SV690: $i,SV413: $i,SV90: $i] :
( ( ! [SY2219: $i] :
( ( c_List_Olist__all @ SV90 @ ( c_List_Oappend @ SV413 @ SV690 @ SY2219 ) @ SY2219 )
| ~ ( c_List_Olist__all @ SV90 @ SV690 @ SY2219 )
| ~ ( c_List_Olist__all @ SV90 @ SV413 @ SY2219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1759,plain,
! [SV414: $i,SV91: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV91 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV414 @ ( c_List_Olist_ONil @ SV91 ) @ SV91 ) @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1760,plain,
! [SV691: $i,SV415: $i,SV92: $i] :
( ( ( c_List_Odistinct @ ( c_List_Otake @ SV92 @ SV415 @ SV691 ) @ SV691 )
| ~ ( c_List_Odistinct @ SV415 @ SV691 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1761,plain,
! [SV692: $i,SV416: $i,SV93: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ SV93 @ SV416 @ SV692 ) @ SV692 )
= ( c_List_Oappend @ ( c_List_Orev @ SV416 @ SV692 ) @ ( c_List_Orev @ SV93 @ SV692 ) @ SV692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1762,plain,
! [SV693: $i,SV417: $i,SV94: $i] :
( ( ! [SY2220: $i,SY2221: $i,SY2222: $i] :
( ( c_List_Ofoldl @ SV94 @ SV417 @ ( c_List_Oappend @ SV693 @ SY2220 @ SY2221 ) @ SY2222 @ SY2221 )
= ( c_List_Ofoldl @ SV94 @ ( c_List_Ofoldl @ SV94 @ SV417 @ SV693 @ SY2222 @ SY2221 ) @ SY2220 @ SY2222 @ SY2221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1763,plain,
! [SV694: $i,SV418: $i,SV95: $i] :
( ( ( c_List_Odistinct @ SV95 @ SV418 )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ SV694 @ SV95 @ SV418 ) @ SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1764,plain,
! [SV695: $i,SV419: $i,SV96: $i] :
( ( ! [SY2223: $i] :
( ( c_List_Ofilter @ SV96 @ ( c_List_Oappend @ SV419 @ SV695 @ SY2223 ) @ SY2223 )
= ( c_List_Oappend @ ( c_List_Ofilter @ SV96 @ SV419 @ SY2223 ) @ ( c_List_Ofilter @ SV96 @ SV695 @ SY2223 ) @ SY2223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1765,plain,
! [SV696: $i,SV420: $i,SV97: $i] :
( ( ! [SY2224: $i,SY2225: $i] :
( ( c_List_Olist__all2 @ SV97 @ ( c_List_Orev @ SV420 @ SV696 ) @ SY2224 @ SV696 @ SY2225 )
| ~ ( c_List_Olist__all2 @ SV97 @ SV420 @ ( c_List_Orev @ SY2224 @ SY2225 ) @ SV696 @ SY2225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1766,plain,
! [SV697: $i,SV421: $i,SV98: $i] :
( ( ! [SY2226: $i,SY2227: $i] :
( ( c_List_Olist__all2 @ SV98 @ SV421 @ ( c_List_Orev @ SV697 @ SY2226 ) @ SY2227 @ SY2226 )
| ~ ( c_List_Olist__all2 @ SV98 @ ( c_List_Orev @ SV421 @ SY2227 ) @ SV697 @ SY2227 @ SY2226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1767,plain,
! [SV698: $i,SV422: $i,SV100: $i] :
( ( c_List_Olist__all2 @ SV100 @ ( c_List_Olist_ONil @ SV422 ) @ ( c_List_Olist_ONil @ SV698 ) @ SV422 @ SV698 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1768,plain,
! [SV423: $i,SV101: $i] :
( ( ( SV101
= ( c_List_Olist_ONil @ SV423 ) )
= $true )
| ( ( ~ ( c_List_Onull @ SV101 @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1769,plain,
! [SV699: $i,SV424: $i,SV104: $i] :
( ( ! [SY2228: $i,SY2229: $i,SY2230: $i] :
( ( SV104 = SV424 )
| ( SV699 = SY2228 )
| ~ ( c_ListOrder_Ostep1 @ SY2229 @ ( c_List_Olist_OCons @ SV424 @ SY2228 @ SY2230 ) @ ( c_List_Olist_OCons @ SV104 @ SV699 @ SY2230 ) @ SY2230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1770,plain,
! [SV700: $i,SV425: $i,SV105: $i] :
( ( ! [SY2231: $i,SY2232: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV425 ) @ SV700 ) )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Olist_OCons @ SV425 @ SY2231 @ SY2232 ) @ ( c_List_Olist_OCons @ SV700 @ SY2231 @ SY2232 ) @ SY2232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1771,plain,
! [SV701: $i,SV426: $i,SV106: $i] :
( ( ! [SY2233: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV106 @ SV426 @ SV701 @ SY2233 ) @ SY2233 )
= ( c_List_Omap @ SV106 @ ( c_List_Orev @ SV426 @ SV701 ) @ SV701 @ SY2233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1772,plain,
! [SV702: $i,SV427: $i,SV107: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV107 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV427 @ SV702 @ SV107 ) @ SV107 )
| ~ ( c_List_Olinorder__class_Osorted @ SV702 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1773,plain,
! [SV703: $i,SV428: $i,SV108: $i] :
( ( ! [SY2234: $i] :
( ~ ( class_Orderings_Olinorder @ SV108 )
| ( c_List_Odistinct @ SV428 @ SV703 )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SY2234 @ SV428 @ SV703 @ SV108 ) @ SV703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1774,plain,
! [SV704: $i,SV429: $i,SV109: $i] :
( ( ! [SY2235: $i] :
( ~ ( class_Orderings_Olinorder @ SV109 )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV429 @ SV704 @ SY2235 @ SV109 ) @ SY2235 )
| ~ ( c_List_Odistinct @ SV704 @ SY2235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1775,plain,
! [SV705: $i,SV430: $i,SV110: $i] :
( ( ! [SY2236: $i,SY2237: $i,SY2238: $i,SY2239: $i] :
( ( c_List_Olist__all2 @ SV110 @ SV430 @ SV705 @ SY2236 @ SY2237 )
| ~ ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SY2238 @ SV430 @ SY2236 ) @ ( c_List_Olist_OCons @ SY2239 @ SV705 @ SY2237 ) @ SY2236 @ SY2237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1776,plain,
! [SV706: $i,SV431: $i,SV111: $i] :
( ( ! [SY2240: $i,SY2241: $i] :
( ( c_List_Orotate @ SV111 @ ( c_List_Omap @ SV431 @ SV706 @ SY2240 @ SY2241 ) @ SY2241 )
= ( c_List_Omap @ SV431 @ ( c_List_Orotate @ SV111 @ SV706 @ SY2240 ) @ SY2240 @ SY2241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1777,plain,
! [SV707: $i,SV432: $i,SV112: $i] :
( ( ( c_List_Odistinct @ SV112 @ SV432 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV112 @ SV707 @ SV432 ) @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1778,plain,
! [SV708: $i,SV433: $i,SV113: $i] :
( ( ( c_List_Odistinct @ SV113 @ SV433 )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV708 @ SV113 @ SV433 ) @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1779,plain,
! [SV709: $i,SV437: $i,SV117: $i] :
( ( ( c_List_Odistinct @ ( c_List_OdropWhile @ SV117 @ SV437 @ SV709 ) @ SV709 )
| ~ ( c_List_Odistinct @ SV437 @ SV709 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1780,plain,
! [SV710: $i,SV438: $i,SV118: $i] :
( ( ! [SY2242: $i,SY2243: $i] :
( ( c_List_Olist__all2 @ SV118 @ SV438 @ SV710 @ SY2242 @ SY2243 )
| ~ ( c_List_Olist__all2 @ SV118 @ ( c_List_Orev @ SV438 @ SY2242 ) @ ( c_List_Orev @ SV710 @ SY2243 ) @ SY2242 @ SY2243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1781,plain,
! [SV711: $i,SV439: $i,SV119: $i] :
( ( ! [SY2244: $i,SY2245: $i] :
( ( c_List_Olist__all2 @ SV119 @ ( c_List_Orev @ SV439 @ SV711 ) @ ( c_List_Orev @ SY2244 @ SY2245 ) @ SV711 @ SY2245 )
| ~ ( c_List_Olist__all2 @ SV119 @ SV439 @ SY2244 @ SV711 @ SY2245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1782,plain,
! [SV712: $i,SV440: $i,SV120: $i] :
( ( ! [SY2246: $i,SY2247: $i] :
( ( c_List_Oconcat__map @ SV120 @ ( c_List_Olist_OCons @ SV440 @ SV712 @ SY2246 ) @ SY2246 @ SY2247 )
= ( c_List_Oappend @ ( hAPP @ SV120 @ SV440 ) @ ( c_List_Oconcat__map @ SV120 @ SV712 @ SY2246 @ SY2247 ) @ SY2247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1783,plain,
! [SV713: $i,SV441: $i,SV121: $i] :
( ( ! [SY2248: $i,SY2249: $i,SY2250: $i] :
( ( c_List_Ofoldr @ SV121 @ ( c_List_Oappend @ SV441 @ SV713 @ SY2248 ) @ SY2249 @ SY2248 @ SY2250 )
= ( c_List_Ofoldr @ SV121 @ SV441 @ ( c_List_Ofoldr @ SV121 @ SV713 @ SY2249 @ SY2248 @ SY2250 ) @ SY2248 @ SY2250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1784,plain,
! [SV714: $i,SV442: $i,SV122: $i] :
( ( ! [SY2251: $i] :
( ( c_List_Olist__ex @ SV122 @ ( c_List_Olist_OCons @ SV442 @ SV714 @ SY2251 ) @ SY2251 )
| ~ ( hBOOL @ ( hAPP @ SV122 @ SV442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1785,plain,
! [SV715: $i,SV443: $i,SV123: $i] :
( ( ! [SY2252: $i,SY2253: $i,SY2254: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV443 ) @ SV715 ) )
| ( SV443 = SV715 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SY2252 @ ( c_List_Olist_OCons @ SV443 @ ( c_List_Olist_ONil @ SY2253 ) @ SY2253 ) @ SY2253 ) @ ( c_List_Oappend @ SY2254 @ ( c_List_Olist_OCons @ SV715 @ ( c_List_Olist_ONil @ SY2253 ) @ SY2253 ) @ SY2253 ) @ SY2253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1786,plain,
! [SV716: $i,SV444: $i,SV124: $i] :
( ( ! [SY2255: $i,SY2256: $i,SY2257: $i,SY2258: $i] :
( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SY2255 ) @ ( c_List_Olist_OCons @ SY2256 @ SY2257 @ SY2258 ) @ SY2255 @ SY2258 )
| ~ ( c_List_Olist__all2 @ SV124 @ SV716 @ SY2257 @ SY2255 @ SY2258 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SY2256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1787,plain,
! [SV717: $i,SV445: $i,SV125: $i] :
( ( ! [SY2259: $i,SY2260: $i,SY2261: $i,SY2262: $i] :
( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SY2259 ) @ ( c_List_Olist_OCons @ SY2260 @ SY2261 @ SY2262 ) @ SY2259 @ SY2262 )
| ~ ( c_List_Olist__all2 @ SV125 @ SV717 @ SY2261 @ SY2259 @ SY2262 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SY2260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1788,plain,
! [SV718: $i,SV446: $i,SV126: $i] :
( ( ! [SY2263: $i,SY2264: $i,SY2265: $i,SY2266: $i] :
( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SY2263 ) @ ( c_List_Olist_OCons @ SY2264 @ SY2265 @ SY2266 ) @ SY2263 @ SY2266 )
| ~ ( c_List_Olist__all2 @ SV126 @ SV718 @ SY2265 @ SY2263 @ SY2266 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SY2264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1789,plain,
! [SV719: $i,SV447: $i,SV127: $i] :
( ( ! [SY2267: $i] :
( ( c_List_Olist__ex @ SV127 @ ( c_List_Olist_OCons @ SV447 @ SV719 @ SY2267 ) @ SY2267 )
| ~ ( c_List_Olist__ex @ SV127 @ SV719 @ SY2267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1790,plain,
! [SV720: $i,SV448: $i,SV128: $i] :
( ( ! [SY2268: $i] :
( ( c_List_Olist__ex @ SV128 @ SV448 @ SV720 )
| ( hBOOL @ ( hAPP @ SV128 @ SY2268 ) )
| ~ ( c_List_Olist__ex @ SV128 @ ( c_List_Olist_OCons @ SY2268 @ SV448 @ SV720 ) @ SV720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1791,plain,
! [SV721: $i,SV449: $i,SV129: $i] :
( ( ! [SY2269: $i,SY2270: $i,SY2271: $i] :
( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SV721 @ SY2269 ) @ ( c_List_Olist_OCons @ SY2270 @ SY2271 @ SY2269 ) @ SY2269 )
| ~ ( c_List_Olistrelp @ SV129 @ SV721 @ SY2271 @ SY2269 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SY2270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1792,plain,
! [SV722: $i,SV450: $i,SV130: $i] :
( ( ! [SY2272: $i] :
( ~ ( class_Lattices_Olattice @ SV130 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ SV722 @ SV130 ) @ SY2272 @ SV130 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV722 @ SY2272 @ SV130 ) @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1793,plain,
! [SV723: $i,SV451: $i,SV131: $i] :
( ( ! [SY2273: $i] :
( ~ ( class_Lattices_Olattice @ SV131 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ SY2273 @ SV131 ) @ SV131 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ SY2273 @ SV131 ) @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1794,plain,
! [SV724: $i,SV452: $i,SV132: $i] :
( ( ! [SY2274: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV132 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV724 @ SY2274 @ SV132 ) @ SV132 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV724 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ SY2274 @ SV132 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1795,plain,
! [SV725: $i,SV453: $i,SV133: $i] :
( ( ! [SY2275: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV133 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ SV725 @ SV133 ) @ SY2275 @ SV133 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SY2275 @ SV133 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1796,plain,
! [SV726: $i,SV454: $i,SV134: $i] :
( ( ! [SY2276: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV134 @ SV454 @ ( tc_fun @ SV726 @ tc_bool ) ) @ SY2276 @ ( tc_fun @ SV726 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV134 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV454 @ SY2276 @ ( tc_fun @ SV726 @ tc_bool ) ) @ ( tc_fun @ SV726 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1797,plain,
! [SV727: $i,SV455: $i,SV135: $i] :
( ( ! [SY2277: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV135 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV455 @ SV727 @ ( tc_fun @ SY2277 @ tc_bool ) ) @ ( tc_fun @ SY2277 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV455 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV135 @ SV727 @ ( tc_fun @ SY2277 @ tc_bool ) ) @ ( tc_fun @ SY2277 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1798,plain,
! [SV728: $i,SV456: $i,SV136: $i] :
( ( ! [SY2278: $i] :
( ( ( c_List_Oremove1 @ SV136 @ ( c_List_Olist_OCons @ SV456 @ SV728 @ SY2278 ) @ SY2278 )
= ( c_List_Olist_OCons @ SV456 @ ( c_List_Oremove1 @ SV136 @ SV728 @ SY2278 ) @ SY2278 ) )
| ( SV136 = SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1799,plain,
! [SV729: $i,SV457: $i,SV137: $i] :
( ( ! [SY2279: $i,SY2280: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV137 @ SV457 @ SV729 ) @ ( c_List_Olist_OCons @ SY2279 @ SY2280 @ SV729 ) @ SV729 )
= ( c_List_Olist_OCons @ SV137 @ ( c_List_Olist_OCons @ SY2279 @ ( c_List_Osplice @ SV457 @ SY2280 @ SV729 ) @ SV729 ) @ SV729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1800,plain,
! [SV730: $i,SV458: $i,SV138: $i] :
( ( ( c_List_Odistinct @ ( c_List_Osublist @ SV138 @ SV458 @ SV730 ) @ SV730 )
| ~ ( c_List_Odistinct @ SV138 @ SV730 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1801,plain,
! [SV731: $i,SV459: $i,SV139: $i] :
( ( ! [SY2281: $i] :
( ( c_List_Omember @ SV139 @ ( c_List_Olist_OCons @ SV459 @ SV731 @ SY2281 ) @ SY2281 )
| ~ ( c_List_Omember @ SV139 @ SV731 @ SY2281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1802,plain,
! [SV732: $i,SV460: $i,SV140: $i] :
( ( ( ( c_List_Otl @ ( c_List_Oappend @ SV140 @ SV460 @ SV732 ) @ SV732 )
= ( c_List_Oappend @ ( c_List_Otl @ SV140 @ SV732 ) @ SV460 @ SV732 ) )
| ( SV140
= ( c_List_Olist_ONil @ SV732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1803,plain,
! [SV733: $i,SV461: $i,SV141: $i] :
( ( ( c_List_Odistinct @ ( c_List_Oremove1 @ SV141 @ SV461 @ SV733 ) @ SV733 )
| ~ ( c_List_Odistinct @ SV461 @ SV733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1804,plain,
! [SV734: $i,SV462: $i,SV142: $i] :
( ( ! [SY2282: $i] :
( ( ( c_List_OdropWhile @ SV142 @ ( c_List_Olist_OCons @ SV462 @ SV734 @ SY2282 ) @ SY2282 )
= ( c_List_OdropWhile @ SV142 @ SV734 @ SY2282 ) )
| ~ ( hBOOL @ ( hAPP @ SV142 @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1805,plain,
! [SV735: $i,SV463: $i,SV143: $i] :
( ( ! [SY2283: $i] :
( ( ( c_List_OdropWhile @ SV143 @ ( c_List_Olist_OCons @ SV463 @ SV735 @ SY2283 ) @ SY2283 )
= ( c_List_Olist_OCons @ SV463 @ SV735 @ SY2283 ) )
| ( hBOOL @ ( hAPP @ SV143 @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1806,plain,
! [SV736: $i,SV464: $i,SV144: $i] :
( ( ! [SY2284: $i,SY2285: $i,SY2286: $i] :
( ( c_ListOrder_Ostep1 @ SV144 @ SV464 @ SV736 @ SY2284 )
| ( SV736 = SV464 )
| ~ ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SY2285 @ SV464 @ SY2284 ) @ ( c_List_Olist_OCons @ SY2286 @ SV736 @ SY2284 ) @ SY2284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1807,plain,
! [SV737: $i,SV465: $i,SV145: $i] :
( ( ( c_List_Otl @ ( c_List_Olist_OCons @ SV145 @ SV465 @ SV737 ) @ SV737 )
= SV465 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1808,plain,
! [SV738: $i,SV466: $i,SV146: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV146 @ SV466 @ SV738 ) @ ( c_List_Olist_ONil @ SV738 ) @ SV738 )
= ( c_List_Olist_OCons @ SV146 @ SV466 @ SV738 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1809,plain,
! [SV739: $i,SV467: $i,SV147: $i] :
( ( ! [SY2287: $i,SY2288: $i] :
( ( c_List_Omap @ SV147 @ ( c_List_Oappend @ SV467 @ SV739 @ SY2287 ) @ SY2287 @ SY2288 )
= ( c_List_Oappend @ ( c_List_Omap @ SV147 @ SV467 @ SY2287 @ SY2288 ) @ ( c_List_Omap @ SV147 @ SV739 @ SY2287 @ SY2288 ) @ SY2288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1810,plain,
! [SV740: $i,SV468: $i,SV148: $i] :
( ( c_List_Omember @ SV148 @ ( c_List_Olist_OCons @ SV148 @ SV468 @ SV740 ) @ SV740 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1811,plain,
! [SV469: $i,SV149: $i] :
( ( ( SV149
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SV469 @ SV149 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SV469 @ SV149 ) @ t_a ) )
= $true )
| ( ( ( SV149
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV469 @ SV149 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1812,plain,
! [SV741: $i,SV470: $i,SV150: $i] :
( ( ! [SY2289: $i,SY2290: $i,SY2291: $i] :
( ( c_List_Olist__all2 @ SV150 @ ( c_List_Odrop @ SV470 @ SV741 @ SY2289 ) @ ( c_List_Odrop @ SV470 @ SY2290 @ SY2291 ) @ SY2289 @ SY2291 )
| ~ ( c_List_Olist__all2 @ SV150 @ SV741 @ SY2290 @ SY2289 @ SY2291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1813,plain,
! [SV742: $i,SV471: $i,SV151: $i] :
( ( ! [SY2292: $i] :
( ( ( c_List_Oremove1 @ SV151 @ ( c_List_Ofilter @ SV471 @ SV742 @ SY2292 ) @ SY2292 )
= ( c_List_Ofilter @ SV471 @ SV742 @ SY2292 ) )
| ( hBOOL @ ( hAPP @ SV471 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1814,plain,
! [SV743: $i,SV472: $i,SV152: $i] :
( ( ! [SY2293: $i,SY2294: $i,SY2295: $i] :
( ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ ( c_List_Olist_OCons @ SV743 @ SY2293 @ SY2294 ) @ SY2295 @ SY2294 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV472 @ SV743 ) @ SY2293 ) @ ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ SY2293 @ SY2295 @ SY2294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1815,plain,
! [SV744: $i,SV473: $i,SV153: $i] :
( ( ! [SY2296: $i] :
( ( c_List_Odistinct @ SV153 @ SV473 )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ SV744 @ SV153 @ SV473 @ SY2296 ) @ SY2296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1816,plain,
! [SV745: $i,SV474: $i,SV154: $i] :
( ( ! [SY2297: $i,SY2298: $i,SY2299: $i] :
( ( SV154 = SV474 )
| ( SV745 = SY2297 )
| ~ ( c_ListOrder_Ostep1 @ SY2298 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SV745 @ ( c_List_Olist_ONil @ SY2299 ) @ SY2299 ) @ SY2299 ) @ ( c_List_Oappend @ SV474 @ ( c_List_Olist_OCons @ SY2297 @ ( c_List_Olist_ONil @ SY2299 ) @ SY2299 ) @ SY2299 ) @ SY2299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1817,plain,
! [SV746: $i,SV475: $i,SV155: $i] :
( ( ( c_List_Odistinct @ SV155 @ SV475 )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ SV746 @ SV155 @ SV475 ) @ SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1818,plain,
! [SV747: $i,SV476: $i,SV156: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate @ SV156 @ SV476 @ SV747 ) @ SV747 )
| ~ ( c_List_Odistinct @ SV476 @ SV747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1819,plain,
! [SV748: $i,SV477: $i,SV157: $i] :
( ( ~ ( c_List_Onull @ ( c_List_Olist_OCons @ SV157 @ SV477 @ SV748 ) @ SV748 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1820,plain,
! [SV749: $i,SV478: $i,SV158: $i] :
( ( ~ ( class_Lattices_Olattice @ SV158 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ SV749 @ SV158 ) @ SV158 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ SV749 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1821,plain,
! [SV750: $i,SV479: $i,SV159: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV159 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV750 @ SV159 ) @ SV159 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV750 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1822,plain,
! [SV751: $i,SV480: $i,SV160: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ SV480 @ ( tc_fun @ SV751 @ tc_bool ) ) @ ( tc_fun @ SV751 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV160 @ SV480 @ ( tc_fun @ SV751 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1823,plain,
! [SV752: $i,SV481: $i,SV161: $i] :
( ( ! [SY2300: $i,SY2301: $i,SY2302: $i] :
( ( c_List_Ofoldr @ SV161 @ ( c_List_Olist_OCons @ SV481 @ SV752 @ SY2300 ) @ SY2301 @ SY2300 @ SY2302 )
= ( hAPP @ ( hAPP @ SV161 @ SV481 ) @ ( c_List_Ofoldr @ SV161 @ SV752 @ SY2301 @ SY2300 @ SY2302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1824,plain,
! [SV753: $i,SV482: $i,SV162: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV162 ) @ ( c_List_Olist_OCons @ SV482 @ SV753 @ SV162 ) @ SV162 )
= ( c_List_Olist_OCons @ SV482 @ SV753 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1825,plain,
! [SV484: $i,SV164: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV164 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV484 @ SV484 @ SV164 )
= SV484 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1826,plain,
! [SV754: $i,SV486: $i,SV166: $i] :
( ( ! [SY2303: $i,SY2304: $i,SY2305: $i] :
( ( c_ListOrder_Ostep1 @ SV166 @ SV486 @ SV754 @ SY2303 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SY2304 ) @ SY2305 ) )
| ~ ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SY2304 @ SV486 @ SY2303 ) @ ( c_List_Olist_OCons @ SY2305 @ SV754 @ SY2303 ) @ SY2303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1827,plain,
! [SV755: $i,SV487: $i,SV167: $i] :
( ( ! [SY2306: $i,SY2307: $i] :
( ( c_ListOrder_Ostep1 @ SV167 @ ( c_List_Olist_OCons @ SV487 @ SV755 @ SY2306 ) @ ( c_List_Olist_OCons @ SV487 @ SY2307 @ SY2306 ) @ SY2306 )
| ~ ( c_ListOrder_Ostep1 @ SV167 @ SV755 @ SY2307 @ SY2306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1828,plain,
! [SV756: $i,SV488: $i,SV168: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV168 )
| ( c_List_Olinorder__class_Osorted @ SV488 @ SV168 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV488 @ SV756 @ SV168 ) @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1829,plain,
! [SV757: $i,SV489: $i,SV169: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV169 )
| ( c_List_Olinorder__class_Osorted @ SV489 @ SV169 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV757 @ SV489 @ SV169 ) @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1830,plain,
! [SV758: $i,SV490: $i,SV170: $i] :
( ( ! [SY2308: $i] :
( ( c_List_Olist__all @ SV170 @ ( c_List_Olist_OCons @ SV490 @ SV758 @ SY2308 ) @ SY2308 )
| ~ ( c_List_Olist__all @ SV170 @ SV758 @ SY2308 )
| ~ ( hBOOL @ ( hAPP @ SV170 @ SV490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1831,plain,
! [SV759: $i,SV491: $i,SV171: $i] :
( ( ! [SY2309: $i,SY2310: $i,SY2311: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV491 @ SV759 @ SY2309 ) @ SY2310 @ SY2311 @ SY2309 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SY2310 @ SY2311 @ SY2309 ) @ SV491 @ SV759 @ SY2309 ) )
| ( SV491 = SY2310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1832,plain,
! [SV492: $i,SV172: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV172 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SV492 @ SV172 ) @ SV172 )
| ~ ( c_List_Olinorder__class_Osorted @ SV492 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1833,plain,
! [SV760: $i,SV493: $i,SV173: $i] :
( ( ( c_List_Olist__all @ SV173 @ SV493 @ SV760 )
| ~ ( c_List_Olist__all @ SV173 @ ( c_List_Orev @ SV493 @ SV760 ) @ SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1834,plain,
! [SV761: $i,SV494: $i,SV174: $i] :
( ( ( c_List_Olist__all @ SV174 @ ( c_List_Orev @ SV494 @ SV761 ) @ SV761 )
| ~ ( c_List_Olist__all @ SV174 @ SV494 @ SV761 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1835,plain,
! [SV762: $i,SV495: $i,SV175: $i] :
( ( ! [SY2312: $i,SY2313: $i] :
( ( c_List_Odrop @ SV175 @ ( c_List_Omap @ SV495 @ SV762 @ SY2312 @ SY2313 ) @ SY2313 )
= ( c_List_Omap @ SV495 @ ( c_List_Odrop @ SV175 @ SV762 @ SY2312 ) @ SY2312 @ SY2313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1836,plain,
! [SV763: $i,SV496: $i,SV176: $i] :
( ( ! [SY2314: $i] :
( ( c_List_Omember @ SV176 @ SV496 @ SV763 )
| ( SV176 = SY2314 )
| ~ ( c_List_Omember @ SV176 @ ( c_List_Olist_OCons @ SY2314 @ SV496 @ SV763 ) @ SV763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1837,plain,
! [SV764: $i,SV497: $i,SV177: $i] :
( ( ! [SY2315: $i] :
( ( ( c_List_Ofilter @ SV177 @ ( c_List_Olist_OCons @ SV497 @ SV764 @ SY2315 ) @ SY2315 )
= ( c_List_Ofilter @ SV177 @ SV764 @ SY2315 ) )
| ( hBOOL @ ( hAPP @ SV177 @ SV497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1838,plain,
! [SV765: $i,SV498: $i,SV178: $i] :
( ( ! [SY2316: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV178 @ SV498 @ ( tc_fun @ SV765 @ tc_bool ) ) @ SY2316 ) )
| ~ ( hBOOL @ ( hAPP @ SV498 @ SY2316 ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ SY2316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1839,plain,
! [SV766: $i,SV499: $i,SV179: $i] :
( ( ( c_List_Orev @ ( c_List_Ofilter @ SV179 @ SV499 @ SV766 ) @ SV766 )
= ( c_List_Ofilter @ SV179 @ ( c_List_Orev @ SV499 @ SV766 ) @ SV766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1840,plain,
! [SV767: $i,SV501: $i,SV181: $i] :
( ( ! [SY2317: $i] :
( ( c_List_Olist__all @ SV181 @ SV501 @ SV767 )
| ~ ( c_List_Olist__all @ SV181 @ ( c_List_Oappend @ SV501 @ SY2317 @ SV767 ) @ SV767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1841,plain,
! [SV768: $i,SV502: $i,SV182: $i] :
( ( ! [SY2318: $i] :
( ( c_List_Olist__all @ SV182 @ SV502 @ SV768 )
| ~ ( c_List_Olist__all @ SV182 @ ( c_List_Oappend @ SY2318 @ SV502 @ SV768 ) @ SV768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1842,plain,
! [SV769: $i,SV503: $i,SV183: $i] :
( ( ( c_List_Orotate1 @ ( c_List_Orotate @ SV183 @ SV503 @ SV769 ) @ SV769 )
= ( c_List_Orotate @ SV183 @ ( c_List_Orotate1 @ SV503 @ SV769 ) @ SV769 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1843,plain,
! [SV770: $i,SV504: $i,SV184: $i] :
( ( ! [SY2319: $i,SY2320: $i] :
( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_Olist__case @ SV504 @ SV770 @ ( c_List_Olist_OCons @ SY2319 @ SY2320 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV184 @ ( hAPP @ ( hAPP @ SV770 @ SY2319 ) @ SY2320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1844,plain,
! [SV771: $i,SV505: $i,SV185: $i] :
( ( ! [SY2321: $i,SY2322: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_List_Olist_Olist__case @ SV505 @ SV771 @ ( c_List_Olist_OCons @ SY2321 @ SY2322 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV185 @ ( hAPP @ ( hAPP @ SV771 @ SY2321 ) @ SY2322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1845,plain,
! [SV772: $i,SV506: $i,SV186: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ SV506 @ SV772 @ SV186 ) @ SV186 )
| ~ ( c_List_Olinorder__class_Osorted @ SV772 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1846,plain,
! [SV773: $i,SV507: $i,SV187: $i] :
( ( ! [SY2323: $i,SY2324: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV187 @ SV507 @ SV773 @ SY2323 ) @ SV507 @ SY2324 @ SY2323 )
= ( c_List_Olist__update @ SV187 @ SV507 @ SY2324 @ SY2323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1847,plain,
! [SV774: $i,SV508: $i,SV188: $i] :
( ( ! [SY2325: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV188 @ SV508 @ SV774 ) @ SY2325 @ SV774 )
= ( c_List_Oappend @ SV188 @ ( c_List_Oappend @ SV508 @ SY2325 @ SV774 ) @ SV774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1848,plain,
! [SV775: $i,SV509: $i,SV189: $i] :
( ( ! [SY2326: $i] :
( ( c_List_Oappend @ SV189 @ ( c_List_Oappend @ SV509 @ SV775 @ SY2326 ) @ SY2326 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV189 @ SV509 @ SY2326 ) @ SV775 @ SY2326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1849,plain,
! [SV776: $i,SV510: $i,SV190: $i] :
( ( ! [SY2327: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV190 @ SV510 @ SV776 ) @ SY2327 @ SV776 )
= ( c_List_Oappend @ SV190 @ ( c_List_Oappend @ SV510 @ SY2327 @ SV776 ) @ SV776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1850,plain,
! [SV777: $i,SV511: $i,SV191: $i] :
( ( ! [SY2328: $i] :
( ( c_List_Oappend @ SV191 @ ( c_List_Oappend @ SV511 @ SV777 @ SY2328 ) @ SY2328 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV191 @ SV511 @ SY2328 ) @ SV777 @ SY2328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1851,plain,
! [SV778: $i,SV512: $i,SV192: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV192 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV512 @ SV778 @ SV192 ) @ SV192 )
| ~ ( c_List_Olinorder__class_Osorted @ SV778 @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1852,plain,
! [SV515: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ SV196 @ SV515 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV196 @ ( v_sko__List__Xrev__Xinduct__2 @ SV196 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV196 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1853,plain,
! [SV516: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ SV197 @ SV516 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV197 @ ( v_sko__List__Xsplice__Xinduct__2 @ SV197 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV197 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1854,plain,
! [SV517: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ SV198 @ SV517 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV198 @ ( v_sko__List__Xset__Xinduct__2 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV198 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1552]) ).
thf(1855,plain,
! [SV518: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ SV199 @ SV518 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV199 @ ( v_sko__List__Xtl__Xinduct__2 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV199 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1856,plain,
! [SV779: $i,SV519: $i,SV200: $i] :
( ( ! [SY2329: $i] :
( ( SV200
= ( c_List_Olist_ONil @ SV519 ) )
| ~ ( c_List_Olist__all2 @ SV779 @ SV200 @ ( c_List_Olist_ONil @ SY2329 ) @ SV519 @ SY2329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1857,plain,
! [SV780: $i,SV520: $i,SV201: $i] :
( ( ! [SY2330: $i] :
( ( SV201
= ( c_List_Olist_ONil @ SV520 ) )
| ~ ( c_List_Olist__all2 @ SV780 @ ( c_List_Olist_ONil @ SY2330 ) @ SV201 @ SY2330 @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1858,plain,
! [SV521: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ SV202 @ SV521 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV202 @ ( v_sko__List__Xlist__Xinducts__2 @ SV202 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV202 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1859,plain,
! [SV522: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ SV203 @ SV522 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV203 @ ( v_sko__List__Xhd__Xinduct__2 @ SV203 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV203 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1860,plain,
! [SV781: $i,SV523: $i,SV205: $i] :
( ( ( c_List_Oconcat__map @ SV205 @ ( c_List_Olist_ONil @ SV523 ) @ SV523 @ SV781 )
= ( c_List_Olist_ONil @ SV781 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1861,plain,
! [SV524: $i,SV206: $i] :
( ( ( hBOOL @ ( hAPP @ SV206 @ SV524 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV206 @ ( v_sko__List__Xremdups__Xinduct__2 @ SV206 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV206 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1862,plain,
! [SV525: $i,SV207: $i] :
( ( c_List_Omember @ SV207 @ ( c_List_Olist_ONil @ SV525 ) @ SV525 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1863,plain,
! [SV782: $i,SV526: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ SV208 @ SV526 ) )
| ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV208 @ SV782 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Olist_ONil @ SV782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1864,plain,
! [SV783: $i,SV527: $i,SV209: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV209 )
| ( ( c_List_Olinorder__class_Osort__key @ SV527 @ ( c_List_Olist_ONil @ SV783 ) @ SV783 @ SV209 )
= ( c_List_Olist_ONil @ SV783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1865,plain,
! [SV528: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ SV210 @ SV528 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV210 @ ( v_sko__List__Xdrop__Xinduct__2 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV210 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1866,plain,
! [SV784: $i,SV529: $i,SV211: $i] :
( ( ! [SY2331: $i] :
( ( c_List_Ofoldl @ SV211 @ SV529 @ ( c_List_Olist_ONil @ SV784 ) @ SY2331 @ SV784 )
= SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1867,plain,
! [SV530: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP @ SV212 @ SV530 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV212 @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV212 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV212 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1868,plain,
! [SV785: $i,SV531: $i,SV213: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV213 @ SV531 @ ( c_List_Olist_ONil @ SV785 ) @ SV785 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1869,plain,
! [SV786: $i,SV532: $i,SV214: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_ONil @ SV532 ) @ SV786 @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1870,plain,
! [SV534: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ SV534 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV217 @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV217 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1871,plain,
! [SV542: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ SV225 @ SV542 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV225 @ ( v_sko__List__Xlast__Xinduct__2 @ SV225 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV225 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1872,plain,
! [SV544: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ SV227 @ SV544 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV227 @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV227 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV227 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1873,plain,
! [SV545: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP @ SV228 @ SV545 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV228 @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV228 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV228 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1580]) ).
thf(1874,plain,
! [SV546: $i,SV229: $i] :
( ( ( hBOOL @ ( hAPP @ SV229 @ SV546 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV229 @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV229 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV229 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1875,plain,
! [SV548: $i,SV232: $i] :
( ( c_List_Olist__ex @ SV232 @ ( c_List_Olist_ONil @ SV548 ) @ SV548 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1876,plain,
! [SV787: $i,SV549: $i,SV234: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV234 @ ( c_List_Olist_Olist__case @ SV549 @ SV787 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV234 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1877,plain,
! [SV788: $i,SV550: $i,SV235: $i] :
( ( ! [SY2332: $i] :
( ( c_List_Ofoldr @ SV235 @ ( c_List_Olist_ONil @ SV550 ) @ SV788 @ SV550 @ SY2332 )
= SV788 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1878,plain,
! [SV551: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ SV236 @ SV551 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV236 @ ( v_sko__List__Xzip__Xinduct__2 @ SV236 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1879,plain,
! [SV789: $i,SV552: $i,SV237: $i] :
( ( ( c_List_Omap @ SV237 @ ( c_List_Olist_ONil @ SV552 ) @ SV552 @ SV789 )
= ( c_List_Olist_ONil @ SV789 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1880,plain,
! [SV554: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ SV239 @ SV554 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV239 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV239 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV239 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1881,plain,
! [SV790: $i,SV555: $i,SV240: $i] :
( ( ! [SY2333: $i] :
( ( c_List_Olist_Olist__rec @ SV240 @ SV555 @ ( c_List_Olist_ONil @ SV790 ) @ SY2333 @ SV790 )
= SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1882,plain,
! [SV556: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ SV556 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV241 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV241 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1883,plain,
! [SV557: $i,SV242: $i] :
( ( ( hBOOL @ ( hAPP @ SV242 @ SV557 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV242 @ ( v_sko__List__Xtake__Xinduct__2 @ SV242 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV242 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1884,plain,
! [SV243: $i] :
( ( ( class_Orderings_Olinorder @ SV243 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV243 ) @ SV243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1885,plain,
! [SV791: $i,SV558: $i,SV244: $i] :
( ( ( c_List_Ofiltermap @ SV244 @ ( c_List_Olist_ONil @ SV558 ) @ SV558 @ SV791 )
= ( c_List_Olist_ONil @ SV791 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1886,plain,
! [SV792: $i,SV560: $i,SV246: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV246 ) @ SV560 @ SV792 @ SV246 )
= ( c_List_Olist_ONil @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1887,plain,
! [SV793: $i,SV561: $i,SV247: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV247 ) @ SV561 @ SV793 @ SV247 )
= ( c_List_Olist_ONil @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1888,plain,
! [SV794: $i,SV562: $i,SV248: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV248 ) @ SV562 @ SV794 @ SV248 )
= ( c_List_Olist_ONil @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1889,plain,
! [SV563: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP @ SV249 @ SV563 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV249 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV249 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV249 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1890,plain,
! [SV565: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ SV251 @ SV565 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV251 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV251 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1891,plain,
! [SV795: $i,SV566: $i,SV252: $i] :
( ( ! [SY2334: $i] :
( ( c_Map_Omap__upds @ SV252 @ SV566 @ ( c_List_Olist_ONil @ SV795 ) @ SY2334 @ SV795 )
= SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1892,plain,
! [SV796: $i,SV567: $i,SV253: $i] :
( ( ! [SY2335: $i] :
( ( c_Map_Omap__upds @ SV253 @ ( c_List_Olist_ONil @ SV567 ) @ SV796 @ SV567 @ SY2335 )
= SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1893,plain,
! [SV568: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ SV254 @ SV568 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV254 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV254 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV254 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1894,plain,
! [SV797: $i,SV569: $i,SV255: $i] :
( ( ! [SY2336: $i] :
( ( c_List_Olist_Olist__case @ SV255 @ SV569 @ ( c_List_Olist_ONil @ SV797 ) @ SY2336 @ SV797 )
= SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1895,plain,
! [SV571: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ SV257 @ SV571 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV257 @ ( v_sko__List__Xlist__Xinduct__2 @ SV257 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1607]) ).
thf(1896,plain,
! [SV798: $i,SV572: $i,SV258: $i] :
( ( ( c_List_Olist_ONil @ SV258 )
= ( c_List_Omap @ SV572 @ ( c_List_Olist_ONil @ SV798 ) @ SV798 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1897,plain,
! [SV574: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ SV574 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV261 @ ( v_sko__List__Xmap__Xinduct__2 @ SV261 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1610]) ).
thf(1898,plain,
! [SV799: $i,SV575: $i,SV263: $i] :
( ( ! [SY2337: $i] :
( ( c_List_Olistsp @ SV263 @ ( c_List_Oappend @ SV575 @ SV799 @ SY2337 ) @ SY2337 )
| ~ ( c_List_Olistsp @ SV263 @ SV799 @ SY2337 )
| ~ ( c_List_Olistsp @ SV263 @ SV575 @ SY2337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1899,plain,
! [SV800: $i,SV576: $i,SV264: $i] :
( ( ( c_List_Olistsp @ SV264 @ SV576 @ SV800 )
| ~ ( hBOOL @ ( hAPP @ SV264 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV264 @ SV576 @ SV800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1900,plain,
! [SV801: $i,SV577: $i,SV265: $i] :
( ( ! [SY2338: $i] :
( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV265 @ SV577 @ ( tc_fun @ SV801 @ tc_bool ) ) @ SY2338 @ SV801 )
| ~ ( c_List_Olistsp @ SV577 @ SY2338 @ SV801 )
| ~ ( c_List_Olistsp @ SV265 @ SY2338 @ SV801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1901,plain,
! [SV802: $i,SV578: $i,SV266: $i] :
( ( ! [SY2339: $i] :
( ( c_List_Olistsp @ SV266 @ SV578 @ SV802 )
| ~ ( c_List_Olistsp @ SV266 @ ( c_List_Oappend @ SY2339 @ SV578 @ SV802 ) @ SV802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1902,plain,
! [SV803: $i,SV579: $i,SV267: $i] :
( ( ! [SY2340: $i] :
( ( c_List_Olistsp @ SV267 @ SV579 @ SV803 )
| ~ ( c_List_Olistsp @ SV267 @ ( c_List_Oappend @ SV579 @ SY2340 @ SV803 ) @ SV803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1903,plain,
! [SV580: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV268 @ SV580 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV268 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1904,plain,
! [SV269: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV269 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1905,plain,
! [SV804: $i,SV581: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ SV270 @ SV581 ) )
| ( hBOOL @ ( hAPP @ SV804 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV804 @ SV270 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV270 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV804 @ SV581 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1906,plain,
! [SV805: $i,SV582: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ SV271 @ SV582 ) )
| ( hBOOL @ ( hAPP @ SV271 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV805 @ SV271 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV805 @ SV582 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1907,plain,
! [SV806: $i,SV583: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ SV272 @ SV583 ) )
| ( hBOOL @ ( hAPP @ SV806 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV806 @ SV272 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV806 @ SV583 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1908,plain,
! [SV807: $i,SV584: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ SV273 @ SV584 ) )
| ( hBOOL @ ( hAPP @ SV273 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV807 @ SV273 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV273 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV807 @ SV584 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1909,plain,
! [SV585: $i,SV274: $i] :
( ( ( c_List_Olistsp @ SV274 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV274 @ SV585 ) @ t_a )
= $true )
| ( ( ( SV585
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV274 @ SV585 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1910,plain,
! [SV586: $i,SV275: $i] :
( ( ( hBOOL @ ( hAPP @ SV275 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV275 @ SV586 ) ) )
= $true )
| ( ( ( SV586
= ( c_List_Olist_ONil @ t_a ) )
| ~ ( c_List_Olistsp @ SV275 @ SV586 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1911,plain,
! [SV808: $i,SV587: $i,SV276: $i] :
( ( ( hBOOL @ ( hAPP @ SV276 @ SV587 ) )
| ( c_List_Olistsp @ SV808 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV808 @ SV276 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV276 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV808 @ SV587 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1912,plain,
! [SV809: $i,SV588: $i,SV277: $i] :
( ( ( hBOOL @ ( hAPP @ SV277 @ SV588 ) )
| ( c_List_Olistsp @ SV809 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV809 @ SV277 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV277 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV809 @ SV588 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1913,plain,
! [SV590: $i,SV279: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV279 @ SV590 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1914,plain,
! [SV591: $i,SV280: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV280 @ SV591 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1915,plain,
! [SV810: $i,SV593: $i,SV282: $i] :
( ( ( SV282 = SV593 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV810 ) @ SV282 ) @ SV593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1916,plain,
! [SV811: $i,SV594: $i,SV283: $i] :
( ( ! [SY2341: $i] :
( ( ( c_List_Orev @ SV283 @ SV594 )
!= ( c_List_Olist_OCons @ SV811 @ SY2341 @ SV594 ) )
| ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SY2341 @ SV594 ) @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1917,plain,
! [SV812: $i,SV595: $i,SV284: $i] :
( ( ( ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 )
!= ( c_List_Orev @ SV812 @ SV595 ) )
| ( SV812
= ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1918,plain,
! [SV813: $i,SV596: $i,SV286: $i] :
( ( ( ( c_List_Oappend @ SV286 @ SV596 @ SV813 )
!= ( c_List_Olist_ONil @ SV813 ) )
| ( SV596
= ( c_List_Olist_ONil @ SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1919,plain,
! [SV814: $i,SV597: $i,SV287: $i] :
( ( ! [SY2342: $i,SY2343: $i] :
( ( ( c_List_Oappend @ SV287 @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 )
!= ( c_List_Oappend @ SY2342 @ ( c_List_Olist_OCons @ SY2343 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 ) )
| ( SV597 = SY2343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1920,plain,
! [SV815: $i,SV598: $i,SV288: $i] :
( ( ( c_List_Olist_OCons @ SV288 @ SV598 @ SV815 )
!= ( c_List_Olist_ONil @ SV815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1921,plain,
! [SV816: $i,SV599: $i,SV289: $i] :
( ( ! [SY2344: $i,SY2345: $i] :
( ( ( c_List_Oappend @ SV289 @ ( c_List_Olist_OCons @ SV599 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 )
!= ( c_List_Oappend @ SY2344 @ ( c_List_Olist_OCons @ SY2345 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 ) )
| ( SV289 = SY2344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1922,plain,
! [SV817: $i,SV600: $i,SV290: $i] :
( ( ( ( c_List_Orotate @ SV290 @ SV600 @ SV817 )
!= ( c_List_Olist_ONil @ SV817 ) )
| ( SV600
= ( c_List_Olist_ONil @ SV817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1923,plain,
! [SV818: $i,SV601: $i,SV291: $i] :
( ( ( c_List_Olist_ONil @ SV291 )
!= ( c_List_Olist_OCons @ SV601 @ SV818 @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1924,plain,
! [SV819: $i,SV602: $i,SV292: $i] :
( ( ( ( c_List_Oappend @ SV292 @ SV602 @ SV819 )
!= ( c_List_Olist_ONil @ SV819 ) )
| ( SV292
= ( c_List_Olist_ONil @ SV819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1925,plain,
! [SV603: $i,SV293: $i] :
( ( ( ( c_List_Oremdups @ SV293 @ SV603 )
!= ( c_List_Olist_ONil @ SV603 ) )
= $true )
| ( ( SV293
= ( c_List_Olist_ONil @ SV603 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1926,plain,
! [SV820: $i,SV604: $i,SV294: $i] :
( ( ( ( c_List_Oappend @ SV294 @ SV604 @ SV820 )
!= SV604 )
| ( SV294
= ( c_List_Olist_ONil @ SV820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1927,plain,
! [SV605: $i,SV296: $i] :
( ( ( ( c_Suc @ SV296 )
!= ( c_Suc @ SV605 ) )
= $true )
| ( ( SV296 = SV605 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1928,plain,
! [SV821: $i,SV606: $i,SV297: $i] :
( ( ! [SY2346: $i,SY2347: $i] :
( ( ( c_List_Olist_OCons @ SV297 @ SV606 @ SV821 )
!= ( c_List_Ofilter @ SY2346 @ SY2347 @ SV821 ) )
| ( hBOOL @ ( hAPP @ SY2346 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1929,plain,
! [SV822: $i,SV607: $i,SV298: $i] :
( ( ! [SY2348: $i,SY2349: $i] :
( ( ( c_List_Olist_OCons @ SV298 @ SV607 @ SV822 )
!= ( c_List_Olist_OCons @ SY2348 @ SY2349 @ SV822 ) )
| ( SV607 = SY2349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1930,plain,
! [SV823: $i,SV608: $i,SV299: $i] :
( ( ( ( c_List_Olist_ONil @ SV299 )
!= ( c_List_Oappend @ SV608 @ SV823 @ SV299 ) )
| ( SV823
= ( c_List_Olist_ONil @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1931,plain,
! [SV824: $i,SV609: $i,SV300: $i] :
( ( ( c_List_Olist_OCons @ SV300 @ SV609 @ SV824 )
!= SV609 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1932,plain,
! [SV610: $i,SV301: $i] :
( ( ( ( c_List_Olist_ONil @ SV301 )
!= ( c_List_Oremdups @ SV610 @ SV301 ) )
= $true )
| ( ( SV610
= ( c_List_Olist_ONil @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1933,plain,
! [SV825: $i,SV611: $i,SV302: $i] :
( ( ! [SY2350: $i] :
( ( ( c_List_Oappend @ SV302 @ SV611 @ SV825 )
!= ( c_List_Oappend @ SY2350 @ SV611 @ SV825 ) )
| ( SV302 = SY2350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1934,plain,
! [SV826: $i,SV612: $i,SV303: $i] :
( ( ( SV303
!= ( c_List_Oappend @ SV612 @ SV303 @ SV826 ) )
| ( SV612
= ( c_List_Olist_ONil @ SV826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1935,plain,
! [SV613: $i,SV304: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV304 )
!= ( c_Lambda_OdB_OAbs @ SV613 ) )
= $true )
| ( ( SV304 = SV613 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1936,plain,
! [SV827: $i,SV614: $i,SV305: $i] :
( ( ! [SY2351: $i] :
( ( ( c_List_Omap @ SV305 @ SV614 @ SV827 @ SY2351 )
!= ( c_List_Olist_ONil @ SY2351 ) )
| ( SV614
= ( c_List_Olist_ONil @ SV827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1937,plain,
! [SV828: $i,SV615: $i,SV306: $i] :
( ( ! [SY2352: $i,SY2353: $i] :
( ( ( c_List_Olist_OCons @ SV306 @ SV615 @ SV828 )
!= ( c_List_Olist_OCons @ SY2352 @ SY2353 @ SV828 ) )
| ( SV306 = SY2352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1938,plain,
! [SV616: $i,SV307: $i] :
( ( ( ( c_List_Olist_ONil @ SV307 )
!= ( c_List_Orev @ SV616 @ SV307 ) )
= $true )
| ( ( SV616
= ( c_List_Olist_ONil @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1939,plain,
! [SV829: $i,SV617: $i,SV308: $i] :
( ( ( ( c_List_Orev @ SV308 @ SV617 )
!= ( c_List_Orev @ SV829 @ SV617 ) )
| ( SV308 = SV829 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1940,plain,
! [SV830: $i,SV618: $i,SV309: $i] :
( ( ! [SY2354: $i] :
( ( ( c_List_Olist__update @ SV309 @ SV618 @ SV830 @ SY2354 )
!= ( c_List_Olist_ONil @ SY2354 ) )
| ( SV309
= ( c_List_Olist_ONil @ SY2354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1941,plain,
! [SV831: $i,SV619: $i,SV310: $i] :
( ( ! [SY2355: $i] :
( ( ( c_List_Olist_ONil @ SV310 )
!= ( c_List_Omap @ SV619 @ SV831 @ SY2355 @ SV310 ) )
| ( SV831
= ( c_List_Olist_ONil @ SY2355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1942,plain,
! [SV620: $i,SV311: $i] :
( ( ( ( c_List_Oremdups @ SV311 @ SV620 )
!= SV311 )
= $true )
| ( ( c_List_Odistinct @ SV311 @ SV620 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1943,plain,
! [SV832: $i,SV621: $i,SV312: $i] :
( ( ( ( c_List_Orev @ SV312 @ SV621 )
!= ( c_List_Olist_OCons @ SV832 @ ( c_List_Olist_ONil @ SV621 ) @ SV621 ) )
| ( SV312
= ( c_List_Olist_OCons @ SV832 @ ( c_List_Olist_ONil @ SV621 ) @ SV621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1944,plain,
! [SV833: $i,SV622: $i,SV313: $i] :
( ( ( ( c_List_Olist_ONil @ SV313 )
!= ( c_List_Oappend @ SV622 @ SV833 @ SV313 ) )
| ( SV622
= ( c_List_Olist_ONil @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1945,plain,
! [SV623: $i,SV314: $i] :
( ( ( ( c_List_Orev @ SV314 @ SV623 )
!= ( c_List_Olist_ONil @ SV623 ) )
= $true )
| ( ( SV314
= ( c_List_Olist_ONil @ SV623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1946,plain,
! [SV834: $i,SV624: $i,SV315: $i] :
( ( ( c_List_Olist_OCons @ SV315 @ SV624 @ SV834 )
!= ( c_List_Olist_ONil @ SV834 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1947,plain,
! [SV835: $i,SV625: $i,SV316: $i] :
( ( ! [SY2356: $i,SY2357: $i] :
( ( ( c_List_OdropWhile @ SV316 @ SV625 @ SV835 )
!= ( c_List_Olist_OCons @ SY2356 @ SY2357 @ SV835 ) )
| ~ ( hBOOL @ ( hAPP @ SV316 @ SY2356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(1948,plain,
! [SV626: $i,SV317: $i] :
( ( ( ( c_Suc @ SV317 )
!= ( c_Suc @ SV626 ) )
= $true )
| ( ( SV317 = SV626 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1949,plain,
! [SV836: $i,SV627: $i,SV318: $i] :
( ( SV318
!= ( c_List_Olist_OCons @ SV627 @ SV318 @ SV836 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1950,plain,
! [SV837: $i,SV628: $i,SV319: $i] :
( ( ! [SY2358: $i] :
( ( ( c_List_Oappend @ SV319 @ SV628 @ SV837 )
!= ( c_List_Oappend @ SV319 @ SY2358 @ SV837 ) )
| ( SV628 = SY2358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1951,plain,
! [SV629: $i,SV320: $i] :
( ( ( ( c_List_Orotate1 @ SV320 @ SV629 )
!= ( c_List_Olist_ONil @ SV629 ) )
= $true )
| ( ( SV320
= ( c_List_Olist_ONil @ SV629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1952,plain,
! [SV838: $i,SV630: $i,SV321: $i] :
( ( ( ( c_List_Oappend @ SV321 @ SV630 @ SV838 )
!= SV321 )
| ( SV630
= ( c_List_Olist_ONil @ SV838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1953,plain,
! [SV839: $i,SV631: $i,SV322: $i] :
( ( ! [SY2359: $i,SY2360: $i] :
( ( ( c_List_Ofilter @ SV322 @ SV631 @ SV839 )
!= ( c_List_Olist_OCons @ SY2359 @ SY2360 @ SV839 ) )
| ( hBOOL @ ( hAPP @ SV322 @ SY2359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1954,plain,
! [SV840: $i,SV632: $i,SV323: $i] :
( ( ( SV323
!= ( c_List_Oappend @ SV323 @ SV632 @ SV840 ) )
| ( SV632
= ( c_List_Olist_ONil @ SV840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1955,plain,
! [SV841: $i,SV635: $i,SV326: $i,SV3: $i] :
( ( ! [SY2361: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV3 @ SV326 @ SV635 ) @ ( c_Suc @ SV841 ) @ SY2361 @ SV635 )
= ( c_List_Olist_OCons @ SV3 @ ( c_List_Olist__update @ SV326 @ SV841 @ SY2361 @ SV635 ) @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1956,plain,
! [SV842: $i,SV636: $i,SV327: $i,SV4: $i] :
( ( ( c_List_Odrop @ ( c_Suc @ SV4 ) @ ( c_List_Olist_OCons @ SV327 @ SV636 @ SV842 ) @ SV842 )
= ( c_List_Odrop @ SV4 @ SV636 @ SV842 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1957,plain,
! [SV843: $i,SV637: $i,SV328: $i,SV5: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV5 ) @ ( c_List_Olist_OCons @ SV328 @ SV637 @ SV843 ) @ SV843 )
= ( c_List_Olist_OCons @ SV328 @ ( c_List_Otake @ SV5 @ SV637 @ SV843 ) @ SV843 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1958,plain,
! [SV330: $i,SV7: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ SV7 ) @ ( v_sko__List__Xdrop__Xinduct__2 @ SV7 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV7 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1959,plain,
! [SV331: $i,SV8: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ SV8 ) @ ( v_sko__List__Xrev__Xinduct__2 @ SV8 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV8 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1960,plain,
! [SV332: $i,SV9: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ SV9 ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV9 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV9 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1961,plain,
! [SV333: $i,SV10: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV10 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV10 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1962,plain,
! [SV640: $i,SV335: $i,SV12: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oappend @ SV12 @ SV335 @ SV640 ) @ SV640 )
= ( c_List_Ohd @ SV12 @ SV640 ) )
= $true )
| ( ( SV12
= ( c_List_Olist_ONil @ SV640 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1963,plain,
! [SV641: $i,SV337: $i,SV14: $i] :
( ( ( ( c_List_Otake @ ( c_Suc @ SV14 ) @ SV337 @ SV641 )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ SV337 @ SV641 ) @ ( c_List_Otake @ SV14 @ ( c_List_Otl @ SV337 @ SV641 ) @ SV641 ) @ SV641 ) )
= $true )
| ( ( SV337
= ( c_List_Olist_ONil @ SV641 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1964,plain,
! [SV642: $i,SV338: $i,SV15: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV15 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV15 @ SV338 @ SV642 ) @ SV642 ) ) ) )
= $true )
| ( ( ( c_List_OdropWhile @ SV15 @ SV338 @ SV642 )
= ( c_List_Olist_ONil @ SV642 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1965,plain,
! [SV339: $i,SV16: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ SV16 ) @ ( v_sko__List__Xhd__Xinduct__2 @ SV16 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV16 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1686]) ).
thf(1966,plain,
! [SV340: $i,SV17: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV17 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV17 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV17 @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1967,plain,
! [SV341: $i,SV18: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ SV18 ) @ ( v_sko__List__Xset__Xinduct__2 @ SV18 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV18 @ SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1968,plain,
! [SV342: $i,SV19: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV19 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV19 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV19 @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(1969,plain,
! [SV343: $i,SV20: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinducts__1 @ SV20 ) @ ( v_sko__List__Xlist__Xinducts__2 @ SV20 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV20 @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1970,plain,
! [SV344: $i,SV21: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV21 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV21 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV21 @ SV344 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1971,plain,
! [SV345: $i,SV22: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ SV22 ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV22 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV22 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1972,plain,
! [SV346: $i,SV23: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ SV23 ) @ ( v_sko__List__Xremdups__Xinduct__2 @ SV23 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV23 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1973,plain,
! [SV347: $i,SV24: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ SV24 ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV24 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV24 @ SV347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1974,plain,
! [SV348: $i,SV25: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ SV25 ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV25 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1975,plain,
! [SV349: $i,SV26: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV26 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV26 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV26 @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1976,plain,
! [SV350: $i,SV27: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV27 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV27 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV27 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1977,plain,
! [SV351: $i,SV28: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV28 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV28 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV28 @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1978,plain,
! [SV352: $i,SV29: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV29 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV29 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ SV352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1979,plain,
! [SV353: $i,SV30: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ SV30 ) @ ( v_sko__List__Xsplice__Xinduct__2 @ SV30 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV30 @ SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(1980,plain,
! [SV354: $i,SV31: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV31 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV31 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV31 @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1981,plain,
! [SV355: $i,SV32: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ SV32 ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV32 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV32 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1982,plain,
! [SV356: $i,SV33: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ SV33 ) @ ( v_sko__List__Xlast__Xinduct__2 @ SV33 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV33 @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1983,plain,
! [SV357: $i,SV34: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ SV34 ) @ ( v_sko__List__Xtl__Xinduct__2 @ SV34 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV34 @ SV357 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1984,plain,
! [SV844: $i,SV643: $i,SV358: $i,SV35: $i] :
( ( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV35 @ SV358 @ SV643 ) @ SV844 @ SV643 )
= ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV844 @ SV643 ) @ ( c_List_Osplice @ SV358 @ ( c_List_Otl @ SV844 @ SV643 ) @ SV643 ) @ SV643 ) @ SV643 ) )
| ( SV844
= ( c_List_Olist_ONil @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1985,plain,
! [SV644: $i,SV359: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP @ SV36 @ SV359 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV36 @ SV644 ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ SV36 @ SV644 ) @ ( c_List_Olist_ONil @ SV644 ) @ SV644 ) @ SV644 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Olist_ONil @ SV644 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1986,plain,
! [SV845: $i,SV645: $i,SV361: $i,SV38: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV38 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV361 @ ( c_List_Olinorder__class_Osort__key @ SV361 @ SV645 @ SV845 @ SV38 ) @ SV845 @ SV38 ) @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1987,plain,
! [SV846: $i,SV647: $i,SV363: $i,SV40: $i] :
( ( ! [SY2362: $i] :
( ( c_ListOrder_Ostep1 @ SV40 @ ( c_List_Oappend @ SV363 @ SV647 @ SV846 ) @ ( c_List_Oappend @ SV363 @ SY2362 @ SV846 ) @ SV846 )
| ~ ( c_ListOrder_Ostep1 @ SV40 @ SV647 @ SY2362 @ SV846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1988,plain,
! [SV847: $i,SV648: $i,SV364: $i,SV41: $i] :
( ( ! [SY2363: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV41 @ SV364 @ SV648 @ SV847 )
| ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Oappend @ SV364 @ SY2363 @ SV847 ) @ ( c_List_Oappend @ SV648 @ SY2363 @ SV847 ) @ SV847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1989,plain,
! [SV848: $i,SV649: $i,SV365: $i,SV42: $i] :
( ( ( ( c_List_Ofilter @ SV42 @ ( c_List_Olist_OCons @ SV365 @ SV649 @ SV848 ) @ SV848 )
= ( c_List_Olist_OCons @ SV365 @ ( c_List_Ofilter @ SV42 @ SV649 @ SV848 ) @ SV848 ) )
| ~ ( hBOOL @ ( hAPP @ SV42 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1990,plain,
! [SV650: $i,SV366: $i,SV43: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV43 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV366 @ SV650 @ SV43 ) @ SV43 )
| ~ ( c_List_Olinorder__class_Osorted @ SV650 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1991,plain,
! [SV849: $i,SV651: $i,SV367: $i,SV44: $i] :
( ( ! [SY2364: $i] :
( ( c_List_Otake @ SV44 @ ( c_List_Omap @ SV367 @ SV651 @ SV849 @ SY2364 ) @ SY2364 )
= ( c_List_Omap @ SV367 @ ( c_List_Otake @ SV44 @ SV651 @ SV849 ) @ SV849 @ SY2364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1992,plain,
! [SV850: $i,SV653: $i,SV369: $i,SV46: $i] :
( ( ! [SY2365: $i,SY2366: $i] :
( ( c_List_Olist__all2 @ SV46 @ ( c_List_Otake @ SV369 @ SV653 @ SV850 ) @ ( c_List_Otake @ SV369 @ SY2365 @ SY2366 ) @ SV850 @ SY2366 )
| ~ ( c_List_Olist__all2 @ SV46 @ SV653 @ SY2365 @ SV850 @ SY2366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1993,plain,
! [SV655: $i,SV371: $i,SV48: $i] :
( ( ( SV48 = SV371 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ ( c_fequal @ SV655 ) @ SV48 @ SV371 @ SV655 @ SV655 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1994,plain,
! [SV851: $i,SV656: $i,SV372: $i,SV49: $i] :
( ( ! [SY2367: $i,SY2368: $i] :
( ( c_List_Ofoldl @ SV49 @ SV372 @ ( c_List_Olist_OCons @ SV656 @ SV851 @ SY2367 ) @ SY2368 @ SY2367 )
= ( c_List_Ofoldl @ SV49 @ ( hAPP @ ( hAPP @ SV49 @ SV372 ) @ SV656 ) @ SV851 @ SY2368 @ SY2367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(1995,plain,
! [SV852: $i,SV657: $i,SV373: $i,SV50: $i] :
( ( ! [SY2369: $i,SY2370: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV373 ) @ SV657 ) )
| ( c_ListOrder_Ostep1 @ SV50 @ SV852 @ SY2369 @ SY2370 )
| ~ ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SV852 @ ( c_List_Olist_OCons @ SV373 @ ( c_List_Olist_ONil @ SY2370 ) @ SY2370 ) @ SY2370 ) @ ( c_List_Oappend @ SY2369 @ ( c_List_Olist_OCons @ SV657 @ ( c_List_Olist_ONil @ SY2370 ) @ SY2370 ) @ SY2370 ) @ SY2370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(1996,plain,
! [SV660: $i,SV377: $i,SV54: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV54 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV377 @ SV660 @ SV54 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV660 @ SV377 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1997,plain,
! [SV661: $i,SV378: $i,SV55: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV55 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 @ SV661 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV661 @ SV378 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1998,plain,
! [SV853: $i,SV662: $i,SV379: $i,SV56: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV56 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(1999,plain,
! [SV854: $i,SV663: $i,SV380: $i,SV57: $i] :
( ( ! [SY2371: $i,SY2372: $i,SY2373: $i] :
( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SV854 ) @ ( c_List_Oappend @ SY2371 @ SY2372 @ SY2373 ) @ SV854 @ SY2373 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV663 @ SY2372 @ SV854 @ SY2373 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SY2371 @ SV854 @ SY2373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2000,plain,
! [SV855: $i,SV664: $i,SV381: $i,SV58: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV58 @ SV381 @ SV664 ) @ SV855 @ SV664 )
= ( c_List_Olist_OCons @ SV58 @ ( c_List_Oappend @ SV381 @ SV855 @ SV664 ) @ SV664 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2001,plain,
! [SV856: $i,SV665: $i,SV382: $i,SV59: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV59 @ SV382 @ SV665 ) @ SV856 @ SV665 )
= ( c_List_Olist_OCons @ SV59 @ ( c_List_Oappend @ SV382 @ SV856 @ SV665 ) @ SV665 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2002,plain,
! [SV383: $i,SV60: $i] :
( ( ( c_List_Odistinct @ SV60 @ SV383 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Orotate1 @ SV60 @ SV383 ) @ SV383 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(2003,plain,
! [SV384: $i,SV61: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate1 @ SV61 @ SV384 ) @ SV384 )
= $false )
| ( ( c_List_Odistinct @ SV61 @ SV384 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(2004,plain,
! [SV666: $i,SV385: $i,SV62: $i] :
( ( ( c_List_Odistinct @ ( c_List_Ofilter @ SV62 @ SV385 @ SV666 ) @ SV666 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV385 @ SV666 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(2005,plain,
! [SV857: $i,SV667: $i,SV386: $i,SV63: $i] :
( ( ! [SY2374: $i] :
( ( c_List_Omap @ SV63 @ ( c_List_Olist_OCons @ SV386 @ SV667 @ SV857 ) @ SV857 @ SY2374 )
= ( c_List_Olist_OCons @ ( hAPP @ SV63 @ SV386 ) @ ( c_List_Omap @ SV63 @ SV667 @ SV857 @ SY2374 ) @ SY2374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2006,plain,
! [SV858: $i,SV668: $i,SV387: $i,SV64: $i] :
( ( ! [SY2375: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV64 @ SV387 ) @ ( c_List_Omap @ SV64 @ SV668 @ SV858 @ SY2375 ) @ SY2375 )
= ( c_List_Omap @ SV64 @ ( c_List_Olist_OCons @ SV387 @ SV668 @ SV858 ) @ SV858 @ SY2375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2007,plain,
! [SV859: $i,SV669: $i,SV388: $i,SV65: $i] :
( ( ! [SY2376: $i] :
( ( c_List_Omap @ SV65 @ ( c_List_Olist_OCons @ SV388 @ SV669 @ SV859 ) @ SV859 @ SY2376 )
= ( c_List_Olist_OCons @ ( hAPP @ SV65 @ SV388 ) @ ( c_List_Omap @ SV65 @ SV669 @ SV859 @ SY2376 ) @ SY2376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2008,plain,
! [SV860: $i,SV670: $i,SV389: $i,SV66: $i] :
( ( ! [SY2377: $i,SY2378: $i] :
( ( c_List_Olist_Olist__case @ SV66 @ SV389 @ ( c_List_Olist_OCons @ SV670 @ SV860 @ SY2377 ) @ SY2378 @ SY2377 )
= ( hAPP @ ( hAPP @ SV389 @ SV670 ) @ SV860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2009,plain,
! [SV861: $i,SV672: $i,SV391: $i,SV68: $i] :
( ( ! [SY2379: $i,SY2380: $i,SY2381: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV391 ) @ SV672 ) )
| ~ ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SV391 @ SV861 @ SY2379 ) @ ( c_List_Olist_OCons @ SV672 @ SY2380 @ SY2381 ) @ SY2379 @ SY2381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2010,plain,
! [SV862: $i,SV673: $i,SV392: $i,SV69: $i] :
( ( ( c_List_Olist_OCons @ SV69 @ ( c_List_Oappend @ SV392 @ SV673 @ SV862 ) @ SV862 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV69 @ SV392 @ SV862 ) @ SV673 @ SV862 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2011,plain,
! [SV863: $i,SV674: $i,SV393: $i,SV70: $i] :
( ( ( c_List_Olist_OCons @ SV70 @ ( c_List_Oappend @ SV393 @ SV674 @ SV863 ) @ SV863 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV70 @ SV393 @ SV863 ) @ SV674 @ SV863 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2012,plain,
! [SV864: $i,SV675: $i,SV394: $i,SV71: $i] :
( ( ! [SY2382: $i,SY2383: $i] :
( ( SV71 = SV394 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV675 @ SV394 ) @ SV71 ) )
| ~ ( c_ListOrder_Ostep1 @ SV675 @ ( c_List_Olist_OCons @ SV394 @ SV864 @ SY2382 ) @ ( c_List_Olist_OCons @ SV71 @ SY2383 @ SY2382 ) @ SY2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2013,plain,
! [SV677: $i,SV396: $i,SV73: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV73 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ SV396 @ SV73 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV677 @ SV396 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(2014,plain,
! [SV679: $i,SV398: $i,SV75: $i] :
( ( ( c_List_Odistinct @ ( c_List_Odrop @ SV75 @ SV398 @ SV679 ) @ SV679 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV398 @ SV679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(2015,plain,
! [SV399: $i,SV76: $i] :
( ( ( c_List_Odistinct @ SV76 @ SV399 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Orev @ SV76 @ SV399 ) @ SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(2016,plain,
! [SV400: $i,SV77: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orev @ SV77 @ SV400 ) @ SV400 )
= $false )
| ( ( c_List_Odistinct @ SV77 @ SV400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(2017,plain,
! [SV865: $i,SV680: $i,SV401: $i,SV78: $i] :
( ( ( c_List_Olist__all @ SV78 @ SV401 @ SV680 )
| ~ ( c_List_Olist__all @ SV78 @ ( c_List_Olist_OCons @ SV865 @ SV401 @ SV680 ) @ SV680 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2018,plain,
! [SV402: $i,SV79: $i] :
( ( ( c_List_Odistinct @ SV79 @ SV402 )
= $false )
| ( ( ( c_List_Oremdups @ SV79 @ SV402 )
= SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(2019,plain,
! [SV681: $i,SV403: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ SV80 @ SV403 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV681 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV681 @ SV80 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV681 @ SV403 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(2020,plain,
! [SV866: $i,SV682: $i,SV404: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ SV81 @ SV404 ) )
| ~ ( c_List_Olist__all @ SV81 @ ( c_List_Olist_OCons @ SV404 @ SV682 @ SV866 ) @ SV866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2021,plain,
! [SV683: $i,SV405: $i,SV82: $i] :
( ( ( hBOOL @ ( hAPP @ SV82 @ SV405 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV683 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV683 @ SV82 ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV683 @ SV405 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(2022,plain,
! [SV867: $i,SV686: $i,SV408: $i,SV85: $i] :
( ( ! [SY2384: $i,SY2385: $i] :
( ( c_List_Omap @ SV85 @ ( c_List_Olist__update @ SV408 @ SV686 @ SV867 @ SY2384 ) @ SY2384 @ SY2385 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV85 @ SV408 @ SY2384 @ SY2385 ) @ SV686 @ ( hAPP @ SV85 @ SV867 ) @ SY2385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2023,plain,
! [SV868: $i,SV687: $i,SV410: $i,SV87: $i] :
( ( ! [SY2386: $i,SY2387: $i] :
( ( SV87 = SV410 )
| ( c_ListOrder_Ostep1 @ SV687 @ SV87 @ SV410 @ SV868 )
| ~ ( c_ListOrder_Ostep1 @ SV687 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SY2386 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ ( c_List_Oappend @ SV410 @ ( c_List_Olist_OCons @ SY2387 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ SV868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2024,plain,
! [SV869: $i,SV688: $i,SV411: $i,SV88: $i] :
( ( ( hBOOL @ ( hAPP @ SV88 @ SV411 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV688 @ SV88 @ ( tc_fun @ SV869 @ tc_bool ) ) @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2025,plain,
! [SV870: $i,SV689: $i,SV412: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ SV89 @ SV412 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV689 @ ( tc_fun @ SV870 @ tc_bool ) ) @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2026,plain,
! [SV871: $i,SV690: $i,SV413: $i,SV90: $i] :
( ( ( c_List_Olist__all @ SV90 @ ( c_List_Oappend @ SV413 @ SV690 @ SV871 ) @ SV871 )
| ~ ( c_List_Olist__all @ SV90 @ SV690 @ SV871 )
| ~ ( c_List_Olist__all @ SV90 @ SV413 @ SV871 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2027,plain,
! [SV414: $i,SV91: $i] :
( ( ( class_Orderings_Olinorder @ SV91 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV414 @ ( c_List_Olist_ONil @ SV91 ) @ SV91 ) @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(2028,plain,
! [SV691: $i,SV415: $i,SV92: $i] :
( ( ( c_List_Odistinct @ ( c_List_Otake @ SV92 @ SV415 @ SV691 ) @ SV691 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV415 @ SV691 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(2029,plain,
! [SV872: $i,SV693: $i,SV417: $i,SV94: $i] :
( ( ! [SY2388: $i,SY2389: $i] :
( ( c_List_Ofoldl @ SV94 @ SV417 @ ( c_List_Oappend @ SV693 @ SV872 @ SY2388 ) @ SY2389 @ SY2388 )
= ( c_List_Ofoldl @ SV94 @ ( c_List_Ofoldl @ SV94 @ SV417 @ SV693 @ SY2389 @ SY2388 ) @ SV872 @ SY2389 @ SY2388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2030,plain,
! [SV694: $i,SV418: $i,SV95: $i] :
( ( ( c_List_Odistinct @ SV95 @ SV418 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ SV694 @ SV95 @ SV418 ) @ SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(2031,plain,
! [SV873: $i,SV695: $i,SV419: $i,SV96: $i] :
( ( ( c_List_Ofilter @ SV96 @ ( c_List_Oappend @ SV419 @ SV695 @ SV873 ) @ SV873 )
= ( c_List_Oappend @ ( c_List_Ofilter @ SV96 @ SV419 @ SV873 ) @ ( c_List_Ofilter @ SV96 @ SV695 @ SV873 ) @ SV873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2032,plain,
! [SV874: $i,SV696: $i,SV420: $i,SV97: $i] :
( ( ! [SY2390: $i] :
( ( c_List_Olist__all2 @ SV97 @ ( c_List_Orev @ SV420 @ SV696 ) @ SV874 @ SV696 @ SY2390 )
| ~ ( c_List_Olist__all2 @ SV97 @ SV420 @ ( c_List_Orev @ SV874 @ SY2390 ) @ SV696 @ SY2390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2033,plain,
! [SV875: $i,SV697: $i,SV421: $i,SV98: $i] :
( ( ! [SY2391: $i] :
( ( c_List_Olist__all2 @ SV98 @ SV421 @ ( c_List_Orev @ SV697 @ SV875 ) @ SY2391 @ SV875 )
| ~ ( c_List_Olist__all2 @ SV98 @ ( c_List_Orev @ SV421 @ SY2391 ) @ SV697 @ SY2391 @ SV875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2034,plain,
! [SV423: $i,SV101: $i] :
( ( ( c_List_Onull @ SV101 @ SV423 )
= $false )
| ( ( SV101
= ( c_List_Olist_ONil @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(2035,plain,
! [SV876: $i,SV699: $i,SV424: $i,SV104: $i] :
( ( ! [SY2392: $i,SY2393: $i] :
( ( SV104 = SV424 )
| ( SV699 = SV876 )
| ~ ( c_ListOrder_Ostep1 @ SY2392 @ ( c_List_Olist_OCons @ SV424 @ SV876 @ SY2393 ) @ ( c_List_Olist_OCons @ SV104 @ SV699 @ SY2393 ) @ SY2393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2036,plain,
! [SV877: $i,SV700: $i,SV425: $i,SV105: $i] :
( ( ! [SY2394: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV425 ) @ SV700 ) )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Olist_OCons @ SV425 @ SV877 @ SY2394 ) @ ( c_List_Olist_OCons @ SV700 @ SV877 @ SY2394 ) @ SY2394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2037,plain,
! [SV878: $i,SV701: $i,SV426: $i,SV106: $i] :
( ( ( c_List_Orev @ ( c_List_Omap @ SV106 @ SV426 @ SV701 @ SV878 ) @ SV878 )
= ( c_List_Omap @ SV106 @ ( c_List_Orev @ SV426 @ SV701 ) @ SV701 @ SV878 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2038,plain,
! [SV702: $i,SV427: $i,SV107: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV107 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV427 @ SV702 @ SV107 ) @ SV107 )
| ~ ( c_List_Olinorder__class_Osorted @ SV702 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(2039,plain,
! [SV879: $i,SV703: $i,SV428: $i,SV108: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV108 )
| ( c_List_Odistinct @ SV428 @ SV703 )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV879 @ SV428 @ SV703 @ SV108 ) @ SV703 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2040,plain,
! [SV880: $i,SV704: $i,SV429: $i,SV109: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV109 )
| ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV429 @ SV704 @ SV880 @ SV109 ) @ SV880 )
| ~ ( c_List_Odistinct @ SV704 @ SV880 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2041,plain,
! [SV881: $i,SV705: $i,SV430: $i,SV110: $i] :
( ( ! [SY2395: $i,SY2396: $i,SY2397: $i] :
( ( c_List_Olist__all2 @ SV110 @ SV430 @ SV705 @ SV881 @ SY2395 )
| ~ ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SY2396 @ SV430 @ SV881 ) @ ( c_List_Olist_OCons @ SY2397 @ SV705 @ SY2395 ) @ SV881 @ SY2395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2042,plain,
! [SV882: $i,SV706: $i,SV431: $i,SV111: $i] :
( ( ! [SY2398: $i] :
( ( c_List_Orotate @ SV111 @ ( c_List_Omap @ SV431 @ SV706 @ SV882 @ SY2398 ) @ SY2398 )
= ( c_List_Omap @ SV431 @ ( c_List_Orotate @ SV111 @ SV706 @ SV882 ) @ SV882 @ SY2398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2043,plain,
! [SV707: $i,SV432: $i,SV112: $i] :
( ( ( c_List_Odistinct @ SV112 @ SV432 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV112 @ SV707 @ SV432 ) @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(2044,plain,
! [SV708: $i,SV433: $i,SV113: $i] :
( ( ( c_List_Odistinct @ SV113 @ SV433 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Oappend @ SV708 @ SV113 @ SV433 ) @ SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(2045,plain,
! [SV709: $i,SV437: $i,SV117: $i] :
( ( ( c_List_Odistinct @ ( c_List_OdropWhile @ SV117 @ SV437 @ SV709 ) @ SV709 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV437 @ SV709 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(2046,plain,
! [SV883: $i,SV710: $i,SV438: $i,SV118: $i] :
( ( ! [SY2399: $i] :
( ( c_List_Olist__all2 @ SV118 @ SV438 @ SV710 @ SV883 @ SY2399 )
| ~ ( c_List_Olist__all2 @ SV118 @ ( c_List_Orev @ SV438 @ SV883 ) @ ( c_List_Orev @ SV710 @ SY2399 ) @ SV883 @ SY2399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2047,plain,
! [SV884: $i,SV711: $i,SV439: $i,SV119: $i] :
( ( ! [SY2400: $i] :
( ( c_List_Olist__all2 @ SV119 @ ( c_List_Orev @ SV439 @ SV711 ) @ ( c_List_Orev @ SV884 @ SY2400 ) @ SV711 @ SY2400 )
| ~ ( c_List_Olist__all2 @ SV119 @ SV439 @ SV884 @ SV711 @ SY2400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2048,plain,
! [SV885: $i,SV712: $i,SV440: $i,SV120: $i] :
( ( ! [SY2401: $i] :
( ( c_List_Oconcat__map @ SV120 @ ( c_List_Olist_OCons @ SV440 @ SV712 @ SV885 ) @ SV885 @ SY2401 )
= ( c_List_Oappend @ ( hAPP @ SV120 @ SV440 ) @ ( c_List_Oconcat__map @ SV120 @ SV712 @ SV885 @ SY2401 ) @ SY2401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2049,plain,
! [SV886: $i,SV713: $i,SV441: $i,SV121: $i] :
( ( ! [SY2402: $i,SY2403: $i] :
( ( c_List_Ofoldr @ SV121 @ ( c_List_Oappend @ SV441 @ SV713 @ SV886 ) @ SY2402 @ SV886 @ SY2403 )
= ( c_List_Ofoldr @ SV121 @ SV441 @ ( c_List_Ofoldr @ SV121 @ SV713 @ SY2402 @ SV886 @ SY2403 ) @ SV886 @ SY2403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2050,plain,
! [SV887: $i,SV714: $i,SV442: $i,SV122: $i] :
( ( ( c_List_Olist__ex @ SV122 @ ( c_List_Olist_OCons @ SV442 @ SV714 @ SV887 ) @ SV887 )
| ~ ( hBOOL @ ( hAPP @ SV122 @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2051,plain,
! [SV888: $i,SV715: $i,SV443: $i,SV123: $i] :
( ( ! [SY2404: $i,SY2405: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV443 ) @ SV715 ) )
| ( SV443 = SV715 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV888 @ ( c_List_Olist_OCons @ SV443 @ ( c_List_Olist_ONil @ SY2404 ) @ SY2404 ) @ SY2404 ) @ ( c_List_Oappend @ SY2405 @ ( c_List_Olist_OCons @ SV715 @ ( c_List_Olist_ONil @ SY2404 ) @ SY2404 ) @ SY2404 ) @ SY2404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2052,plain,
! [SV889: $i,SV716: $i,SV444: $i,SV124: $i] :
( ( ! [SY2406: $i,SY2407: $i,SY2408: $i] :
( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SV889 ) @ ( c_List_Olist_OCons @ SY2406 @ SY2407 @ SY2408 ) @ SV889 @ SY2408 )
| ~ ( c_List_Olist__all2 @ SV124 @ SV716 @ SY2407 @ SV889 @ SY2408 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SY2406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2053,plain,
! [SV890: $i,SV717: $i,SV445: $i,SV125: $i] :
( ( ! [SY2409: $i,SY2410: $i,SY2411: $i] :
( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SV890 ) @ ( c_List_Olist_OCons @ SY2409 @ SY2410 @ SY2411 ) @ SV890 @ SY2411 )
| ~ ( c_List_Olist__all2 @ SV125 @ SV717 @ SY2410 @ SV890 @ SY2411 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SY2409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2054,plain,
! [SV891: $i,SV718: $i,SV446: $i,SV126: $i] :
( ( ! [SY2412: $i,SY2413: $i,SY2414: $i] :
( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SV891 ) @ ( c_List_Olist_OCons @ SY2412 @ SY2413 @ SY2414 ) @ SV891 @ SY2414 )
| ~ ( c_List_Olist__all2 @ SV126 @ SV718 @ SY2413 @ SV891 @ SY2414 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SY2412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2055,plain,
! [SV892: $i,SV719: $i,SV447: $i,SV127: $i] :
( ( ( c_List_Olist__ex @ SV127 @ ( c_List_Olist_OCons @ SV447 @ SV719 @ SV892 ) @ SV892 )
| ~ ( c_List_Olist__ex @ SV127 @ SV719 @ SV892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2056,plain,
! [SV893: $i,SV720: $i,SV448: $i,SV128: $i] :
( ( ( c_List_Olist__ex @ SV128 @ SV448 @ SV720 )
| ( hBOOL @ ( hAPP @ SV128 @ SV893 ) )
| ~ ( c_List_Olist__ex @ SV128 @ ( c_List_Olist_OCons @ SV893 @ SV448 @ SV720 ) @ SV720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2057,plain,
! [SV894: $i,SV721: $i,SV449: $i,SV129: $i] :
( ( ! [SY2415: $i,SY2416: $i] :
( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SV721 @ SV894 ) @ ( c_List_Olist_OCons @ SY2415 @ SY2416 @ SV894 ) @ SV894 )
| ~ ( c_List_Olistrelp @ SV129 @ SV721 @ SY2416 @ SV894 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SY2415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2058,plain,
! [SV895: $i,SV722: $i,SV450: $i,SV130: $i] :
( ( ~ ( class_Lattices_Olattice @ SV130 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ SV722 @ SV130 ) @ SV895 @ SV130 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV722 @ SV895 @ SV130 ) @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2059,plain,
! [SV896: $i,SV723: $i,SV451: $i,SV131: $i] :
( ( ~ ( class_Lattices_Olattice @ SV131 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ SV896 @ SV131 ) @ SV131 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ SV896 @ SV131 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2060,plain,
! [SV897: $i,SV724: $i,SV452: $i,SV132: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV132 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV724 @ SV897 @ SV132 ) @ SV132 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV724 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ SV897 @ SV132 ) @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2061,plain,
! [SV898: $i,SV725: $i,SV453: $i,SV133: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV133 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ SV725 @ SV133 ) @ SV898 @ SV133 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV898 @ SV133 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2062,plain,
! [SV899: $i,SV726: $i,SV454: $i,SV134: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV134 @ SV454 @ ( tc_fun @ SV726 @ tc_bool ) ) @ SV899 @ ( tc_fun @ SV726 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV134 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV454 @ SV899 @ ( tc_fun @ SV726 @ tc_bool ) ) @ ( tc_fun @ SV726 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2063,plain,
! [SV900: $i,SV727: $i,SV455: $i,SV135: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV135 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV455 @ SV727 @ ( tc_fun @ SV900 @ tc_bool ) ) @ ( tc_fun @ SV900 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV455 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV135 @ SV727 @ ( tc_fun @ SV900 @ tc_bool ) ) @ ( tc_fun @ SV900 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2064,plain,
! [SV901: $i,SV728: $i,SV456: $i,SV136: $i] :
( ( ( ( c_List_Oremove1 @ SV136 @ ( c_List_Olist_OCons @ SV456 @ SV728 @ SV901 ) @ SV901 )
= ( c_List_Olist_OCons @ SV456 @ ( c_List_Oremove1 @ SV136 @ SV728 @ SV901 ) @ SV901 ) )
| ( SV136 = SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2065,plain,
! [SV902: $i,SV729: $i,SV457: $i,SV137: $i] :
( ( ! [SY2417: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV137 @ SV457 @ SV729 ) @ ( c_List_Olist_OCons @ SV902 @ SY2417 @ SV729 ) @ SV729 )
= ( c_List_Olist_OCons @ SV137 @ ( c_List_Olist_OCons @ SV902 @ ( c_List_Osplice @ SV457 @ SY2417 @ SV729 ) @ SV729 ) @ SV729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2066,plain,
! [SV730: $i,SV458: $i,SV138: $i] :
( ( ( c_List_Odistinct @ ( c_List_Osublist @ SV138 @ SV458 @ SV730 ) @ SV730 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV138 @ SV730 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(2067,plain,
! [SV903: $i,SV731: $i,SV459: $i,SV139: $i] :
( ( ( c_List_Omember @ SV139 @ ( c_List_Olist_OCons @ SV459 @ SV731 @ SV903 ) @ SV903 )
| ~ ( c_List_Omember @ SV139 @ SV731 @ SV903 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2068,plain,
! [SV732: $i,SV460: $i,SV140: $i] :
( ( ( ( c_List_Otl @ ( c_List_Oappend @ SV140 @ SV460 @ SV732 ) @ SV732 )
= ( c_List_Oappend @ ( c_List_Otl @ SV140 @ SV732 ) @ SV460 @ SV732 ) )
= $true )
| ( ( SV140
= ( c_List_Olist_ONil @ SV732 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(2069,plain,
! [SV733: $i,SV461: $i,SV141: $i] :
( ( ( c_List_Odistinct @ ( c_List_Oremove1 @ SV141 @ SV461 @ SV733 ) @ SV733 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV461 @ SV733 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(2070,plain,
! [SV904: $i,SV734: $i,SV462: $i,SV142: $i] :
( ( ( ( c_List_OdropWhile @ SV142 @ ( c_List_Olist_OCons @ SV462 @ SV734 @ SV904 ) @ SV904 )
= ( c_List_OdropWhile @ SV142 @ SV734 @ SV904 ) )
| ~ ( hBOOL @ ( hAPP @ SV142 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2071,plain,
! [SV905: $i,SV735: $i,SV463: $i,SV143: $i] :
( ( ( ( c_List_OdropWhile @ SV143 @ ( c_List_Olist_OCons @ SV463 @ SV735 @ SV905 ) @ SV905 )
= ( c_List_Olist_OCons @ SV463 @ SV735 @ SV905 ) )
| ( hBOOL @ ( hAPP @ SV143 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2072,plain,
! [SV906: $i,SV736: $i,SV464: $i,SV144: $i] :
( ( ! [SY2418: $i,SY2419: $i] :
( ( c_ListOrder_Ostep1 @ SV144 @ SV464 @ SV736 @ SV906 )
| ( SV736 = SV464 )
| ~ ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SY2418 @ SV464 @ SV906 ) @ ( c_List_Olist_OCons @ SY2419 @ SV736 @ SV906 ) @ SV906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2073,plain,
! [SV907: $i,SV739: $i,SV467: $i,SV147: $i] :
( ( ! [SY2420: $i] :
( ( c_List_Omap @ SV147 @ ( c_List_Oappend @ SV467 @ SV739 @ SV907 ) @ SV907 @ SY2420 )
= ( c_List_Oappend @ ( c_List_Omap @ SV147 @ SV467 @ SV907 @ SY2420 ) @ ( c_List_Omap @ SV147 @ SV739 @ SV907 @ SY2420 ) @ SY2420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2074,plain,
! [SV469: $i,SV149: $i] :
( ( ( SV149
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV469 @ SV149 @ t_a ) )
= $true )
| ( ( SV149
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SV469 @ SV149 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SV469 @ SV149 ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(2075,plain,
! [SV908: $i,SV741: $i,SV470: $i,SV150: $i] :
( ( ! [SY2421: $i,SY2422: $i] :
( ( c_List_Olist__all2 @ SV150 @ ( c_List_Odrop @ SV470 @ SV741 @ SV908 ) @ ( c_List_Odrop @ SV470 @ SY2421 @ SY2422 ) @ SV908 @ SY2422 )
| ~ ( c_List_Olist__all2 @ SV150 @ SV741 @ SY2421 @ SV908 @ SY2422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2076,plain,
! [SV909: $i,SV742: $i,SV471: $i,SV151: $i] :
( ( ( ( c_List_Oremove1 @ SV151 @ ( c_List_Ofilter @ SV471 @ SV742 @ SV909 ) @ SV909 )
= ( c_List_Ofilter @ SV471 @ SV742 @ SV909 ) )
| ( hBOOL @ ( hAPP @ SV471 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2077,plain,
! [SV910: $i,SV743: $i,SV472: $i,SV152: $i] :
( ( ! [SY2423: $i,SY2424: $i] :
( ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ ( c_List_Olist_OCons @ SV743 @ SV910 @ SY2423 ) @ SY2424 @ SY2423 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV472 @ SV743 ) @ SV910 ) @ ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ SV910 @ SY2424 @ SY2423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2078,plain,
! [SV911: $i,SV744: $i,SV473: $i,SV153: $i] :
( ( ( c_List_Odistinct @ SV153 @ SV473 )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ SV744 @ SV153 @ SV473 @ SV911 ) @ SV911 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2079,plain,
! [SV912: $i,SV745: $i,SV474: $i,SV154: $i] :
( ( ! [SY2425: $i,SY2426: $i] :
( ( SV154 = SV474 )
| ( SV745 = SV912 )
| ~ ( c_ListOrder_Ostep1 @ SY2425 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SV745 @ ( c_List_Olist_ONil @ SY2426 ) @ SY2426 ) @ SY2426 ) @ ( c_List_Oappend @ SV474 @ ( c_List_Olist_OCons @ SV912 @ ( c_List_Olist_ONil @ SY2426 ) @ SY2426 ) @ SY2426 ) @ SY2426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2080,plain,
! [SV746: $i,SV475: $i,SV155: $i] :
( ( ( c_List_Odistinct @ SV155 @ SV475 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Orotate @ SV746 @ SV155 @ SV475 ) @ SV475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(2081,plain,
! [SV747: $i,SV476: $i,SV156: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate @ SV156 @ SV476 @ SV747 ) @ SV747 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV476 @ SV747 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(2082,plain,
! [SV748: $i,SV477: $i,SV157: $i] :
( ( c_List_Onull @ ( c_List_Olist_OCons @ SV157 @ SV477 @ SV748 ) @ SV748 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(2083,plain,
! [SV749: $i,SV478: $i,SV158: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV158 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ SV749 @ SV158 ) @ SV158 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ SV749 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2084,plain,
! [SV750: $i,SV479: $i,SV159: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV159 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV750 @ SV159 ) @ SV159 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV750 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2085,plain,
! [SV913: $i,SV752: $i,SV481: $i,SV161: $i] :
( ( ! [SY2427: $i,SY2428: $i] :
( ( c_List_Ofoldr @ SV161 @ ( c_List_Olist_OCons @ SV481 @ SV752 @ SV913 ) @ SY2427 @ SV913 @ SY2428 )
= ( hAPP @ ( hAPP @ SV161 @ SV481 ) @ ( c_List_Ofoldr @ SV161 @ SV752 @ SY2427 @ SV913 @ SY2428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2086,plain,
! [SV484: $i,SV164: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV164 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV484 @ SV484 @ SV164 )
= SV484 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(2087,plain,
! [SV914: $i,SV754: $i,SV486: $i,SV166: $i] :
( ( ! [SY2429: $i,SY2430: $i] :
( ( c_ListOrder_Ostep1 @ SV166 @ SV486 @ SV754 @ SV914 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SY2429 ) @ SY2430 ) )
| ~ ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SY2429 @ SV486 @ SV914 ) @ ( c_List_Olist_OCons @ SY2430 @ SV754 @ SV914 ) @ SV914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2088,plain,
! [SV915: $i,SV755: $i,SV487: $i,SV167: $i] :
( ( ! [SY2431: $i] :
( ( c_ListOrder_Ostep1 @ SV167 @ ( c_List_Olist_OCons @ SV487 @ SV755 @ SV915 ) @ ( c_List_Olist_OCons @ SV487 @ SY2431 @ SV915 ) @ SV915 )
| ~ ( c_ListOrder_Ostep1 @ SV167 @ SV755 @ SY2431 @ SV915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2089,plain,
! [SV756: $i,SV488: $i,SV168: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV168 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ SV488 @ SV168 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV488 @ SV756 @ SV168 ) @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2090,plain,
! [SV757: $i,SV489: $i,SV169: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV169 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ SV489 @ SV169 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV757 @ SV489 @ SV169 ) @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2091,plain,
! [SV916: $i,SV758: $i,SV490: $i,SV170: $i] :
( ( ( c_List_Olist__all @ SV170 @ ( c_List_Olist_OCons @ SV490 @ SV758 @ SV916 ) @ SV916 )
| ~ ( c_List_Olist__all @ SV170 @ SV758 @ SV916 )
| ~ ( hBOOL @ ( hAPP @ SV170 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2092,plain,
! [SV917: $i,SV759: $i,SV491: $i,SV171: $i] :
( ( ! [SY2432: $i,SY2433: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV491 @ SV759 @ SV917 ) @ SY2432 @ SY2433 @ SV917 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SY2432 @ SY2433 @ SV917 ) @ SV491 @ SV759 @ SV917 ) )
| ( SV491 = SY2432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2093,plain,
! [SV492: $i,SV172: $i] :
( ( ( class_Orderings_Olinorder @ SV172 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SV492 @ SV172 ) @ SV172 )
| ~ ( c_List_Olinorder__class_Osorted @ SV492 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(2094,plain,
! [SV760: $i,SV493: $i,SV173: $i] :
( ( ( c_List_Olist__all @ SV173 @ SV493 @ SV760 )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV173 @ ( c_List_Orev @ SV493 @ SV760 ) @ SV760 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2095,plain,
! [SV761: $i,SV494: $i,SV174: $i] :
( ( ( c_List_Olist__all @ SV174 @ ( c_List_Orev @ SV494 @ SV761 ) @ SV761 )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV174 @ SV494 @ SV761 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2096,plain,
! [SV918: $i,SV762: $i,SV495: $i,SV175: $i] :
( ( ! [SY2434: $i] :
( ( c_List_Odrop @ SV175 @ ( c_List_Omap @ SV495 @ SV762 @ SV918 @ SY2434 ) @ SY2434 )
= ( c_List_Omap @ SV495 @ ( c_List_Odrop @ SV175 @ SV762 @ SV918 ) @ SV918 @ SY2434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2097,plain,
! [SV919: $i,SV763: $i,SV496: $i,SV176: $i] :
( ( ( c_List_Omember @ SV176 @ SV496 @ SV763 )
| ( SV176 = SV919 )
| ~ ( c_List_Omember @ SV176 @ ( c_List_Olist_OCons @ SV919 @ SV496 @ SV763 ) @ SV763 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2098,plain,
! [SV920: $i,SV764: $i,SV497: $i,SV177: $i] :
( ( ( ( c_List_Ofilter @ SV177 @ ( c_List_Olist_OCons @ SV497 @ SV764 @ SV920 ) @ SV920 )
= ( c_List_Ofilter @ SV177 @ SV764 @ SV920 ) )
| ( hBOOL @ ( hAPP @ SV177 @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2099,plain,
! [SV921: $i,SV765: $i,SV498: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV178 @ SV498 @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV921 ) )
| ~ ( hBOOL @ ( hAPP @ SV498 @ SV921 ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ SV921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2100,plain,
! [SV922: $i,SV767: $i,SV501: $i,SV181: $i] :
( ( ( c_List_Olist__all @ SV181 @ SV501 @ SV767 )
| ~ ( c_List_Olist__all @ SV181 @ ( c_List_Oappend @ SV501 @ SV922 @ SV767 ) @ SV767 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2101,plain,
! [SV923: $i,SV768: $i,SV502: $i,SV182: $i] :
( ( ( c_List_Olist__all @ SV182 @ SV502 @ SV768 )
| ~ ( c_List_Olist__all @ SV182 @ ( c_List_Oappend @ SV923 @ SV502 @ SV768 ) @ SV768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2102,plain,
! [SV924: $i,SV770: $i,SV504: $i,SV184: $i] :
( ( ! [SY2435: $i] :
( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_Olist__case @ SV504 @ SV770 @ ( c_List_Olist_OCons @ SV924 @ SY2435 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV184 @ ( hAPP @ ( hAPP @ SV770 @ SV924 ) @ SY2435 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2103,plain,
! [SV925: $i,SV771: $i,SV505: $i,SV185: $i] :
( ( ! [SY2436: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_List_Olist_Olist__case @ SV505 @ SV771 @ ( c_List_Olist_OCons @ SV925 @ SY2436 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV185 @ ( hAPP @ ( hAPP @ SV771 @ SV925 ) @ SY2436 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2104,plain,
! [SV772: $i,SV506: $i,SV186: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV186 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ SV506 @ SV772 @ SV186 ) @ SV186 )
| ~ ( c_List_Olinorder__class_Osorted @ SV772 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(2105,plain,
! [SV926: $i,SV773: $i,SV507: $i,SV187: $i] :
( ( ! [SY2437: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV187 @ SV507 @ SV773 @ SV926 ) @ SV507 @ SY2437 @ SV926 )
= ( c_List_Olist__update @ SV187 @ SV507 @ SY2437 @ SV926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2106,plain,
! [SV927: $i,SV774: $i,SV508: $i,SV188: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV188 @ SV508 @ SV774 ) @ SV927 @ SV774 )
= ( c_List_Oappend @ SV188 @ ( c_List_Oappend @ SV508 @ SV927 @ SV774 ) @ SV774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2107,plain,
! [SV928: $i,SV775: $i,SV509: $i,SV189: $i] :
( ( ( c_List_Oappend @ SV189 @ ( c_List_Oappend @ SV509 @ SV775 @ SV928 ) @ SV928 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV189 @ SV509 @ SV928 ) @ SV775 @ SV928 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2108,plain,
! [SV929: $i,SV776: $i,SV510: $i,SV190: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV190 @ SV510 @ SV776 ) @ SV929 @ SV776 )
= ( c_List_Oappend @ SV190 @ ( c_List_Oappend @ SV510 @ SV929 @ SV776 ) @ SV776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2109,plain,
! [SV930: $i,SV777: $i,SV511: $i,SV191: $i] :
( ( ( c_List_Oappend @ SV191 @ ( c_List_Oappend @ SV511 @ SV777 @ SV930 ) @ SV930 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV191 @ SV511 @ SV930 ) @ SV777 @ SV930 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2110,plain,
! [SV778: $i,SV512: $i,SV192: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV192 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV512 @ SV778 @ SV192 ) @ SV192 )
| ~ ( c_List_Olinorder__class_Osorted @ SV778 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2111,plain,
! [SV515: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ SV196 @ ( v_sko__List__Xrev__Xinduct__2 @ SV196 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV196 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV196 @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(2112,plain,
! [SV516: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ SV197 @ ( v_sko__List__Xsplice__Xinduct__2 @ SV197 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV197 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV197 @ SV516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2113,plain,
! [SV517: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ SV198 @ ( v_sko__List__Xset__Xinduct__2 @ SV198 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV198 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV198 @ SV517 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(2114,plain,
! [SV518: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ SV199 @ ( v_sko__List__Xtl__Xinduct__2 @ SV199 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV199 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV199 @ SV518 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2115,plain,
! [SV931: $i,SV779: $i,SV519: $i,SV200: $i] :
( ( ( SV200
= ( c_List_Olist_ONil @ SV519 ) )
| ~ ( c_List_Olist__all2 @ SV779 @ SV200 @ ( c_List_Olist_ONil @ SV931 ) @ SV519 @ SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2116,plain,
! [SV932: $i,SV780: $i,SV520: $i,SV201: $i] :
( ( ( SV201
= ( c_List_Olist_ONil @ SV520 ) )
| ~ ( c_List_Olist__all2 @ SV780 @ ( c_List_Olist_ONil @ SV932 ) @ SV201 @ SV932 @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2117,plain,
! [SV521: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ SV202 @ ( v_sko__List__Xlist__Xinducts__2 @ SV202 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV202 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV202 @ SV521 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(2118,plain,
! [SV522: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ SV203 @ ( v_sko__List__Xhd__Xinduct__2 @ SV203 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV203 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV203 @ SV522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(2119,plain,
! [SV524: $i,SV206: $i] :
( ( ( hBOOL @ ( hAPP @ SV206 @ ( v_sko__List__Xremdups__Xinduct__2 @ SV206 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV206 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV206 @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2120,plain,
! [SV782: $i,SV526: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ SV208 @ SV526 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV208 @ SV782 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Olist_ONil @ SV782 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(2121,plain,
! [SV783: $i,SV527: $i,SV209: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV209 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osort__key @ SV527 @ ( c_List_Olist_ONil @ SV783 ) @ SV783 @ SV209 )
= ( c_List_Olist_ONil @ SV783 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(2122,plain,
! [SV528: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ SV210 @ ( v_sko__List__Xdrop__Xinduct__2 @ SV210 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV210 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV210 @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(2123,plain,
! [SV933: $i,SV784: $i,SV529: $i,SV211: $i] :
( ( ( c_List_Ofoldl @ SV211 @ SV529 @ ( c_List_Olist_ONil @ SV784 ) @ SV933 @ SV784 )
= SV529 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2124,plain,
! [SV530: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP @ SV212 @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV212 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV212 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV212 @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2125,plain,
! [SV785: $i,SV531: $i,SV213: $i] :
( ( c_ListOrder_Ostep1 @ SV213 @ SV531 @ ( c_List_Olist_ONil @ SV785 ) @ SV785 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(2126,plain,
! [SV786: $i,SV532: $i,SV214: $i] :
( ( c_ListOrder_Ostep1 @ SV214 @ ( c_List_Olist_ONil @ SV532 ) @ SV786 @ SV532 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(2127,plain,
! [SV534: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV217 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV217 @ SV534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(2128,plain,
! [SV542: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ SV225 @ ( v_sko__List__Xlast__Xinduct__2 @ SV225 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV225 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV225 @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2129,plain,
! [SV544: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ SV227 @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV227 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV227 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV227 @ SV544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2130,plain,
! [SV545: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP @ SV228 @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV228 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV228 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV228 @ SV545 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2131,plain,
! [SV546: $i,SV229: $i] :
( ( ( hBOOL @ ( hAPP @ SV229 @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV229 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV229 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV229 @ SV546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2132,plain,
! [SV787: $i,SV549: $i,SV234: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV234 @ ( c_List_Olist_Olist__case @ SV549 @ SV787 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV234 @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2133,plain,
! [SV934: $i,SV788: $i,SV550: $i,SV235: $i] :
( ( ( c_List_Ofoldr @ SV235 @ ( c_List_Olist_ONil @ SV550 ) @ SV788 @ SV550 @ SV934 )
= SV788 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2134,plain,
! [SV551: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ SV236 @ ( v_sko__List__Xzip__Xinduct__2 @ SV236 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV236 @ SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(2135,plain,
! [SV554: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ SV239 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV239 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV239 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV239 @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2136,plain,
! [SV935: $i,SV790: $i,SV555: $i,SV240: $i] :
( ( ( c_List_Olist_Olist__rec @ SV240 @ SV555 @ ( c_List_Olist_ONil @ SV790 ) @ SV935 @ SV790 )
= SV240 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2137,plain,
! [SV556: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV241 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV241 @ SV556 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2138,plain,
! [SV557: $i,SV242: $i] :
( ( ( hBOOL @ ( hAPP @ SV242 @ ( v_sko__List__Xtake__Xinduct__2 @ SV242 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV242 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV242 @ SV557 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2139,plain,
! [SV563: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP @ SV249 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV249 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV249 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV249 @ SV563 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2140,plain,
! [SV565: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ SV251 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV251 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV251 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV251 @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2141,plain,
! [SV936: $i,SV795: $i,SV566: $i,SV252: $i] :
( ( ( c_Map_Omap__upds @ SV252 @ SV566 @ ( c_List_Olist_ONil @ SV795 ) @ SV936 @ SV795 )
= SV252 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2142,plain,
! [SV937: $i,SV796: $i,SV567: $i,SV253: $i] :
( ( ( c_Map_Omap__upds @ SV253 @ ( c_List_Olist_ONil @ SV567 ) @ SV796 @ SV567 @ SV937 )
= SV253 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2143,plain,
! [SV568: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ SV254 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV254 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV254 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV254 @ SV568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2144,plain,
! [SV938: $i,SV797: $i,SV569: $i,SV255: $i] :
( ( ( c_List_Olist_Olist__case @ SV255 @ SV569 @ ( c_List_Olist_ONil @ SV797 ) @ SV938 @ SV797 )
= SV255 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2145,plain,
! [SV571: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ SV257 @ ( v_sko__List__Xlist__Xinduct__2 @ SV257 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV257 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV257 @ SV571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2146,plain,
! [SV574: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ ( v_sko__List__Xmap__Xinduct__2 @ SV261 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV261 @ SV574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2147,plain,
! [SV939: $i,SV799: $i,SV575: $i,SV263: $i] :
( ( ( c_List_Olistsp @ SV263 @ ( c_List_Oappend @ SV575 @ SV799 @ SV939 ) @ SV939 )
| ~ ( c_List_Olistsp @ SV263 @ SV799 @ SV939 )
| ~ ( c_List_Olistsp @ SV263 @ SV575 @ SV939 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2148,plain,
! [SV800: $i,SV576: $i,SV264: $i] :
( ( ( c_List_Olistsp @ SV264 @ SV576 @ SV800 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV264 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV264 @ SV576 @ SV800 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2149,plain,
! [SV940: $i,SV801: $i,SV577: $i,SV265: $i] :
( ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV265 @ SV577 @ ( tc_fun @ SV801 @ tc_bool ) ) @ SV940 @ SV801 )
| ~ ( c_List_Olistsp @ SV577 @ SV940 @ SV801 )
| ~ ( c_List_Olistsp @ SV265 @ SV940 @ SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2150,plain,
! [SV941: $i,SV802: $i,SV578: $i,SV266: $i] :
( ( ( c_List_Olistsp @ SV266 @ SV578 @ SV802 )
| ~ ( c_List_Olistsp @ SV266 @ ( c_List_Oappend @ SV941 @ SV578 @ SV802 ) @ SV802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2151,plain,
! [SV942: $i,SV803: $i,SV579: $i,SV267: $i] :
( ( ( c_List_Olistsp @ SV267 @ SV579 @ SV803 )
| ~ ( c_List_Olistsp @ SV267 @ ( c_List_Oappend @ SV579 @ SV942 @ SV803 ) @ SV803 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2152,plain,
! [SV580: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV268 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV268 @ SV580 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2153,plain,
! [SV804: $i,SV581: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ SV270 @ SV581 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV804 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV804 @ SV270 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV270 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV804 @ SV581 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2154,plain,
! [SV805: $i,SV582: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ SV271 @ SV582 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV271 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV805 @ SV271 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV271 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV805 @ SV582 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2155,plain,
! [SV806: $i,SV583: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ SV272 @ SV583 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV806 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV806 @ SV272 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV806 @ SV583 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2156,plain,
! [SV807: $i,SV584: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ SV273 @ SV584 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV273 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV807 @ SV273 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV273 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV807 @ SV584 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1908]) ).
thf(2157,plain,
! [SV274: $i,SV585: $i] :
( ( ( SV585
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV274 @ SV585 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV274 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV274 @ SV585 ) @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(2158,plain,
! [SV275: $i,SV586: $i] :
( ( ( SV586
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV275 @ SV586 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV275 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV275 @ SV586 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2159,plain,
! [SV808: $i,SV587: $i,SV276: $i] :
( ( ( hBOOL @ ( hAPP @ SV276 @ SV587 ) )
= $true )
| ( ( ( c_List_Olistsp @ SV808 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV808 @ SV276 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV276 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV808 @ SV587 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2160,plain,
! [SV809: $i,SV588: $i,SV277: $i] :
( ( ( hBOOL @ ( hAPP @ SV277 @ SV588 ) )
= $true )
| ( ( ( c_List_Olistsp @ SV809 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV809 @ SV277 ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ SV277 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV809 @ SV588 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(2161,plain,
! [SV279: $i,SV590: $i] :
( ( ( class_Lattices_Olattice @ SV590 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV279 @ SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(2162,plain,
! [SV280: $i,SV591: $i] :
( ( ( class_Lattices_Olattice @ SV591 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV280 @ SV591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2163,plain,
! [SV810: $i,SV593: $i,SV282: $i] :
( ( ( SV282 = SV593 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV810 ) @ SV282 ) @ SV593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2164,plain,
! [SV943: $i,SV811: $i,SV594: $i,SV283: $i] :
( ( ( ( c_List_Orev @ SV283 @ SV594 )
!= ( c_List_Olist_OCons @ SV811 @ SV943 @ SV594 ) )
| ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SV943 @ SV594 ) @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2165,plain,
! [SV812: $i,SV595: $i,SV284: $i] :
( ( ( ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 )
!= ( c_List_Orev @ SV812 @ SV595 ) )
= $true )
| ( ( SV812
= ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2166,plain,
! [SV813: $i,SV596: $i,SV286: $i] :
( ( ( ( c_List_Oappend @ SV286 @ SV596 @ SV813 )
!= ( c_List_Olist_ONil @ SV813 ) )
= $true )
| ( ( SV596
= ( c_List_Olist_ONil @ SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2167,plain,
! [SV944: $i,SV814: $i,SV597: $i,SV287: $i] :
( ( ! [SY2438: $i] :
( ( ( c_List_Oappend @ SV287 @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 )
!= ( c_List_Oappend @ SV944 @ ( c_List_Olist_OCons @ SY2438 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 ) )
| ( SV597 = SY2438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2168,plain,
! [SV815: $i,SV598: $i,SV288: $i] :
( ( ( c_List_Olist_OCons @ SV288 @ SV598 @ SV815 )
= ( c_List_Olist_ONil @ SV815 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2169,plain,
! [SV945: $i,SV816: $i,SV599: $i,SV289: $i] :
( ( ! [SY2439: $i] :
( ( ( c_List_Oappend @ SV289 @ ( c_List_Olist_OCons @ SV599 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 )
!= ( c_List_Oappend @ SV945 @ ( c_List_Olist_OCons @ SY2439 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 ) )
| ( SV289 = SV945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2170,plain,
! [SV817: $i,SV600: $i,SV290: $i] :
( ( ( ( c_List_Orotate @ SV290 @ SV600 @ SV817 )
!= ( c_List_Olist_ONil @ SV817 ) )
= $true )
| ( ( SV600
= ( c_List_Olist_ONil @ SV817 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2171,plain,
! [SV818: $i,SV601: $i,SV291: $i] :
( ( ( c_List_Olist_ONil @ SV291 )
= ( c_List_Olist_OCons @ SV601 @ SV818 @ SV291 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2172,plain,
! [SV819: $i,SV602: $i,SV292: $i] :
( ( ( ( c_List_Oappend @ SV292 @ SV602 @ SV819 )
!= ( c_List_Olist_ONil @ SV819 ) )
= $true )
| ( ( SV292
= ( c_List_Olist_ONil @ SV819 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2173,plain,
! [SV603: $i,SV293: $i] :
( ( ( ( c_List_Oremdups @ SV293 @ SV603 )
= ( c_List_Olist_ONil @ SV603 ) )
= $false )
| ( ( SV293
= ( c_List_Olist_ONil @ SV603 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2174,plain,
! [SV820: $i,SV604: $i,SV294: $i] :
( ( ( ( c_List_Oappend @ SV294 @ SV604 @ SV820 )
!= SV604 )
= $true )
| ( ( SV294
= ( c_List_Olist_ONil @ SV820 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2175,plain,
! [SV605: $i,SV296: $i] :
( ( ( ( c_Suc @ SV296 )
= ( c_Suc @ SV605 ) )
= $false )
| ( ( SV296 = SV605 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(2176,plain,
! [SV946: $i,SV821: $i,SV606: $i,SV297: $i] :
( ( ! [SY2440: $i] :
( ( ( c_List_Olist_OCons @ SV297 @ SV606 @ SV821 )
!= ( c_List_Ofilter @ SV946 @ SY2440 @ SV821 ) )
| ( hBOOL @ ( hAPP @ SV946 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2177,plain,
! [SV947: $i,SV822: $i,SV607: $i,SV298: $i] :
( ( ! [SY2441: $i] :
( ( ( c_List_Olist_OCons @ SV298 @ SV607 @ SV822 )
!= ( c_List_Olist_OCons @ SV947 @ SY2441 @ SV822 ) )
| ( SV607 = SY2441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2178,plain,
! [SV823: $i,SV608: $i,SV299: $i] :
( ( ( ( c_List_Olist_ONil @ SV299 )
!= ( c_List_Oappend @ SV608 @ SV823 @ SV299 ) )
= $true )
| ( ( SV823
= ( c_List_Olist_ONil @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2179,plain,
! [SV824: $i,SV609: $i,SV300: $i] :
( ( ( c_List_Olist_OCons @ SV300 @ SV609 @ SV824 )
= SV609 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2180,plain,
! [SV610: $i,SV301: $i] :
( ( ( ( c_List_Olist_ONil @ SV301 )
= ( c_List_Oremdups @ SV610 @ SV301 ) )
= $false )
| ( ( SV610
= ( c_List_Olist_ONil @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2181,plain,
! [SV948: $i,SV825: $i,SV611: $i,SV302: $i] :
( ( ( ( c_List_Oappend @ SV302 @ SV611 @ SV825 )
!= ( c_List_Oappend @ SV948 @ SV611 @ SV825 ) )
| ( SV302 = SV948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2182,plain,
! [SV826: $i,SV612: $i,SV303: $i] :
( ( ( SV303
!= ( c_List_Oappend @ SV612 @ SV303 @ SV826 ) )
= $true )
| ( ( SV612
= ( c_List_Olist_ONil @ SV826 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2183,plain,
! [SV613: $i,SV304: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV304 )
= ( c_Lambda_OdB_OAbs @ SV613 ) )
= $false )
| ( ( SV304 = SV613 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2184,plain,
! [SV949: $i,SV827: $i,SV614: $i,SV305: $i] :
( ( ( ( c_List_Omap @ SV305 @ SV614 @ SV827 @ SV949 )
!= ( c_List_Olist_ONil @ SV949 ) )
| ( SV614
= ( c_List_Olist_ONil @ SV827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2185,plain,
! [SV950: $i,SV828: $i,SV615: $i,SV306: $i] :
( ( ! [SY2442: $i] :
( ( ( c_List_Olist_OCons @ SV306 @ SV615 @ SV828 )
!= ( c_List_Olist_OCons @ SV950 @ SY2442 @ SV828 ) )
| ( SV306 = SV950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2186,plain,
! [SV616: $i,SV307: $i] :
( ( ( ( c_List_Olist_ONil @ SV307 )
= ( c_List_Orev @ SV616 @ SV307 ) )
= $false )
| ( ( SV616
= ( c_List_Olist_ONil @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2187,plain,
! [SV829: $i,SV617: $i,SV308: $i] :
( ( ( ( c_List_Orev @ SV308 @ SV617 )
!= ( c_List_Orev @ SV829 @ SV617 ) )
= $true )
| ( ( SV308 = SV829 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2188,plain,
! [SV951: $i,SV830: $i,SV618: $i,SV309: $i] :
( ( ( ( c_List_Olist__update @ SV309 @ SV618 @ SV830 @ SV951 )
!= ( c_List_Olist_ONil @ SV951 ) )
| ( SV309
= ( c_List_Olist_ONil @ SV951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2189,plain,
! [SV952: $i,SV831: $i,SV619: $i,SV310: $i] :
( ( ( ( c_List_Olist_ONil @ SV310 )
!= ( c_List_Omap @ SV619 @ SV831 @ SV952 @ SV310 ) )
| ( SV831
= ( c_List_Olist_ONil @ SV952 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2190,plain,
! [SV620: $i,SV311: $i] :
( ( ( ( c_List_Oremdups @ SV311 @ SV620 )
= SV311 )
= $false )
| ( ( c_List_Odistinct @ SV311 @ SV620 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2191,plain,
! [SV832: $i,SV621: $i,SV312: $i] :
( ( ( ( c_List_Orev @ SV312 @ SV621 )
!= ( c_List_Olist_OCons @ SV832 @ ( c_List_Olist_ONil @ SV621 ) @ SV621 ) )
= $true )
| ( ( SV312
= ( c_List_Olist_OCons @ SV832 @ ( c_List_Olist_ONil @ SV621 ) @ SV621 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(2192,plain,
! [SV833: $i,SV622: $i,SV313: $i] :
( ( ( ( c_List_Olist_ONil @ SV313 )
!= ( c_List_Oappend @ SV622 @ SV833 @ SV313 ) )
= $true )
| ( ( SV622
= ( c_List_Olist_ONil @ SV313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(2193,plain,
! [SV623: $i,SV314: $i] :
( ( ( ( c_List_Orev @ SV314 @ SV623 )
= ( c_List_Olist_ONil @ SV623 ) )
= $false )
| ( ( SV314
= ( c_List_Olist_ONil @ SV623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(2194,plain,
! [SV834: $i,SV624: $i,SV315: $i] :
( ( ( c_List_Olist_OCons @ SV315 @ SV624 @ SV834 )
= ( c_List_Olist_ONil @ SV834 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2195,plain,
! [SV953: $i,SV835: $i,SV625: $i,SV316: $i] :
( ( ! [SY2443: $i] :
( ( ( c_List_OdropWhile @ SV316 @ SV625 @ SV835 )
!= ( c_List_Olist_OCons @ SV953 @ SY2443 @ SV835 ) )
| ~ ( hBOOL @ ( hAPP @ SV316 @ SV953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2196,plain,
! [SV626: $i,SV317: $i] :
( ( ( ( c_Suc @ SV317 )
= ( c_Suc @ SV626 ) )
= $false )
| ( ( SV317 = SV626 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2197,plain,
! [SV836: $i,SV627: $i,SV318: $i] :
( ( SV318
= ( c_List_Olist_OCons @ SV627 @ SV318 @ SV836 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2198,plain,
! [SV954: $i,SV837: $i,SV628: $i,SV319: $i] :
( ( ( ( c_List_Oappend @ SV319 @ SV628 @ SV837 )
!= ( c_List_Oappend @ SV319 @ SV954 @ SV837 ) )
| ( SV628 = SV954 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2199,plain,
! [SV629: $i,SV320: $i] :
( ( ( ( c_List_Orotate1 @ SV320 @ SV629 )
= ( c_List_Olist_ONil @ SV629 ) )
= $false )
| ( ( SV320
= ( c_List_Olist_ONil @ SV629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2200,plain,
! [SV838: $i,SV630: $i,SV321: $i] :
( ( ( ( c_List_Oappend @ SV321 @ SV630 @ SV838 )
!= SV321 )
= $true )
| ( ( SV630
= ( c_List_Olist_ONil @ SV838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1952]) ).
thf(2201,plain,
! [SV955: $i,SV839: $i,SV631: $i,SV322: $i] :
( ( ! [SY2444: $i] :
( ( ( c_List_Ofilter @ SV322 @ SV631 @ SV839 )
!= ( c_List_Olist_OCons @ SV955 @ SY2444 @ SV839 ) )
| ( hBOOL @ ( hAPP @ SV322 @ SV955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2202,plain,
! [SV840: $i,SV632: $i,SV323: $i] :
( ( ( SV323
!= ( c_List_Oappend @ SV323 @ SV632 @ SV840 ) )
= $true )
| ( ( SV632
= ( c_List_Olist_ONil @ SV840 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2203,plain,
! [SV956: $i,SV841: $i,SV635: $i,SV326: $i,SV3: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV3 @ SV326 @ SV635 ) @ ( c_Suc @ SV841 ) @ SV956 @ SV635 )
= ( c_List_Olist_OCons @ SV3 @ ( c_List_Olist__update @ SV326 @ SV841 @ SV956 @ SV635 ) @ SV635 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2204,plain,
! [SV330: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ SV7 ) @ ( v_sko__List__Xdrop__Xinduct__2 @ SV7 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV7 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2205,plain,
! [SV331: $i,SV8: $i] :
( ( ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ SV8 ) @ ( v_sko__List__Xrev__Xinduct__2 @ SV8 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV8 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2206,plain,
! [SV332: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ SV9 ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV9 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV9 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2207,plain,
! [SV333: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV10 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV10 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2208,plain,
! [SV642: $i,SV338: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ SV15 @ ( c_List_Ohd @ ( c_List_OdropWhile @ SV15 @ SV338 @ SV642 ) @ SV642 ) ) )
= $false )
| ( ( ( c_List_OdropWhile @ SV15 @ SV338 @ SV642 )
= ( c_List_Olist_ONil @ SV642 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2209,plain,
! [SV339: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ SV16 ) @ ( v_sko__List__Xhd__Xinduct__2 @ SV16 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV16 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2210,plain,
! [SV340: $i,SV17: $i] :
( ( ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV17 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV17 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV17 @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2211,plain,
! [SV341: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ SV18 ) @ ( v_sko__List__Xset__Xinduct__2 @ SV18 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV18 @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2212,plain,
! [SV342: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV19 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV19 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV19 @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2213,plain,
! [SV343: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinducts__1 @ SV20 ) @ ( v_sko__List__Xlist__Xinducts__2 @ SV20 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV20 @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2214,plain,
! [SV344: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV21 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV21 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV21 @ SV344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2215,plain,
! [SV345: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ SV22 ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV22 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV22 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1971]) ).
thf(2216,plain,
! [SV346: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ SV23 ) @ ( v_sko__List__Xremdups__Xinduct__2 @ SV23 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV23 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2217,plain,
! [SV347: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ SV24 ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV24 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV24 @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2218,plain,
! [SV348: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ SV25 ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV25 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2219,plain,
! [SV349: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV26 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV26 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV26 @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2220,plain,
! [SV350: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV27 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV27 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV27 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2221,plain,
! [SV351: $i,SV28: $i] :
( ( ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV28 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV28 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV28 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2222,plain,
! [SV352: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV29 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV29 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2223,plain,
! [SV353: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ SV30 ) @ ( v_sko__List__Xsplice__Xinduct__2 @ SV30 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV30 @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2224,plain,
! [SV354: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV31 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV31 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV31 @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2225,plain,
! [SV355: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ SV32 ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV32 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV32 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2226,plain,
! [SV356: $i,SV33: $i] :
( ( ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ SV33 ) @ ( v_sko__List__Xlast__Xinduct__2 @ SV33 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV33 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2227,plain,
! [SV357: $i,SV34: $i] :
( ( ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ SV34 ) @ ( v_sko__List__Xtl__Xinduct__2 @ SV34 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV34 @ SV357 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2228,plain,
! [SV844: $i,SV643: $i,SV358: $i,SV35: $i] :
( ( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV35 @ SV358 @ SV643 ) @ SV844 @ SV643 )
= ( c_List_Olist_OCons @ SV35 @ ( c_List_Olist_OCons @ ( c_List_Ohd @ SV844 @ SV643 ) @ ( c_List_Osplice @ SV358 @ ( c_List_Otl @ SV844 @ SV643 ) @ SV643 ) @ SV643 ) @ SV643 ) )
= $true )
| ( ( SV844
= ( c_List_Olist_ONil @ SV643 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2229,plain,
! [SV359: $i,SV644: $i,SV36: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV36 @ SV644 ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ SV36 @ SV644 ) @ ( c_List_Olist_ONil @ SV644 ) @ SV644 ) @ SV644 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Olist_ONil @ SV644 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV36 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2230,plain,
! [SV845: $i,SV645: $i,SV361: $i,SV38: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV38 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV361 @ ( c_List_Olinorder__class_Osort__key @ SV361 @ SV645 @ SV845 @ SV38 ) @ SV845 @ SV38 ) @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2231,plain,
! [SV957: $i,SV846: $i,SV647: $i,SV363: $i,SV40: $i] :
( ( ( c_ListOrder_Ostep1 @ SV40 @ ( c_List_Oappend @ SV363 @ SV647 @ SV846 ) @ ( c_List_Oappend @ SV363 @ SV957 @ SV846 ) @ SV846 )
| ~ ( c_ListOrder_Ostep1 @ SV40 @ SV647 @ SV957 @ SV846 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2232,plain,
! [SV958: $i,SV847: $i,SV648: $i,SV364: $i,SV41: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV41 @ SV364 @ SV648 @ SV847 )
| ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Oappend @ SV364 @ SV958 @ SV847 ) @ ( c_List_Oappend @ SV648 @ SV958 @ SV847 ) @ SV847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2233,plain,
! [SV848: $i,SV649: $i,SV365: $i,SV42: $i] :
( ( ( ( c_List_Ofilter @ SV42 @ ( c_List_Olist_OCons @ SV365 @ SV649 @ SV848 ) @ SV848 )
= ( c_List_Olist_OCons @ SV365 @ ( c_List_Ofilter @ SV42 @ SV649 @ SV848 ) @ SV848 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV42 @ SV365 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2234,plain,
! [SV650: $i,SV366: $i,SV43: $i] :
( ( ( class_Orderings_Olinorder @ SV43 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV366 @ SV650 @ SV43 ) @ SV43 )
| ~ ( c_List_Olinorder__class_Osorted @ SV650 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2235,plain,
! [SV959: $i,SV849: $i,SV651: $i,SV367: $i,SV44: $i] :
( ( ( c_List_Otake @ SV44 @ ( c_List_Omap @ SV367 @ SV651 @ SV849 @ SV959 ) @ SV959 )
= ( c_List_Omap @ SV367 @ ( c_List_Otake @ SV44 @ SV651 @ SV849 ) @ SV849 @ SV959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2236,plain,
! [SV960: $i,SV850: $i,SV653: $i,SV369: $i,SV46: $i] :
( ( ! [SY2445: $i] :
( ( c_List_Olist__all2 @ SV46 @ ( c_List_Otake @ SV369 @ SV653 @ SV850 ) @ ( c_List_Otake @ SV369 @ SV960 @ SY2445 ) @ SV850 @ SY2445 )
| ~ ( c_List_Olist__all2 @ SV46 @ SV653 @ SV960 @ SV850 @ SY2445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2237,plain,
! [SV371: $i,SV48: $i,SV655: $i] :
( ( ( c_List_Olist__all2 @ ( c_fequal @ SV655 ) @ SV48 @ SV371 @ SV655 @ SV655 )
= $false )
| ( ( SV48 = SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2238,plain,
! [SV961: $i,SV851: $i,SV656: $i,SV372: $i,SV49: $i] :
( ( ! [SY2446: $i] :
( ( c_List_Ofoldl @ SV49 @ SV372 @ ( c_List_Olist_OCons @ SV656 @ SV851 @ SV961 ) @ SY2446 @ SV961 )
= ( c_List_Ofoldl @ SV49 @ ( hAPP @ ( hAPP @ SV49 @ SV372 ) @ SV656 ) @ SV851 @ SY2446 @ SV961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2239,plain,
! [SV962: $i,SV852: $i,SV657: $i,SV373: $i,SV50: $i] :
( ( ! [SY2447: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV373 ) @ SV657 ) )
| ( c_ListOrder_Ostep1 @ SV50 @ SV852 @ SV962 @ SY2447 )
| ~ ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SV852 @ ( c_List_Olist_OCons @ SV373 @ ( c_List_Olist_ONil @ SY2447 ) @ SY2447 ) @ SY2447 ) @ ( c_List_Oappend @ SV962 @ ( c_List_Olist_OCons @ SV657 @ ( c_List_Olist_ONil @ SY2447 ) @ SY2447 ) @ SY2447 ) @ SY2447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2240,plain,
! [SV660: $i,SV377: $i,SV54: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV54 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV377 @ SV660 @ SV54 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV660 @ SV377 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2241,plain,
! [SV661: $i,SV378: $i,SV55: $i] :
( ( ( class_Lattices_Olattice @ SV55 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 @ SV661 @ SV55 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV661 @ SV378 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2242,plain,
! [SV853: $i,SV662: $i,SV379: $i,SV56: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV56 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2243,plain,
! [SV963: $i,SV854: $i,SV663: $i,SV380: $i,SV57: $i] :
( ( ! [SY2448: $i,SY2449: $i] :
( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SV854 ) @ ( c_List_Oappend @ SV963 @ SY2448 @ SY2449 ) @ SV854 @ SY2449 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV663 @ SY2448 @ SV854 @ SY2449 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SV963 @ SV854 @ SY2449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2244,plain,
! [SV62: $i,SV666: $i,SV385: $i] :
( ( ( c_List_Odistinct @ SV385 @ SV666 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Ofilter @ SV62 @ SV385 @ SV666 ) @ SV666 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2245,plain,
! [SV964: $i,SV857: $i,SV667: $i,SV386: $i,SV63: $i] :
( ( ( c_List_Omap @ SV63 @ ( c_List_Olist_OCons @ SV386 @ SV667 @ SV857 ) @ SV857 @ SV964 )
= ( c_List_Olist_OCons @ ( hAPP @ SV63 @ SV386 ) @ ( c_List_Omap @ SV63 @ SV667 @ SV857 @ SV964 ) @ SV964 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2246,plain,
! [SV965: $i,SV858: $i,SV668: $i,SV387: $i,SV64: $i] :
( ( ( c_List_Olist_OCons @ ( hAPP @ SV64 @ SV387 ) @ ( c_List_Omap @ SV64 @ SV668 @ SV858 @ SV965 ) @ SV965 )
= ( c_List_Omap @ SV64 @ ( c_List_Olist_OCons @ SV387 @ SV668 @ SV858 ) @ SV858 @ SV965 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2247,plain,
! [SV966: $i,SV859: $i,SV669: $i,SV388: $i,SV65: $i] :
( ( ( c_List_Omap @ SV65 @ ( c_List_Olist_OCons @ SV388 @ SV669 @ SV859 ) @ SV859 @ SV966 )
= ( c_List_Olist_OCons @ ( hAPP @ SV65 @ SV388 ) @ ( c_List_Omap @ SV65 @ SV669 @ SV859 @ SV966 ) @ SV966 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2248,plain,
! [SV967: $i,SV860: $i,SV670: $i,SV389: $i,SV66: $i] :
( ( ! [SY2450: $i] :
( ( c_List_Olist_Olist__case @ SV66 @ SV389 @ ( c_List_Olist_OCons @ SV670 @ SV860 @ SV967 ) @ SY2450 @ SV967 )
= ( hAPP @ ( hAPP @ SV389 @ SV670 ) @ SV860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2249,plain,
! [SV968: $i,SV861: $i,SV672: $i,SV391: $i,SV68: $i] :
( ( ! [SY2451: $i,SY2452: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV391 ) @ SV672 ) )
| ~ ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SV391 @ SV861 @ SV968 ) @ ( c_List_Olist_OCons @ SV672 @ SY2451 @ SY2452 ) @ SV968 @ SY2452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2250,plain,
! [SV969: $i,SV864: $i,SV675: $i,SV394: $i,SV71: $i] :
( ( ! [SY2453: $i] :
( ( SV71 = SV394 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV675 @ SV394 ) @ SV71 ) )
| ~ ( c_ListOrder_Ostep1 @ SV675 @ ( c_List_Olist_OCons @ SV394 @ SV864 @ SV969 ) @ ( c_List_Olist_OCons @ SV71 @ SY2453 @ SV969 ) @ SV969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2251,plain,
! [SV677: $i,SV396: $i,SV73: $i] :
( ( ( class_Orderings_Olinorder @ SV73 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ SV396 @ SV73 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV677 @ SV396 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2252,plain,
! [SV75: $i,SV679: $i,SV398: $i] :
( ( ( c_List_Odistinct @ SV398 @ SV679 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Odrop @ SV75 @ SV398 @ SV679 ) @ SV679 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2253,plain,
! [SV865: $i,SV680: $i,SV401: $i,SV78: $i] :
( ( ( c_List_Olist__all @ SV78 @ SV401 @ SV680 )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV78 @ ( c_List_Olist_OCons @ SV865 @ SV401 @ SV680 ) @ SV680 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2254,plain,
! [SV403: $i,SV681: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV681 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV681 @ SV80 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV681 @ SV403 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV80 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2255,plain,
! [SV866: $i,SV682: $i,SV404: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ SV81 @ SV404 ) )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV81 @ ( c_List_Olist_OCons @ SV404 @ SV682 @ SV866 ) @ SV866 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2256,plain,
! [SV405: $i,SV683: $i,SV82: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV683 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV683 @ SV82 ) @ t_a ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV683 @ SV405 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV82 @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2257,plain,
! [SV970: $i,SV867: $i,SV686: $i,SV408: $i,SV85: $i] :
( ( ! [SY2454: $i] :
( ( c_List_Omap @ SV85 @ ( c_List_Olist__update @ SV408 @ SV686 @ SV867 @ SV970 ) @ SV970 @ SY2454 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV85 @ SV408 @ SV970 @ SY2454 ) @ SV686 @ ( hAPP @ SV85 @ SV867 ) @ SY2454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2258,plain,
! [SV971: $i,SV868: $i,SV687: $i,SV410: $i,SV87: $i] :
( ( ! [SY2455: $i] :
( ( SV87 = SV410 )
| ( c_ListOrder_Ostep1 @ SV687 @ SV87 @ SV410 @ SV868 )
| ~ ( c_ListOrder_Ostep1 @ SV687 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ ( c_List_Oappend @ SV410 @ ( c_List_Olist_OCons @ SY2455 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ SV868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2259,plain,
! [SV869: $i,SV688: $i,SV411: $i,SV88: $i] :
( ( ( hBOOL @ ( hAPP @ SV88 @ SV411 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV688 @ SV88 @ ( tc_fun @ SV869 @ tc_bool ) ) @ SV411 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2260,plain,
! [SV870: $i,SV689: $i,SV412: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ SV89 @ SV412 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV689 @ ( tc_fun @ SV870 @ tc_bool ) ) @ SV412 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2261,plain,
! [SV871: $i,SV690: $i,SV413: $i,SV90: $i] :
( ( ( c_List_Olist__all @ SV90 @ ( c_List_Oappend @ SV413 @ SV690 @ SV871 ) @ SV871 )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV90 @ SV690 @ SV871 )
| ~ ( c_List_Olist__all @ SV90 @ SV413 @ SV871 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2262,plain,
! [SV92: $i,SV691: $i,SV415: $i] :
( ( ( c_List_Odistinct @ SV415 @ SV691 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Otake @ SV92 @ SV415 @ SV691 ) @ SV691 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2263,plain,
! [SV972: $i,SV872: $i,SV693: $i,SV417: $i,SV94: $i] :
( ( ! [SY2456: $i] :
( ( c_List_Ofoldl @ SV94 @ SV417 @ ( c_List_Oappend @ SV693 @ SV872 @ SV972 ) @ SY2456 @ SV972 )
= ( c_List_Ofoldl @ SV94 @ ( c_List_Ofoldl @ SV94 @ SV417 @ SV693 @ SY2456 @ SV972 ) @ SV872 @ SY2456 @ SV972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2264,plain,
! [SV418: $i,SV95: $i,SV694: $i] :
( ( ( c_List_Odistinct @ ( c_List_Olist_OCons @ SV694 @ SV95 @ SV418 ) @ SV418 )
= $false )
| ( ( c_List_Odistinct @ SV95 @ SV418 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2265,plain,
! [SV973: $i,SV874: $i,SV696: $i,SV420: $i,SV97: $i] :
( ( ( c_List_Olist__all2 @ SV97 @ ( c_List_Orev @ SV420 @ SV696 ) @ SV874 @ SV696 @ SV973 )
| ~ ( c_List_Olist__all2 @ SV97 @ SV420 @ ( c_List_Orev @ SV874 @ SV973 ) @ SV696 @ SV973 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2266,plain,
! [SV974: $i,SV875: $i,SV697: $i,SV421: $i,SV98: $i] :
( ( ( c_List_Olist__all2 @ SV98 @ SV421 @ ( c_List_Orev @ SV697 @ SV875 ) @ SV974 @ SV875 )
| ~ ( c_List_Olist__all2 @ SV98 @ ( c_List_Orev @ SV421 @ SV974 ) @ SV697 @ SV974 @ SV875 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2267,plain,
! [SV975: $i,SV876: $i,SV699: $i,SV424: $i,SV104: $i] :
( ( ! [SY2457: $i] :
( ( SV104 = SV424 )
| ( SV699 = SV876 )
| ~ ( c_ListOrder_Ostep1 @ SV975 @ ( c_List_Olist_OCons @ SV424 @ SV876 @ SY2457 ) @ ( c_List_Olist_OCons @ SV104 @ SV699 @ SY2457 ) @ SY2457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2268,plain,
! [SV976: $i,SV877: $i,SV700: $i,SV425: $i,SV105: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV425 ) @ SV700 ) )
| ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Olist_OCons @ SV425 @ SV877 @ SV976 ) @ ( c_List_Olist_OCons @ SV700 @ SV877 @ SV976 ) @ SV976 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2269,plain,
! [SV702: $i,SV427: $i,SV107: $i] :
( ( ( class_Orderings_Olinorder @ SV107 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV427 @ SV702 @ SV107 ) @ SV107 )
| ~ ( c_List_Olinorder__class_Osorted @ SV702 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2270,plain,
! [SV879: $i,SV703: $i,SV428: $i,SV108: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV108 ) )
= $true )
| ( ( ( c_List_Odistinct @ SV428 @ SV703 )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV879 @ SV428 @ SV703 @ SV108 ) @ SV703 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2039]) ).
thf(2271,plain,
! [SV880: $i,SV704: $i,SV429: $i,SV109: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV109 ) )
= $true )
| ( ( ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV429 @ SV704 @ SV880 @ SV109 ) @ SV880 )
| ~ ( c_List_Odistinct @ SV704 @ SV880 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2272,plain,
! [SV977: $i,SV881: $i,SV705: $i,SV430: $i,SV110: $i] :
( ( ! [SY2458: $i,SY2459: $i] :
( ( c_List_Olist__all2 @ SV110 @ SV430 @ SV705 @ SV881 @ SV977 )
| ~ ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SY2458 @ SV430 @ SV881 ) @ ( c_List_Olist_OCons @ SY2459 @ SV705 @ SV977 ) @ SV881 @ SV977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2273,plain,
! [SV978: $i,SV882: $i,SV706: $i,SV431: $i,SV111: $i] :
( ( ( c_List_Orotate @ SV111 @ ( c_List_Omap @ SV431 @ SV706 @ SV882 @ SV978 ) @ SV978 )
= ( c_List_Omap @ SV431 @ ( c_List_Orotate @ SV111 @ SV706 @ SV882 ) @ SV882 @ SV978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2274,plain,
! [SV432: $i,SV707: $i,SV112: $i] :
( ( ( c_List_Odistinct @ ( c_List_Oappend @ SV112 @ SV707 @ SV432 ) @ SV432 )
= $false )
| ( ( c_List_Odistinct @ SV112 @ SV432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2275,plain,
! [SV433: $i,SV113: $i,SV708: $i] :
( ( ( c_List_Odistinct @ ( c_List_Oappend @ SV708 @ SV113 @ SV433 ) @ SV433 )
= $false )
| ( ( c_List_Odistinct @ SV113 @ SV433 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2276,plain,
! [SV117: $i,SV709: $i,SV437: $i] :
( ( ( c_List_Odistinct @ SV437 @ SV709 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_OdropWhile @ SV117 @ SV437 @ SV709 ) @ SV709 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2277,plain,
! [SV979: $i,SV883: $i,SV710: $i,SV438: $i,SV118: $i] :
( ( ( c_List_Olist__all2 @ SV118 @ SV438 @ SV710 @ SV883 @ SV979 )
| ~ ( c_List_Olist__all2 @ SV118 @ ( c_List_Orev @ SV438 @ SV883 ) @ ( c_List_Orev @ SV710 @ SV979 ) @ SV883 @ SV979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2278,plain,
! [SV980: $i,SV884: $i,SV711: $i,SV439: $i,SV119: $i] :
( ( ( c_List_Olist__all2 @ SV119 @ ( c_List_Orev @ SV439 @ SV711 ) @ ( c_List_Orev @ SV884 @ SV980 ) @ SV711 @ SV980 )
| ~ ( c_List_Olist__all2 @ SV119 @ SV439 @ SV884 @ SV711 @ SV980 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2279,plain,
! [SV981: $i,SV885: $i,SV712: $i,SV440: $i,SV120: $i] :
( ( ( c_List_Oconcat__map @ SV120 @ ( c_List_Olist_OCons @ SV440 @ SV712 @ SV885 ) @ SV885 @ SV981 )
= ( c_List_Oappend @ ( hAPP @ SV120 @ SV440 ) @ ( c_List_Oconcat__map @ SV120 @ SV712 @ SV885 @ SV981 ) @ SV981 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2280,plain,
! [SV982: $i,SV886: $i,SV713: $i,SV441: $i,SV121: $i] :
( ( ! [SY2460: $i] :
( ( c_List_Ofoldr @ SV121 @ ( c_List_Oappend @ SV441 @ SV713 @ SV886 ) @ SV982 @ SV886 @ SY2460 )
= ( c_List_Ofoldr @ SV121 @ SV441 @ ( c_List_Ofoldr @ SV121 @ SV713 @ SV982 @ SV886 @ SY2460 ) @ SV886 @ SY2460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2281,plain,
! [SV887: $i,SV714: $i,SV442: $i,SV122: $i] :
( ( ( c_List_Olist__ex @ SV122 @ ( c_List_Olist_OCons @ SV442 @ SV714 @ SV887 ) @ SV887 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV122 @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2282,plain,
! [SV983: $i,SV888: $i,SV715: $i,SV443: $i,SV123: $i] :
( ( ! [SY2461: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV443 ) @ SV715 ) )
| ( SV443 = SV715 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV888 @ ( c_List_Olist_OCons @ SV443 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ ( c_List_Oappend @ SY2461 @ ( c_List_Olist_OCons @ SV715 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ SV983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2283,plain,
! [SV984: $i,SV889: $i,SV716: $i,SV444: $i,SV124: $i] :
( ( ! [SY2462: $i,SY2463: $i] :
( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SV889 ) @ ( c_List_Olist_OCons @ SV984 @ SY2462 @ SY2463 ) @ SV889 @ SY2463 )
| ~ ( c_List_Olist__all2 @ SV124 @ SV716 @ SY2462 @ SV889 @ SY2463 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SV984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2284,plain,
! [SV985: $i,SV890: $i,SV717: $i,SV445: $i,SV125: $i] :
( ( ! [SY2464: $i,SY2465: $i] :
( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SV890 ) @ ( c_List_Olist_OCons @ SV985 @ SY2464 @ SY2465 ) @ SV890 @ SY2465 )
| ~ ( c_List_Olist__all2 @ SV125 @ SV717 @ SY2464 @ SV890 @ SY2465 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SV985 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2285,plain,
! [SV986: $i,SV891: $i,SV718: $i,SV446: $i,SV126: $i] :
( ( ! [SY2466: $i,SY2467: $i] :
( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SV891 ) @ ( c_List_Olist_OCons @ SV986 @ SY2466 @ SY2467 ) @ SV891 @ SY2467 )
| ~ ( c_List_Olist__all2 @ SV126 @ SV718 @ SY2466 @ SV891 @ SY2467 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SV986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2286,plain,
! [SV892: $i,SV719: $i,SV447: $i,SV127: $i] :
( ( ( c_List_Olist__ex @ SV127 @ ( c_List_Olist_OCons @ SV447 @ SV719 @ SV892 ) @ SV892 )
= $true )
| ( ( ~ ( c_List_Olist__ex @ SV127 @ SV719 @ SV892 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2287,plain,
! [SV893: $i,SV720: $i,SV448: $i,SV128: $i] :
( ( ( c_List_Olist__ex @ SV128 @ SV448 @ SV720 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV128 @ SV893 ) )
| ~ ( c_List_Olist__ex @ SV128 @ ( c_List_Olist_OCons @ SV893 @ SV448 @ SV720 ) @ SV720 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2288,plain,
! [SV987: $i,SV894: $i,SV721: $i,SV449: $i,SV129: $i] :
( ( ! [SY2468: $i] :
( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SV721 @ SV894 ) @ ( c_List_Olist_OCons @ SV987 @ SY2468 @ SV894 ) @ SV894 )
| ~ ( c_List_Olistrelp @ SV129 @ SV721 @ SY2468 @ SV894 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SV987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2289,plain,
! [SV895: $i,SV722: $i,SV450: $i,SV130: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV130 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ SV722 @ SV130 ) @ SV895 @ SV130 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV722 @ SV895 @ SV130 ) @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2290,plain,
! [SV896: $i,SV723: $i,SV451: $i,SV131: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV131 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ SV896 @ SV131 ) @ SV131 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ SV896 @ SV131 ) @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2291,plain,
! [SV897: $i,SV724: $i,SV452: $i,SV132: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV132 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV724 @ SV897 @ SV132 ) @ SV132 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV724 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ SV897 @ SV132 ) @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2060]) ).
thf(2292,plain,
! [SV898: $i,SV725: $i,SV453: $i,SV133: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV133 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ SV725 @ SV133 ) @ SV898 @ SV133 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV898 @ SV133 ) @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2293,plain,
! [SV901: $i,SV728: $i,SV456: $i,SV136: $i] :
( ( ( ( c_List_Oremove1 @ SV136 @ ( c_List_Olist_OCons @ SV456 @ SV728 @ SV901 ) @ SV901 )
= ( c_List_Olist_OCons @ SV456 @ ( c_List_Oremove1 @ SV136 @ SV728 @ SV901 ) @ SV901 ) )
= $true )
| ( ( SV136 = SV456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2294,plain,
! [SV988: $i,SV902: $i,SV729: $i,SV457: $i,SV137: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV137 @ SV457 @ SV729 ) @ ( c_List_Olist_OCons @ SV902 @ SV988 @ SV729 ) @ SV729 )
= ( c_List_Olist_OCons @ SV137 @ ( c_List_Olist_OCons @ SV902 @ ( c_List_Osplice @ SV457 @ SV988 @ SV729 ) @ SV729 ) @ SV729 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2295,plain,
! [SV458: $i,SV730: $i,SV138: $i] :
( ( ( c_List_Odistinct @ SV138 @ SV730 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Osublist @ SV138 @ SV458 @ SV730 ) @ SV730 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2296,plain,
! [SV903: $i,SV731: $i,SV459: $i,SV139: $i] :
( ( ( c_List_Omember @ SV139 @ ( c_List_Olist_OCons @ SV459 @ SV731 @ SV903 ) @ SV903 )
= $true )
| ( ( ~ ( c_List_Omember @ SV139 @ SV731 @ SV903 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2067]) ).
thf(2297,plain,
! [SV141: $i,SV733: $i,SV461: $i] :
( ( ( c_List_Odistinct @ SV461 @ SV733 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Oremove1 @ SV141 @ SV461 @ SV733 ) @ SV733 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2298,plain,
! [SV904: $i,SV734: $i,SV462: $i,SV142: $i] :
( ( ( ( c_List_OdropWhile @ SV142 @ ( c_List_Olist_OCons @ SV462 @ SV734 @ SV904 ) @ SV904 )
= ( c_List_OdropWhile @ SV142 @ SV734 @ SV904 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV142 @ SV462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2299,plain,
! [SV905: $i,SV735: $i,SV463: $i,SV143: $i] :
( ( ( ( c_List_OdropWhile @ SV143 @ ( c_List_Olist_OCons @ SV463 @ SV735 @ SV905 ) @ SV905 )
= ( c_List_Olist_OCons @ SV463 @ SV735 @ SV905 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV143 @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2300,plain,
! [SV989: $i,SV906: $i,SV736: $i,SV464: $i,SV144: $i] :
( ( ! [SY2469: $i] :
( ( c_ListOrder_Ostep1 @ SV144 @ SV464 @ SV736 @ SV906 )
| ( SV736 = SV464 )
| ~ ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SV989 @ SV464 @ SV906 ) @ ( c_List_Olist_OCons @ SY2469 @ SV736 @ SV906 ) @ SV906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2301,plain,
! [SV990: $i,SV907: $i,SV739: $i,SV467: $i,SV147: $i] :
( ( ( c_List_Omap @ SV147 @ ( c_List_Oappend @ SV467 @ SV739 @ SV907 ) @ SV907 @ SV990 )
= ( c_List_Oappend @ ( c_List_Omap @ SV147 @ SV467 @ SV907 @ SV990 ) @ ( c_List_Omap @ SV147 @ SV739 @ SV907 @ SV990 ) @ SV990 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2302,plain,
! [SV149: $i,SV469: $i] :
( ( ( c_List_Olistsp @ SV469 @ SV149 @ t_a )
= $false )
| ( ( SV149
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( SV149
= ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xcases__1 @ SV469 @ SV149 ) @ ( v_sko__List__Xlistsp__Xcases__2 @ SV469 @ SV149 ) @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2303,plain,
! [SV991: $i,SV908: $i,SV741: $i,SV470: $i,SV150: $i] :
( ( ! [SY2470: $i] :
( ( c_List_Olist__all2 @ SV150 @ ( c_List_Odrop @ SV470 @ SV741 @ SV908 ) @ ( c_List_Odrop @ SV470 @ SV991 @ SY2470 ) @ SV908 @ SY2470 )
| ~ ( c_List_Olist__all2 @ SV150 @ SV741 @ SV991 @ SV908 @ SY2470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2304,plain,
! [SV909: $i,SV742: $i,SV471: $i,SV151: $i] :
( ( ( ( c_List_Oremove1 @ SV151 @ ( c_List_Ofilter @ SV471 @ SV742 @ SV909 ) @ SV909 )
= ( c_List_Ofilter @ SV471 @ SV742 @ SV909 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV471 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2305,plain,
! [SV992: $i,SV910: $i,SV743: $i,SV472: $i,SV152: $i] :
( ( ! [SY2471: $i] :
( ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ ( c_List_Olist_OCons @ SV743 @ SV910 @ SV992 ) @ SY2471 @ SV992 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV472 @ SV743 ) @ SV910 ) @ ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ SV910 @ SY2471 @ SV992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2306,plain,
! [SV911: $i,SV744: $i,SV473: $i,SV153: $i] :
( ( ( c_List_Odistinct @ SV153 @ SV473 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Omap @ SV744 @ SV153 @ SV473 @ SV911 ) @ SV911 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2307,plain,
! [SV993: $i,SV912: $i,SV745: $i,SV474: $i,SV154: $i] :
( ( ! [SY2472: $i] :
( ( SV154 = SV474 )
| ( SV745 = SV912 )
| ~ ( c_ListOrder_Ostep1 @ SV993 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SV745 @ ( c_List_Olist_ONil @ SY2472 ) @ SY2472 ) @ SY2472 ) @ ( c_List_Oappend @ SV474 @ ( c_List_Olist_OCons @ SV912 @ ( c_List_Olist_ONil @ SY2472 ) @ SY2472 ) @ SY2472 ) @ SY2472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2308,plain,
! [SV475: $i,SV155: $i,SV746: $i] :
( ( ( c_List_Odistinct @ ( c_List_Orotate @ SV746 @ SV155 @ SV475 ) @ SV475 )
= $false )
| ( ( c_List_Odistinct @ SV155 @ SV475 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2309,plain,
! [SV156: $i,SV747: $i,SV476: $i] :
( ( ( c_List_Odistinct @ SV476 @ SV747 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Orotate @ SV156 @ SV476 @ SV747 ) @ SV747 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2310,plain,
! [SV749: $i,SV478: $i,SV158: $i] :
( ( ( class_Lattices_Olattice @ SV158 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ SV749 @ SV158 ) @ SV158 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV478 @ SV749 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2311,plain,
! [SV750: $i,SV479: $i,SV159: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV159 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV750 @ SV159 ) @ SV159 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV750 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2312,plain,
! [SV994: $i,SV913: $i,SV752: $i,SV481: $i,SV161: $i] :
( ( ! [SY2473: $i] :
( ( c_List_Ofoldr @ SV161 @ ( c_List_Olist_OCons @ SV481 @ SV752 @ SV913 ) @ SV994 @ SV913 @ SY2473 )
= ( hAPP @ ( hAPP @ SV161 @ SV481 ) @ ( c_List_Ofoldr @ SV161 @ SV752 @ SV994 @ SV913 @ SY2473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2313,plain,
! [SV995: $i,SV914: $i,SV754: $i,SV486: $i,SV166: $i] :
( ( ! [SY2474: $i] :
( ( c_ListOrder_Ostep1 @ SV166 @ SV486 @ SV754 @ SV914 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV995 ) @ SY2474 ) )
| ~ ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SV995 @ SV486 @ SV914 ) @ ( c_List_Olist_OCons @ SY2474 @ SV754 @ SV914 ) @ SV914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2314,plain,
! [SV996: $i,SV915: $i,SV755: $i,SV487: $i,SV167: $i] :
( ( ( c_ListOrder_Ostep1 @ SV167 @ ( c_List_Olist_OCons @ SV487 @ SV755 @ SV915 ) @ ( c_List_Olist_OCons @ SV487 @ SV996 @ SV915 ) @ SV915 )
| ~ ( c_ListOrder_Ostep1 @ SV167 @ SV755 @ SV996 @ SV915 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2315,plain,
! [SV756: $i,SV488: $i,SV168: $i] :
( ( ( class_Orderings_Olinorder @ SV168 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ SV488 @ SV168 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV488 @ SV756 @ SV168 ) @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2316,plain,
! [SV757: $i,SV489: $i,SV169: $i] :
( ( ( class_Orderings_Olinorder @ SV169 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ SV489 @ SV169 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV757 @ SV489 @ SV169 ) @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2317,plain,
! [SV916: $i,SV758: $i,SV490: $i,SV170: $i] :
( ( ( c_List_Olist__all @ SV170 @ ( c_List_Olist_OCons @ SV490 @ SV758 @ SV916 ) @ SV916 )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV170 @ SV758 @ SV916 )
| ~ ( hBOOL @ ( hAPP @ SV170 @ SV490 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2318,plain,
! [SV997: $i,SV917: $i,SV759: $i,SV491: $i,SV171: $i] :
( ( ! [SY2475: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV491 @ SV759 @ SV917 ) @ SV997 @ SY2475 @ SV917 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV997 @ SY2475 @ SV917 ) @ SV491 @ SV759 @ SV917 ) )
| ( SV491 = SV997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2319,plain,
! [SV172: $i,SV492: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SV492 @ SV172 ) @ SV172 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV492 @ SV172 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2320,plain,
! [SV760: $i,SV493: $i,SV173: $i] :
( ( ( c_List_Olist__all @ SV173 @ ( c_List_Orev @ SV493 @ SV760 ) @ SV760 )
= $false )
| ( ( c_List_Olist__all @ SV173 @ SV493 @ SV760 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2321,plain,
! [SV761: $i,SV494: $i,SV174: $i] :
( ( ( c_List_Olist__all @ SV174 @ SV494 @ SV761 )
= $false )
| ( ( c_List_Olist__all @ SV174 @ ( c_List_Orev @ SV494 @ SV761 ) @ SV761 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2322,plain,
! [SV998: $i,SV918: $i,SV762: $i,SV495: $i,SV175: $i] :
( ( ( c_List_Odrop @ SV175 @ ( c_List_Omap @ SV495 @ SV762 @ SV918 @ SV998 ) @ SV998 )
= ( c_List_Omap @ SV495 @ ( c_List_Odrop @ SV175 @ SV762 @ SV918 ) @ SV918 @ SV998 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2323,plain,
! [SV919: $i,SV763: $i,SV496: $i,SV176: $i] :
( ( ( c_List_Omember @ SV176 @ SV496 @ SV763 )
= $true )
| ( ( ( SV176 = SV919 )
| ~ ( c_List_Omember @ SV176 @ ( c_List_Olist_OCons @ SV919 @ SV496 @ SV763 ) @ SV763 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2324,plain,
! [SV920: $i,SV764: $i,SV497: $i,SV177: $i] :
( ( ( ( c_List_Ofilter @ SV177 @ ( c_List_Olist_OCons @ SV497 @ SV764 @ SV920 ) @ SV920 )
= ( c_List_Ofilter @ SV177 @ SV764 @ SV920 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV177 @ SV497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2325,plain,
! [SV921: $i,SV765: $i,SV498: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV178 @ SV498 @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV921 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV498 @ SV921 ) )
| ~ ( hBOOL @ ( hAPP @ SV178 @ SV921 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2326,plain,
! [SV922: $i,SV767: $i,SV501: $i,SV181: $i] :
( ( ( c_List_Olist__all @ SV181 @ SV501 @ SV767 )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV181 @ ( c_List_Oappend @ SV501 @ SV922 @ SV767 ) @ SV767 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2327,plain,
! [SV923: $i,SV768: $i,SV502: $i,SV182: $i] :
( ( ( c_List_Olist__all @ SV182 @ SV502 @ SV768 )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV182 @ ( c_List_Oappend @ SV923 @ SV502 @ SV768 ) @ SV768 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2328,plain,
! [SV999: $i,SV924: $i,SV770: $i,SV504: $i,SV184: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_Olist__case @ SV504 @ SV770 @ ( c_List_Olist_OCons @ SV924 @ SV999 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV184 @ ( hAPP @ ( hAPP @ SV770 @ SV924 ) @ SV999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2329,plain,
! [SV1000: $i,SV925: $i,SV771: $i,SV505: $i,SV185: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_List_Olist_Olist__case @ SV505 @ SV771 @ ( c_List_Olist_OCons @ SV925 @ SV1000 @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ SV185 @ ( hAPP @ ( hAPP @ SV771 @ SV925 ) @ SV1000 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2330,plain,
! [SV772: $i,SV506: $i,SV186: $i] :
( ( ( class_Orderings_Olinorder @ SV186 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ SV506 @ SV772 @ SV186 ) @ SV186 )
| ~ ( c_List_Olinorder__class_Osorted @ SV772 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2331,plain,
! [SV1001: $i,SV926: $i,SV773: $i,SV507: $i,SV187: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV187 @ SV507 @ SV773 @ SV926 ) @ SV507 @ SV1001 @ SV926 )
= ( c_List_Olist__update @ SV187 @ SV507 @ SV1001 @ SV926 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2332,plain,
! [SV778: $i,SV512: $i,SV192: $i] :
( ( ( class_Orderings_Olinorder @ SV192 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV512 @ SV778 @ SV192 ) @ SV192 )
| ~ ( c_List_Olinorder__class_Osorted @ SV778 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2333,plain,
! [SV515: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ SV196 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV196 @ ( v_sko__List__Xrev__Xinduct__2 @ SV196 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV196 @ SV515 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2334,plain,
! [SV516: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ SV197 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV197 @ ( v_sko__List__Xsplice__Xinduct__2 @ SV197 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV197 @ SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2335,plain,
! [SV517: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ SV198 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV198 @ ( v_sko__List__Xset__Xinduct__2 @ SV198 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV198 @ SV517 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2336,plain,
! [SV518: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ SV199 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV199 @ ( v_sko__List__Xtl__Xinduct__2 @ SV199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV199 @ SV518 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2337,plain,
! [SV931: $i,SV779: $i,SV519: $i,SV200: $i] :
( ( ( SV200
= ( c_List_Olist_ONil @ SV519 ) )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV779 @ SV200 @ ( c_List_Olist_ONil @ SV931 ) @ SV519 @ SV931 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2338,plain,
! [SV932: $i,SV780: $i,SV520: $i,SV201: $i] :
( ( ( SV201
= ( c_List_Olist_ONil @ SV520 ) )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV780 @ ( c_List_Olist_ONil @ SV932 ) @ SV201 @ SV932 @ SV520 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2339,plain,
! [SV521: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ SV202 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV202 @ ( v_sko__List__Xlist__Xinducts__2 @ SV202 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV202 @ SV521 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2340,plain,
! [SV522: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ SV203 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV203 @ ( v_sko__List__Xhd__Xinduct__2 @ SV203 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV203 @ SV522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2341,plain,
! [SV524: $i,SV206: $i] :
( ( ( hBOOL @ ( hAPP @ SV206 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV206 @ ( v_sko__List__Xremdups__Xinduct__2 @ SV206 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV206 @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2342,plain,
! [SV526: $i,SV782: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV208 @ SV782 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Olist_ONil @ SV782 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV208 @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2343,plain,
! [SV783: $i,SV527: $i,SV209: $i] :
( ( ( class_Orderings_Olinorder @ SV209 )
= $false )
| ( ( ( c_List_Olinorder__class_Osort__key @ SV527 @ ( c_List_Olist_ONil @ SV783 ) @ SV783 @ SV209 )
= ( c_List_Olist_ONil @ SV783 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2344,plain,
! [SV528: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ SV210 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV210 @ ( v_sko__List__Xdrop__Xinduct__2 @ SV210 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV210 @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2345,plain,
! [SV530: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP @ SV212 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV212 @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV212 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV212 @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2346,plain,
! [SV534: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ SV217 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV217 @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV217 @ SV534 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2347,plain,
! [SV542: $i,SV225: $i] :
( ( ( hBOOL @ ( hAPP @ SV225 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV225 @ ( v_sko__List__Xlast__Xinduct__2 @ SV225 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV225 @ SV542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2348,plain,
! [SV544: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP @ SV227 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV227 @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV227 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV227 @ SV544 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2349,plain,
! [SV545: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP @ SV228 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV228 @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV228 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV228 @ SV545 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2350,plain,
! [SV546: $i,SV229: $i] :
( ( ( hBOOL @ ( hAPP @ SV229 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV229 @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV229 @ SV546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2351,plain,
! [SV787: $i,SV549: $i,SV234: $i] :
( ( ( hBOOL @ ( hAPP @ SV234 @ ( c_List_Olist_Olist__case @ SV549 @ SV787 @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV234 @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2352,plain,
! [SV551: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ SV236 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV236 @ ( v_sko__List__Xzip__Xinduct__2 @ SV236 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV236 @ SV551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2353,plain,
! [SV554: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ SV239 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV239 @ ( v_sko__List__Xlistset__Xinduct__2 @ SV239 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV239 @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2354,plain,
! [SV556: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV241 @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV241 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV241 @ SV556 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2355,plain,
! [SV557: $i,SV242: $i] :
( ( ( hBOOL @ ( hAPP @ SV242 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV242 @ ( v_sko__List__Xtake__Xinduct__2 @ SV242 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV242 @ SV557 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2356,plain,
! [SV563: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP @ SV249 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV249 @ ( v_sko__List__Xconcat__Xinduct__2 @ SV249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV249 @ SV563 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2357,plain,
! [SV565: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ SV251 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV251 @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV251 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV251 @ SV565 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2358,plain,
! [SV568: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ SV254 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV254 @ ( v_sko__List__Xremove1__Xinduct__2 @ SV254 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV254 @ SV568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2359,plain,
! [SV571: $i,SV257: $i] :
( ( ( hBOOL @ ( hAPP @ SV257 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV257 @ ( v_sko__List__Xlist__Xinduct__2 @ SV257 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV257 @ SV571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2360,plain,
! [SV574: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV261 @ ( v_sko__List__Xmap__Xinduct__2 @ SV261 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV261 @ SV574 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2361,plain,
! [SV939: $i,SV799: $i,SV575: $i,SV263: $i] :
( ( ( c_List_Olistsp @ SV263 @ ( c_List_Oappend @ SV575 @ SV799 @ SV939 ) @ SV939 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV263 @ SV799 @ SV939 )
| ~ ( c_List_Olistsp @ SV263 @ SV575 @ SV939 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2362,plain,
! [SV800: $i,SV576: $i,SV264: $i] :
( ( ( hBOOL @ ( hAPP @ SV264 @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ SV264 @ SV576 @ SV800 ) ) )
= $false )
| ( ( c_List_Olistsp @ SV264 @ SV576 @ SV800 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2363,plain,
! [SV940: $i,SV801: $i,SV577: $i,SV265: $i] :
( ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV265 @ SV577 @ ( tc_fun @ SV801 @ tc_bool ) ) @ SV940 @ SV801 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV577 @ SV940 @ SV801 )
| ~ ( c_List_Olistsp @ SV265 @ SV940 @ SV801 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2364,plain,
! [SV941: $i,SV802: $i,SV578: $i,SV266: $i] :
( ( ( c_List_Olistsp @ SV266 @ SV578 @ SV802 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV266 @ ( c_List_Oappend @ SV941 @ SV578 @ SV802 ) @ SV802 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2365,plain,
! [SV942: $i,SV803: $i,SV579: $i,SV267: $i] :
( ( ( c_List_Olistsp @ SV267 @ SV579 @ SV803 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV267 @ ( c_List_Oappend @ SV579 @ SV942 @ SV803 ) @ SV803 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2366,plain,
! [SV581: $i,SV270: $i,SV804: $i] :
( ( ( hBOOL @ ( hAPP @ SV804 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV804 @ SV270 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV270 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV804 @ SV581 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV581 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2367,plain,
! [SV582: $i,SV805: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ SV271 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV805 @ SV271 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV271 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV805 @ SV582 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2368,plain,
! [SV583: $i,SV272: $i,SV806: $i] :
( ( ( hBOOL @ ( hAPP @ SV806 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV806 @ SV272 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV272 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV806 @ SV583 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV583 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2369,plain,
! [SV584: $i,SV807: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ SV273 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV807 @ SV273 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV273 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV807 @ SV584 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV273 @ SV584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2370,plain,
! [SV585: $i,SV274: $i] :
( ( ( c_List_Olistsp @ SV274 @ SV585 @ t_a )
= $false )
| ( ( SV585
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV274 @ ( v_sko__List__Xlistsp__Xcases__2 @ SV274 @ SV585 ) @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2371,plain,
! [SV586: $i,SV275: $i] :
( ( ( c_List_Olistsp @ SV275 @ SV586 @ t_a )
= $false )
| ( ( SV586
= ( c_List_Olist_ONil @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV275 @ ( v_sko__List__Xlistsp__Xcases__1 @ SV275 @ SV586 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2372,plain,
! [SV587: $i,SV276: $i,SV808: $i] :
( ( ( c_List_Olistsp @ SV808 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV808 @ SV276 ) @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV276 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV808 @ SV587 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV276 @ SV587 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2373,plain,
! [SV588: $i,SV277: $i,SV809: $i] :
( ( ( c_List_Olistsp @ SV809 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV809 @ SV277 ) @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV277 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV809 @ SV588 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV277 @ SV588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2374,plain,
! [SV593: $i,SV282: $i,SV810: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV810 ) @ SV282 ) @ SV593 ) )
= $false )
| ( ( SV282 = SV593 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2375,plain,
! [SV943: $i,SV811: $i,SV594: $i,SV283: $i] :
( ( ( ( c_List_Orev @ SV283 @ SV594 )
!= ( c_List_Olist_OCons @ SV811 @ SV943 @ SV594 ) )
= $true )
| ( ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SV943 @ SV594 ) @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2376,plain,
! [SV812: $i,SV595: $i,SV284: $i] :
( ( ( ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 )
= ( c_List_Orev @ SV812 @ SV595 ) )
= $false )
| ( ( SV812
= ( c_List_Olist_OCons @ SV284 @ ( c_List_Olist_ONil @ SV595 ) @ SV595 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2377,plain,
! [SV813: $i,SV596: $i,SV286: $i] :
( ( ( ( c_List_Oappend @ SV286 @ SV596 @ SV813 )
= ( c_List_Olist_ONil @ SV813 ) )
= $false )
| ( ( SV596
= ( c_List_Olist_ONil @ SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2378,plain,
! [SV1002: $i,SV944: $i,SV814: $i,SV597: $i,SV287: $i] :
( ( ( ( c_List_Oappend @ SV287 @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 )
!= ( c_List_Oappend @ SV944 @ ( c_List_Olist_OCons @ SV1002 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 ) )
| ( SV597 = SV1002 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2379,plain,
! [SV1003: $i,SV945: $i,SV816: $i,SV599: $i,SV289: $i] :
( ( ( ( c_List_Oappend @ SV289 @ ( c_List_Olist_OCons @ SV599 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 )
!= ( c_List_Oappend @ SV945 @ ( c_List_Olist_OCons @ SV1003 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 ) )
| ( SV289 = SV945 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2380,plain,
! [SV817: $i,SV600: $i,SV290: $i] :
( ( ( ( c_List_Orotate @ SV290 @ SV600 @ SV817 )
= ( c_List_Olist_ONil @ SV817 ) )
= $false )
| ( ( SV600
= ( c_List_Olist_ONil @ SV817 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2381,plain,
! [SV819: $i,SV602: $i,SV292: $i] :
( ( ( ( c_List_Oappend @ SV292 @ SV602 @ SV819 )
= ( c_List_Olist_ONil @ SV819 ) )
= $false )
| ( ( SV292
= ( c_List_Olist_ONil @ SV819 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2382,plain,
! [SV820: $i,SV604: $i,SV294: $i] :
( ( ( ( c_List_Oappend @ SV294 @ SV604 @ SV820 )
= SV604 )
= $false )
| ( ( SV294
= ( c_List_Olist_ONil @ SV820 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2383,plain,
! [SV1004: $i,SV946: $i,SV821: $i,SV606: $i,SV297: $i] :
( ( ( ( c_List_Olist_OCons @ SV297 @ SV606 @ SV821 )
!= ( c_List_Ofilter @ SV946 @ SV1004 @ SV821 ) )
| ( hBOOL @ ( hAPP @ SV946 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2384,plain,
! [SV1005: $i,SV947: $i,SV822: $i,SV607: $i,SV298: $i] :
( ( ( ( c_List_Olist_OCons @ SV298 @ SV607 @ SV822 )
!= ( c_List_Olist_OCons @ SV947 @ SV1005 @ SV822 ) )
| ( SV607 = SV1005 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2385,plain,
! [SV823: $i,SV608: $i,SV299: $i] :
( ( ( ( c_List_Olist_ONil @ SV299 )
= ( c_List_Oappend @ SV608 @ SV823 @ SV299 ) )
= $false )
| ( ( SV823
= ( c_List_Olist_ONil @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2386,plain,
! [SV948: $i,SV825: $i,SV611: $i,SV302: $i] :
( ( ( ( c_List_Oappend @ SV302 @ SV611 @ SV825 )
!= ( c_List_Oappend @ SV948 @ SV611 @ SV825 ) )
= $true )
| ( ( SV302 = SV948 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2387,plain,
! [SV826: $i,SV612: $i,SV303: $i] :
( ( ( SV303
= ( c_List_Oappend @ SV612 @ SV303 @ SV826 ) )
= $false )
| ( ( SV612
= ( c_List_Olist_ONil @ SV826 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2388,plain,
! [SV949: $i,SV827: $i,SV614: $i,SV305: $i] :
( ( ( ( c_List_Omap @ SV305 @ SV614 @ SV827 @ SV949 )
!= ( c_List_Olist_ONil @ SV949 ) )
= $true )
| ( ( SV614
= ( c_List_Olist_ONil @ SV827 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2389,plain,
! [SV1006: $i,SV950: $i,SV828: $i,SV615: $i,SV306: $i] :
( ( ( ( c_List_Olist_OCons @ SV306 @ SV615 @ SV828 )
!= ( c_List_Olist_OCons @ SV950 @ SV1006 @ SV828 ) )
| ( SV306 = SV950 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2390,plain,
! [SV829: $i,SV617: $i,SV308: $i] :
( ( ( ( c_List_Orev @ SV308 @ SV617 )
= ( c_List_Orev @ SV829 @ SV617 ) )
= $false )
| ( ( SV308 = SV829 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2391,plain,
! [SV951: $i,SV830: $i,SV618: $i,SV309: $i] :
( ( ( ( c_List_Olist__update @ SV309 @ SV618 @ SV830 @ SV951 )
!= ( c_List_Olist_ONil @ SV951 ) )
= $true )
| ( ( SV309
= ( c_List_Olist_ONil @ SV951 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2188]) ).
thf(2392,plain,
! [SV952: $i,SV831: $i,SV619: $i,SV310: $i] :
( ( ( ( c_List_Olist_ONil @ SV310 )
!= ( c_List_Omap @ SV619 @ SV831 @ SV952 @ SV310 ) )
= $true )
| ( ( SV831
= ( c_List_Olist_ONil @ SV952 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2393,plain,
! [SV832: $i,SV621: $i,SV312: $i] :
( ( ( ( c_List_Orev @ SV312 @ SV621 )
= ( c_List_Olist_OCons @ SV832 @ ( c_List_Olist_ONil @ SV621 ) @ SV621 ) )
= $false )
| ( ( SV312
= ( c_List_Olist_OCons @ SV832 @ ( c_List_Olist_ONil @ SV621 ) @ SV621 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2394,plain,
! [SV833: $i,SV622: $i,SV313: $i] :
( ( ( ( c_List_Olist_ONil @ SV313 )
= ( c_List_Oappend @ SV622 @ SV833 @ SV313 ) )
= $false )
| ( ( SV622
= ( c_List_Olist_ONil @ SV313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2395,plain,
! [SV1007: $i,SV953: $i,SV835: $i,SV625: $i,SV316: $i] :
( ( ( ( c_List_OdropWhile @ SV316 @ SV625 @ SV835 )
!= ( c_List_Olist_OCons @ SV953 @ SV1007 @ SV835 ) )
| ~ ( hBOOL @ ( hAPP @ SV316 @ SV953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2396,plain,
! [SV954: $i,SV837: $i,SV628: $i,SV319: $i] :
( ( ( ( c_List_Oappend @ SV319 @ SV628 @ SV837 )
!= ( c_List_Oappend @ SV319 @ SV954 @ SV837 ) )
= $true )
| ( ( SV628 = SV954 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2397,plain,
! [SV838: $i,SV630: $i,SV321: $i] :
( ( ( ( c_List_Oappend @ SV321 @ SV630 @ SV838 )
= SV321 )
= $false )
| ( ( SV630
= ( c_List_Olist_ONil @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2398,plain,
! [SV1008: $i,SV955: $i,SV839: $i,SV631: $i,SV322: $i] :
( ( ( ( c_List_Ofilter @ SV322 @ SV631 @ SV839 )
!= ( c_List_Olist_OCons @ SV955 @ SV1008 @ SV839 ) )
| ( hBOOL @ ( hAPP @ SV322 @ SV955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2399,plain,
! [SV840: $i,SV632: $i,SV323: $i] :
( ( ( SV323
= ( c_List_Oappend @ SV323 @ SV632 @ SV840 ) )
= $false )
| ( ( SV632
= ( c_List_Olist_ONil @ SV840 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2400,plain,
! [SV330: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV7 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdrop__Xinduct__1 @ SV7 ) @ ( v_sko__List__Xdrop__Xinduct__2 @ SV7 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV7 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2401,plain,
! [SV331: $i,SV8: $i] :
( ( ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV8 @ ( c_List_Olist_OCons @ ( v_sko__List__Xrev__Xinduct__1 @ SV8 ) @ ( v_sko__List__Xrev__Xinduct__2 @ SV8 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV8 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2402,plain,
! [SV332: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV9 @ ( c_List_Olist_OCons @ ( v_sko__List__Xfoldl__Xinduct__1 @ SV9 ) @ ( v_sko__List__Xfoldl__Xinduct__2 @ SV9 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV9 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2403,plain,
! [SV333: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV10 @ ( c_List_Olist_OCons @ ( v_sko__List__Xconcat__Xinduct__1 @ SV10 ) @ ( v_sko__List__Xconcat__Xinduct__2 @ SV10 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2404,plain,
! [SV339: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV16 @ ( c_List_Olist_OCons @ ( v_sko__List__Xhd__Xinduct__1 @ SV16 ) @ ( v_sko__List__Xhd__Xinduct__2 @ SV16 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV16 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2405,plain,
! [SV340: $i,SV17: $i] :
( ( ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV17 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtake__Xinduct__1 @ SV17 ) @ ( v_sko__List__Xtake__Xinduct__2 @ SV17 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV17 @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2406,plain,
! [SV341: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV18 @ ( c_List_Olist_OCons @ ( v_sko__List__Xset__Xinduct__1 @ SV18 ) @ ( v_sko__List__Xset__Xinduct__2 @ SV18 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV18 @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2407,plain,
! [SV342: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV19 @ ( c_List_Olist_OCons @ ( v_sko__List__Xmap__Xinduct__1 @ SV19 ) @ ( v_sko__List__Xmap__Xinduct__2 @ SV19 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV19 @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2408,plain,
! [SV343: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV20 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinducts__1 @ SV20 ) @ ( v_sko__List__Xlist__Xinducts__2 @ SV20 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV20 @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2409,plain,
! [SV344: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV21 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ SV21 ) @ ( v_sko__List__Xlist__Xinduct__2 @ SV21 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV21 @ SV344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2410,plain,
! [SV345: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV22 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ SV22 ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ SV22 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV22 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2411,plain,
! [SV346: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV23 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremdups__Xinduct__1 @ SV23 ) @ ( v_sko__List__Xremdups__Xinduct__2 @ SV23 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV23 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2412,plain,
! [SV347: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV24 @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ SV24 ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ SV24 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV24 @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2413,plain,
! [SV348: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV25 @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ SV25 ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ SV25 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV25 @ SV348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2414,plain,
! [SV349: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV26 @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ SV26 ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ SV26 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV26 @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2415,plain,
! [SV350: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV27 @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ SV27 ) @ ( v_sko__List__Xzip__Xinduct__2 @ SV27 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV27 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2416,plain,
! [SV351: $i,SV28: $i] :
( ( ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV28 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ SV28 ) @ ( v_sko__List__Xlistset__Xinduct__2 @ SV28 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV28 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2417,plain,
! [SV352: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV29 @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ SV29 ) @ ( v_sko__List__Xremove1__Xinduct__2 @ SV29 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV29 @ SV352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2418,plain,
! [SV353: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV30 @ ( c_List_Olist_OCons @ ( v_sko__List__Xsplice__Xinduct__1 @ SV30 ) @ ( v_sko__List__Xsplice__Xinduct__2 @ SV30 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV30 @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2419,plain,
! [SV354: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV31 @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ SV31 ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ SV31 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV31 @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2420,plain,
! [SV355: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV32 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ SV32 ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ SV32 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV32 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2421,plain,
! [SV356: $i,SV33: $i] :
( ( ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV33 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ SV33 ) @ ( v_sko__List__Xlast__Xinduct__2 @ SV33 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV33 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2422,plain,
! [SV357: $i,SV34: $i] :
( ( ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV34 @ ( c_List_Olist_OCons @ ( v_sko__List__Xtl__Xinduct__1 @ SV34 ) @ ( v_sko__List__Xtl__Xinduct__2 @ SV34 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV34 @ SV357 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2423,plain,
! [SV359: $i,SV644: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV36 @ SV644 ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ SV36 @ SV644 ) @ ( c_List_Olist_ONil @ SV644 ) @ SV644 ) @ SV644 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Olist_ONil @ SV644 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV36 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2424,plain,
! [SV845: $i,SV645: $i,SV361: $i,SV38: $i] :
( ( ( class_Orderings_Olinorder @ SV38 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV361 @ ( c_List_Olinorder__class_Osort__key @ SV361 @ SV645 @ SV845 @ SV38 ) @ SV845 @ SV38 ) @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2425,plain,
! [SV957: $i,SV846: $i,SV647: $i,SV363: $i,SV40: $i] :
( ( ( c_ListOrder_Ostep1 @ SV40 @ ( c_List_Oappend @ SV363 @ SV647 @ SV846 ) @ ( c_List_Oappend @ SV363 @ SV957 @ SV846 ) @ SV846 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV40 @ SV647 @ SV957 @ SV846 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2426,plain,
! [SV958: $i,SV847: $i,SV648: $i,SV364: $i,SV41: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV41 @ SV364 @ SV648 @ SV847 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Oappend @ SV364 @ SV958 @ SV847 ) @ ( c_List_Oappend @ SV648 @ SV958 @ SV847 ) @ SV847 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2427,plain,
! [SV848: $i,SV649: $i,SV365: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ SV42 @ SV365 ) )
= $false )
| ( ( ( c_List_Ofilter @ SV42 @ ( c_List_Olist_OCons @ SV365 @ SV649 @ SV848 ) @ SV848 )
= ( c_List_Olist_OCons @ SV365 @ ( c_List_Ofilter @ SV42 @ SV649 @ SV848 ) @ SV848 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2428,plain,
! [SV43: $i,SV650: $i,SV366: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV366 @ SV650 @ SV43 ) @ SV43 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV650 @ SV43 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2429,plain,
! [SV1009: $i,SV960: $i,SV850: $i,SV653: $i,SV369: $i,SV46: $i] :
( ( ( c_List_Olist__all2 @ SV46 @ ( c_List_Otake @ SV369 @ SV653 @ SV850 ) @ ( c_List_Otake @ SV369 @ SV960 @ SV1009 ) @ SV850 @ SV1009 )
| ~ ( c_List_Olist__all2 @ SV46 @ SV653 @ SV960 @ SV850 @ SV1009 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2430,plain,
! [SV1010: $i,SV961: $i,SV851: $i,SV656: $i,SV372: $i,SV49: $i] :
( ( ( c_List_Ofoldl @ SV49 @ SV372 @ ( c_List_Olist_OCons @ SV656 @ SV851 @ SV961 ) @ SV1010 @ SV961 )
= ( c_List_Ofoldl @ SV49 @ ( hAPP @ ( hAPP @ SV49 @ SV372 ) @ SV656 ) @ SV851 @ SV1010 @ SV961 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2431,plain,
! [SV1011: $i,SV962: $i,SV852: $i,SV657: $i,SV373: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV373 ) @ SV657 ) )
| ( c_ListOrder_Ostep1 @ SV50 @ SV852 @ SV962 @ SV1011 )
| ~ ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SV852 @ ( c_List_Olist_OCons @ SV373 @ ( c_List_Olist_ONil @ SV1011 ) @ SV1011 ) @ SV1011 ) @ ( c_List_Oappend @ SV962 @ ( c_List_Olist_OCons @ SV657 @ ( c_List_Olist_ONil @ SV1011 ) @ SV1011 ) @ SV1011 ) @ SV1011 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2432,plain,
! [SV853: $i,SV662: $i,SV379: $i,SV56: $i] :
( ( ( class_Orderings_Olinorder @ SV56 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2433,plain,
! [SV1012: $i,SV963: $i,SV854: $i,SV663: $i,SV380: $i,SV57: $i] :
( ( ! [SY2476: $i] :
( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SV854 ) @ ( c_List_Oappend @ SV963 @ SV1012 @ SY2476 ) @ SV854 @ SY2476 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV663 @ SV1012 @ SV854 @ SY2476 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SV963 @ SV854 @ SY2476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2434,plain,
! [SV1013: $i,SV967: $i,SV860: $i,SV670: $i,SV389: $i,SV66: $i] :
( ( ( c_List_Olist_Olist__case @ SV66 @ SV389 @ ( c_List_Olist_OCons @ SV670 @ SV860 @ SV967 ) @ SV1013 @ SV967 )
= ( hAPP @ ( hAPP @ SV389 @ SV670 ) @ SV860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2435,plain,
! [SV1014: $i,SV968: $i,SV861: $i,SV672: $i,SV391: $i,SV68: $i] :
( ( ! [SY2477: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV391 ) @ SV672 ) )
| ~ ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SV391 @ SV861 @ SV968 ) @ ( c_List_Olist_OCons @ SV672 @ SV1014 @ SY2477 ) @ SV968 @ SY2477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2436,plain,
! [SV1015: $i,SV969: $i,SV864: $i,SV675: $i,SV394: $i,SV71: $i] :
( ( ( SV71 = SV394 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV675 @ SV394 ) @ SV71 ) )
| ~ ( c_ListOrder_Ostep1 @ SV675 @ ( c_List_Olist_OCons @ SV394 @ SV864 @ SV969 ) @ ( c_List_Olist_OCons @ SV71 @ SV1015 @ SV969 ) @ SV969 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2437,plain,
! [SV677: $i,SV73: $i,SV396: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV396 @ SV73 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV677 @ SV396 @ SV73 ) @ SV73 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2438,plain,
! [SV680: $i,SV401: $i,SV865: $i,SV78: $i] :
( ( ( c_List_Olist__all @ SV78 @ ( c_List_Olist_OCons @ SV865 @ SV401 @ SV680 ) @ SV680 )
= $false )
| ( ( c_List_Olist__all @ SV78 @ SV401 @ SV680 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2439,plain,
! [SV403: $i,SV681: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV681 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV681 @ SV80 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV681 @ SV403 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV80 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2440,plain,
! [SV866: $i,SV682: $i,SV404: $i,SV81: $i] :
( ( ( c_List_Olist__all @ SV81 @ ( c_List_Olist_OCons @ SV404 @ SV682 @ SV866 ) @ SV866 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV81 @ SV404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2441,plain,
! [SV405: $i,SV683: $i,SV82: $i] :
( ( ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV683 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV683 @ SV82 ) @ t_a ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) )
| ~ ( c_List_Olistsp @ SV683 @ SV405 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV82 @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2442,plain,
! [SV1016: $i,SV970: $i,SV867: $i,SV686: $i,SV408: $i,SV85: $i] :
( ( ( c_List_Omap @ SV85 @ ( c_List_Olist__update @ SV408 @ SV686 @ SV867 @ SV970 ) @ SV970 @ SV1016 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV85 @ SV408 @ SV970 @ SV1016 ) @ SV686 @ ( hAPP @ SV85 @ SV867 ) @ SV1016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2443,plain,
! [SV1017: $i,SV971: $i,SV868: $i,SV687: $i,SV410: $i,SV87: $i] :
( ( ( SV87 = SV410 )
| ( c_ListOrder_Ostep1 @ SV687 @ SV87 @ SV410 @ SV868 )
| ~ ( c_ListOrder_Ostep1 @ SV687 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ ( c_List_Oappend @ SV410 @ ( c_List_Olist_OCons @ SV1017 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ SV868 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2444,plain,
! [SV411: $i,SV869: $i,SV88: $i,SV688: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV688 @ SV88 @ ( tc_fun @ SV869 @ tc_bool ) ) @ SV411 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV88 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2445,plain,
! [SV412: $i,SV870: $i,SV689: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV689 @ ( tc_fun @ SV870 @ tc_bool ) ) @ SV412 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV89 @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2446,plain,
! [SV413: $i,SV871: $i,SV690: $i,SV90: $i] :
( ( ( ~ ( c_List_Olist__all @ SV90 @ SV690 @ SV871 ) )
= $true )
| ( ( ~ ( c_List_Olist__all @ SV90 @ SV413 @ SV871 ) )
= $true )
| ( ( c_List_Olist__all @ SV90 @ ( c_List_Oappend @ SV413 @ SV690 @ SV871 ) @ SV871 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2447,plain,
! [SV1018: $i,SV972: $i,SV872: $i,SV693: $i,SV417: $i,SV94: $i] :
( ( ( c_List_Ofoldl @ SV94 @ SV417 @ ( c_List_Oappend @ SV693 @ SV872 @ SV972 ) @ SV1018 @ SV972 )
= ( c_List_Ofoldl @ SV94 @ ( c_List_Ofoldl @ SV94 @ SV417 @ SV693 @ SV1018 @ SV972 ) @ SV872 @ SV1018 @ SV972 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2448,plain,
! [SV973: $i,SV874: $i,SV696: $i,SV420: $i,SV97: $i] :
( ( ( c_List_Olist__all2 @ SV97 @ ( c_List_Orev @ SV420 @ SV696 ) @ SV874 @ SV696 @ SV973 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV97 @ SV420 @ ( c_List_Orev @ SV874 @ SV973 ) @ SV696 @ SV973 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2449,plain,
! [SV974: $i,SV875: $i,SV697: $i,SV421: $i,SV98: $i] :
( ( ( c_List_Olist__all2 @ SV98 @ SV421 @ ( c_List_Orev @ SV697 @ SV875 ) @ SV974 @ SV875 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV98 @ ( c_List_Orev @ SV421 @ SV974 ) @ SV697 @ SV974 @ SV875 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2450,plain,
! [SV1019: $i,SV975: $i,SV876: $i,SV699: $i,SV424: $i,SV104: $i] :
( ( ( SV104 = SV424 )
| ( SV699 = SV876 )
| ~ ( c_ListOrder_Ostep1 @ SV975 @ ( c_List_Olist_OCons @ SV424 @ SV876 @ SV1019 ) @ ( c_List_Olist_OCons @ SV104 @ SV699 @ SV1019 ) @ SV1019 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2451,plain,
! [SV976: $i,SV877: $i,SV700: $i,SV425: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV425 ) @ SV700 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Olist_OCons @ SV425 @ SV877 @ SV976 ) @ ( c_List_Olist_OCons @ SV700 @ SV877 @ SV976 ) @ SV976 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2452,plain,
! [SV107: $i,SV702: $i,SV427: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV427 @ SV702 @ SV107 ) @ SV107 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV702 @ SV107 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2453,plain,
! [SV879: $i,SV703: $i,SV428: $i,SV108: $i] :
( ( ( class_Orderings_Olinorder @ SV108 )
= $false )
| ( ( ( c_List_Odistinct @ SV428 @ SV703 )
| ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV879 @ SV428 @ SV703 @ SV108 ) @ SV703 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2454,plain,
! [SV880: $i,SV704: $i,SV429: $i,SV109: $i] :
( ( ( class_Orderings_Olinorder @ SV109 )
= $false )
| ( ( ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV429 @ SV704 @ SV880 @ SV109 ) @ SV880 )
| ~ ( c_List_Odistinct @ SV704 @ SV880 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2455,plain,
! [SV1020: $i,SV977: $i,SV881: $i,SV705: $i,SV430: $i,SV110: $i] :
( ( ! [SY2478: $i] :
( ( c_List_Olist__all2 @ SV110 @ SV430 @ SV705 @ SV881 @ SV977 )
| ~ ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SV1020 @ SV430 @ SV881 ) @ ( c_List_Olist_OCons @ SY2478 @ SV705 @ SV977 ) @ SV881 @ SV977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2456,plain,
! [SV979: $i,SV883: $i,SV710: $i,SV438: $i,SV118: $i] :
( ( ( c_List_Olist__all2 @ SV118 @ SV438 @ SV710 @ SV883 @ SV979 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV118 @ ( c_List_Orev @ SV438 @ SV883 ) @ ( c_List_Orev @ SV710 @ SV979 ) @ SV883 @ SV979 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2457,plain,
! [SV980: $i,SV884: $i,SV711: $i,SV439: $i,SV119: $i] :
( ( ( c_List_Olist__all2 @ SV119 @ ( c_List_Orev @ SV439 @ SV711 ) @ ( c_List_Orev @ SV884 @ SV980 ) @ SV711 @ SV980 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV119 @ SV439 @ SV884 @ SV711 @ SV980 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2458,plain,
! [SV1021: $i,SV982: $i,SV886: $i,SV713: $i,SV441: $i,SV121: $i] :
( ( ( c_List_Ofoldr @ SV121 @ ( c_List_Oappend @ SV441 @ SV713 @ SV886 ) @ SV982 @ SV886 @ SV1021 )
= ( c_List_Ofoldr @ SV121 @ SV441 @ ( c_List_Ofoldr @ SV121 @ SV713 @ SV982 @ SV886 @ SV1021 ) @ SV886 @ SV1021 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2459,plain,
! [SV887: $i,SV714: $i,SV442: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ SV122 @ SV442 ) )
= $false )
| ( ( c_List_Olist__ex @ SV122 @ ( c_List_Olist_OCons @ SV442 @ SV714 @ SV887 ) @ SV887 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2460,plain,
! [SV1022: $i,SV983: $i,SV888: $i,SV715: $i,SV443: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV443 ) @ SV715 ) )
| ( SV443 = SV715 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV888 @ ( c_List_Olist_OCons @ SV443 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ ( c_List_Oappend @ SV1022 @ ( c_List_Olist_OCons @ SV715 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ SV983 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2461,plain,
! [SV1023: $i,SV984: $i,SV889: $i,SV716: $i,SV444: $i,SV124: $i] :
( ( ! [SY2479: $i] :
( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SV889 ) @ ( c_List_Olist_OCons @ SV984 @ SV1023 @ SY2479 ) @ SV889 @ SY2479 )
| ~ ( c_List_Olist__all2 @ SV124 @ SV716 @ SV1023 @ SV889 @ SY2479 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SV984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2462,plain,
! [SV1024: $i,SV985: $i,SV890: $i,SV717: $i,SV445: $i,SV125: $i] :
( ( ! [SY2480: $i] :
( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SV890 ) @ ( c_List_Olist_OCons @ SV985 @ SV1024 @ SY2480 ) @ SV890 @ SY2480 )
| ~ ( c_List_Olist__all2 @ SV125 @ SV717 @ SV1024 @ SV890 @ SY2480 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SV985 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2463,plain,
! [SV1025: $i,SV986: $i,SV891: $i,SV718: $i,SV446: $i,SV126: $i] :
( ( ! [SY2481: $i] :
( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SV891 ) @ ( c_List_Olist_OCons @ SV986 @ SV1025 @ SY2481 ) @ SV891 @ SY2481 )
| ~ ( c_List_Olist__all2 @ SV126 @ SV718 @ SV1025 @ SV891 @ SY2481 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SV986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2464,plain,
! [SV447: $i,SV892: $i,SV719: $i,SV127: $i] :
( ( ( c_List_Olist__ex @ SV127 @ SV719 @ SV892 )
= $false )
| ( ( c_List_Olist__ex @ SV127 @ ( c_List_Olist_OCons @ SV447 @ SV719 @ SV892 ) @ SV892 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2465,plain,
! [SV720: $i,SV448: $i,SV893: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ SV128 @ SV893 ) )
= $true )
| ( ( ~ ( c_List_Olist__ex @ SV128 @ ( c_List_Olist_OCons @ SV893 @ SV448 @ SV720 ) @ SV720 ) )
= $true )
| ( ( c_List_Olist__ex @ SV128 @ SV448 @ SV720 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2466,plain,
! [SV1026: $i,SV987: $i,SV894: $i,SV721: $i,SV449: $i,SV129: $i] :
( ( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SV721 @ SV894 ) @ ( c_List_Olist_OCons @ SV987 @ SV1026 @ SV894 ) @ SV894 )
| ~ ( c_List_Olistrelp @ SV129 @ SV721 @ SV1026 @ SV894 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SV987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2467,plain,
! [SV895: $i,SV722: $i,SV450: $i,SV130: $i] :
( ( ( class_Lattices_Olattice @ SV130 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ SV722 @ SV130 ) @ SV895 @ SV130 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV450 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV722 @ SV895 @ SV130 ) @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2468,plain,
! [SV896: $i,SV723: $i,SV451: $i,SV131: $i] :
( ( ( class_Lattices_Olattice @ SV131 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ SV896 @ SV131 ) @ SV131 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV451 @ SV896 @ SV131 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2469,plain,
! [SV897: $i,SV724: $i,SV452: $i,SV132: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV132 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV724 @ SV897 @ SV132 ) @ SV132 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV724 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV452 @ SV897 @ SV132 ) @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2470,plain,
! [SV898: $i,SV725: $i,SV453: $i,SV133: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV133 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ SV725 @ SV133 ) @ SV898 @ SV133 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV453 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV898 @ SV133 ) @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2471,plain,
! [SV459: $i,SV903: $i,SV731: $i,SV139: $i] :
( ( ( c_List_Omember @ SV139 @ SV731 @ SV903 )
= $false )
| ( ( c_List_Omember @ SV139 @ ( c_List_Olist_OCons @ SV459 @ SV731 @ SV903 ) @ SV903 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2472,plain,
! [SV904: $i,SV734: $i,SV462: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP @ SV142 @ SV462 ) )
= $false )
| ( ( ( c_List_OdropWhile @ SV142 @ ( c_List_Olist_OCons @ SV462 @ SV734 @ SV904 ) @ SV904 )
= ( c_List_OdropWhile @ SV142 @ SV734 @ SV904 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2473,plain,
! [SV1027: $i,SV989: $i,SV906: $i,SV736: $i,SV464: $i,SV144: $i] :
( ( ( c_ListOrder_Ostep1 @ SV144 @ SV464 @ SV736 @ SV906 )
| ( SV736 = SV464 )
| ~ ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SV989 @ SV464 @ SV906 ) @ ( c_List_Olist_OCons @ SV1027 @ SV736 @ SV906 ) @ SV906 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2474,plain,
! [SV1028: $i,SV991: $i,SV908: $i,SV741: $i,SV470: $i,SV150: $i] :
( ( ( c_List_Olist__all2 @ SV150 @ ( c_List_Odrop @ SV470 @ SV741 @ SV908 ) @ ( c_List_Odrop @ SV470 @ SV991 @ SV1028 ) @ SV908 @ SV1028 )
| ~ ( c_List_Olist__all2 @ SV150 @ SV741 @ SV991 @ SV908 @ SV1028 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2475,plain,
! [SV1029: $i,SV992: $i,SV910: $i,SV743: $i,SV472: $i,SV152: $i] :
( ( ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ ( c_List_Olist_OCons @ SV743 @ SV910 @ SV992 ) @ SV1029 @ SV992 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV472 @ SV743 ) @ SV910 ) @ ( c_List_Olist_Olist__rec @ SV152 @ SV472 @ SV910 @ SV1029 @ SV992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2476,plain,
! [SV911: $i,SV473: $i,SV153: $i,SV744: $i] :
( ( ( c_List_Odistinct @ ( c_List_Omap @ SV744 @ SV153 @ SV473 @ SV911 ) @ SV911 )
= $false )
| ( ( c_List_Odistinct @ SV153 @ SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2477,plain,
! [SV1030: $i,SV993: $i,SV912: $i,SV745: $i,SV474: $i,SV154: $i] :
( ( ( SV154 = SV474 )
| ( SV745 = SV912 )
| ~ ( c_ListOrder_Ostep1 @ SV993 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SV745 @ ( c_List_Olist_ONil @ SV1030 ) @ SV1030 ) @ SV1030 ) @ ( c_List_Oappend @ SV474 @ ( c_List_Olist_OCons @ SV912 @ ( c_List_Olist_ONil @ SV1030 ) @ SV1030 ) @ SV1030 ) @ SV1030 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2478,plain,
! [SV1031: $i,SV994: $i,SV913: $i,SV752: $i,SV481: $i,SV161: $i] :
( ( ( c_List_Ofoldr @ SV161 @ ( c_List_Olist_OCons @ SV481 @ SV752 @ SV913 ) @ SV994 @ SV913 @ SV1031 )
= ( hAPP @ ( hAPP @ SV161 @ SV481 ) @ ( c_List_Ofoldr @ SV161 @ SV752 @ SV994 @ SV913 @ SV1031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2479,plain,
! [SV1032: $i,SV995: $i,SV914: $i,SV754: $i,SV486: $i,SV166: $i] :
( ( ( c_ListOrder_Ostep1 @ SV166 @ SV486 @ SV754 @ SV914 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV995 ) @ SV1032 ) )
| ~ ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SV995 @ SV486 @ SV914 ) @ ( c_List_Olist_OCons @ SV1032 @ SV754 @ SV914 ) @ SV914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2480,plain,
! [SV996: $i,SV915: $i,SV755: $i,SV487: $i,SV167: $i] :
( ( ( c_ListOrder_Ostep1 @ SV167 @ ( c_List_Olist_OCons @ SV487 @ SV755 @ SV915 ) @ ( c_List_Olist_OCons @ SV487 @ SV996 @ SV915 ) @ SV915 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV167 @ SV755 @ SV996 @ SV915 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2481,plain,
! [SV756: $i,SV168: $i,SV488: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV488 @ SV168 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV488 @ SV756 @ SV168 ) @ SV168 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2482,plain,
! [SV757: $i,SV169: $i,SV489: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV489 @ SV169 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV757 @ SV489 @ SV169 ) @ SV169 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2483,plain,
! [SV490: $i,SV916: $i,SV758: $i,SV170: $i] :
( ( ( ~ ( c_List_Olist__all @ SV170 @ SV758 @ SV916 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV170 @ SV490 ) ) )
= $true )
| ( ( c_List_Olist__all @ SV170 @ ( c_List_Olist_OCons @ SV490 @ SV758 @ SV916 ) @ SV916 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2484,plain,
! [SV1033: $i,SV997: $i,SV917: $i,SV759: $i,SV491: $i,SV171: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV491 @ SV759 @ SV917 ) @ SV997 @ SV1033 @ SV917 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV997 @ SV1033 @ SV917 ) @ SV491 @ SV759 @ SV917 ) )
| ( SV491 = SV997 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2485,plain,
! [SV172: $i,SV492: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV492 @ SV172 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ SV492 @ SV172 ) @ SV172 )
= $true )
| ( ( class_Orderings_Olinorder @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2486,plain,
! [SV763: $i,SV496: $i,SV919: $i,SV176: $i] :
( ( ( SV176 = SV919 )
= $true )
| ( ( ~ ( c_List_Omember @ SV176 @ ( c_List_Olist_OCons @ SV919 @ SV496 @ SV763 ) @ SV763 ) )
= $true )
| ( ( c_List_Omember @ SV176 @ SV496 @ SV763 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2487,plain,
! [SV765: $i,SV178: $i,SV921: $i,SV498: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV498 @ SV921 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV178 @ SV921 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV178 @ SV498 @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV921 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2488,plain,
! [SV767: $i,SV922: $i,SV501: $i,SV181: $i] :
( ( ( c_List_Olist__all @ SV181 @ ( c_List_Oappend @ SV501 @ SV922 @ SV767 ) @ SV767 )
= $false )
| ( ( c_List_Olist__all @ SV181 @ SV501 @ SV767 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2489,plain,
! [SV768: $i,SV502: $i,SV923: $i,SV182: $i] :
( ( ( c_List_Olist__all @ SV182 @ ( c_List_Oappend @ SV923 @ SV502 @ SV768 ) @ SV768 )
= $false )
| ( ( c_List_Olist__all @ SV182 @ SV502 @ SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2490,plain,
! [SV999: $i,SV924: $i,SV770: $i,SV504: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_Olist__case @ SV504 @ SV770 @ ( c_List_Olist_OCons @ SV924 @ SV999 @ t_b ) @ t_a @ t_b ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV184 @ ( hAPP @ ( hAPP @ SV770 @ SV924 ) @ SV999 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2491,plain,
! [SV1000: $i,SV925: $i,SV771: $i,SV505: $i,SV185: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_List_Olist_Olist__case @ SV505 @ SV771 @ ( c_List_Olist_OCons @ SV925 @ SV1000 @ t_b ) @ t_a @ t_b ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV185 @ ( hAPP @ ( hAPP @ SV771 @ SV925 ) @ SV1000 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2492,plain,
! [SV186: $i,SV772: $i,SV506: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ SV506 @ SV772 @ SV186 ) @ SV186 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV772 @ SV186 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2493,plain,
! [SV192: $i,SV778: $i,SV512: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV512 @ SV778 @ SV192 ) @ SV192 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV778 @ SV192 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2494,plain,
! [SV519: $i,SV931: $i,SV200: $i,SV779: $i] :
( ( ( c_List_Olist__all2 @ SV779 @ SV200 @ ( c_List_Olist_ONil @ SV931 ) @ SV519 @ SV931 )
= $false )
| ( ( SV200
= ( c_List_Olist_ONil @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2495,plain,
! [SV520: $i,SV201: $i,SV932: $i,SV780: $i] :
( ( ( c_List_Olist__all2 @ SV780 @ ( c_List_Olist_ONil @ SV932 ) @ SV201 @ SV932 @ SV520 )
= $false )
| ( ( SV201
= ( c_List_Olist_ONil @ SV520 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2496,plain,
! [SV526: $i,SV782: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Olist_ONil @ SV782 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV208 @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV208 @ SV782 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV208 @ SV526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2497,plain,
! [SV575: $i,SV939: $i,SV799: $i,SV263: $i] :
( ( ( ~ ( c_List_Olistsp @ SV263 @ SV799 @ SV939 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV263 @ SV575 @ SV939 ) )
= $true )
| ( ( c_List_Olistsp @ SV263 @ ( c_List_Oappend @ SV575 @ SV799 @ SV939 ) @ SV939 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2498,plain,
! [SV265: $i,SV801: $i,SV940: $i,SV577: $i] :
( ( ( ~ ( c_List_Olistsp @ SV577 @ SV940 @ SV801 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV265 @ SV940 @ SV801 ) )
= $true )
| ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV265 @ SV577 @ ( tc_fun @ SV801 @ tc_bool ) ) @ SV940 @ SV801 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2499,plain,
! [SV802: $i,SV578: $i,SV941: $i,SV266: $i] :
( ( ( c_List_Olistsp @ SV266 @ ( c_List_Oappend @ SV941 @ SV578 @ SV802 ) @ SV802 )
= $false )
| ( ( c_List_Olistsp @ SV266 @ SV578 @ SV802 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2500,plain,
! [SV803: $i,SV942: $i,SV579: $i,SV267: $i] :
( ( ( c_List_Olistsp @ SV267 @ ( c_List_Oappend @ SV579 @ SV942 @ SV803 ) @ SV803 )
= $false )
| ( ( c_List_Olistsp @ SV267 @ SV579 @ SV803 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2501,plain,
! [SV581: $i,SV804: $i,SV270: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV270 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV804 @ SV581 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV804 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV804 @ SV270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV581 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2502,plain,
! [SV582: $i,SV805: $i,SV271: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV271 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV805 @ SV582 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV805 @ SV271 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2503,plain,
! [SV583: $i,SV806: $i,SV272: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV272 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV806 @ SV583 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV806 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV806 @ SV272 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV583 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2504,plain,
! [SV584: $i,SV807: $i,SV273: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV273 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV807 @ SV584 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV273 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV807 @ SV273 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV273 @ SV584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2505,plain,
! [SV587: $i,SV808: $i,SV276: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV276 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV808 @ SV587 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV808 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV808 @ SV276 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV276 @ SV587 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2506,plain,
! [SV588: $i,SV809: $i,SV277: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV277 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV809 @ SV588 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV809 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV809 @ SV277 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV277 @ SV588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2507,plain,
! [SV943: $i,SV811: $i,SV594: $i,SV283: $i] :
( ( ( ( c_List_Orev @ SV283 @ SV594 )
= ( c_List_Olist_OCons @ SV811 @ SV943 @ SV594 ) )
= $false )
| ( ( SV283
= ( c_List_Oappend @ ( c_List_Orev @ SV943 @ SV594 ) @ ( c_List_Olist_OCons @ SV811 @ ( c_List_Olist_ONil @ SV594 ) @ SV594 ) @ SV594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2508,plain,
! [SV1002: $i,SV944: $i,SV814: $i,SV597: $i,SV287: $i] :
( ( ( ( c_List_Oappend @ SV287 @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 )
!= ( c_List_Oappend @ SV944 @ ( c_List_Olist_OCons @ SV1002 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 ) )
= $true )
| ( ( SV597 = SV1002 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2509,plain,
! [SV1003: $i,SV945: $i,SV816: $i,SV599: $i,SV289: $i] :
( ( ( ( c_List_Oappend @ SV289 @ ( c_List_Olist_OCons @ SV599 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 )
!= ( c_List_Oappend @ SV945 @ ( c_List_Olist_OCons @ SV1003 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 ) )
= $true )
| ( ( SV289 = SV945 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2510,plain,
! [SV1004: $i,SV946: $i,SV821: $i,SV606: $i,SV297: $i] :
( ( ( ( c_List_Olist_OCons @ SV297 @ SV606 @ SV821 )
!= ( c_List_Ofilter @ SV946 @ SV1004 @ SV821 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV946 @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2511,plain,
! [SV1005: $i,SV947: $i,SV822: $i,SV607: $i,SV298: $i] :
( ( ( ( c_List_Olist_OCons @ SV298 @ SV607 @ SV822 )
!= ( c_List_Olist_OCons @ SV947 @ SV1005 @ SV822 ) )
= $true )
| ( ( SV607 = SV1005 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2512,plain,
! [SV948: $i,SV825: $i,SV611: $i,SV302: $i] :
( ( ( ( c_List_Oappend @ SV302 @ SV611 @ SV825 )
= ( c_List_Oappend @ SV948 @ SV611 @ SV825 ) )
= $false )
| ( ( SV302 = SV948 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2513,plain,
! [SV949: $i,SV827: $i,SV614: $i,SV305: $i] :
( ( ( ( c_List_Omap @ SV305 @ SV614 @ SV827 @ SV949 )
= ( c_List_Olist_ONil @ SV949 ) )
= $false )
| ( ( SV614
= ( c_List_Olist_ONil @ SV827 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2514,plain,
! [SV1006: $i,SV950: $i,SV828: $i,SV615: $i,SV306: $i] :
( ( ( ( c_List_Olist_OCons @ SV306 @ SV615 @ SV828 )
!= ( c_List_Olist_OCons @ SV950 @ SV1006 @ SV828 ) )
= $true )
| ( ( SV306 = SV950 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2515,plain,
! [SV951: $i,SV830: $i,SV618: $i,SV309: $i] :
( ( ( ( c_List_Olist__update @ SV309 @ SV618 @ SV830 @ SV951 )
= ( c_List_Olist_ONil @ SV951 ) )
= $false )
| ( ( SV309
= ( c_List_Olist_ONil @ SV951 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2516,plain,
! [SV952: $i,SV831: $i,SV619: $i,SV310: $i] :
( ( ( ( c_List_Olist_ONil @ SV310 )
= ( c_List_Omap @ SV619 @ SV831 @ SV952 @ SV310 ) )
= $false )
| ( ( SV831
= ( c_List_Olist_ONil @ SV952 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2517,plain,
! [SV1007: $i,SV953: $i,SV835: $i,SV625: $i,SV316: $i] :
( ( ( ( c_List_OdropWhile @ SV316 @ SV625 @ SV835 )
!= ( c_List_Olist_OCons @ SV953 @ SV1007 @ SV835 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV316 @ SV953 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2518,plain,
! [SV954: $i,SV837: $i,SV628: $i,SV319: $i] :
( ( ( ( c_List_Oappend @ SV319 @ SV628 @ SV837 )
= ( c_List_Oappend @ SV319 @ SV954 @ SV837 ) )
= $false )
| ( ( SV628 = SV954 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2519,plain,
! [SV1008: $i,SV955: $i,SV839: $i,SV631: $i,SV322: $i] :
( ( ( ( c_List_Ofilter @ SV322 @ SV631 @ SV839 )
!= ( c_List_Olist_OCons @ SV955 @ SV1008 @ SV839 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV322 @ SV955 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2520,plain,
! [SV359: $i,SV644: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Olist_ONil @ SV644 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV36 @ ( c_List_Oappend @ ( c_List_Osko__List__Xrev__induct__1__2 @ SV36 @ SV644 ) @ ( c_List_Olist_OCons @ ( c_List_Osko__List__Xrev__induct__1__1 @ SV36 @ SV644 ) @ ( c_List_Olist_ONil @ SV644 ) @ SV644 ) @ SV644 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV36 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2521,plain,
! [SV363: $i,SV846: $i,SV957: $i,SV647: $i,SV40: $i] :
( ( ( c_ListOrder_Ostep1 @ SV40 @ SV647 @ SV957 @ SV846 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV40 @ ( c_List_Oappend @ SV363 @ SV647 @ SV846 ) @ ( c_List_Oappend @ SV363 @ SV957 @ SV846 ) @ SV846 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2522,plain,
! [SV958: $i,SV847: $i,SV648: $i,SV364: $i,SV41: $i] :
( ( ( c_ListOrder_Ostep1 @ SV41 @ SV364 @ SV648 @ SV847 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV41 @ ( c_List_Oappend @ SV364 @ SV958 @ SV847 ) @ ( c_List_Oappend @ SV648 @ SV958 @ SV847 ) @ SV847 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2523,plain,
! [SV366: $i,SV43: $i,SV650: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV650 @ SV43 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV366 @ SV650 @ SV43 ) @ SV43 )
= $true )
| ( ( class_Orderings_Olinorder @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2524,plain,
! [SV1009: $i,SV960: $i,SV850: $i,SV653: $i,SV369: $i,SV46: $i] :
( ( ( c_List_Olist__all2 @ SV46 @ ( c_List_Otake @ SV369 @ SV653 @ SV850 ) @ ( c_List_Otake @ SV369 @ SV960 @ SV1009 ) @ SV850 @ SV1009 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV46 @ SV653 @ SV960 @ SV850 @ SV1009 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2525,plain,
! [SV1011: $i,SV962: $i,SV852: $i,SV657: $i,SV373: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV373 ) @ SV657 ) )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV50 @ SV852 @ SV962 @ SV1011 )
| ~ ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SV852 @ ( c_List_Olist_OCons @ SV373 @ ( c_List_Olist_ONil @ SV1011 ) @ SV1011 ) @ SV1011 ) @ ( c_List_Oappend @ SV962 @ ( c_List_Olist_OCons @ SV657 @ ( c_List_Olist_ONil @ SV1011 ) @ SV1011 ) @ SV1011 ) @ SV1011 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2526,plain,
! [SV853: $i,SV56: $i,SV662: $i,SV379: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 ) @ SV56 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2527,plain,
! [SV1034: $i,SV1012: $i,SV963: $i,SV854: $i,SV663: $i,SV380: $i,SV57: $i] :
( ( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SV854 ) @ ( c_List_Oappend @ SV963 @ SV1012 @ SV1034 ) @ SV854 @ SV1034 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV663 @ SV1012 @ SV854 @ SV1034 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SV963 @ SV854 @ SV1034 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2528,plain,
! [SV1035: $i,SV1014: $i,SV968: $i,SV861: $i,SV672: $i,SV391: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV391 ) @ SV672 ) )
| ~ ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SV391 @ SV861 @ SV968 ) @ ( c_List_Olist_OCons @ SV672 @ SV1014 @ SV1035 ) @ SV968 @ SV1035 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(2529,plain,
! [SV1015: $i,SV969: $i,SV864: $i,SV675: $i,SV394: $i,SV71: $i] :
( ( ( SV71 = SV394 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV675 @ SV394 ) @ SV71 ) )
| ~ ( c_ListOrder_Ostep1 @ SV675 @ ( c_List_Olist_OCons @ SV394 @ SV864 @ SV969 ) @ ( c_List_Olist_OCons @ SV71 @ SV1015 @ SV969 ) @ SV969 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2530,plain,
! [SV73: $i,SV396: $i,SV677: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV677 @ SV396 @ SV73 ) @ SV73 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV396 @ SV73 )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2531,plain,
! [SV403: $i,SV681: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV681 @ SV403 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV681 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV681 @ SV80 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV80 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(2532,plain,
! [SV405: $i,SV683: $i,SV82: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV683 @ SV405 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV683 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV683 @ SV82 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV82 @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2533,plain,
! [SV1017: $i,SV971: $i,SV868: $i,SV687: $i,SV410: $i,SV87: $i] :
( ( ( SV87 = SV410 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV687 @ SV87 @ SV410 @ SV868 )
| ~ ( c_ListOrder_Ostep1 @ SV687 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ ( c_List_Oappend @ SV410 @ ( c_List_Olist_OCons @ SV1017 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ SV868 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2534,plain,
! [SV413: $i,SV871: $i,SV690: $i,SV90: $i] :
( ( ( c_List_Olist__all @ SV90 @ SV690 @ SV871 )
= $false )
| ( ( ~ ( c_List_Olist__all @ SV90 @ SV413 @ SV871 ) )
= $true )
| ( ( c_List_Olist__all @ SV90 @ ( c_List_Oappend @ SV413 @ SV690 @ SV871 ) @ SV871 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2535,plain,
! [SV696: $i,SV973: $i,SV874: $i,SV420: $i,SV97: $i] :
( ( ( c_List_Olist__all2 @ SV97 @ SV420 @ ( c_List_Orev @ SV874 @ SV973 ) @ SV696 @ SV973 )
= $false )
| ( ( c_List_Olist__all2 @ SV97 @ ( c_List_Orev @ SV420 @ SV696 ) @ SV874 @ SV696 @ SV973 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2536,plain,
! [SV875: $i,SV697: $i,SV974: $i,SV421: $i,SV98: $i] :
( ( ( c_List_Olist__all2 @ SV98 @ ( c_List_Orev @ SV421 @ SV974 ) @ SV697 @ SV974 @ SV875 )
= $false )
| ( ( c_List_Olist__all2 @ SV98 @ SV421 @ ( c_List_Orev @ SV697 @ SV875 ) @ SV974 @ SV875 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2537,plain,
! [SV1019: $i,SV975: $i,SV876: $i,SV699: $i,SV424: $i,SV104: $i] :
( ( ( SV104 = SV424 )
= $true )
| ( ( ( SV699 = SV876 )
| ~ ( c_ListOrder_Ostep1 @ SV975 @ ( c_List_Olist_OCons @ SV424 @ SV876 @ SV1019 ) @ ( c_List_Olist_OCons @ SV104 @ SV699 @ SV1019 ) @ SV1019 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(2538,plain,
! [SV976: $i,SV877: $i,SV700: $i,SV425: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV105 @ SV425 ) @ SV700 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV105 @ ( c_List_Olist_OCons @ SV425 @ SV877 @ SV976 ) @ ( c_List_Olist_OCons @ SV700 @ SV877 @ SV976 ) @ SV976 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2539,plain,
! [SV427: $i,SV107: $i,SV702: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV702 @ SV107 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV427 @ SV702 @ SV107 ) @ SV107 )
= $true )
| ( ( class_Orderings_Olinorder @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2540,plain,
! [SV108: $i,SV879: $i,SV703: $i,SV428: $i] :
( ( ( c_List_Odistinct @ SV428 @ SV703 )
= $true )
| ( ( ~ ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV879 @ SV428 @ SV703 @ SV108 ) @ SV703 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2541,plain,
! [SV109: $i,SV880: $i,SV704: $i,SV429: $i] :
( ( ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV429 @ SV704 @ SV880 @ SV109 ) @ SV880 )
= $true )
| ( ( ~ ( c_List_Odistinct @ SV704 @ SV880 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2542,plain,
! [SV1036: $i,SV1020: $i,SV977: $i,SV881: $i,SV705: $i,SV430: $i,SV110: $i] :
( ( ( c_List_Olist__all2 @ SV110 @ SV430 @ SV705 @ SV881 @ SV977 )
| ~ ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SV1020 @ SV430 @ SV881 ) @ ( c_List_Olist_OCons @ SV1036 @ SV705 @ SV977 ) @ SV881 @ SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2543,plain,
! [SV979: $i,SV710: $i,SV883: $i,SV438: $i,SV118: $i] :
( ( ( c_List_Olist__all2 @ SV118 @ ( c_List_Orev @ SV438 @ SV883 ) @ ( c_List_Orev @ SV710 @ SV979 ) @ SV883 @ SV979 )
= $false )
| ( ( c_List_Olist__all2 @ SV118 @ SV438 @ SV710 @ SV883 @ SV979 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2544,plain,
! [SV980: $i,SV711: $i,SV884: $i,SV439: $i,SV119: $i] :
( ( ( c_List_Olist__all2 @ SV119 @ SV439 @ SV884 @ SV711 @ SV980 )
= $false )
| ( ( c_List_Olist__all2 @ SV119 @ ( c_List_Orev @ SV439 @ SV711 ) @ ( c_List_Orev @ SV884 @ SV980 ) @ SV711 @ SV980 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2545,plain,
! [SV1022: $i,SV983: $i,SV888: $i,SV715: $i,SV443: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV443 ) @ SV715 ) )
= $true )
| ( ( ( SV443 = SV715 )
| ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV888 @ ( c_List_Olist_OCons @ SV443 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ ( c_List_Oappend @ SV1022 @ ( c_List_Olist_OCons @ SV715 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ SV983 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2546,plain,
! [SV1037: $i,SV1023: $i,SV984: $i,SV889: $i,SV716: $i,SV444: $i,SV124: $i] :
( ( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SV889 ) @ ( c_List_Olist_OCons @ SV984 @ SV1023 @ SV1037 ) @ SV889 @ SV1037 )
| ~ ( c_List_Olist__all2 @ SV124 @ SV716 @ SV1023 @ SV889 @ SV1037 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SV984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2547,plain,
! [SV1038: $i,SV1024: $i,SV985: $i,SV890: $i,SV717: $i,SV445: $i,SV125: $i] :
( ( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SV890 ) @ ( c_List_Olist_OCons @ SV985 @ SV1024 @ SV1038 ) @ SV890 @ SV1038 )
| ~ ( c_List_Olist__all2 @ SV125 @ SV717 @ SV1024 @ SV890 @ SV1038 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SV985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(2548,plain,
! [SV1039: $i,SV1025: $i,SV986: $i,SV891: $i,SV718: $i,SV446: $i,SV126: $i] :
( ( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SV891 ) @ ( c_List_Olist_OCons @ SV986 @ SV1025 @ SV1039 ) @ SV891 @ SV1039 )
| ~ ( c_List_Olist__all2 @ SV126 @ SV718 @ SV1025 @ SV891 @ SV1039 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SV986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2549,plain,
! [SV720: $i,SV448: $i,SV893: $i,SV128: $i] :
( ( ( c_List_Olist__ex @ SV128 @ ( c_List_Olist_OCons @ SV893 @ SV448 @ SV720 ) @ SV720 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV128 @ SV893 ) )
= $true )
| ( ( c_List_Olist__ex @ SV128 @ SV448 @ SV720 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2550,plain,
! [SV1026: $i,SV987: $i,SV894: $i,SV721: $i,SV449: $i,SV129: $i] :
( ( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SV721 @ SV894 ) @ ( c_List_Olist_OCons @ SV987 @ SV1026 @ SV894 ) @ SV894 )
= $true )
| ( ( ~ ( c_List_Olistrelp @ SV129 @ SV721 @ SV1026 @ SV894 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SV987 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2466]) ).
thf(2551,plain,
! [SV1027: $i,SV989: $i,SV906: $i,SV736: $i,SV464: $i,SV144: $i] :
( ( ( c_ListOrder_Ostep1 @ SV144 @ SV464 @ SV736 @ SV906 )
= $true )
| ( ( ( SV736 = SV464 )
| ~ ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SV989 @ SV464 @ SV906 ) @ ( c_List_Olist_OCons @ SV1027 @ SV736 @ SV906 ) @ SV906 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2552,plain,
! [SV1028: $i,SV991: $i,SV908: $i,SV741: $i,SV470: $i,SV150: $i] :
( ( ( c_List_Olist__all2 @ SV150 @ ( c_List_Odrop @ SV470 @ SV741 @ SV908 ) @ ( c_List_Odrop @ SV470 @ SV991 @ SV1028 ) @ SV908 @ SV1028 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV150 @ SV741 @ SV991 @ SV908 @ SV1028 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2553,plain,
! [SV1030: $i,SV993: $i,SV912: $i,SV745: $i,SV474: $i,SV154: $i] :
( ( ( SV154 = SV474 )
= $true )
| ( ( ( SV745 = SV912 )
| ~ ( c_ListOrder_Ostep1 @ SV993 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SV745 @ ( c_List_Olist_ONil @ SV1030 ) @ SV1030 ) @ SV1030 ) @ ( c_List_Oappend @ SV474 @ ( c_List_Olist_OCons @ SV912 @ ( c_List_Olist_ONil @ SV1030 ) @ SV1030 ) @ SV1030 ) @ SV1030 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2554,plain,
! [SV1032: $i,SV995: $i,SV914: $i,SV754: $i,SV486: $i,SV166: $i] :
( ( ( c_ListOrder_Ostep1 @ SV166 @ SV486 @ SV754 @ SV914 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV995 ) @ SV1032 ) )
| ~ ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SV995 @ SV486 @ SV914 ) @ ( c_List_Olist_OCons @ SV1032 @ SV754 @ SV914 ) @ SV914 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(2555,plain,
! [SV487: $i,SV915: $i,SV996: $i,SV755: $i,SV167: $i] :
( ( ( c_ListOrder_Ostep1 @ SV167 @ SV755 @ SV996 @ SV915 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV167 @ ( c_List_Olist_OCons @ SV487 @ SV755 @ SV915 ) @ ( c_List_Olist_OCons @ SV487 @ SV996 @ SV915 ) @ SV915 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2556,plain,
! [SV168: $i,SV756: $i,SV488: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV488 @ SV756 @ SV168 ) @ SV168 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV488 @ SV168 )
= $true )
| ( ( class_Orderings_Olinorder @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2557,plain,
! [SV169: $i,SV489: $i,SV757: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV757 @ SV489 @ SV169 ) @ SV169 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV489 @ SV169 )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2558,plain,
! [SV490: $i,SV916: $i,SV758: $i,SV170: $i] :
( ( ( c_List_Olist__all @ SV170 @ SV758 @ SV916 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV170 @ SV490 ) ) )
= $true )
| ( ( c_List_Olist__all @ SV170 @ ( c_List_Olist_OCons @ SV490 @ SV758 @ SV916 ) @ SV916 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2559,plain,
! [SV1033: $i,SV997: $i,SV917: $i,SV759: $i,SV491: $i,SV171: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV491 @ SV759 @ SV917 ) @ SV997 @ SV1033 @ SV917 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV171 @ SV997 @ SV1033 @ SV917 ) @ SV491 @ SV759 @ SV917 ) )
= $true )
| ( ( SV491 = SV997 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2560,plain,
! [SV763: $i,SV496: $i,SV919: $i,SV176: $i] :
( ( ( c_List_Omember @ SV176 @ ( c_List_Olist_OCons @ SV919 @ SV496 @ SV763 ) @ SV763 )
= $false )
| ( ( SV176 = SV919 )
= $true )
| ( ( c_List_Omember @ SV176 @ SV496 @ SV763 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2561,plain,
! [SV765: $i,SV178: $i,SV921: $i,SV498: $i] :
( ( ( hBOOL @ ( hAPP @ SV498 @ SV921 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV178 @ SV921 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV178 @ SV498 @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV921 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2562,plain,
! [SV999: $i,SV924: $i,SV770: $i,SV504: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ SV184 @ ( c_List_Olist_Olist__case @ SV504 @ SV770 @ ( c_List_Olist_OCons @ SV924 @ SV999 @ t_b ) @ t_a @ t_b ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV184 @ ( hAPP @ ( hAPP @ SV770 @ SV924 ) @ SV999 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2563,plain,
! [SV1000: $i,SV925: $i,SV771: $i,SV505: $i,SV185: $i] :
( ( ( hBOOL @ ( hAPP @ SV185 @ ( c_List_Olist_Olist__case @ SV505 @ SV771 @ ( c_List_Olist_OCons @ SV925 @ SV1000 @ t_b ) @ t_a @ t_b ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV185 @ ( hAPP @ ( hAPP @ SV771 @ SV925 ) @ SV1000 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2564,plain,
! [SV506: $i,SV186: $i,SV772: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV772 @ SV186 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ SV506 @ SV772 @ SV186 ) @ SV186 )
= $true )
| ( ( class_Orderings_Olinorder @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2565,plain,
! [SV512: $i,SV192: $i,SV778: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV778 @ SV192 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ SV512 @ SV778 @ SV192 ) @ SV192 )
= $true )
| ( ( class_Orderings_Olinorder @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2566,plain,
! [SV575: $i,SV939: $i,SV799: $i,SV263: $i] :
( ( ( c_List_Olistsp @ SV263 @ SV799 @ SV939 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV263 @ SV575 @ SV939 ) )
= $true )
| ( ( c_List_Olistsp @ SV263 @ ( c_List_Oappend @ SV575 @ SV799 @ SV939 ) @ SV939 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2567,plain,
! [SV265: $i,SV801: $i,SV940: $i,SV577: $i] :
( ( ( c_List_Olistsp @ SV577 @ SV940 @ SV801 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV265 @ SV940 @ SV801 ) )
= $true )
| ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV265 @ SV577 @ ( tc_fun @ SV801 @ tc_bool ) ) @ SV940 @ SV801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2568,plain,
! [SV581: $i,SV804: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ SV270 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV804 @ SV581 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV804 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV804 @ SV270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV581 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2569,plain,
! [SV582: $i,SV805: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ SV271 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV805 @ SV582 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV805 @ SV271 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV582 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2570,plain,
! [SV583: $i,SV806: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ SV272 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV806 @ SV583 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV806 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV806 @ SV272 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV583 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2571,plain,
! [SV584: $i,SV807: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ SV273 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV807 @ SV584 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV273 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV807 @ SV273 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV273 @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2572,plain,
! [SV587: $i,SV808: $i,SV276: $i] :
( ( ( hBOOL @ ( hAPP @ SV276 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV808 @ SV587 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV808 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV808 @ SV276 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV276 @ SV587 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2573,plain,
! [SV588: $i,SV809: $i,SV277: $i] :
( ( ( hBOOL @ ( hAPP @ SV277 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV809 @ SV588 @ t_a ) )
= $true )
| ( ( c_List_Olistsp @ SV809 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV809 @ SV277 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV277 @ SV588 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2574,plain,
! [SV1002: $i,SV944: $i,SV814: $i,SV597: $i,SV287: $i] :
( ( ( ( c_List_Oappend @ SV287 @ ( c_List_Olist_OCons @ SV597 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 )
= ( c_List_Oappend @ SV944 @ ( c_List_Olist_OCons @ SV1002 @ ( c_List_Olist_ONil @ SV814 ) @ SV814 ) @ SV814 ) )
= $false )
| ( ( SV597 = SV1002 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2575,plain,
! [SV1003: $i,SV945: $i,SV816: $i,SV599: $i,SV289: $i] :
( ( ( ( c_List_Oappend @ SV289 @ ( c_List_Olist_OCons @ SV599 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 )
= ( c_List_Oappend @ SV945 @ ( c_List_Olist_OCons @ SV1003 @ ( c_List_Olist_ONil @ SV816 ) @ SV816 ) @ SV816 ) )
= $false )
| ( ( SV289 = SV945 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2509]) ).
thf(2576,plain,
! [SV1004: $i,SV946: $i,SV821: $i,SV606: $i,SV297: $i] :
( ( ( ( c_List_Olist_OCons @ SV297 @ SV606 @ SV821 )
= ( c_List_Ofilter @ SV946 @ SV1004 @ SV821 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV946 @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2577,plain,
! [SV1005: $i,SV947: $i,SV822: $i,SV607: $i,SV298: $i] :
( ( ( ( c_List_Olist_OCons @ SV298 @ SV607 @ SV822 )
= ( c_List_Olist_OCons @ SV947 @ SV1005 @ SV822 ) )
= $false )
| ( ( SV607 = SV1005 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2578,plain,
! [SV1006: $i,SV950: $i,SV828: $i,SV615: $i,SV306: $i] :
( ( ( ( c_List_Olist_OCons @ SV306 @ SV615 @ SV828 )
= ( c_List_Olist_OCons @ SV950 @ SV1006 @ SV828 ) )
= $false )
| ( ( SV306 = SV950 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2579,plain,
! [SV1007: $i,SV953: $i,SV835: $i,SV625: $i,SV316: $i] :
( ( ( ( c_List_OdropWhile @ SV316 @ SV625 @ SV835 )
= ( c_List_Olist_OCons @ SV953 @ SV1007 @ SV835 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV316 @ SV953 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2580,plain,
! [SV1008: $i,SV955: $i,SV839: $i,SV631: $i,SV322: $i] :
( ( ( ( c_List_Ofilter @ SV322 @ SV631 @ SV839 )
= ( c_List_Olist_OCons @ SV955 @ SV1008 @ SV839 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV322 @ SV955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2581,plain,
! [SV369: $i,SV1009: $i,SV850: $i,SV960: $i,SV653: $i,SV46: $i] :
( ( ( c_List_Olist__all2 @ SV46 @ SV653 @ SV960 @ SV850 @ SV1009 )
= $false )
| ( ( c_List_Olist__all2 @ SV46 @ ( c_List_Otake @ SV369 @ SV653 @ SV850 ) @ ( c_List_Otake @ SV369 @ SV960 @ SV1009 ) @ SV850 @ SV1009 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2582,plain,
! [SV657: $i,SV373: $i,SV1011: $i,SV962: $i,SV852: $i,SV50: $i] :
( ( ( c_ListOrder_Ostep1 @ SV50 @ SV852 @ SV962 @ SV1011 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SV852 @ ( c_List_Olist_OCons @ SV373 @ ( c_List_Olist_ONil @ SV1011 ) @ SV1011 ) @ SV1011 ) @ ( c_List_Oappend @ SV962 @ ( c_List_Olist_OCons @ SV657 @ ( c_List_Olist_ONil @ SV1011 ) @ SV1011 ) @ SV1011 ) @ SV1011 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV373 ) @ SV657 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2583,plain,
! [SV56: $i,SV662: $i,SV379: $i,SV853: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV853 @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 ) @ SV56 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV379 @ SV662 @ SV56 ) @ SV56 )
= $true )
| ( ( class_Orderings_Olinorder @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2584,plain,
! [SV1034: $i,SV1012: $i,SV963: $i,SV854: $i,SV663: $i,SV380: $i,SV57: $i] :
( ( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SV854 ) @ ( c_List_Oappend @ SV963 @ SV1012 @ SV1034 ) @ SV854 @ SV1034 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV57 @ SV663 @ SV1012 @ SV854 @ SV1034 )
| ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SV963 @ SV854 @ SV1034 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2585,plain,
! [SV1035: $i,SV1014: $i,SV968: $i,SV861: $i,SV672: $i,SV391: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV391 ) @ SV672 ) )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SV391 @ SV861 @ SV968 ) @ ( c_List_Olist_OCons @ SV672 @ SV1014 @ SV1035 ) @ SV968 @ SV1035 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2586,plain,
! [SV1015: $i,SV969: $i,SV864: $i,SV71: $i,SV394: $i,SV675: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV675 @ SV394 ) @ SV71 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV675 @ ( c_List_Olist_OCons @ SV394 @ SV864 @ SV969 ) @ ( c_List_Olist_OCons @ SV71 @ SV1015 @ SV969 ) @ SV969 ) )
= $true )
| ( ( SV71 = SV394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2529]) ).
thf(2587,plain,
! [SV403: $i,SV681: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV681 @ SV403 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV681 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV681 @ SV80 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV80 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2588,plain,
! [SV405: $i,SV683: $i,SV82: $i] :
( ( ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV683 @ SV405 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV683 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV683 @ SV82 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV82 @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2589,plain,
! [SV1017: $i,SV971: $i,SV868: $i,SV410: $i,SV87: $i,SV687: $i] :
( ( ( c_ListOrder_Ostep1 @ SV687 @ SV87 @ SV410 @ SV868 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV687 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ ( c_List_Oappend @ SV410 @ ( c_List_Olist_OCons @ SV1017 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ SV868 ) )
= $true )
| ( ( SV87 = SV410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2590,plain,
! [SV690: $i,SV871: $i,SV413: $i,SV90: $i] :
( ( ( c_List_Olist__all @ SV90 @ SV413 @ SV871 )
= $false )
| ( ( c_List_Olist__all @ SV90 @ SV690 @ SV871 )
= $false )
| ( ( c_List_Olist__all @ SV90 @ ( c_List_Oappend @ SV413 @ SV690 @ SV871 ) @ SV871 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2591,plain,
! [SV104: $i,SV1019: $i,SV424: $i,SV975: $i,SV876: $i,SV699: $i] :
( ( ( SV699 = SV876 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV975 @ ( c_List_Olist_OCons @ SV424 @ SV876 @ SV1019 ) @ ( c_List_Olist_OCons @ SV104 @ SV699 @ SV1019 ) @ SV1019 ) )
= $true )
| ( ( SV104 = SV424 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2592,plain,
! [SV108: $i,SV703: $i,SV428: $i,SV879: $i] :
( ( ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV879 @ SV428 @ SV703 @ SV108 ) @ SV703 )
= $false )
| ( ( c_List_Odistinct @ SV428 @ SV703 )
= $true )
| ( ( class_Orderings_Olinorder @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2593,plain,
! [SV109: $i,SV429: $i,SV880: $i,SV704: $i] :
( ( ( c_List_Odistinct @ SV704 @ SV880 )
= $false )
| ( ( c_List_Odistinct @ ( c_List_Olinorder__class_Osort__key @ SV429 @ SV704 @ SV880 @ SV109 ) @ SV880 )
= $true )
| ( ( class_Orderings_Olinorder @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2594,plain,
! [SV1036: $i,SV1020: $i,SV977: $i,SV881: $i,SV705: $i,SV430: $i,SV110: $i] :
( ( ( c_List_Olist__all2 @ SV110 @ SV430 @ SV705 @ SV881 @ SV977 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SV1020 @ SV430 @ SV881 ) @ ( c_List_Olist_OCons @ SV1036 @ SV705 @ SV977 ) @ SV881 @ SV977 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2542]) ).
thf(2595,plain,
! [SV1022: $i,SV983: $i,SV888: $i,SV123: $i,SV715: $i,SV443: $i] :
( ( ( SV443 = SV715 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV888 @ ( c_List_Olist_OCons @ SV443 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ ( c_List_Oappend @ SV1022 @ ( c_List_Olist_OCons @ SV715 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ SV983 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV443 ) @ SV715 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2596,plain,
! [SV1037: $i,SV1023: $i,SV984: $i,SV889: $i,SV716: $i,SV444: $i,SV124: $i] :
( ( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SV889 ) @ ( c_List_Olist_OCons @ SV984 @ SV1023 @ SV1037 ) @ SV889 @ SV1037 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV124 @ SV716 @ SV1023 @ SV889 @ SV1037 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SV984 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2597,plain,
! [SV1038: $i,SV1024: $i,SV985: $i,SV890: $i,SV717: $i,SV445: $i,SV125: $i] :
( ( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SV890 ) @ ( c_List_Olist_OCons @ SV985 @ SV1024 @ SV1038 ) @ SV890 @ SV1038 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV125 @ SV717 @ SV1024 @ SV890 @ SV1038 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SV985 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2598,plain,
! [SV1039: $i,SV1025: $i,SV986: $i,SV891: $i,SV718: $i,SV446: $i,SV126: $i] :
( ( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SV891 ) @ ( c_List_Olist_OCons @ SV986 @ SV1025 @ SV1039 ) @ SV891 @ SV1039 )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV126 @ SV718 @ SV1025 @ SV891 @ SV1039 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SV986 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2548]) ).
thf(2599,plain,
! [SV987: $i,SV449: $i,SV894: $i,SV1026: $i,SV721: $i,SV129: $i] :
( ( ( ~ ( c_List_Olistrelp @ SV129 @ SV721 @ SV1026 @ SV894 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SV987 ) ) )
= $true )
| ( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SV721 @ SV894 ) @ ( c_List_Olist_OCons @ SV987 @ SV1026 @ SV894 ) @ SV894 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2600,plain,
! [SV1027: $i,SV906: $i,SV989: $i,SV144: $i,SV464: $i,SV736: $i] :
( ( ( SV736 = SV464 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SV989 @ SV464 @ SV906 ) @ ( c_List_Olist_OCons @ SV1027 @ SV736 @ SV906 ) @ SV906 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV144 @ SV464 @ SV736 @ SV906 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2601,plain,
! [SV470: $i,SV1028: $i,SV908: $i,SV991: $i,SV741: $i,SV150: $i] :
( ( ( c_List_Olist__all2 @ SV150 @ SV741 @ SV991 @ SV908 @ SV1028 )
= $false )
| ( ( c_List_Olist__all2 @ SV150 @ ( c_List_Odrop @ SV470 @ SV741 @ SV908 ) @ ( c_List_Odrop @ SV470 @ SV991 @ SV1028 ) @ SV908 @ SV1028 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2602,plain,
! [SV474: $i,SV1030: $i,SV154: $i,SV993: $i,SV912: $i,SV745: $i] :
( ( ( SV745 = SV912 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV993 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SV745 @ ( c_List_Olist_ONil @ SV1030 ) @ SV1030 ) @ SV1030 ) @ ( c_List_Oappend @ SV474 @ ( c_List_Olist_OCons @ SV912 @ ( c_List_Olist_ONil @ SV1030 ) @ SV1030 ) @ SV1030 ) @ SV1030 ) )
= $true )
| ( ( SV154 = SV474 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2603,plain,
! [SV754: $i,SV914: $i,SV486: $i,SV1032: $i,SV995: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV995 ) @ SV1032 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SV995 @ SV486 @ SV914 ) @ ( c_List_Olist_OCons @ SV1032 @ SV754 @ SV914 ) @ SV914 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV166 @ SV486 @ SV754 @ SV914 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2604,plain,
! [SV916: $i,SV758: $i,SV490: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ SV170 @ SV490 ) )
= $false )
| ( ( c_List_Olist__all @ SV170 @ SV758 @ SV916 )
= $false )
| ( ( c_List_Olist__all @ SV170 @ ( c_List_Olist_OCons @ SV490 @ SV758 @ SV916 ) @ SV916 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2605,plain,
! [SV765: $i,SV498: $i,SV921: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ SV178 @ SV921 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV498 @ SV921 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV178 @ SV498 @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV921 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2606,plain,
! [SV799: $i,SV939: $i,SV575: $i,SV263: $i] :
( ( ( c_List_Olistsp @ SV263 @ SV575 @ SV939 )
= $false )
| ( ( c_List_Olistsp @ SV263 @ SV799 @ SV939 )
= $false )
| ( ( c_List_Olistsp @ SV263 @ ( c_List_Oappend @ SV575 @ SV799 @ SV939 ) @ SV939 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2607,plain,
! [SV577: $i,SV801: $i,SV940: $i,SV265: $i] :
( ( ( c_List_Olistsp @ SV265 @ SV940 @ SV801 )
= $false )
| ( ( c_List_Olistsp @ SV577 @ SV940 @ SV801 )
= $false )
| ( ( c_List_Olistsp @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV265 @ SV577 @ ( tc_fun @ SV801 @ tc_bool ) ) @ SV940 @ SV801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2608,plain,
! [SV270: $i,SV581: $i,SV804: $i] :
( ( ( c_List_Olistsp @ SV804 @ SV581 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV270 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV804 @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV804 @ SV270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV581 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(2609,plain,
! [SV271: $i,SV582: $i,SV805: $i] :
( ( ( c_List_Olistsp @ SV805 @ SV582 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV271 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV271 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV805 @ SV271 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV271 @ SV582 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2610,plain,
! [SV272: $i,SV583: $i,SV806: $i] :
( ( ( c_List_Olistsp @ SV806 @ SV583 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV272 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV806 @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV806 @ SV272 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV272 @ SV583 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2611,plain,
! [SV273: $i,SV584: $i,SV807: $i] :
( ( ( c_List_Olistsp @ SV807 @ SV584 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV273 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV273 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV807 @ SV273 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV273 @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2612,plain,
! [SV276: $i,SV587: $i,SV808: $i] :
( ( ( c_List_Olistsp @ SV808 @ SV587 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV276 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( c_List_Olistsp @ SV808 @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV808 @ SV276 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV276 @ SV587 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2613,plain,
! [SV277: $i,SV588: $i,SV809: $i] :
( ( ( c_List_Olistsp @ SV809 @ SV588 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV277 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( c_List_Olistsp @ SV809 @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV809 @ SV277 ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV277 @ SV588 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2614,plain,
! [SV1007: $i,SV835: $i,SV625: $i,SV953: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ SV316 @ SV953 ) )
= $false )
| ( ( ( c_List_OdropWhile @ SV316 @ SV625 @ SV835 )
= ( c_List_Olist_OCons @ SV953 @ SV1007 @ SV835 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2615,plain,
! [SV657: $i,SV962: $i,SV1011: $i,SV373: $i,SV852: $i,SV50: $i] :
( ( ( c_ListOrder_Ostep1 @ SV50 @ ( c_List_Oappend @ SV852 @ ( c_List_Olist_OCons @ SV373 @ ( c_List_Olist_ONil @ SV1011 ) @ SV1011 ) @ SV1011 ) @ ( c_List_Oappend @ SV962 @ ( c_List_Olist_OCons @ SV657 @ ( c_List_Olist_ONil @ SV1011 ) @ SV1011 ) @ SV1011 ) @ SV1011 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV50 @ SV852 @ SV962 @ SV1011 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV373 ) @ SV657 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2616,plain,
! [SV963: $i,SV380: $i,SV1034: $i,SV854: $i,SV1012: $i,SV663: $i,SV57: $i] :
( ( ( ~ ( c_List_Olist__all2 @ SV57 @ SV663 @ SV1012 @ SV854 @ SV1034 ) )
= $true )
| ( ( ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SV963 @ SV854 @ SV1034 ) )
= $true )
| ( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SV854 ) @ ( c_List_Oappend @ SV963 @ SV1012 @ SV1034 ) @ SV854 @ SV1034 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2617,plain,
! [SV1035: $i,SV1014: $i,SV672: $i,SV968: $i,SV861: $i,SV391: $i,SV68: $i] :
( ( ( c_List_Olist__all2 @ SV68 @ ( c_List_Olist_OCons @ SV391 @ SV861 @ SV968 ) @ ( c_List_Olist_OCons @ SV672 @ SV1014 @ SV1035 ) @ SV968 @ SV1035 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV68 @ SV391 ) @ SV672 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2618,plain,
! [SV1015: $i,SV71: $i,SV969: $i,SV864: $i,SV394: $i,SV675: $i] :
( ( ( c_ListOrder_Ostep1 @ SV675 @ ( c_List_Olist_OCons @ SV394 @ SV864 @ SV969 ) @ ( c_List_Olist_OCons @ SV71 @ SV1015 @ SV969 ) @ SV969 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV675 @ SV394 ) @ SV71 ) )
= $true )
| ( ( SV71 = SV394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2619,plain,
! [SV80: $i,SV403: $i,SV681: $i] :
( ( ( c_List_Olistsp @ SV681 @ SV403 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV80 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinduct__1 @ SV681 @ SV80 ) @ ( v_sko__List__Xlistsp__Xinduct__2 @ SV681 @ SV80 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV80 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2620,plain,
! [SV82: $i,SV405: $i,SV683: $i] :
( ( ( c_List_Olistsp @ SV683 @ SV405 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_ONil @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV82 @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsp__Xinducts__1 @ SV683 @ SV82 ) @ ( v_sko__List__Xlistsp__Xinducts__2 @ SV683 @ SV82 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV82 @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2621,plain,
! [SV1017: $i,SV410: $i,SV868: $i,SV971: $i,SV87: $i,SV687: $i] :
( ( ( c_ListOrder_Ostep1 @ SV687 @ ( c_List_Oappend @ SV87 @ ( c_List_Olist_OCons @ SV971 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ ( c_List_Oappend @ SV410 @ ( c_List_Olist_OCons @ SV1017 @ ( c_List_Olist_ONil @ SV868 ) @ SV868 ) @ SV868 ) @ SV868 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV687 @ SV87 @ SV410 @ SV868 )
= $true )
| ( ( SV87 = SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(2622,plain,
! [SV699: $i,SV104: $i,SV1019: $i,SV876: $i,SV424: $i,SV975: $i] :
( ( ( c_ListOrder_Ostep1 @ SV975 @ ( c_List_Olist_OCons @ SV424 @ SV876 @ SV1019 ) @ ( c_List_Olist_OCons @ SV104 @ SV699 @ SV1019 ) @ SV1019 )
= $false )
| ( ( SV699 = SV876 )
= $true )
| ( ( SV104 = SV424 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2623,plain,
! [SV977: $i,SV705: $i,SV1036: $i,SV881: $i,SV430: $i,SV1020: $i,SV110: $i] :
( ( ( c_List_Olist__all2 @ SV110 @ ( c_List_Olist_OCons @ SV1020 @ SV430 @ SV881 ) @ ( c_List_Olist_OCons @ SV1036 @ SV705 @ SV977 ) @ SV881 @ SV977 )
= $false )
| ( ( c_List_Olist__all2 @ SV110 @ SV430 @ SV705 @ SV881 @ SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2624,plain,
! [SV715: $i,SV1022: $i,SV983: $i,SV443: $i,SV888: $i,SV123: $i] :
( ( ( c_ListOrder_Ostep1 @ SV123 @ ( c_List_Oappend @ SV888 @ ( c_List_Olist_OCons @ SV443 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ ( c_List_Oappend @ SV1022 @ ( c_List_Olist_OCons @ SV715 @ ( c_List_Olist_ONil @ SV983 ) @ SV983 ) @ SV983 ) @ SV983 )
= $false )
| ( ( SV443 = SV715 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV443 ) @ SV715 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2625,plain,
! [SV984: $i,SV444: $i,SV1037: $i,SV889: $i,SV1023: $i,SV716: $i,SV124: $i] :
( ( ( ~ ( c_List_Olist__all2 @ SV124 @ SV716 @ SV1023 @ SV889 @ SV1037 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SV984 ) ) )
= $true )
| ( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SV889 ) @ ( c_List_Olist_OCons @ SV984 @ SV1023 @ SV1037 ) @ SV889 @ SV1037 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2626,plain,
! [SV985: $i,SV445: $i,SV1038: $i,SV890: $i,SV1024: $i,SV717: $i,SV125: $i] :
( ( ( ~ ( c_List_Olist__all2 @ SV125 @ SV717 @ SV1024 @ SV890 @ SV1038 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SV985 ) ) )
= $true )
| ( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SV890 ) @ ( c_List_Olist_OCons @ SV985 @ SV1024 @ SV1038 ) @ SV890 @ SV1038 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2627,plain,
! [SV986: $i,SV446: $i,SV1039: $i,SV891: $i,SV1025: $i,SV718: $i,SV126: $i] :
( ( ( ~ ( c_List_Olist__all2 @ SV126 @ SV718 @ SV1025 @ SV891 @ SV1039 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SV986 ) ) )
= $true )
| ( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SV891 ) @ ( c_List_Olist_OCons @ SV986 @ SV1025 @ SV1039 ) @ SV891 @ SV1039 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2628,plain,
! [SV987: $i,SV449: $i,SV894: $i,SV1026: $i,SV721: $i,SV129: $i] :
( ( ( c_List_Olistrelp @ SV129 @ SV721 @ SV1026 @ SV894 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SV987 ) ) )
= $true )
| ( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SV721 @ SV894 ) @ ( c_List_Olist_OCons @ SV987 @ SV1026 @ SV894 ) @ SV894 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2629,plain,
! [SV736: $i,SV1027: $i,SV906: $i,SV464: $i,SV989: $i,SV144: $i] :
( ( ( c_ListOrder_Ostep1 @ SV144 @ ( c_List_Olist_OCons @ SV989 @ SV464 @ SV906 ) @ ( c_List_Olist_OCons @ SV1027 @ SV736 @ SV906 ) @ SV906 )
= $false )
| ( ( SV736 = SV464 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV144 @ SV464 @ SV736 @ SV906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2630,plain,
! [SV912: $i,SV474: $i,SV1030: $i,SV745: $i,SV154: $i,SV993: $i] :
( ( ( c_ListOrder_Ostep1 @ SV993 @ ( c_List_Oappend @ SV154 @ ( c_List_Olist_OCons @ SV745 @ ( c_List_Olist_ONil @ SV1030 ) @ SV1030 ) @ SV1030 ) @ ( c_List_Oappend @ SV474 @ ( c_List_Olist_OCons @ SV912 @ ( c_List_Olist_ONil @ SV1030 ) @ SV1030 ) @ SV1030 ) @ SV1030 )
= $false )
| ( ( SV745 = SV912 )
= $true )
| ( ( SV154 = SV474 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2631,plain,
! [SV754: $i,SV1032: $i,SV914: $i,SV486: $i,SV995: $i,SV166: $i] :
( ( ( c_ListOrder_Ostep1 @ SV166 @ ( c_List_Olist_OCons @ SV995 @ SV486 @ SV914 ) @ ( c_List_Olist_OCons @ SV1032 @ SV754 @ SV914 ) @ SV914 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV166 @ SV995 ) @ SV1032 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV166 @ SV486 @ SV754 @ SV914 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2632,plain,
! [SV963: $i,SV380: $i,SV1034: $i,SV854: $i,SV1012: $i,SV663: $i,SV57: $i] :
( ( ( c_List_Olist__all2 @ SV57 @ SV663 @ SV1012 @ SV854 @ SV1034 )
= $false )
| ( ( ~ ( c_List_Olist__all2 @ SV57 @ SV380 @ SV963 @ SV854 @ SV1034 ) )
= $true )
| ( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SV854 ) @ ( c_List_Oappend @ SV963 @ SV1012 @ SV1034 ) @ SV854 @ SV1034 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2633,plain,
! [SV984: $i,SV444: $i,SV1037: $i,SV889: $i,SV1023: $i,SV716: $i,SV124: $i] :
( ( ( c_List_Olist__all2 @ SV124 @ SV716 @ SV1023 @ SV889 @ SV1037 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SV984 ) ) )
= $true )
| ( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SV889 ) @ ( c_List_Olist_OCons @ SV984 @ SV1023 @ SV1037 ) @ SV889 @ SV1037 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2634,plain,
! [SV985: $i,SV445: $i,SV1038: $i,SV890: $i,SV1024: $i,SV717: $i,SV125: $i] :
( ( ( c_List_Olist__all2 @ SV125 @ SV717 @ SV1024 @ SV890 @ SV1038 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SV985 ) ) )
= $true )
| ( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SV890 ) @ ( c_List_Olist_OCons @ SV985 @ SV1024 @ SV1038 ) @ SV890 @ SV1038 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2635,plain,
! [SV986: $i,SV446: $i,SV1039: $i,SV891: $i,SV1025: $i,SV718: $i,SV126: $i] :
( ( ( c_List_Olist__all2 @ SV126 @ SV718 @ SV1025 @ SV891 @ SV1039 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SV986 ) ) )
= $true )
| ( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SV891 ) @ ( c_List_Olist_OCons @ SV986 @ SV1025 @ SV1039 ) @ SV891 @ SV1039 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2636,plain,
! [SV894: $i,SV1026: $i,SV721: $i,SV987: $i,SV449: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV129 @ SV449 ) @ SV987 ) )
= $false )
| ( ( c_List_Olistrelp @ SV129 @ SV721 @ SV1026 @ SV894 )
= $false )
| ( ( c_List_Olistrelp @ SV129 @ ( c_List_Olist_OCons @ SV449 @ SV721 @ SV894 ) @ ( c_List_Olist_OCons @ SV987 @ SV1026 @ SV894 ) @ SV894 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(2637,plain,
! [SV1012: $i,SV663: $i,SV1034: $i,SV854: $i,SV963: $i,SV380: $i,SV57: $i] :
( ( ( c_List_Olist__all2 @ SV57 @ SV380 @ SV963 @ SV854 @ SV1034 )
= $false )
| ( ( c_List_Olist__all2 @ SV57 @ SV663 @ SV1012 @ SV854 @ SV1034 )
= $false )
| ( ( c_List_Olist__all2 @ SV57 @ ( c_List_Oappend @ SV380 @ SV663 @ SV854 ) @ ( c_List_Oappend @ SV963 @ SV1012 @ SV1034 ) @ SV854 @ SV1034 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2638,plain,
! [SV1037: $i,SV889: $i,SV1023: $i,SV716: $i,SV984: $i,SV444: $i,SV124: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV124 @ SV444 ) @ SV984 ) )
= $false )
| ( ( c_List_Olist__all2 @ SV124 @ SV716 @ SV1023 @ SV889 @ SV1037 )
= $false )
| ( ( c_List_Olist__all2 @ SV124 @ ( c_List_Olist_OCons @ SV444 @ SV716 @ SV889 ) @ ( c_List_Olist_OCons @ SV984 @ SV1023 @ SV1037 ) @ SV889 @ SV1037 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2639,plain,
! [SV1038: $i,SV890: $i,SV1024: $i,SV717: $i,SV985: $i,SV445: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV125 @ SV445 ) @ SV985 ) )
= $false )
| ( ( c_List_Olist__all2 @ SV125 @ SV717 @ SV1024 @ SV890 @ SV1038 )
= $false )
| ( ( c_List_Olist__all2 @ SV125 @ ( c_List_Olist_OCons @ SV445 @ SV717 @ SV890 ) @ ( c_List_Olist_OCons @ SV985 @ SV1024 @ SV1038 ) @ SV890 @ SV1038 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2640,plain,
! [SV1039: $i,SV891: $i,SV1025: $i,SV718: $i,SV986: $i,SV446: $i,SV126: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV126 @ SV446 ) @ SV986 ) )
= $false )
| ( ( c_List_Olist__all2 @ SV126 @ SV718 @ SV1025 @ SV891 @ SV1039 )
= $false )
| ( ( c_List_Olist__all2 @ SV126 @ ( c_List_Olist_OCons @ SV446 @ SV718 @ SV891 ) @ ( c_List_Olist_OCons @ SV986 @ SV1025 @ SV1039 ) @ SV891 @ SV1039 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2641,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[985,2640,2639,2638,2637,2636,2631,2630,2629,2624,2623,2622,2621,2620,2619,2618,2617,2615,2614,2613,2612,2611,2610,2609,2608,2607,2606,2605,2604,2601,2593,2592,2590,2583,2581,2580,2578,2577,2576,2575,2574,2565,2564,2563,2562,2560,2559,2557,2556,2555,2549,2544,2543,2539,2538,2536,2535,2530,2523,2522,2521,2520,2518,2516,2515,2513,2512,2507,2500,2499,2496,2495,2494,2489,2488,2485,2478,2476,2475,2472,2471,2470,2469,2468,2467,2464,2459,2458,2447,2445,2444,2442,2440,2438,2434,2430,2427,2424,2422,2421,2420,2419,2418,2417,2416,2415,2414,2413,2412,2411,2410,2409,2408,2407,2406,2405,2404,2403,2402,2401,2400,2399,2397,2394,2393,2390,2387,2385,2382,2381,2380,2377,2376,2374,2371,2370,2362,2360,2359,2358,2357,2356,2355,2354,2353,2352,2351,2350,2349,2348,2347,2346,2345,2344,2343,2341,2340,2339,2336,2335,2334,2333,2331,2324,2322,2321,2320,2311,2310,2309,2308,2304,2302,2301,2299,2297,2295,2294,2293,2279,2276,2275,2274,2273,2264,2262,2252,2247,2246,2245,2244,2241,2240,2237,2235,2228,2208,2203,2199,2197,2196,2194,2193,2190,2186,2183,2180,2179,2175,2173,2171,2168,2162,2161,2152,2144,2142,2141,2136,2133,2126,2125,2123,2109,2108,2107,2106,2086,2082,2068,2063,2062,2037,2034,2031,2027,2018,2016,2015,2011,2010,2003,2002,2001,2000,1963,1962,1957,1956,1904,1896,1888,1887,1886,1885,1884,1879,1875,1862,1860,1842,1839,1824,1822,1810,1808,1807,1767,1761,1753,1752,1743,1741,1736,1722,1721,1717,1715,1709,1707,1682,1677,1673,1672,1643,1633,1629,1626,1609,1606,1600,1595,1588,1582,1578,1576,1575,1574,1573,1572,1571,1570,1568,1549,1548,1535,1520,1518,1471,1470,1469,1444,1410,1371,1317,1296,1293,1267,1265,1249,1238,1229,1137,1136,1133,1034,989,988,987,986]) ).
thf(2642,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL764-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 12:33:16 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.37/3.24 ..
% 18.37/3.24
% 18.37/3.24 No.of.Axioms: 329
% 18.37/3.24
% 18.37/3.24 Length.of.Defs: 0
% 18.37/3.24
% 18.37/3.24 Contains.Choice.Funs: false
% 18.37/3.24 ...................................................................................
% 18.37/3.24
% 18.37/3.24 ********************************
% 18.37/3.24 * All subproblems solved! *
% 18.37/3.24 ********************************
% 18.37/3.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:329,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2641,loop_count:0,foatp_calls:1,translation:fof_full)
% 18.37/3.24
% 18.37/3.24 %**** Beginning of derivation protocol ****
% 18.37/3.24 % SZS output start CNFRefutation
% See solution above
% 18.37/3.25
% 18.37/3.25 %**** End of derivation protocol ****
% 18.37/3.25 %**** no. of clauses in derivation: 2642 ****
% 18.37/3.25 %**** clause counter: 2641 ****
% 18.37/3.25
% 18.37/3.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:329,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2641,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------